Selecting the Discount Rate (2017)

by Christopher J. Bruce, Derek W. Aldridge, Kelly Rathje, Laura Weir

When calculating the lump sum award that is to replace a stream of losses in the future, it is first necessary to determine the rate of interest, or discount rate, at which the award will be invested. In Canada, this rate is set equal to the real rate of interest, that is, to the nominal (or “observed”) interest rate net of the rate of inflation.1

Whereas most provinces mandate the discount rate that is to be used when calculating the present value of future losses, Alberta has left the determination of that rate to the courts. Accordingly, the testimony of financial experts on this matter has become an important element of most personal injury actions.

Over the last forty years, Economica has made important contributions to the debate concerning the choice of a discount rate. These contributions have come in the form of chapters in our textbook, Assessment of Personal Injury Damages (now in its fifth edition), articles in this newsletter, and submissions to reviews of the mandated rates in Ontario, Saskatchewan, and British Columbia.

In this article, we argue that whereas virtually all financial experts (including ourselves) have implicitly applied what we will call here the active management approach to the determination of the discount rate, it can be argued that an alternative technique, which we will call the annuity approach, is often more appropriate.

In Section I of this article, we describe these two approaches and investigate their relative merits. In Section II, we employ the principles developed in the first section, to examine how numerical measures of the discount rate might be obtained when discounting two types of future costs: medical expenses and losses of earnings. Finally, in Section III, we summarise our findings.

In that Section, we argue that:

  • if the plaintiff chooses to self-manage the investment of his or her award, the appropriate discount rate (net of inflation) is 2.5 percent; whereas
  • if the plaintiff chooses to purchase a life annuity, or have the defendant purchase a structured settlement, the appropriate discount rate (net of inflation) is zero percent. We argue that it is to the advantage of plaintiffs to make this choice in most cases in which their losses are expected to continue into ages of high mortality (usually after age 75 or so).

I. Two Approaches to Selecting the Discount Rate

There are two broad approaches to the determination of the discount rate, the annuity approach and the active management approach. In the former, it is assumed that plaintiffs will use their lump sum awards to purchase annuities. In the latter, it is assumed that they will invest their awards in a portfolio of stocks, bonds, mutual funds, and other financial assets.

In this section, we define the two approaches and investigate their relative merits. We conclude by identifying the circumstances in which each approach might be preferred to the other.

1. The Two Approaches Defined

The Annuity Approach

If the plaintiff has been awarded a lump sum award to replace a stream of losses from the date of trial until some specified termination date – most often the plaintiff’s projected date of retirement or date of death – he or she will be able to replace the future losses by purchasing an annuity, usually from a life insurance company. This purchase can take the form of either a life annuity or, under the auspices of the court, a structured settlement. In either case, the plaintiff will receive a specified stream of benefits until the termination date.

The purchase price of the annuity will be determined by three main factors: the value of the annual payments, the number of years to the termination date (which will, in part, be determined by the life expectancy of the plaintiff), and the rate of interest at which the insurance company is able to invest the funds received from the plaintiff (or defendant, in the case of a structured settlement).

It is this rate of interest that is known as the discount rate. In the case of an annuity, the discount rate is determined primarily by the requirement (arising both from regulation and accepted accounting practices) that the stream of payments the insurance company has contracted to make is matched by the stream of income that the company will receive from its investment. That is, at the time the annuity contract is signed, the insurance company will invest a sufficient amount, in secure financial instruments, that the income generated from that investment will be sufficient to fund the stream of payments the company has contracted to pay.

What this implies is that for each promised future payment, the insurance company will, implicitly make a separate investment that will generate sufficient returns that it will be able to cover the contracted payment at the appropriate date. For example, if it has contracted to pay $50,000 per year for ten years, it will make ten separate investments, each of which has a maturity value of $50,000.

The discount rate applicable to the payment that must be made one year from now is the interest rate currently available on one-year investments (such as one-year bonds); the rate applicable to the payment to be made two years from now is the interest rate currently available on two-year investments; etc. Thus, there could, in principle, be as many discount rates as there are time periods in the plaintiff’s stream of losses. (In practice, however, investments for more than ten or fifteen years tend to have the same interest rate, so a thirty-year annuity might require ten discount rates.)

Note, first, that there is not “a” discount rate. Rather, there is one rate for each year over which the stream of payments is to be made into the future.

More importantly, note also that it is not necessary to “predict” the discount rate(s). As the investments are to be purchased today (i.e. at the date of settlement), it is the interest rates that are available today that are to be used – and these rates are readily available.

Structured settlement: If it is assumed that a structured settlement is to be purchased, the argument concerning choice of a discount rate is similar to that for a life annuity. Again, the insurance company will place the lump sum received from the defendant in a series of investments, each of which will mature on the date that the payment is due. As the insurance company can be expected, once again, to purchase secure investments, the rates of return that are currently available on such investments can be used to determine the discount rate(s).

The Active Management Approach

Alternatively, the plaintiff might use his or her award to purchase a mixed portfolio of financial assets – for example, stocks, bonds, and mutual funds – selling and buying components within that portfolio as changes occur in financial markets. Because the individual is continuously selling old investments and purchasing new ones, the returns on those investments will reflect rising (and falling) rates that are available in the financial markets.

The complication that this approach introduces is that the rates of return that will be available at the times the plaintiff reinvests his or her funds are not known at the time that the court award is made. These rates must be predicted – in contrast to the rates employed in the annuity approach, which are known at the time the award is made.

2. Comparison of the Two Approaches

As the plaintiff’s award is intended to replace an ongoing loss, it is important that the income the plaintiff receives from investment of that award is sufficient, in each period, to provide the desired compensation. In turn, this requires that the rate of return on that investment be as predictable as possible. The less predictable is the rate of return, the less certain can the courts be that the award will be sufficient for its purposes.

The predictability of the rates of return obtained under the annuity and active management approaches differs with respect to three characteristics: volatility of the rate of return on the invested funds, uncertainty concerning the plaintiff’s life expectancy, and protection against unanticipated increases in the rate of inflation. In this section, we compare the two investment approaches with respect to each of these characteristics in turn.

Volatility

The volatility of a class of investments refers to the variability in the rate of return earned on those investments over time. According to one source:

… volatility refers to the amount of uncertainty or risk about the size of changes in a security’s value. A higher volatility means that a security’s value can potentially be spread out over a larger range of values. This means that the price of the security can change dramatically over a short time period in either direction. A lower volatility means that a security’s value does not fluctuate dramatically, but changes in value at a steady pace over a period of time. [investopedia.com, emphasis added]

The more volatile is the price of a security, the more likely it is that the rate of return on that security will deviate from its long run average. In some periods the return will rise above the average and investors will experience a windfall; but in other periods, the return will fall below average and investors will experience a shortfall.

In the very long run, high returns and low returns may average out, and the rate of return obtained will trend towards the long run value. However, many plaintiffs do not invest for a period long enough that they can be confident that the rate of return on investment of their awards will settle on the long run average. This will particularly be true if plaintiffs are unlucky enough to make a major investment shortly before markets enter a sharp downturn such as was experienced in 2008, (or lucky enough to invest shortly before an upturn, such as in 2010).

To avoid the uncertainty that may result if the plaintiff’s award is invested in volatile financial instruments, it is often recommended that they concentrate their investments on secure, non-volatile stocks, bonds, and mutual funds. The Canadian courts have confirmed this recommendation. For example, in its seminal decision in Lewis v. Todd (1980 CarswellOnt 617), the Supreme Court of Canada approved of an expert witness’s use of “high grade investments [of] long duration.” [para. 17]

Investments in life annuities offer the lowest volatility possible: essentially, the rate of return is guaranteed as long as the insurer, and its re-insurers, remains viable.

Investments in an actively managed portfolio experience two forms of volatility that are not found with annuities. First, all but the most conservative, high grade investments experience variations in returns from year to year.

Second, even if a sophisticated investor could avoid most year-to-year variations in the rate of return, no investor can protect him- or herself against variations that occur due to long-term changes in the economy. For example, assume that it had been anticipated that the plaintiff would be able to obtain a two percent rate of return on investment of his/her award, because the economy was expected to grow at that rate. If broad economic fundamentals should change, such that long run growth fell to one percent per year, it is unlikely that the individual investor would be able to maintain a two percent return on investments.

To conclude, if the goal is to minimize volatility in the returns on the plaintiff’s investments, life annuities and structured settlements are superior to active management, especially in the long run. For short periods of time, perhaps five or ten years, an actively managed “portfolio of high grade investments” may offer almost as much security as an annuity.

Life Expectancy

Assume that a plaintiff will require medical expenses of $50,000 per year for the rest of his life. In a personal injury action, his award will be calculated to ensure that if he invests that amount in a fund composed of secure investments, it will provide $50,000 per year for the lifetime of the average Canadian of his age and sex. For example, if he is a 50-year-old Canadian male his life expectancy is approximately 31 years, to age 81. Thus, his award will be calculated to ensure that he can remove $50,000 per year until his age 81, at which point the award have been drawn down (approximately) to zero.

This puts the plaintiff in a quandary: that the life expectancy of 50-year-old males is 31 years implies that (approximately) half of 50 year old males will live longer than 31 years (and half less than that). Thus, if the plaintiff spends $50,000 per year on medical expenses there is a 50 percent chance that his investment fund will be exhausted before he dies.

Alternatively, if he spends less than $50,000 per year, to leave money in the fund for the possibility that he will live beyond age 81, he will have insufficient funds in every year to pay for his required expenses. Even if it happens that the plaintiff lives less than 31 years, he will have been inadequately compensated for his necessary expenses, because he will have been taking the (reasonable) precaution of spending less than $50,000 per year to create a buffer for the possibility he will live longer than average.

In short, if plaintiffs invest their awards in actively managed investment funds, it is virtually certain that their awards will be insufficient to compensate them fully.

Furthermore, it can easily be shown that this outcome also arises when the amount to be replaced is a loss of income – although the shortfall will be less in this case than in the case of most medical expenses, because the impact of mortality is much lower when the loss continues only to retirement ages (when mortality rates are still low) than when it continues to the end of life.

If the plaintiff’s award is placed in a life annuity or structured settlement, however, payment of the desired annual compensation will be guaranteed from the date of settlement to the end date of the compensation period.

In short, whereas a life annuity will pay the plaintiff an amount equal to his or her loss in every year, an award invested in a portfolio of funds will, in most cases, undercompensate the plaintiff. This under-compensation will often be less when the award is intended to compensate for a loss of earned income than when it is to compensate for long term costs of care. Thus, on this ground, life annuities are slightly preferred to mixed portfolios of investments when there has been a loss of earnings; but annuities are definitely preferred when there is a long-term requirement for payment of medical expenses.

Unanticipated Inflation

A drawback to the annuity approach is that the stream of income that it provides may prove to be inadequate if inflation rates rise unexpectedly. For example, if an annuity provided for $10,000 per year, increasing each year at two percent (to allow for anticipated inflation), it would pay $12,190 in year ten. But if inflation proves to be four percent per year, the plaintiff will require $14,800 in year ten to buy what $10,000 would have bought in year one. The annuity will pay $12,190 when $14,800 is required.

It is often possible to buy annuities whose annual payouts increase with the actual rate of inflation. However, as the risk facing the sellers of annuities is quite high in this case, the price of these annuities may be higher than many buyers are willing to pay.

An alternative method of protecting against the effect of unanticipated inflation is to invest in an actively managed portfolio of assets. Under this approach, the individual is assumed to buy and sell financial assets on a continuing basis, replacing low-earning assets with higher-earning ones as market conditions change. If inflation increases, so will the returns on investments, particularly bonds, allowing the plaintiff to maintain a real rate of return (i.e. a rate net of inflation) that is consistent over time.

On this ground, if the rate of inflation cannot be predicted easily, the active management approach may be preferred to the annuity approach. However, central banks around the world have become convinced that one of their primary functions is to maintain a steady, low rate of inflation. The Bank of Canada, for example, has successfully targeted a rate of two percent since the early 1990s. This policy has been so well received that virtually all financial analysts expect this rate to be maintained well into the future.

As there is no reason to expect that the future rate of inflation will deviate significantly from the rate that has been experienced for the last twenty years, there is little reason to base the selection of the investment approach on the need to protect against unanticipated changes in the rate of inflation.

We conclude, therefore, that the ability of the active management approach to provide protection against unanticipated inflation does not offer a compelling reason to choose that approach in preference to the life annuity approach.

3. Summary

We summarise this section by investigating the merits of using the two investment approaches to replace (i) costs of medical care and (ii) losses of earnings.

Costs of Medical Care

For two reasons, if the plaintiff’s award is intended to provide compensation for medical expenses, particularly expenses that extend well into the future, we recommend that the award be invested in a life annuity (or structured settlement). First, as medical expenses are often required for the plaintiff’s entire life, it is important that the award is able to provide benefits should the plaintiff live beyond the average life expectancy. Whereas this can be achieved easily using a life annuity, it cannot be done through the active management approach.

Second, as the requirement for medical expenses often extends many decades into the future, the returns on awards invested in actively managed funds may be subjected to significant volatility, hence placing the risk of inadequate compensation on the plaintiff. The returns on a life annuity, however, are guaranteed by the insurer, thereby removing the risk of volatility from the plaintiff.

The contrary argument, for using the active management approach to the funding of future medical expenses, is that this approach allows for protection against unanticipated inflationary changes. We have argued, however, that such changes are not expected to be so large as to counter the arguments for use of life annuities. Furthermore, if the courts decide that inflation is likely to become an important factor, they can require that plaintiffs purchase inflation-protected life annuities.

We conclude that, in most cases, it should be assumed that when the plaintiff’s award is to provide for medical expenses, it will not be invested in actively managed funds but will, instead, be used to purchase life annuities. The exception occurs when medical expenses are required for only a short period of time.

Loss of Earnings

When the purpose of the plaintiff’s award is to replace a future stream of lost earnings, the argument in favour of life annuities is weaker than it was with respect to medical expenses. The reason for this is that earnings losses will generally end at an age at which the annual rate of mortality is still quite low.

For example, as we argued above, if a 50-year-old man has a life expectancy of 81, there is (approximately) a fifty percent chance that he will live beyond that age and will exhaust any award for medical expenses. Assume, however, that that individual had planned to retire at age 60, bringing any loss of earnings to an end at that age. As the probability of dying before age 60 is very small, the difference between an award that allowed for that probability and one that did not would also be small. Thus, any “error” that arose from using the active management approach might be compensated by other factors.

If we assume again that the risk of unexpected changes in inflation is small, then the primary difference between the annuity approach and the active management approach (with respect to losses of earnings) will arise with respect to volatility. On this basis alone, the annuity approach will be preferred as it offers less risk that an unanticipated fall in interest rates will leave the plaintiff’s award inadequate.

However, it is possible that this uncertainty concerning the rate of return on investments might be offset if the active management approach provided higher average rates of return. For example, if those rates were two or three percentage points higher than those offered by the sellers of life annuities, plaintiffs might prefer to manage their own funds rather than rely on an annuity.

For this reason, we suggest that the active management approach be employed only if it is clear that the plaintiff does not wish to invest his or her award in an annuity (as, in this case, the plaintiff has signaled that the rate of return on actively managed assets is high enough to compensate for the increased risk).

II. Evidence Concerning the Value of the Discount Rate

1. The Annuity Approach

If it is assumed that the plaintiff will purchase a life annuity, the appropriate discount rate will be the rate(s) of return that life insurance companies use when pricing those annuities. In this section, we argue that these rates will approximate the rates of interest that are available on Government of Canada bonds of the appropriate durations.

In Table 1, we summarise those rates for five-year, ten-year, long-term, and real rate of return bonds and for GICs of one-year, three-year, and five-year terms. In this table, the term “long-term bond” applies to government bonds with maturation dates of fifteen years or more. “Real rate of return bonds” are bonds whose rate of return is specified as a fixed value (the real rate of return) plus the actual rate of inflation. Thus, for example, if the fixed value is 1.0 percent and the rate of inflation proves to be 2.5 percent, the bond will pay (approximately) 3.5 percent.2

Table 1 reports both the nominal (observed) and real (net of inflation) rates of return on five- and ten-year bonds, long-term bonds, and GICs. In each case, the real rate has been calculated by reducing the nominal rate by the expected rate of inflation, two percent.3 As the interest rate on real rate of return bonds is reported as a real rate, we report only the real rate of return on those bonds.

In Table 1 it can be seen, first, that the real rates of return on government bonds increase as the duration of those bonds increase; thus confirming that there is not a single discount rate but rather a different rate for each length of investment.

Second, it is also seen that the real interest rates on secure bonds have not recently risen above 0.5 percent for investments of any duration; and have risen above 0.0 percent only on real rate of return bonds.

Our contention is that these rates can be used as indicators of the rates at which life insurance companies will invest the funds they receive for life annuities and structured settlements. We can test this contention by comparing the interest rates employed to determine the prices of structured settlements against the rates reported in Table 1.

This we have done by obtaining quotes for several alternative structured settlements. From these we have been able to determine the interest rates that were employed to obtain those quotes. In Table 2 we report six such structured settlements, for males receiving $1,000 per month ($12,000 per year).4

Three scenarios represent payments that end at age 60 and three represent payments that continue to the date of the plaintiff’s death. (Those that end at age 60 are assumed to be typical of awards for loss of earnings; and those that continue for life are assumed to be typical of awards for medical expenses.) The assumed ages for the plaintiffs, at the date of trial, are, respectively, 20, 35, and 60. Furthermore, in each case we report quotes for both the situation in which the annual payment is to increase by two percent per year and for that in which it will increase by the actual rate of inflation.

Column (4) of Table 2 reports the quotes we received, assuming that the annual payment was to increase by the actual rate of inflation; while column (6) reports the quotes assuming that the annual payment was to increase by two percent per year. Columns (5) and (7) then report our calculation of the implied interest rates that were used to obtain the costs of the various annuities.

For example, the first figure in column (4) indicates that it would cost $489,176 to purchase an annuity that paid a male plaintiff $12,000 per year, indexed for inflation, for the next 40 years (i.e. from age 20 to age 60). The first figure in column (5) then indicates that the insurance company that quoted this amount had implicitly assumed that its investments would earn an average real rate of interest, (i.e. nominal interest net of inflation), of -0.27 percent over the 40-year period in question. Similar costs and real interest rates are reported for the other eleven scenarios.

Notably, in every case in which the payments were fully indexed for future inflation (column 5), the implied real rate of interest was negative – between -1.24 percent and -0.27 percent. It is only when the payments did not provide full protection against inflation – column 7, in which increases were limited to two percent per year – that insurers offered a positive real interest rate. Even then, rates were less than one percent.

We would note that the implied discount rates of the annuities presented in Table 2 are consistent with the implied discount rates of annuities offered  by private insurance firms such as Sun Life Financial and RBC Insurance. For example, the Sun Life Financial annuity calculator indicates that as of April 2017, a $1,000,000 annuity for a 50-year old female will provide an annual income of approximately $41,819 per year (with no inflation adjustment). This implies a discount rate of approximately 0.13 percent. The annuity calculator provided by RBC Insurance indicates that as of April 2017, a $1,000,000 annuity will provide a 55-year old male with annual payments of approximately $50,931 (with no inflation adjustment), for an implied discount rate of 0.15 percent.5

It is informative to compare the rates employed in the calculation of structured settlements (and private annuities) with the rates reported for government bonds, in Table 1. The two annuities with the shortest durations – ten years, from age 50 to 60 – had implied discount rates of -1.24 and -1.02 percent, both very similar to the figure of -1.23 percent reported in Table 1 for five-year bonds in 2016. Similarly, the two annuities with the longest durations – from age 20 for life – had implied discount rates of -0.57 percent and +0.65 percent, with an average very close to the figure of -0.08 percent reported in Table 1 for long-term government bonds.

We conclude from Tables 1 and 2 that, in cases in which the plaintiff purchases a life annuity or structured settlement – particularly one that is fully indexed for inflation – the discount rate can be estimated with some accuracy from the real rates of return currently available on Government of Canada bonds of appropriate durations.

2. Active Management Approach

In the active management approach, it is assumed that plaintiffs will re-allocate funds within their investment portfolios as conditions in financial markets change. Because these changes will be made in the future, the active management approach requires that estimates of future rates of return be calculated.

In this section, we first identify the type of financial instrument in which we assume the plaintiff will invest. We then contrast two methods of forecasting the rates of return on those instruments. Finally, we provide estimates of those rates of return.

Selection of the Appropriate Financial Instrument

The courts have been clear that, as the lump-sum award is intended to replace the plaintiff’s lost earnings, the investments in the plaintiff’s portfolio must not expose the plaintiff to unreasonable risk. For example, in its seminal decision in Lewis v. Todd (1980 CarswellOnt 617), the Supreme Court of Canada approved of the expert’s use of “high grade investments [of] long duration” [para. 17].

As the rates of return on investments in the stock market have historically been very volatile, it is usually recommended that plaintiffs do not restrict their investments to equities. Table 3, for example, reports the value of the Toronto Stock Exchange composite index for July of each year since 2000. It can be seen there that rates of return have been highly volatile, indicating that the rate available to an individual whose investments tracked the market would have depended importantly on the year in which those investments were made. For example, whereas the nominal return on investment in such a portfolio would have averaged 2.2 percent per year between 2000 and 2015, a similar investment would have averaged 6.2 percent per year between 2002 and 2015.

In light of this issue, two approaches might meet the court’s requirement that plaintiffs invest in high grade investments: it could be assumed that plaintiffs will purchase long-term Government of Canada bonds; or that they will invest their awards in financial instruments that offer higher yields than government bonds, but with greater risk – for example, in a mixed portfolio of “blue chip” stocks, corporate bonds, and mutual funds. In the discussion that follows, we will consider both.

Forecasting the Returns on Government Bonds

Two methods have commonly been used to forecast the rate of interest that will be available on government bonds. The first of these, the historical approach assumes that future rates will equal those that were observed in the past. The second, the efficient market approach, assumes that the rates that are currently available in the market reflect the rates that investors believe will prevail in the long run. We explain here why we prefer the efficient market approach.

The historical approach: A fundamental problem with the historical approach is that real interest rates have varied significantly over the last sixty years. As can be seen from Table 4, real rates were as low as 1.50 percent in two decades (1951-1960 and 1971-1980) and as high as 4.70 percent in two others (1981-2000). From this record, it would be possible to find support for almost any long-run rate between 2.0 and 5.0 percent.

More importantly, as indicated in Figure 1, real rates of return have declined virtually continuously for the past twenty years, from approximately 5.5 percent to -0.5 percent. Even if it was to be argued that real rates of interest will return to, say, 3.0 percent over the next twenty years, most plaintiffs will experience rates of return well below that over most of the period in which their award is invested.

A third problem with the use of historical rates is that there is no theory to support it. Adherents simply assume that because real rates took some value in the past, rates will return to that value in the future. Furthermore, they make this assumption in the face of the long run decline in real interest rates reported in Figure 1. If the markets expected the real rate of interest to return to “long-run” levels soon, sophisticated investors would not continue to purchase financial instruments that paid long-run rates as low as -0.08 percent (Table 1).

Finally, the evidence is not just that the real interest rate has declined significantly; this decline is consistent with theoretical predictions. Importantly, as central banks have adopted a policy of maintaining inflation within a narrow band of rates (in Canada, between 1.0 and 3.0 percent), uncertainty about the rate of inflation has been minimized. This reduction in risk has led to an increase in demand for bonds, and an associated reduction in real interest rates.

The Congressional Budget Office of the United States also predicts that interest rates will be lower in the future than in the past, resulting in part from slower growth rates of both the labour force and of productivity, thereby reducing the rate of return on capital; and in part from a shift of income to high-income households who tend to have high savings, thereby increasing the supply of money to the bond market.

The efficient market approach: The second source of information concerning future real rates of interest is the money market. When an investment firm that believes that inflation will average two percent per year purchases twenty-year Government of Canada bonds paying three percent, it is revealing that it expects the real rate of interest on those bonds will average approximately one percent over those twenty years. Thus, if the rate of inflation that investors were forecasting was known, that forecast could be used to deflate the nominal rates of interest observed in the market to obtain the implicit, underlying forecasts of real rates.

A strong case can be made for using an expected inflation rate of two percent. The reason for this is that in the last decade the Bank of Canada has not only made this its target rate of inflation, it has been successful in keeping the actual (long-run) rate of inflation very close to that target (which, in turn, has led most financial institutions to predict that future inflation will average two percent).6

Furthermore, in choosing to target a low rate of inflation, the Bank has been following a view that has achieved widespread acceptance in the economics community – that is, that control of inflation, at a low level, should be one of central banks’ primary roles.

On this basis, at the end of 2016 the real rate of interest on long-term government of Canada bonds appeared to be as little as 0.00 percent. (See the figures for long-term bond rates in Table 1.)

An alternative approach is to rely on information concerning bonds whose rate of return is denominated in terms of real interest rates – called real return bonds, or RRBs. By observing the rates of return at which these bonds sell, the risk free real rate of return that investors believe will prevail over the long run can easily be determined. That is, even if plaintiffs do not purchase RRBs, the real rate of interest that is observed on those bonds provides an unbiased indicator of the rate of interest that is expected by sophisticated investors. In Table 1, it is seen that the return on these bonds has recently fallen to as little as 0.41 percent.7

Forecasting Returns on a Mixed Portfolio

Forecasting the returns on a conservative, mixed portfolio is complicated by the fact that there is no common agreement about what the components of such a portfolio should be. Hence, not only is it difficult to obtain the current rates of return on conservative investments, there is also very little information about how such returns have varied over the past. Both issues complicate the forecasting process.

An approach that we suggest might mitigate this problem would be to rely on the rates of return that have been available on conservative portfolios offered by Canadian banks. We have been able to obtain information about four of these: the RBC Select Very Conservative Portfolio, CIBC Managed Income Portfolio, TD Comfort Conservative Income Portfolio, and ScotiaBank Selected Income Portfolio-Series A. Although these funds differ from one another in their details, they all have investment objectives similar to those stated for the RBC portfolio:

To provide income and the potential for modest capital growth by investing primarily in funds managed by RBC Global Asset Management, emphasizing mutual funds that invest in fixed-income securities with some exposure to mutual funds that invest in equity securities. The portfolio invests in a mix of Canadian, U.S. and international funds.

To achieve this goal, RBC invests primarily in bond funds. The result, seen in the first columns of Table 5 below, is that since 2011 this fund has consistently earned a nominal rate of return between 2.5 and 5.0 percent – with one deviation, to 6.74 percent, in 2014 – suggesting a real rate of return over that period of approximately 1.0 to 3.5 percent. Table 5 reports similar results for the other three portfolios (again, with 2014 being the only year that each of them achieved a nominal return that exceeded 5.00 percent).

The volatility in the rates of return on all four portfolios reported in Table 5 is considerably less than that on investments in the Toronto Stock Exchange, as reported in Table 3.

But that does not necessarily mean that plaintiffs would be advised to invest in a conservative mixed portfolio. Although the returns on such portfolios may be higher than that on life annuities, the returns on the latter are fixed once they are purchased, and hence have lower (zero) volatility than the returns on all other investments. The question remains: do the higher rates of return on mixed portfolios compensate the plaintiff for the higher volatility of their returns? This is a question that cannot be answered by financial experts, but only by the courts or government regulators.

What Table 5 does suggest, however, is that if plaintiffs had purchased mixed conservative portfolios in the last five years they would have achieved average nominal returns of between 3.5 and 4.5 percent per annum – or approximately 2.0 to 3.0 percent in real terms. This suggests that 2.5 percent represents a conservative estimate of the real rate available to plaintiffs seeking conservative investments.

III. Summary

In personal injury and fatal accident actions, the plaintiffs are assumed to invest their awards in such a way as to provide streams of returns that will replace their future annual losses. Two factors may intervene to hinder plaintiffs’ ability to achieve this goal. First, they may live longer than average. Second, the rate of return on investments may fall below the level that was anticipated when calculating their awards. In both cases, the award will be exhausted before the plaintiff’s death.

One approach plaintiffs can employ to avoid these problems is to invest their awards in life annuities or structured settlements, as these instruments guarantee a specified annual payment for life, and as the rates of return available on them are fixed.

The drawback to annuities is that the interest rates that insurance companies use to price their products are much lower than the rates of return that have been available on conservative mixed portfolios of financial assets. We showed in Section II that, whereas the implicit interest rates on life annuities are similar to the rates available on long-term Government of Canada bonds, or approximately 0.0 to 0.5 percent, the interest rates available on conservative portfolios of assets have been approximately 2.0 to 3.0 percent.

If a loss will not continue into the years beyond which mortality rates begin to rise substantially, the advantage of buying a life annuity may be relatively small compared to investing in a portfolio of assets. In that case, it may be appropriate to assume that that the discount rate can be estimated from the return on a portfolio of assets.

If the loss will continue into years of high mortality, however, the benefits of a life annuity (protection against exhaustion of the award) may exceed the costs (a lower rate of interest).

As it is only the plaintiff who can determine whether the benefits of a life annuity exceed the costs, it seems appropriate that the discount rate be chosen based on the plaintiff’s decision whether to self-manage the investment of his or her award or to use that award to purchase a life annuity (or structured settlement).

  • If the plaintiff chooses to self-manage his or her award, we recommend that the discount rate be set at 2.5 percent.
  • If the plaintiff chooses a life annuity or structured settlement, we recommend that the discount rate be set at zero percent.
  • We anticipate that plaintiffs will make the latter choice in virtually all cases in which their losses will continue into years of high mortality.

 

Implied Rates of Return on Structured Settlements

by Derek Aldridge & Christopher Bruce

The purpose of a lump sum award in a personal injury or fatal accident case is to provide a fund that, when invested, will generate a stream of benefits equal to the plaintiff’s future stream of losses. One method of generating such a stream would be to purchase a life annuity. This, for example, is what is anticipated by Section 19.1 of the Judicature Act (RSA 2000) when it provides that:

(2)  On application by any party to a proceeding, the Court may order that damages awarded be paid in whole or in part by periodic payments…

This type of periodic payment has come to be known as a structured settlement annuity. Such annuities are sold by insurance companies. When calculating the price it is going to charge for an annuity, the insurer determines how much it would have to invest, at current interest rates, in order to generate a stream of income at least equal to the required periodic payments. For example, if it had promised to pay $10,000 per year indefinitely , and the rate of interest that it thought it could earn was 10 percent, it would charge at least $100,000 – as $100,000, invested at 10 percent per year, would generate a stream of income of $10,000 per year.

Conversely, therefore, if we observe the lump sum that an insurance company charges for an annuity that promises a specified stream of payments, we can calculate the rate of interest that the insurance company expects to obtain on the investment of that sum. For example, if it was observed that the company had charged $100,000 for a periodic payment of $10,000 per year (indefinitely)¹, we would be able to calculate that the rate of return it expected to obtain on investment of that $100,000 was at least 10 percent.

We have used this principle to calculate the rate of return that insurers expect to obtain on a series of standard structured settlements. By contrasting these rates of return with the rates that Economica has been using, we can check whether Economica’s rates are consistent with those that sophisticated investors – insurance companies – expect to earn on low-risk investments.

With the assistance of Heber Smith, of Smith Structured Settlements (www.structuredsettlements.ca), in August 2011 we obtained quotes on an annuity that provided payments of $1,000 per month to a male plaintiff. These quotes were for

  • three different ages of plaintiffs: 20, 35, and 50;
  • two different termination dates: the plaintiff’s age 60 and his age of death; and
  • two different assumptions concerning inflation indexation: one in which the insurer increased the annual payment each year by the rate of consumer price inflation and one in which the payment was increased each year by a fixed 2 percent.

We report the quotes that we obtained for twelve different scenarios in columns 6 and 8 of the table below. As an example of how to read this table, the $127,064 figure in column 6 of the first row in the table, indicates that we were quoted a price of $127,064 to purchase an annuity that paid $1,000 per month, increasing at the rate of consumer price inflation, from the plaintiff’s age 50 to his age 60. Similarly, it is seen from column 8 of the first row that that annuity would have cost $121,255 if the payments had been adjusted by 2 percent per year instead of by the prevailing rate of inflation. (If we assume that insurers believe that inflation will be 2 percent on average, the difference be $5,809 difference between columns 6 and 8 in the first row is a “premium” the insurer charges to compensate it for taking the risk that inflation might prove to be higher than 2 percent.)

The comparable figures in columns 6 and 8 of the third row of the table report the cost of an annuity that extends to the end of the plaintiff’s life, instead of to age 60 (as in the first row). The figures in the third row would be relevant if an annuity was being purchased to pay for costs of care, instead of for loss of earnings (first row). The remaining rows in the table report the costs of annuities paying $12,000 per year to a 20-year old and a 35-year old.

Given the quotes reported in columns 6 and 8, we were able to calculate the real rate of interest (interest rate net of a two percent expected rate of inflation) the insurance company was expecting to receive from investment of each annuity. These rates are reported in columns 7 and 9, with the figures in column 7 referring to the quotes in column 6 and the figures in column 9 referring to the quotes in column 8. As an example, the figure of -0.95% in column 9 of the first row indicates that the insurance company anticipated that it would receive a nominal interest rate of approximately 1.05% (i.e. 1.05% nominal interest – 2.00% inflation = -0.95% real rate of interest, or discount rate).

Of the twelve discount rates reported in the table, only one – the 2.10 percent rate of return in column 9 of the second row – exceeds the lowest rate used by Economica, as reported in Table 2 of the first article in this newsletter – 1.80 percent on investments of less than four years; and most of the remaining discount rates are significantly lower than the rates that we recommend.

The result is that the present discounted values quoted by insurance companies for the purchase of structured settlements are considerably higher than the comparable values that would have been calculated by Economica. The latter values are reported in column 4 of the table. It is seen in column 4 of row four, for example, that whereas Economica would have calculated that a plaintiff would need $277,538 to replace $12,000 per year from age 20 to age 60; the quote we received for a structured settlement was $506,890 – 82.6 percent more.

The differentials are even greater if we use the discount rate that some other expert economists have recommended – 3.50 percent. In the fourth row of column 5, for example, we report that the present value of $12,000 from age 20 to age 60 would be $252,895 if 3.50 percent is used – less than half of the $506,890 that we were quoted for a structured settlement.

To conclude: in every case, the present values that we would estimate using our discount rate assumptions are considerably lower than the actual cost that a plaintiff would incur if he were to buy an annuity to fund his future losses. This is very strong evidence in support of the claims that we have made over the last several years that our discount rate approach is a conservative one. Based on the costs to purchase structured settlement annuities, and the plaintiff’s ability to demand that his/her loss be funded using this “periodic payment” approach (given Section 19.1 of the Judicature Act), it follows that any reasonable change to our discount rate approach would be to use lower rates, not higher (as some other experts have argued).

Acknowledgment

As noted above, Heber Smith, of Smith Structured Settlements generously provided us with quotes on various annuities which we used in the creation of this article. On previous cases, we have worked together with Mr. Smith when the plaintiff’s lawyer chose to argue that damages should be satisfied by periodic payments (in accordance with Section 19.1 of the Judicature Amendments Act), rather than a conventional present value. An advantage of having future losses assessed in this manner is that it removes the subjective nature of opinions concerning the discount rate. Instead of relying on opinion concerning the rate of return that a plaintiff will earn on his or her investments, we can determine precisely how much it will cost the plaintiff to purchase annuities to fund the future losses.

Smith Structured Settlements serves the personal injury community as an annuity brokerage specializing in the preparation of fee-based Section 19.1 damages reports. Should you wish to investigate such an option they may be reached at www.structuredsettlements.ca.

 

 

Footnote:

  1. Of course, structured settlements never continue indefinitely. We use this example because of its mathematical simplicity. [back to text of article]

The Discount Rate Simplified

by Christopher Bruce, Laura Weir, Derek Aldridge, and Kelly Rathje

In every personal injury or fatal accident case in which the plaintiff’s loss continues into the future, it is necessary to calculate the rate of interest at which the damages will be invested. This interest rate is commonly called the discount rate, and it is calculated as the nominal (or observed) rate of interest net of the expected rate of price inflation.

As Alberta has no mandated discount rate, the determination of that rate is left to the courts. In this article, we propose to offer a simple technique for identifying this rate.

We proceed in two steps. First, we discuss the criteria that we believe must be met when selecting the discount rate. Second, we apply these criteria to the relevant data, to make that selection. In a separate article following this one, Derek Aldridge and Christopher Bruce contrast the rates that we propose with those that are available on structured settlements.

1. Criteria

The first step in selecting a discount rate is to recognise that the plaintiff is expected to invest his or her award in such a way that the stream of income generated from that award will exactly reflect the stream of losses that the plaintiff has suffered. If the plaintiff has lost $50,000 per year for twenty years, investment of the lump-sum award should produce $50,000 per year, with the principal being exhausted by the end of the twentieth year.

As this stream of investment income is intended to replace a significant portion of the plaintiff’s lifetime earnings, the courts have ruled that the lump-sum should be invested in low-risk financial instruments. Hence:

The discount rate must be based on an investment portfolio that is of low risk.

Although this requirement does not mean that the plaintiff must put all of his or her award into government bonds or guaranteed investment certificates (the lowest-risk investments available), we argue that the interest rate available on those investments provides the most reliable indicator of the rate of return required by the courts.

The plaintiff may well include in his/her portfolio non-government or non-guaranteed investments, such as corporate bonds, mutual funds, and blue chip stocks; but, that the returns on such investments are higher than those obtained from government bonds results primarily from the higher level of risk associated with them – as was seen with devastating results in the post-2008 stock market crash.

The difference between the rate of interest on a government bond or a GIC and, say, a corporate bond is a measure of the compensation that investors demand for accepting a higher degree of risk on the latter investment than on the former. Once that level of “compensation” is deducted, the net, risk-free, interest rate is approximately the same on both. Hence:

The rates of return on Government of Canada bonds and GICs represent reliable indicators of the rate of interest sought by the courts.

Once it has been decided that it is government bond and GIC rates that are to be used, it is necessary to select from among the various options that are available to the plaintiff. Financial advisors recommend that, in order to reduce risk, investors should purchase a mix of bond durations. In that way, if interest rates should rise, investors can sell their short-term bonds and purchase newly-issued bonds at the higher rates; and if interest rates should fall, although investors will have to accept reduced interest rates on any new investments, they will still experience relatively high rates on their long-term (locked-in) investments. Hence:

Plaintiffs should purchase a mix of short-, medium-, and long-term investments.

If the duration of the plaintiff’s loss is less than ten years, the plaintiff will minimize risk by purchasing investments that have durations that mature on the dates on which the losses are incurred. For example, a one-year bond might be purchased to replace the loss one year in the future, a two-year bond to replace the loss two years from now, etc. Hence:

For losses that will occur in the next ten years, the relevant interest rate for any year is the rate of interest on a Government of Canada bond (or GIC) that has a term equal to that number of years.

But if the plaintiff’s loss extends for more than ten years, it will be wise to adopt an investment strategy in which bonds are purchased for shorter terms than the duration of the loss, and then re-invested periodically. To replace a loss twenty years from now, for example, the plaintiff might purchase five-year bonds today and re-invest the returns every five years until the funds were needed. If a similar practice is followed for every duration of loss, the risk that interest rates will rise or fall, relative to what is expected at the time of the initial investment, will be minimised.

Such a strategy, of rolling over short-term investments in order to generate a long-term return, means that the effective discount rate over the term of the investment will be determined not only by the rates that are available today but also by rates that will become available in the future. Thus, the court must predict what those future rates will be.

Contrary to what many experts argue, this prediction can be made simply and with confidence: the most reliable prediction of the rate of interest that will prevail in the long-run is that it will equal the rate of return currently available on long-run bonds. For example, if the current rate on 15-year government bonds is 3.0 percent, the best prediction of the rate of return that will prevail over the next fifteen years is 3.0 percent.

The argument for basing the prediction on this rate can most easily be understood by showing that the contrary cannot be true. For example, it might be argued that “as interest rates are unusually low today, it can be expected that they will eventually rise above current rates.” If this argument is correct, then individuals who wished to invest their funds for long periods of time (for example, individuals who are saving for their retirement) would not purchase long-term bonds today – they would purchase short-term bonds while waiting for interest rates to rise, and then purchase bonds at the new, higher rates once the interest rate had risen.

But if investors behaved this way, the demand for long-term bonds would decrease; and when demand for a bond decreases, its interest rate rises. (Issuers have to raise the rate of return in order to attract investors.) That is, if investors predict that the long-term interest rate will exceed the rate currently available on long-term bonds, they will act in such a way as to drive up the interest rate on long-term bonds. A bond rate that is less than the expected rate cannot be maintained.

Similarly, if investors believed that interest rates were about to fall, they would sell their short-term bonds and purchase long-term. But this would decrease the demand for short-term funds, driving up short-term interest rates, and increase the demand for long-term funds, driving down long-term interest rates.

In short, if the rate of interest that is currently available on long-term bonds is different from the rate that investors expect will prevail in the future, the long-term bond rate will change “towards” the rate that investors predict. As a result, the interest rate available on long-term bonds will always adjust until it equals the rate that investors predict will prevail in the long run. And, as investors have a strong incentive to make correct predictions about the bond market, it is likely that their predictions are the best that are available. Hence, we conclude that:

The best predictor of the rate of interest that will prevail in the long-run is the rate of interest that is currently offered on long-term bonds.

Finally, as we noted in the introduction to this article, the discount rate is found by netting out the forecasted rate of price inflation from the observed nominal rate of interest. Hence, before the discount rate can be determined:

The long-run rate of price inflation must be forecast.

Fortunately, there is a clear consensus that the long-run rate of inflation in Canada will be two percent. This consensus has developed because, since the early 1990s, the Bank of Canada has not only set two percent as its long-run target, it has both met that target and expressed satisfaction with the results of its policy.

That participants in the “money markets” have come to accept that the Bank will achieve this goal over the long-run is seen in two surveys of business leaders that have been conducted annually since 1994. Consistently, respondents have reported that they expect the long-run rate to be 2.0 percent. Indeed, not only has the average, expected rate been 2.0 percent in most years that the surveys were conducted, the variation of responses “around” 2.0 percent has decreased continuously. Hence:

There is a strong consensus that, in the long run, the rate of inflation will average 2.0 percent in Canada. Hence, the discount rate can be found by reducing the forecasted nominal rate by 2.0 percent.

2. Data

In Figure 1 and Table 1 we report the annual rates of return that have been available since 1995 on five Government of Canada bonds: 2-, 5-, and 10-year bonds, long-term bonds (an average of bonds with a maturity date longer than 10 years), and “real rate of return” bonds (bonds whose rates of return are stated net of inflation). It is seen there that both nominal and real interest rates on Government of Canada bonds have decreased almost continuously since the Bank of Canada introduced its policy of targeting a two percent rate of inflation. Whereas real interest rates were between 4.5 and 7.5 percent in 1995, they have fallen below one percent on most bonds, and even below zero percent on some, in recent years.

 

 

What these figures indicate is that investments in government bonds are unlikely to provide real rates of return above zero percent over the next five years; that bonds of five to ten year durations are unlikely to produce rates in excess of 1.0 percent; and that the market expects long-term real interest rates on government bonds to be less than two percent.

Nevertheless, in recognition of the fact that current rates are at a historical low, we have left our assumed rates at the same values we have employed for the past five years. Those rates, which we report in Table 2, are: 1.8 percent per year on funds invested for three years or less; rising in equal increments to 3.0 percent per year on funds invested for more than fifteen years.

 

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.

Kelly Rathje is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Calgary.

Laura Weir is a consultant with Economica and has a Bachelor of Arts in economics (with a minor in actuarial science) and a Master of Arts degree from the University of Calgary.

The Discount Rate Revisited (Spring 2008)

by Laura Weir, Derek Aldridge, Kelly Rathje, and Christopher Bruce

This article first appeared in the spring 2008 issue of the Expert Witness.

Our readers will recall that every year or two we review our standard discount rate assumptions and publish our findings. It is time to repeat this exercise.

In the Summer 2006 issue of the Expert Witness, we reported that real rates of interest (that is, the rates of return net of inflation) had increased slightly from those outlined in our Summer 2005 article. We responded by increasing our forecast of the short-term (one to six years) real rates of interest. Our forecasted interest rates for the medium to long-term (seven to 15 years or more) remained unchanged – although these rates were slightly higher than the observed real rates of return on Government of Canada bonds, long-term real rate of return bonds, and the long-term rate mandated in Ontario. (Higher rates lead to lower present values, so our estimates can be considered conservative.)

In our 2006 article we specified our assumptions for real interest rates for periods ranging from one-year to 15 years or more. Our assumptions were based on the observed rates of interest on Government of Canada bonds of various terms. We now have more rates to observe and we see that these rates have continued their long-term downward trend. Real rates of interest for five bond series over the last 14 years are depicted in the figure below (with the rates for 2008 estimated using an average of the January through June interest rates).

Figure 1

From the figure we see that real rates have decreased slightly from their 2006 and 2007 levels. However, the decrease in real interest rates is not sufficient to warrant a change in our discount rate assumptions. In particular, we note that the average real rates for the past 12 and 24 months are very similar to the corresponding averages at the time we wrote the previous article. One exception is the long-term rate, whose 24-month average (2.23 percent) is a third of a percent less than the corresponding 24-month average at the time of our previous article.

Although we do not show the comparable interest rates on guaranteed investment certificates (GICs), we have examined them and they are consistently lower than the rates of return on bonds. For example, the rate currently offered for 5-year GICs is approximately three percent, corresponding to a real rate of only one percent.

Our discount rate assumptions, unchanged from our 2006 article, are shown in the table below.

Table 1

Over the years, our approach to forecasting an appropriate discount rate has been criticized by other economists who prefer to rely on historical interest rates in making their forecasts. Below, we address some of these critiques and provide support for our approach.

Our approach, often called the “conservative investment” approach (which assumes a plaintiff will use his damage award to purchase a financial instrument with an appropriate term to maturity and hold that instrument to maturity), has been criticized by other economists who argue for a “market-based” approach (that assumes a plaintiff will buy and sell bonds as interest rates vary instead of holding the bond to maturity). One of us (Bruce) addressed this issue in an article written for the Spring 2007 issue of the Expert Witness entitled “Forecasting the long-term interest rate on Government of Canada bonds: “market-based” versus “conservative” investment“. We summarize his conclusions here as this issue continues to arise.

Some economists suggest that our approach ignores the price changes resulting from changes in the interest rate within the bond market, arguing for the market-based approach that assumes the plaintiff can earn a higher rate of return by actively buying and selling bonds as interest rates change. As a simple example, suppose a plaintiff will incur a loss of income of $100,000, 20 years from now. The conservative approach assumes that he will purchase a 20-year bond, paying five percent in interest per year, for $37,689 and redeem it at maturity for $100,000 to fund his loss in that year.

Assume, however, that the interest rate decreases to four percent one year after purchase. The market-based approach suggests that at four percent, the plaintiff could sell his bond (that has 19 years left to maturity) for $47,464 (= $100,000/1.0419) and earn $9,775 (= $47,464 – $37,689) in profit, for an effective rate of return of 25.94 percent in one year. However, this is actually not a profit because the plaintiff still has to purchase a 19-year bond (at a cost of $47,464) to fund his $100,000 loss of income 19 years from now. Thus, there is no real benefit to actively trading bonds as the interest rate changes.

In addition to the fact that the effective rates of return under the market-based approach are illusory, effective rates of interest are extremely variable. For example, a publication by the Canadian Institute of Actuaries entitled Report on Canadian Economic Statistics 1924-2005 indicates that the 10-year average (1996-2005) effective real rate of return on long-term Government of Canada bonds was 7.36 percent. However, the standard deviation was 9.01 percent, suggesting an average effective real rate of return that could fluctuate between -1.65 percent and 16.37 percent. This suggests that the plaintiff will almost certainly earn a rate of return different from the average long-term rate. Further, while a “profit” can be made by selling a bond when the interest rate decreases, a “loss” would occur if the interest rate increased (say) to six percent, where the 19-year bond would now only cost $33,051, for a net loss of $4,638 (or an effective rate of return of -12.31 percent).

Finally, if we were to rely on an average of past effective rates of interest then what period should we rely on? For example, the Canadian Institute of Actuaries report noted above indicates that the real effective rate of return on Government of Canada long-term bonds averaged -1.31 percent for the period 1956-1980, +8.74 percent for the period 1981-2005, and +6.79 percent for the period 2001-2005. There would be no justification for relying on any one of the above periods over the others, or for averaging these periods together, in attempting to obtain a forecast of the rate of return in the future.

We use the observed rates on government bonds as an indicator of the rates that are anticipated by large institutional investors, with billions of dollars at stake. While one might find that a forecaster is suggesting that (say) 3½ percent is the appropriate real long-term rate, this prediction is contradicted by the fact that the Government of Canada is presently able to sell its long-term bonds which offer a real return of less than three percent. (If expert institutional investors anticipated that real rates on secure investments will average, say 3½ percent over the next ten years, then they would not buy bonds that pay only 2½ percent, and the Government of Canada would be forced to adjust its bond rates.)

Other economists suggest that it would be simpler to assume that a plaintiff will hold a long-term security and then liquidate portions of this security to fund his/her losses in each year. This is simply another version of the market-based approach and, as discussed, there is a great amount of risk inherent in this strategy. Under our approach, if a plaintiff purchases a 5-year government bond with a value at maturity of $10,000, then in five years he is virtually guaranteed to receive $10,000 after redeeming his bond. However, if he were to buy a 20-year bond with the idea that he would liquidate portions of it to fund losses in each year, then he would be at the mercy of the bond prices available in each year. That is, he would be selling portions of his bond (as opposed to redeeming bonds for the guaranteed maturity value) and so, would be relying on the price of bonds attainable at the date he needed to fund his losses. As our discussion regarding the “conservative” versus “market-based” approaches illustrates, a plaintiff trying to fund his losses during periods of high interest rates would likely be selling portions of his bond at prices lower than his original purchase price and so, may not be able to fund his losses in each future year. If there is pressure on interest rates to increase in the next few years, as many economists feel is the case, then it is likely that plaintiffs investing awards from trials occurring in the next year or two would find themselves in this situation. We do not believe it is reasonable to impose this level of risk on a plaintiff.

Over the last ten years our prediction concerning the long-term interest rate has gradually declined from 4¼ percent to three percent. This decline has been in step with the observed rates, which can be seen in the above chart. Other economists have commented on our changes, with the implication that these changes demonstrate a weakness in our methodology. Our response is that the long-term rate has been changing over the past ten years, and it is important to reflect these changes in our calculations. To do otherwise would result in us using interest rates that are inconsistent with the rates that are actually available to plaintiffs.

Even if one finds that over the past few decades, long-term real interest rates have averaged 3½ percent, that rate is not now available to plaintiffs. Today’s plaintiff seeking secure investments simply cannot obtain a guaranteed long-term rate as high as the rates that were available 10 or 20 years ago. Even if the long-term rate rises to 3½ percent in five years, it does not follow that today’s plaintiff will be able to earn a long-term rate of 3½ percent, since he will be limited to the lower rates for the first five years.

Finally, many economists argue that plaintiffs should invest in equities, as well as bonds, and argue that this would result in a portfolio that is less volatile than investing in bonds alone. We find it difficult to justify the assertion that a portfolio that includes equities would be less volatile, given that the value at maturity of Government of Canada bonds is virtually guaranteed. Remember, the purpose behind the plaintiff’s investment of an award is to fund his losses in each future year and this is much different from investing for (say) retirement. The plaintiff must be able to fund his future losses in each year, whereas retirement can be delayed (or retirement plans changed) if there are insufficient funds. A plaintiff who invests in a series of bonds that provide the amount needed to fund his loss in each year, will receive the necessary amount with little to no risk of default. The same can not be said of equities, which carry a very real risk of default. The inclusion of equities can only increase the risk that a plaintiff will not be able to fund their future losses in each year.

We will re-examine our assumptions next year, and expect that some minor adjustments in our shorter-term rates may be warranted, depending on the movement of rates between now and then. As noted, minor changes in our assumptions regarding short-term interest rates will typically lead to negligible changes to our present value estimates. The assumed longer-term rates have a greater influence on our calculations, and if the rate on long-term bonds remains significantly below three percent (as it has since 2004), it may be appropriate to adjust our long-term rates as well.

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Laura Weir, Derek Aldridge, Kelly Rathje, and Christopher Bruce are consultants with Economica.

Forecasting the long-term interest rate on Government of Canada bonds: “market-based” versus “conservative” investment

by Christopher Bruce

This article first appeared in the spring 2007 issue of the Expert Witness.

Introduction

In order to calculate the lump-sum, or discounted, value of a future stream of earnings, the financial expert must forecast the rate of interest (or discount rate) at which the plaintiff’s damages will be invested. Although most experts now base this forecast, to a large extent, on the rates of interest available on Government of Canada bonds, disputes have arisen concerning the manner in which the data concerning these bonds should be interpreted.

Fundamentally, the question comes down to one of whether the plaintiff can be assumed to take a “conservative” approach, in which she invests her damages in long-term bonds and holds those bonds to maturity; or whether she can be assumed to follow a “market-based” (or “speculative”) approach in which she buys and sells bonds as market conditions change.

Whereas Economica favours what I have called the conservative approach, some other economists employ the market-based approach. In this article, I first describe how interest rates are determined under each of these approaches and then I explain why I believe that the market-based approach is inappropriate.

Definitions

Imagine the following scenario: the court has ruled (i) that one component of the plaintiff’s damages is a loss of $50,000 twenty years from now; and (ii) that the interest rate to be used to discount this loss is five percent. In this case, the lump sum value of the loss can be determined to be $18,844 (= $50,000/1.0520).

It is possible that the court could have obtained its interest rate assumption simply by observing the rates offered on twenty-year bonds – what I will call the “posted” rates. Implicitly, in that case, it would have been assuming that the plaintiff will use his damages to purchase a twenty-year bond (or similar, long-term financial instrument) that pays five percent per annum; and that he will hold that bond until maturity. I call this the “conservative” approach.

Alternatively, however, the court might have assumed that the plaintiff will not hold his bond until maturity, but will buy and sell bonds as interest rates vary. In this approach, the effective interest rate will be the average of the rates that the plaintiff can expect to earn over the twenty year period. I call this approach the “market-based investment” approach.

Market-based investment in bonds operates in the following way: Imagine that, at a time when posted interest rates are five percent, the plaintiff has paid $18,844 to purchase a twenty-year bond worth $50,000 on maturity. Assume also that, one year later, interest rates have fallen to four percent. At that rate, it would cost $23,732 (= $50,000/1.0419) to purchase a bond that paid $50,000 nineteen years in the future. The plaintiff could now sell his twenty-year bond, (which, after a year, has nineteen years left on it), for this amount – making a profit of $4,888 (= $23,732 – $18,844), or an effective rate of return of 25.94 percent, in one year.

Rates such as this can be earned on long-term bonds as long as the interest rates on those bonds are falling. For example, a bond that pays $10,000 ten years from now will cost $5,584 when interest rates are six percent; and a bond that pays $10,000 nine years from now will cost $6,446 when interest rates are five percent. Thus, the investor who purchases a ten-year bond at six percent will be able to sell it one year from now for a profit of $862 (= $6,446 – $5,584), or an effective return of 15.44 percent (= $862/$5,584), if interest rates fall to five percent.

Whenever interest rates are falling, the investor who actively trades long-term bonds will make effective rates of return that exceed the rates that would be obtained if those bonds were held to maturity.

Conversely, however, if interest rates are rising, the market-based trader will earn effective rates that are lower than the posted rates. For example, if the interest rate is seven percent, a bond that pays $10,000 nine years from now will cost $5,439 (= $10,000/1.079). It was seen above, however, that a bond that pays $10,000 ten years in the future will cost $5,584 when interest rates are six percent. Thus, an investor who purchases a ten-year bond at six percent will lose $145 (= $5,439 – $5,584), for an effective “return” of -2.6 percent, if interest rates fall to seven percent and he sells it one year later.

What is less clear from these examples is that, if the effective interest rates are averaged over a long period of time, they will equal the rates that investors would have obtained had they held their bonds to maturity. Over the long-run, the investor who sells multi-year bonds after one year, and replaces them each time with other multi-year bonds, will average the same rate of return as an investor who buys and holds bonds to maturity.

Data

Table 1 reports both the posted and the effective rates of interest on Government of Canada bonds of 10+ years to maturity, for the last 25 years. It is seen in the first column of this table that posted interest rates have fallen almost continuously over the entire period: from 15.22 percent in 1981 to 4.39 percent in 2005.

Table 1

Given the discussion above, therefore, we expect to see that effective interest rates over most of this period would exceed the posted rates. It is seen in the second column of Table 1 that this is what happened. Particularly noticeable is the effective rate in 2005: 15.05 percent at a time when posted rates were in the four to five percent range.

As those who argue for the use of effective rates anticipate that the average of those rates will equal the average of the posted rates over the long run, Table 2 reports average posted and effective rates, both in nominal and “real” terms, for various sub-periods in the last 50 years.

Table 2

It is seen there that, whether nominal or real (i.e. net of inflation) rates are used, effective rates have exceeded posted rates in every sub-period in the last 25 years. For example, whereas the average effective nominal rate was 12.49 percent between 1981 and 2005, the average posted rate was 8.64 percent. The comparable real rates were 8.74 and 5.00 percent, respectively, a difference of over three percentage points in each case.

Only if a fifty year period is used do the effective and posted rates begin to approach one another – primarily because the 25 year period from 1956 to 1980 experienced extremely low effective rates of return (hence balancing the high rates from 1981-2005 in the calculation of the fifty-year average).

Drawbacks to Use of the Effective Rate

A review of the information contained in Tables 1 and 2 makes it clear that there are many disadvantages to the use of the effective rate as an indicator of the rate of return that plaintiffs will be able to obtain in the future.

1. The most serious difficulty with this rate is that it has been extremely variable. As a result, one can obtain almost any estimate of the real effective rate that one wishes, simply by choosing the appropriate time period.

Those who wish to argue for a very high rate might choose the fifteen-year period 1991-2005, with an average rate of 9.39 percent, for example. Whereas those who wish to argue for a much lower rate could choose the fifty-year period 1956-2005, with an average rate of 3.71 percent – or even the 60-year period 1946-2005, with an average of 2.44 percent.

There is no sound reason for choosing any one of these periods over the other. For example, it would be difficult to justify averaging together the 1956-1980 average, of -1.31 percent, with the 1981-2005 average, of 8.74 percent, to obtain a forecast of the rate of return obtainable over the next ten years.

2. A related problem is that the extreme variability of the effective rate virtually guarantees that the rate of return the investor will actually earn will differ significantly from the average rate obtainable over the long run. Hence, it would never be prudent to advise plaintiffs to adopt the market-based investment approach on which the effective rate is based.

3. Because long-term interest rates have been falling for 25 years, they have reached levels so low that most analysts believe they will not fall further – they certainly cannot fall by more than ten percentage points, as they did between 1981 (15.22 percent) and 2005 (4.39 percent). This means that the very high effective rates that have been observed in the last 25 years will not be observed again. Indeed, it is highly likely that nominal rates will rise over the near future, causing effective rates to fall, perhaps even into negative figures. As a result, plaintiffs would not be well-advised to engage in market-based investment in bonds.

4. Even if effective rates are positive, and above posted rates, the effective rate is not an appropriate rate for determining long-term rates of return on investments.

Return to the example developed in the first section of this article: The court has found that the plaintiff will lose $50,000 twenty years from now. Hence, if the interest rate is five percent, the lump-sum value of the plaintiff’s damages amount to $18,844. If, between now and one year from now, the interest rate falls to four percent, the plaintiff will be able to sell his bond for $23,732, earning a one-year rate of return of 25.94 percent.

But the plaintiff still needs to set aside enough money to replace his future $50,000 loss. At the new four percent interest rate, this will cost him $23,732. The money he has “earned” by selling his bond now has to be spent to replace it. Thus, the high effective rate of interest is illusory.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

The Discount Rate Revisited (Summer 2006)

by Derek Aldridge

This article first appeared in the summer 2006 issue of the Expert Witness.

Our readers will recall that every year or two we review our standard discount rate assumption and publish our findings. It is time to repeat this exercise.

One year ago, in the Summer 2005 issue of the Expert Witness, we reported that real rates of interest (that is, the rate of return net of inflation) had continued their downward trend. We responded by lowering our forecast of the long-term real rate of interest to three percent – a rate that was slightly higher than the observed real rate of return on long-term Government of Canada bonds, long-term real rate of return bonds, and the long-term rate mandated in Ontario. (Higher rates lead to lower present values, so our estimates can be considered conservative.)

In addition, we made a change to how we applied our discount rate assumptions in our calculations. Previously we had assumed that the plaintiff’s entire lump sum award would earn a given interest rate, regardless of the fact that part of the award might be needed to fund next year’s losses and another part might be needed to fund losses 20 years from now. Our revised approach was to assume that the plaintiff will invest part of his award in short-term investments, part in medium-term investments, part in long-term investments, and so forth. This more accurately reflects the behaviour that would be expected from a plaintiff, and it more accurately reflects the different returns he can expect from his short-term investments versus his long-term investments. [*]

In our previous article we specified our assumptions for real interest rates for periods ranging from one-year to investments of 15 years or more. Our assumptions were based on the observed rates of interest on Government of Canada bonds of various terms. We now have four more quarters of rates to observe and we see that, except for the returns on long-term bonds, rates have increased. The trend in real rates over the last ten years is depicted in the chart below.

Figure 1

Note that to determine the real interest rate we deduct two percentage points from the “nominal” or observed interest rates to reflect inflation anticipated by investors. As the Bank of Canada has managed to keep the core rate of inflation within a small band around this target since the early 1990s, and as it has been the stated intention of not only the Bank of Canada but most other central banks (most notably that of the European Union) to keep the inflation rate at that level, there is now virtual unanimity among investors that two percent will be the long run rate of inflation in Canada. Accordingly, it can be concluded that investors have been acting as if the real rate of interest is the observed, nominal rate less two percent.

From the chart we see that most real rates began to rise with the third quarter of 2005. Long-term government bonds did not begin their rise until the second quarter of 2006 and are now only slightly higher than they were a year ago. The pattern has been similar for real rate of return bonds. Given these changes, we believe a slight increase in our shorter-term rates is warranted, though we will not change our longer-term rates. The most recent two years of real rates are shown in the table below, along with the rates that we will use in our calculations.

Table 1

The change from the rates we have been using for the past year is very modest. Only the rates for years 1-6 have changed at all, and these changes will have a negligible impact on our calculations. The present value of losses that will end within five years will decrease by about one percent relative to our previous assumption, while losses that extend for more than five years will fall by an even smaller amount.

Although we do not show the comparable interest rates on guaranteed investment certificates (GICs), we have examined them and they are consistently lower that the rates of return on bonds. For example, the real rates on 1-year GICs are currently about one percent, while the real rate on 5-year GICs is only about 1½ percent.

Note that we are not specifically assuming that plaintiffs will invest their awards in government bonds and hold them to maturity. There are a variety of reasonable investment strategies they could pursue. We use the observed rates on government bonds as an indicator of the rates that are anticipated by large institutional investors, with billions of dollars at stake. While one might find that a forecaster is suggesting that (say) 3½ percent is the appropriate real long-term rate, this prediction is contradicted by the fact that the Government of Canada is presently able to sell its long-term bonds which offer a real return of less than three percent. (If expert institutional investors anticipated that real rates on secure investments will average, say 3½ percent over the next ten years, then they would not buy bonds that pay only 2½ percent, and the Government of Canada would be forced to adjust its bond rates.)

Over the last ten years our assumption regarding the long-term interest rate has gradually declined from 4¼ percent to three percent. This decline has been in step with the observed rates, which can be seen in the above chart. Other economists have commented on our changes, with the implication that these changes demonstrate a weakness in our methodology. Our response is that the long-term rate has been changing over the past ten years, and it is important to reflect these changes in our calculations. To do otherwise would result in us using interest rates that are inconsistent with the rates that are actually available to plaintiffs.

Even if one finds that over the past few decades, long-term real interest rates have averaged 3½ percent, that rate is not now available to plaintiffs. Today’s plaintiff seeking secure investments simply cannot obtain a guaranteed long-term rate as high as the rates that were available 10 or 20 years ago. Even if the long-term rate rises to 3½ percent in five years, it does not follow that today’s plaintiff will be able to earn a long-term rate of 3½ percent, since he will be limited to the lower rates for the first five years.

As noted, we have changed our assumptions regarding the shorter-term discount rates, but not the longer-term rates. We expect that our estimates of the long-term rate discount rate will change less frequently and to a lesser extent than our estimates of the shorter term rates. This simply reflects that shorter-term rates are inherently more volatile than long-term rates. This can be seen in these charts (Figure 2), which show the percentage point changes in the quarterly real interest rates over the last ten years.

Figure 2

We will re-examine our assumptions next year, and expect that some minor adjustments in our shorter-term rates may be warranted, depending on the movement of rates between now and then. As noted, minor changes in our assumptions regarding short-term interest rates will typically lead to negligible changes to our present value estimates. The assumed longer-term rates have a greater influence on our calculations, and if the rate on long-term bonds remains significantly below three percent (as it has since 2004), it may be appropriate to adjust our long-term rates as well.

Footnotes

* To illustrate the effect of this approach, note that a child plaintiff who will not experience a loss of income for ten years will manage to earn a relatively high rate of return because he will be able to invest in “long-term” investments, and he will be more likely to benefit from possible future increases in interest rates. On the other hand, an older plaintiff who will experience a loss of income over the next five years only, will not be able to benefit from long-term investments or from possible increases in interest rates. She will face the low rates available on short-term investments. [back to text of article]

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Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.

The Discount Rate Revisited

by Christopher Bruce, Derek Aldridge, Kelly Rathje, and Hugh Finnigan

This article first appeared in the summer 2005 issue of the Expert Witness.

In the Autumn 2000 issue of this newsletter, we conducted an extensive review of the various methods of measuring the real rate of interest, or discount rate, and presented evidence concerning the movement of those measures over the period 1995-2000. (That article is available on our website, at economica.ca/ew53p1.htm.)

That survey was subsequently updated in our Winter 2001/02 and Spring 2003 issues. What we found in both of those updates was that interest rates had begun to fall relative to the historically high levels that had persisted over most of the 1990s.

At the time of our Spring 2003 article, we concluded that the best estimate of the long-run discount rate was 3¼ percent. But we also argued that, as interest rates on short-term bonds and GICs were lower than those on longer term investments, it would be appropriate to employ an interest rate of 2¼ percent on the first five years of any investment.

The primary purpose of this article is to examine nine additional quarters (27 months) of data to determine whether the trend we observed in our earlier articles has continued, or whether a revision in our recommended interest rate is appropriate. We also report on recent changes to Ontario’s mandated discount rate; and we revisit the question of whether forecasts of future interest rates should be based on information about past interest rates or on information about current, long-run interest rates.

Revised Data

Instead of providing tables of data comparable to those presented in our earlier articles, we now present a chart that shows the trend in interest rates since 1995. The complete data set can be found on our web site (see www.economica.ca/ew102p1.htm). Figure 1 shows the trend in real interest rates on government bonds of various term lengths, as well as the rate of return on real rate of return bonds.

Figure 1

Note: We deduct two percentage points from the “nominal” or observed interest rates to reflect inflation anticipated by investors. As the Bank of Canada has managed to keep the core rate of inflation within a small band around this target since the early 1990s, and as it has been the stated intention of not only the Bank of Canada but most other central banks (most notably that of the European Union) to keep the inflation rate at that level, there is now virtual unanimity among investors that two percent will be the long run rate of inflation in Canada. Accordingly, it can be concluded that investors have been acting as if the real rate of interest is the observed, nominal rate less two percent.

The data in Figure 1 indicate that real rates of interest have continued the downward trend that began in 1996/97. Whereas we concluded two years ago that long-term real interest rates were approximately 3¼ percent and short-term rates approximately 2¼ percent; it now appears that real rates have fallen substantially below those levels. In particular, note that the rate of return on 10-year Government of Canada bonds, net of the 2 percent expected rate of inflation, is now below 2 percent and has not exceeded 3¼ percent (our earlier prediction of the “long-term” rate) since early 2002. Even the real rate on long-term (30-year) Government of Canada bonds has fallen below 2½ percent in the most recent quarter. And the rate of return on real rate of return bonds is now below 2 percent and has not been above 3 percent since mid-2003.

Although we do not show the comparable interest rates on guaranteed investment certificates (GICs), we have examined them and they are consistently lower that the rates of return on bonds. For example, the real rates on 1-year GICs have been consistently negative since late-2001, meaning that investments in one-year GICs are not keeping pace with inflation. The real rate on 5-year GICs has been below one percent for all but two of the last eight quarters and has not exceeded two percent since early 2002.

Forecasting the Real Rate of Interest

For some time now, Economica has been arguing that current interest rates, net of the two percent expected rate of inflation, provide the most reliable basis on which to predict future interest rates. Some other economic experts in Western Canada disagree with us, and base their forecasts on information about historical interest rates. We consider their position to be unjustified. We explain why here:

The continued dramatic fall in interest rates.

First, as a glance at Figure 1 will indicate, the real rate of interest in the last decade has fallen continuously and dramatically: the long-term rate has fallen from about 7 percent to below 2½, while the short-term rate has fallen from about 6 percent to below 1 percent. Clearly, any prediction that was based on an average of the figures in this period (or any other period extending back to the early 1980s) would seriously overstate the rates that will be available to a plaintiff investing his or her award today.

It is important to note that although rates are low by historic standards, today’s investors who seek the security of investments comparable to government bonds and GICs cannot avoid these low rates. The fact that average interest rates over the last 30 years were much higher does not help today’s plaintiff-investor. Even if one believed that long-term real rates will rebound to (say) 3.5 percent in the next 5-10 years, the best that today’s investor will be able to do is place his funds in 5-10 year investments earning 1.5-2 percent and then hopefully reinvest at the higher 3.5 percent rate. This of course will not yield nearly the same result as if he had been able to invest at 3.5 percent right from the start.

Economic theory.

Second, the fall in real interest rates is consistent with macroeconomic theory. Specifically, many macroeconomists are arguing that the relatively high real interest rates that were observed in the 1980s resulted from the high volatility in expectations concerning the nominal rate of inflation. That is, when inflation is unpredictable, investors who place their funds in long-term bonds face a considerable amount of uncertainty. If inflation proves to be higher than expected, the real rate of return that they realise may be very low or even negative. To compensate for this uncertainty, investors demand a relatively high expected rate of return. Conversely, when inflation becomes predictable, as has happened in the last five to ten years, investors face much less uncertainty and are willing to accept lower real rates of return. Accordingly, there is sound reason to believe that, as long as the Bank of Canada maintains its current course[*] (which it is expected to do), both nominal inflation and real interest rates will remain at the low levels that have been observed recently.

Furthermore, most economists believe that real interest rates will be higher in a period in which governments run large deficits – and, therefore, have to borrow heavily – than in those in which revenues exceed expenditures. As is well known, although the Canadian government ran sizeable deficits in the late 1980s and 1990s, it has now adopted a goal of achieving a balanced (or, even, surplus) budget. Again, this leads us to believe that real interest rates will be lower in the future than they were in the 1980s and 1990s.

The actions of large, institutional investors.

Most of the bonds reported in Figure 1 are purchased by large, institutional investors, such as pension funds. That these investors are willing to purchase, say, ten-year bonds paying a real rate of approximately two percent, or real rate of return bonds that are paying below two percent (as of the second quarter of 2005) indicates that they do not anticipate that they can obtain better rates of return on other secure investments. That is, regardless of whether private investors actually purchase the government bonds identified in Figure 1, the returns on those bonds indicate that the institutions that base millions of dollars of investment on their predictions of the financial markets are forecasting that real rates of return will remain low in the foreseeable future. (If expert institutional investors anticipated that rates on secure investments will average, say 3½ percent over the next ten years, then they would not buy bonds that pay only two percent, and the Government of Canada would be forced to adjust its bond rates.)

A future increase in rates will have little effect on most plaintiffs.

Even if real interest rates were to increase substantially in the next ten years or so, (against expectations), that would have relatively little effect on the investments of many plaintiffs, for two reasons. First, it is the rates of return that are available today that will dictate the average rate that plaintiffs will be able to obtain over at least the first 5-10 years of the period of their loss. As noted above, if rates increase in the future, the best that today’s plaintiff can do is place his funds in 5-10 year investments at today’s low rates and then later reinvest at the (hopefully) higher future rates. Even if rates return to their historical average, this investment approach will still yield an average rate of return that is below the historical average. Second, since most plaintiffs will need to begin consuming their award immediately (to replace their lost income and fund their costs of care), the most substantial portion of the interest that they will earn on the investment of their awards will occur in the first half of their period of loss, before they have drawn down much of their capital (that is, during the period in which they are funding most of their annual losses from interest income). If the period of loss is 20 years or less (like most plaintiffs), then the interest they earn in the first ten years will have a much greater impact on their investments than the interest they earn in the next ten years. Thus a return to higher interest rates after 10 years or so will have only a small impact on these plaintiffs. For plaintiffs with a period of loss that is only ten years or less, future increases in interest rates will have almost no effect on their investments.

Note that one implication of relying heavily on current interest rates is that it requires that we change our discount rate assumption more frequently than if we simply relied on historical averages. However, making changes to our discount rate assumption does not imply a weakness in our methodology. To do otherwise would result in us using interest rates that we know are inconsistent with the rates that are actually available to plaintiffs. Even if one believed that over the long-term, real interest rates will average (say) 3 or 3½ percent, it does not necessarily follow that our discount rate assumptions should remain fixed. This is because (as we explained above), the rates of return over the next ten or so years will have a substantial impact on the investment results of most plaintiffs. Thus, it is important to account for the rates that are available to plaintiffs now, as well as the rates that will be available (on average) over the long-term.

Ontario’s mandated discount rate

Following a detailed review, Ontario (in year 2000) revised its regulations concerning its mandated discount rate. The new methodology that was chosen yields a discount rate of 1.5 percent for the first fifteen years of any award and 2.5 percent for all years beyond that point. Specifically, Ontario’s revised regulation 53.09 states:

53.09 (1) The discount rate to be used in determining the amount of an award in respect of future pecuniary damages, to the extent that it reflects the difference between estimated investment and price inflation rates, is,

(a) for the 15-year period that follows the start of the trial, the average of the value for the last Wednesday in each month of the real rate of interest on long-term Government of Canada real return bonds (Series V121808, formerly Series B113911), as published in the Bank of Canada Weekly Financial Statistics for the 12 months ending on August 31 in the year before the year in which the trial begins, less 1 per cent and rounded to the nearest ¼ per cent; and

(b) for any later period covered by the award, 2.5 per cent per year. O. Reg. 488/99, s. 2; O. Reg. 263/03, s. 4 (1).

The average month-end rate of return on real rate of interest bonds from September 2003 through August 2004 was 2.58 percent. Deducting one percentage point and rounding to the nearest quarter percent yields a mandated discount rate of 1.5 percent for trials that occur in 2005. Given the rates on real rate of interest bonds since September 2005, we can also be almost certain that Ontario’s mandated discount rate (for the first 15 years of loss) will fall to 1.0 percent for trials that occur in 2006.

As discussed in an earlier article (see “Ontario’s Mandated Discount Rate – Rule 53.09(1)” that appeared in the Autumn 2000 issue of the Expert Witness), we have a concern with Ontario’s policy of deducting one percentage point from the one-year average of the rate on real rate of return bonds. What is perhaps more interesting is their finding that 2.5 percent reflects the long-term real rate of interest. This rate is lower than the long-term rate we have been using, though it is consistent with the current rate on long-term Government of Canada bonds.

Conclusion

Our review of the empirical and theoretical sources suggests that it would be appropriate to adjust our discount rate assumption. We also propose to make a change in how we apply our discount rate assumptions in our calculations. Whereas we previously assumed that the real rate of return on all of a plaintiff’s investments would be 2.25 percent for the first five years and 3.25 percent thereafter, we now assume that for income required in the first few years, an investment will be made at short-term rates, while for income needed in the more distant future, investments will be made that will earn the predicted long-term rates. Below we will further explain the approach we will use for our calculations, and then we will outline the discount rate assumptions we will use.

To illustrate the effect of this approach, note that a child plaintiff who will not experience a loss of income for ten years will manage to earn a relatively high rate of return because he will be able to invest in “long-term” investments, and he will be more likely to benefit from possible future increases in interest rates. On the other hand, an older plaintiff who will experience a loss of income over the next five years only, will not be able to benefit from long-term investments or from possible increases in interest rates. She will face the low rates available on short-term investments.

Consider the following example of a plaintiff who will incur a loss of income of $10,000 seven years from now. If she is compensated for the future loss today, she could use her award to purchase a government bond with a seven-year term, and not touch the award until it is needed in seven years, when the bond matures. We will see in Table 1 (below) that such a bond has been paying about 2.2 percent, net of inflation over the last two years. This plaintiff will not need to invest at the lower rates offered by shorter-term assets, but she will also not benefit from the rates offered on longer-term bonds, nor will she benefit from a possible future increase in interest rates. To invest her award in secure assets she faces two options: she can make successive short-term investments in hopes that the rates will increase in the near future, or she can make a longer-term (seven-year) investment and accept the interest rate that is available to her. Given her investment-obligations as a plaintiff, we would expect that that latter option would be more appropriate. Even if she chose the former option we would not expect her overall return to improve, unless we knew that rates would increase in the near future. (And if it was known that rates will increase in the near future, then this increase would already be reflected in the current rate of return offered on seven-year bonds.)

For our calculations we will choose an average rate of return that will be earned on investments that are held until each future year of the period of loss. For example, we assume that the portion of the plaintiff’s award that is held for seven years to compensate her for her loss in year 7 will earn an average rate of return of 2.2 percent. Similarly, we assume that the portion of the plaintiff’s award that is held for 15 years to compensate her for her loss in year 15 will earn an average rate of return of 3.0 percent. And so forth.

To obtain the discount rates for use in our calculations, we propose to take an average of the most recent two years of quarterly interest rates (using two years of monthly rates would yield the same results), for the Government of Canada benchmark bond yields for 2-, 3-, 5-, 7-, 10-year, and long-term bonds. After deducting two percentage points for anticipated inflation and rounding to the nearest tenth of a percent, this will give us our assumed real interest rates for various future terms. We assume the one-year rate is the same as the reported two-year rate, and for the “in-between” years we simply extrapolate. We assume that the long-term rate applies to year 15 and beyond. The rates that result from this approach are shown in Table 1.

Table 1

Note that we believe that the rates proposed in Table 1 (above) remain conservative (that is, they may understate future losses) since they reflect interest rates that have been available over the past two years, instead of only the rates that are available now (even though only the rates available now can be assured to today’s investor).

Footnotes

* Since approximately December 1993, the Bank of Canada has successfully maintained a policy of keeping inflation at a two percent target (the midpoint of its 1-3 percent target range). [back to text of article]

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.

Kelly Rathje is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Calgary.

From 2003 through 2005, Hugh Finnigan was a consulting economist at Economica, with a Master of Arts degree from the University of Calgary.

Selecting the Discount Rate – An Update

by Christopher Bruce, Derek Aldridge, Kelly Rathje, and Scott Beesley

This article first appeared in the spring 2003 issue of the Expert Witness.

In the Autumn 2000 issue of this newsletter, we conducted an extensive review of the various methods of measuring the real rate of interest, or discount rate, and presented evidence concerning the movement of those measures over the period 1995-2000.

That survey was subsequently updated in our Winter 2001/2002 issue (Vol. 6, No. 4). What we found was that interest rates had begun to fall, relative to the historically high levels that had persisted over most of the 1990s.

At that time, we concluded that the best estimate of the long-run discount rate was 3½ percent. But we also argued that, as interest rates on short-term bonds and GICs were lower than those on longer term investments, it would be appropriate to employ an interest rate of 2½ percent on the first five years of any investment.

The purpose of this article will be to provide five additional quarters (15 months) of data to determine whether the trend we observed at the beginning of 2002 has continued, or whether a revision in our recommended interest rate is appropriate.

Revised data

Tables 1 and 2 provide updates of the information contained in the equivalent tables of the Winter 2001/2002 article. In particular, we have added data for all four quarters of 2002 plus the first quarter of 2003.

Table 1 reports the “raw” data from which some of the real interest rate figures in Table 2 have been calculated. The first column reports the “core rate of inflation” – a measure of the rate of inflation that removes the effects of change in those components of the price index that often move erratically, such as food, energy, and taxes. It is often argued that this measure offers a more reliable predictor of future changes in prices than does the “standard” measure of price inflation. (See the Autumn 2000 article for a detailed description of the core rate of inflation.)

The next three columns in Table 1 report the rates of return on Government of Canada 5-year and 10-year bonds and on 5-year Guaranteed Investment Certificates (GICs). The former represent the minimum rates of return that investors can expect on safe investments. The rate of return on GICs, on the other hand, represents the interest rate available on a mixed, low-risk portfolio of stocks and bonds.

Table 1

Table 2 reports seven measures of the real rate of interest – that is, the rate of interest net of the expected rate of inflation. The first of these is the market-determined rate of return on “real rate of return bonds” – bonds whose value is denominated in terms of the real rate of interest. These bonds are of particular importance because they are purchased by sophisticated investors and because they tend to held for long periods of time.

The second, fourth, and sixth columns report the 5- and 10-year government bond interest rates and 5-year GIC rates net of the core inflation measure.

Finally, columns three, five, and seven report the government bond and GIC rates net of the Bank of Canada’s target rate of inflation of 2 percent. As the Bank has managed to keep the core rate of inflation within a small band around this target for the last eight years, it is widely believed that 2 percent is the rate that is expected by most investors. That is, investors are believed to act as if the real rate of interest is the observed, nominal rate less 2 percent.

Table 2

Interpretation of the data

The data in Table 2 indicate that real rates of interest have continued the downward trend that began in 1996/1997. Whereas we concluded a year ago that long-term interest rates were approximately 3½ percent and short-term rates approximately 2½ percent; it appears that those rates have now fallen to 3 percent and 2¼ percent, respectively.

Note that the latter rate is close to the rates reported in the Bank of Canada’s Monetary Policy Report of April 2003 (Chart 19, p. 24).

In addition, 3 percent is the rate at which the Bank of Canada recently issued a new set of 33-year real rate of interest bonds. As we argued in the Autumn 2000 issue of the Expert Witness, the rate of return on these bonds is a particularly reliable estimate of the expected real interest rate as they are purchased primarily by large institutional investors (like pension funds) that have made considerable investments in the prediction of future rates of interest and inflation.

For this reason, we believe that it would be appropriate to revise our existing 2½ and 3½ percent two-part forecast of real interest rates. Based primarily on the observed rate on 5-year Government of Canada bonds, we propose to use a rate of 2¼ percent for the first five years of all calculations. For all subsequent years we propose to use a rate of 3¼ percent – though we note that a rate as low as 3 percent could be supported based on the most recent observed rates on 10-year Government of Canada bonds and based on the Bank of Canada’s current issue of real rate of return bonds. Our long-term rate is perhaps slightly conservative, but we will re-examine this issue next year and decide then if changes are warranted.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.

Scott Beesley is a consultant with Economica and has a Master of Arts degree (in economics) from the University of British Columbia.

Kelly Rathje is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Calgary.

Selecting the Discount Rate – An Update

by Christopher Bruce, Derek Aldridge, Scott Beesley, and Kelly Rathje

This article was originally published in the Winter 2001/02 issue of the Expert Witness.

In the Autumn 2000 issue of this newsletter, we conducted an extensive review of the various methods of measuring the real rate of interest, or discount rate, and presented evidence concerning the movement of those measures over the period 1995-2000.

At that time, we concluded that our best estimate of the long-run discount rate was 4.0 percent. But we added the caveat that, as interest rates in 2000 had deviated significantly from the average of the preceding years, it would be important to maintain a close watch on those rates – to determine whether 2000 was an aberration or whether it represented the beginning of a new trend.

In particular, we concluded that article with the statement:

If bond rates do not rise relative to the rate of inflation in the near future, we will be revising our real rate of interest forecast downward.

The purpose of this article will be to provide five additional quarters (15 months) of data to determine whether such a revision is appropriate.

Revised data

Tables 1 and 2 provide updates of the information contained in Tables 1 and 2 of the Autumn 2000 article. Four changes have been made to the latter tables. First, we have added data for the fourth quarter of 2000 and for all four quarters of 2001. Second, in some cases, the relevant statistical authorities have revised their estimates of the figures we reported previously. In those cases, we have provided the revised figures.

Third, we have added information concerning interest rates on five-year Government of Canada bonds. Finally, in the interest of space, we have omitted the estimates of the real rate of interest that relied on information concerning the “standard” inflation rate.

Table 1

Table 1 reports the “raw” data from which some of the real interest rate figures in Table 2 have been calculated. The first column reports the “core rate of inflation” – a measure of the rate of inflation that removes the effects of change in those components of the price index that often move erratically – such as food, energy, and taxes. It is often argued that this measure offers a more reliable predictor of future changes in prices than does the “standard” measure of price inflation.

The next three columns in Table 1 report the rates of return on Government of Canada 5-year and 10-year bonds and on 5-year Guaranteed Investment Certificates (GICs). The former represent the minimum rates of return that investors can expect on safe investments. The rate of return on GICs, on the other hand, represents the interest rate available on a mixed, low-risk portfolio of stocks and bonds.

Table 2 reports seven measures of the real rate of interest – that is, the rate of interest net of the expected rate of inflation. The first of these is the market-determined rate of return on “real rate of return bonds” – bonds whose value is denominated in terms of the real rate of interest. These bonds are of particular importance because they are purchased by sophisticated investors and because they tend to be held for long periods of time.

The second, fourth, and sixth columns report the 5- and 10-year government bond interest rates and 5-year GIC rates net of the core inflation measure.

Finally, columns three, five, and seven report the government bond and GIC rates net of the Bank of Canada’s target rate of inflation of 2 percent. As the Bank has managed to keep the core rate of inflation within a small band around this target for the last six years, it is widely believed that 2 percent is the rate that is expected by most investors. That is, investors are believed to act as if the real rate of interest is the observed, nominal rate less 2 percent.

Table 2

Interpretation of the data

The data in Table 2 indicate that real rates of interest are lowest on the shortest-term investments, GICs and 5-year bonds, and highest on the longest-term investments, 10-year bonds and real rate of interest bonds. This suggests to us that investors believe that the current slowdown in the economy, which has induced central banks to lower interest rates very significantly, may continue for two or three years but will not continue in the long term.

For this reason, we believe that it would be appropriate to adopt a two part forecast of real interest rates. Based primarily on the observed rate on 5-year Government of Canada bonds, we propose to use a rate of 2.50 percent for the first five years of all calculations. Based primarily on the observed rate on 10-year Government of Canada bonds, we propose to use a rate of 3.50 percent for all subsequent years. Note that the latter rate is close to the average real rate of return on GICs over the period 1964 to 1998, (3.58 percent), reported in Bruce, Assessment of Personal Injury Damages, Third Edition, at page 231.

Once again, however, in recognition of the uncertainty facing our economy, we will revisit this question at the end of this year.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.

Scott Beesley is a consultant with Economica and has a Master of Arts degree (in economics) from the University of British Columbia.

Kelly Rathje is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Calgary.

Selecting the Discount Rate

by Christopher Bruce, Derek Aldridge, Scott Beesley, & Kelly Rathje

This article was originally published in the Autumn 2000 issue of the Expert Witness.

One of the most important determinants of the lump sum award for future losses is the discount rate, or real rate of interest. Simply put, this is the rate of interest at which the plaintiff is assumed to invest the award, after the effects of price inflation have been removed.

For example, assume that the court has found that if the plaintiff was to incur a loss today, the value of that loss would be $10,000. But, because the loss will occur one year from now, and the rate of inflation between today and one year from now will be 2 percent, the loss will actually be $10,200.

The court must determine how much the plaintiff will have to invest today in order to ensure that he or she will have $10,200 available one year from now. The discount rate is the interest rate that is used to make this calculation. The purpose of this article is to determine the current value of the discount rate.

We proceed in four steps. First, we distinguish between “nominal” interest rates and “real” interest rates and explain why the latter are generally used in preference to the former. Second, we review a number of alternative methods of measuring the interest rate. Third, we review a number of methods of estimating the expected rate of inflation. Finally, we report the values of these alternative measures for the years 1997-2000 and we conclude with a recommendation concerning the appropriate value to be used today.

Real versus nominal interest rates

There are two methods of calculating the present value of a future loss. The first is to “discount” the loss by the “nominal” rate of interest – that is, by the rate of interest that is observed at financial institutions. The second is to remove the inflationary estimate from the projected loss, to obtain what is called a “real” loss, and then discount that loss by the “real” rate of interest – that is, the nominal rate after the rate of inflation has been removed. The two methods yield identical results.

For example, assume that the nominal rate of interest is 6 percent. The first method of determining the award is to divide $10,200 by 1.06, (that is, by 1 plus the interest rate). That number is found to be $9,623. It can easily be confirmed that if 6 percent of $9,623 is added to $9,623 one obtains $10,200. That is, if the plaintiff was to invest an award of $9,623 at 6 percent, he or she would have $10,200 at the end of one year.

In the second method, one first “removes” inflation, here 2 percent, from both the future loss and the nominal interest rate. In both cases, this is done by dividing by 1.02, (that is, by 1 plus the inflation rate). Thus, as intuition would suggest, the real level of damages is found to be $10,200/1.02 = $10,000. The real interest rate is found to be 1.06/1.02 = 1.0392, or 3.92 percent. (Note that, in the same way that 1.06 is 1 plus the nominal interest rate, 1.0392 is 1 plus the real interest rate.) When $10,000 is divided by 1 plus the real interest rate, 1.0392, one obtains $9,623, exactly the same answer that was obtained using the nominal method.

Economists generally prefer to use the real loss/real interest rate approach when calculating lump sum awards for future losses. The primary reason for this is that real interest rates tend to be much more stable and, therefore, much more easily predicted, than either inflation rates or nominal interest rates.

Alternative measures of the interest rate

Because plaintiffs often have to rely on the investment of their awards to provide a significant portion of their future incomes, it is important that they place their awards in relatively risk-free investments. For this reason, the discount rate is usually based on the rate of return on either long-term government bonds or secure private sector investments. Once a nominal rate has been determined for one of these investments, it is then necessary to determine an expected rate of inflation (over the duration of the investment) in order to calculate the real rate of return.

In this section, we will consider three types of secure investments. In the following section, we will discuss three methods of estimating the expected inflation rate.

Real return bonds The first investment vehicle is Government of Canada real return bonds. These are long-term, secure bonds whose rate of return is denominated in terms of a real interest rate. (That is, the government guarantees that the investor will receive a specified (real) interest rate plus the actual rate of inflation.) There are a number of advantages to using the rate of return on these bonds.

First, when that rate is used, it is not necessary to make a separate projection of the rate of inflation.

Second, these bonds are guaranteed by the government of Canada.

Third, the estimate of the real rate of interest that is obtained by observing the prices at which these bonds are traded in the financial markets provides an objective measure of the real rate of interest that is forecast by sophisticated investors. Note, we are not suggesting that plaintiffs should, or will, invest their awards in real return bonds. Rather, we are arguing that the observed returns on these bonds provides an excellent, objective measure of the expected real rate of return – as these bonds are purchased primarily by individuals who are close observers of money markets and who have a great deal of money at stake when selecting their investments. (Generally, it is pension fund administrators who purchase real return bonds.)

Recently, Ontario revised its Rules of Court concerning the selection of the discount rate. Whereas the previous rule required that the courts use a fixed rate of 2.5 percent, the new rule bases the rate on current observations of the interest rate on real return bonds. For further analysis of Ontario’s new rule, see the accompanying article “Ontario’s Mandated Discount Rate – Rule 53.09(1).”

Guaranteed investment certificates A second approach to the determination of the real discount rate is to identify a measure of the rate of return on a “safe portfolio” of investments (i.e. the kind of portfolio in which a plaintiff could be expected to invest) and to deduct from that rate the expected rate of inflation. We have long recommended that the rate of return on five year guaranteed investment certificates, GICs, be used for this purpose.

Again, as we commented with respect to real return bonds, we are not suggesting that the plaintiff should use his or her award to purchase GICs. Rather, as the types of investments contained in GICs are similar to those that one would expect a prudent investor to purchase, the rate of return on GICs provides an objective measure of the rate of return that plaintiffs can expect to obtain. (Furthermore, as the quoted rate on GICs is net of investment management fees, there is no need to make a separate calculation of the management fee.)

Long-term Government of Canada bonds The rate of return on long-term government bonds can be used as a benchmark against which to measure the returns on other investments. As these bonds are widely held by private citizens (unlike real return bonds) and as they are among the most secure investments available, it would be expected that plaintiffs would never earn a nominal rate of return less than that obtainable from Government of Canada bonds. (If the plaintiff’s investments began to obtain a lower rate of return, the plaintiff could always, easily, transfer his or her investments to government bonds.) Hence, any suggested discount rate must pass the test that it is not lower than the rate obtainable on government bonds. Conversely, we would suggest that the discount rate used should also not significantly exceed the government bond rate, as that would imply that plaintiffs should place their awards in unacceptably risky investments.

Estimating the rate of inflation

The real rate of interest is calculated by removing the effects of price inflation from the nominal rate of interest. As the interest rate is to apply to investments that will continue for many years into the future, the relevant rate of inflation is the average rate that is expected to apply over that future. We will discuss three methods of forecasting this rate.

Current rate of inflation One simple method is to assume that the current rate of inflation will continue into the future. Use of this rate is based on the observation that investors appear to adjust their expectations of the future when current conditions change. Often it is assumed that this shift of expectations occurs with a short “lag,” of six months to two years. But, in periods in which the rate of inflation is not changing quickly, only small errors will be produced if the current rate is used.

Core rate of inflation In Canada, the reported rate of inflation is measured as the change in the price level of a representative “basket” of goods over a 12 month period. For example, the rate of inflation reported for January 2001 will be the percentage change in prices between January 2000 and January 2001.

What this means is that if there is a large, one-time increase in prices in January 2000, measured inflation will be relatively high in each month from January 2000 to December 2000 and then will fall significantly in subsequent months. The reason for this is that the increased price level produced by the January 2000 price increase will continue to be in effect in every future month. Hence, in every month between January 2000 and December 2000, prices will be higher than in the corresponding month a year earlier. Inflation in those months will be correspondingly high.

For example, assume that the CPI had been 100 in every month during 1999, had risen to 110 in January 2000, and stayed at that level for the rest of the year. Then, in every month during 2000 the CPI would be 110, in comparison with 100 in the same month the year before. Hence, in every month in 2000 the rate of inflation would be reported as 10 percent – even though there had not been a price increase since January.

But, when calculating the January 2001 inflation rate, the price level for that month will be compared to a price level (January 2000) that already contains the one-time increase of January 2000. Hence, the measured rate of inflation in January 2001 (i.e. between January 2000 and January 2001) will drop back to the long-run maintainable rate.

In our example, if the CPI remains at 110 in January 2001, inflation between January 2000 and January 2001 will be 0 percent. The one time increase in January 2000 will have had only a temporary impact on the rate of inflation.

What this observation implies is that if we wish to use the current rate of inflation to forecast the long-run rate of inflation, we must first remove the effect of one-time price increases. The Bank of Canada attempts to provide such a measure of long-run price inflation with what it calls its core rate of inflation. In particular, this measure removes movements in the costs of food and energy and movements in prices due to the effects of indirect taxes.

For example, the core rate of inflation would not include the effects of the doubling of oil prices during 2000. Why? Because, although a doubling of prices from $15 a barrel to $30 (and higher) was not completely unexpected, very few observers expect to see prices rise much higher. Hence, even if prices remain at their current level, within 12 months of the initial increases, inflation (the change in the level of prices) will fall. (The increase in oil prices is an example of the one-time increase we discussed above.)

And, of course, if prices should fall back to their pre-2000 levels, short-term inflation will fall even more – perhaps into negative numbers – for the next 12 months. But no one will expect those low levels of inflation to continue any more than they expect the current high levels to continue.

The implication, then, is that the core rate of inflation may be a better indicator of the long-run, expected rate of inflation than is the measure that is usually reported in the press. For this reason, in the tables below, we report both the core rate and the published rate.

The Bank of Canada’s target rate For the last decade, the Bank of Canada’s monetary policy has been directed at producing a rate of inflation of 2 percent (plus or minus 1 percent). As anyone who can remember the 1970s and 1980s can attest, the Bank has been singularly successful in reaching this goal.

Indeed, it has been so successful, that we believe that it can be argued that most investors have come to believe that the long-run rate of inflation will be (approximately) 2 percent. (The Bank itself reports that most financial analysts are predicting inflation rates of approximately 2 percent. See Bank of Canada Monetary Policy Report, November 2000, p. 32.) For this reason, when determining the real interest rate, in the tables below, we report calculations employing an inflation rate of 2 percent.

The data

We present two tables. Table 1 reports quarterly values of the two nominal interest rates – 10-year Government of Canada bonds and GICs – and two of the measures of expected inflation – the standard version and core inflation – for 1997, 1998, 1999, and the first three quarters of 2000. (We do not report the Bank of Canada target rate of inflation, as it did not change over this period.)

Table 1

Table 2 reports the real rates of interest obtained, first, from the real return bonds and, second, from adjusting the two nominal interest rates by each of the three measures of expected inflation. This produces seven measures of the real rate of interest.

Table 2

What these figures suggest is, first, that the interest rate on real return bonds has been remarkably constant over the last three and a half years, rarely deviating very far from the 4.0 to 4.1 percent range until 2000, when it fell to approximately 3.7 percent.

Second, it is seen that the real rate of interest on 10-year government bonds has also fluctuated around 4.0 percent, but with far larger deviations than was seen with respect to the rate on real return bonds. Some of the wider of these deviations can easily be explained, however.

Note, for example, that the low real rates produced in 1998 and 1999 when the 2 percent inflation factor is used may have resulted because a long period of below-2 percent inflation had caused financial markets to believe that the Bank had lowered its target rate. (The conventional measure of inflation exceeded 2.0 percent only once between the first quarter of 1996 and the third quarter of 1999, when it was reported to be 2.1 percent in the first quarter of 1997.) If the markets had come to expect inflation rates of 1.5 percent in 1998 and 1999, for example, most of the real rates in those years would have been close to 4.0 percent.

The relatively high rates found in 2000 when long-run bond rates are discounted by core inflation, and the relatively low rates found in that year when they are discounted by the standard measure of inflation, could both be “explained” if it was found that financial markets had begun to accept the Bank of Canada’s statement that it was targeting a long-run inflation rate of 2 percent.

The consistently low rates found on GICs, however, are disconcerting. Over the entire period reported in Table 2, and for a number of years prior to that, the rates of return on GICs were significantly lower than those on government bonds. This suggests that plaintiffs would be extremely unwise to invest in GICs for the foreseeable future.

We conclude, therefore, that current estimates of the discount rate should be based on the rates observed on real return bonds and on long-term Government of Canada bonds. Arguably, these rates fluctuated around 4.0 percent for most of the last four years. They have, however, fallen slightly during 2000.

This raises the question of whether 2000 is an aberration, or whether the recent decline in real rates is the beginning of a long-term trend. Some evidence that the decline is expected to be short-lived comes from the Alberta government’s Budget 2000 documents. There, it is reported that nine respected forecasting agencies predicted an average interest rate on Government of Canada 10-year bonds of approximately 6.21 percent (over the years 2000-2003). As it is unlikely that those agencies would have forecast an inflation rate in excess of 2 percent, implicitly they have forecast a real rate of interest of approximately 4.1 percent.

In this light, we believe that a rate of 4.0 percent is the best, current estimate of long-run real interest rates. However, Economica will be monitoring movements in the interest rates on real return and 10-year Government bonds closely. If bond rates do not rise relative to the rate of inflation in the near future, we will be revising our real rate of interest forecast downward.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Derek Aldridge is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Victoria.

Scott Beesley is a consultant with Economica and has a Master of Arts degree (in economics) from the University of British Columbia.

Kelly Rathje is a consultant with Economica and has a Master of Arts degree (in economics) from the University of Calgary.

Ontario’s Mandated Discount Rate – Rule 53.09(1)

by Christopher Bruce

This article was originally published in the Autumn 2000 issue of the Expert Witness.

Recently, Ontario changed its Rules of Court concerning selection of the discount rate. Previously, Rule 53.09(1) required that the courts use a real interest rate of 2.5 percent when discounting future earnings.

The new rule divides the future into two periods – the next 15 years, and beyond 15 years. In the first period, Rule 53.09(1) requires that the courts use the rate observed on real return bonds for the 12 months ending August of the year preceding the date of calculation, less one percent, rounded to the nearest one quarter percent.

For example, as the average rate for the 12 months ending August 2000 was 3.87 percent, all calculations performed in 2001 must use a discount rate of 2.75 percent – that is, 3.87 minus 1.00 rounded to the nearest 0.25.

In the second period, for losses beyond 15 years into the future, 2.5 percent is still to be used.

The wording of Rule 53.09(1) clearly states that the figure obtained by deducting 1 percent from the rate on real return bonds is to represent the discount rate. The committee that recommended the changes to Rule 53.09(1), (the Subcommittee of the Civil Rules Committee on the Discount Rate and Other Matters), deliberately selected this wording.

It was their view that because real return bonds are not traded very frequently and because they receive “unfavourable tax treatment,” “economic and risk factors” biased the reported rate upwards. That is, it was felt that a risk free investment would have a lower rate of return – by 1 percent – than that reported for real return bonds.

I do not agree with the committee’s conclusions on this matter. The committee seems to have been confused about the rationale for using the rate on real return bonds. As was indicated in the article “Selecting the Discount Rate” in this issue, the proposal is not that plaintiffs purchase real return bonds. Rather, the rate of return on those bonds is to be used as an objective indicator of the forecast that sophisticated investors are making of the real rate of interest.

This is not to say that some discount should not be made for the fact that so few of these bonds are bought and sold. But a discount of 1 percent seems well out of line. This was seen clearly in the last section of “Selecting the Discount Rate,” in which recent statistics concerning real interest rates in Canada were summarised.

There it was reported that real rates of interest on risk-free Government of Canada bonds have been very similar to the rates reported on real return bonds in the last three years. It appears that the committee was reluctant to choose an interest rate that would differ significantly from the previous mandated rate of 2.5 percent.

Interestingly, the Ontario Court of Appeal, in Martin v. Listowel Memorial Hospital (Docket C31222, November 1, 2000), concluded that the current real rate of interest is approximately 4 percent, not the 2.75 percent implied by its own Rules of Court. Indeed, in the Martin decision, the Court seemed to signal that it was willing to accept evidence concerning the discount rate on a case-by-case basis – hardly a ringing endorsement of the newly-established Rule 53.09.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

Selecting the Discount Rate

by Christopher Bruce

This article first appeared in the autumn 1996 issue of the Expert Witness.

The discount rate is the interest rate at which it is assumed plaintiffs will invest their awards in order to replace their future streams of losses. As was explained in the first issue of this newsletter, it is the “real” rate of interest – or observed rate of interest net of the expected rate of inflation – which most financial experts prefer to use for this purpose.

In six provinces, the discount rate has been set by regulation. In the remaining four, including Alberta, however, the expert must provide evidence concerning the forecasted value of the real interest/discount rate. The purpose of this article will be to review a number of techniques for obtaining such a forecast and to provide an estimate of the real rate of interest based on the most reliable of these techniques.

The article will be divided into three sections. In the first, I list the rates in the six provinces which mandate a discount rate. In the second section, I summarise three methods which have been used to forecast real interest (discount) rates and identify the strengths and weaknesses of each of those methods. Finally, I select one method and use it to select a discount rate for use in Alberta.

Mandated Discount Rates

Mandated discounted rates in Canada
Province Discount Rate
British Columbia 3.5% (cost of care)
2.5% (loss of income)
Saskatchewan 3.0%
Manitoba 3.0%
Ontario 2.5%
New Brunswick 2.5%
Nova Scotia 2.5%
Prince Edward Island 2.5%

The discount rates shown in the previous table have been mandated in Canada.

Three Methods for Determining Discount Rates

1. The historical approach: The approach which, implicitly, has been favoured by those provinces which have mandated their discount rates is to assume that the average rate which has been observed in the past will continue into the future. Typically, those who use this approach rely on the real interest rates which have been reported over the entire post-World War II period. What analysis of these rates indicates is that real rates were fairly stable over the period 1950-1970, at approximately 3 percent. During the oil crisis, of the early 1970s, real interest rates fell, sometimes becoming negative. Towards the end of that decade, however, they began to rise again and it appeared that they would return to their historical level. But the rise continued beyond 3 percent and since 1983 real interest rates have consistently remained above that level. Indeed, real interest rates have remained above 4 percent for so long that it is now difficult to justify the use of a rate lower than that. At the very least, any expert who attempted to rely on the historical 3 percent average to forecast future rates of interest would have to explain why the 1980s and 1990s were such an anomaly.

2. Forecasting agencies: There is a small number of consulting firms in Canada which provide forecasts of such economic variables as GNP, the unemployment rate, and inflation. They will also forecast other variables, including the real rate of interest. Extreme caution must be used when employing these firms’ long-term forecasts, however. First, the mathematical models which they employ were built specifically to make short- term forecasts. Second, long-term forecasts cannot be made without imposing assumptions about many factors which are outside the mathematical models developed by these agencies, such as foreign interest rates, exchange rates, and government monetary and fiscal policy. Finally, private forecasters have little incentive to produce accurate long-term forecasts. A consulting firm’s reputation will not hinge in any way on the accuracy of its current forecasts concerning, say, the level of unemployment in 2020. The forecasts which customers use to evaluate the agencies’ accuracy are those which have been made into the near future, not the distant future. Hence, it is forecasts of one or two years on which consulting firms concentrate their resources. The real rate of interest, on the other hand, must commonly be forecast twenty or thirty years into the future.

3. Market rates: The third source of information concerning future real rates of interest is the money market. When an investment firm which believes that inflation will average 2 percent per year purchases 20 year bonds paying 6 percent, it is revealing that it expects the real rate of interest will average 4 percent over those 20 years. (The real rate of interest is the 6 percent observed, or “nominal,” rate of interest net of the 2 percent inflation.) Thus, if we knew the rate of inflation which investors were forecasting, that forecast could be used to deflate the nominal rates of interest observed in the market in order to obtain the implicit, underlying real rates. At the moment, such forecasts can be obtained with some accuracy. Not only do surveys of investors conclude that there is considerable agreement among them with respect to their forecasts of inflation – generally between 2 and 3 percent – but we know that the government is strongly committed to maintaining a long-run inflation rate below 3 percent. Thus, we can be confident that investors predict real rates of interest which are no less than the observed, nominal rates less 3 percent. (For information concerning the long-run expected rate of inflation, see Bank of Canada, Monetary Policy Report, May 1996.)

Alternatively, the Canadian government has for some time issued bonds which are denominated in terms of real interest rates, (real rate of interest bonds, or RRBs). By observing the rates of return at which these bonds sell, the real rate of interest which investors believe will prevail over the future can easily be determined. There are two drawbacks to the use of market interest rates to forecast future real rates of interest. First, the rate which is obtained from this method has not been stable, but has generally fluctuated between 4 and 6 percent since 1983. Hence, no definitive conclusion can be drawn. Second, as very few RRBs have been issued, the rates of return which they have obtained may not accurately reflect the rates in the market as a whole.

Forecasting the Discount Rate

Of the three techniques for forecasting real interest rates discussed in the previous section, the least satisfactory is the first one, based on historical rates. As those rates have varied so widely since the early 1970s, they convey little reliable information concerning the future. Of the remaining two, most economists prefer the market-based technique. A simple analogy will explain why.

Imagine that you wished to determine the average price which potential purchasers were willing to pay for twenty-year old, three bedroom bungalows in Edmonton. One approach would be to conduct a telephone survey of Edmontonians, asking them what they would be willing to pay for such homes. A second approach would be to observe the actual prices at which such homes sold in Edmonton. Clearly, the second approach is preferable. Why? Because rather than asking individuals how they think they will behave in some hypothetical situation, it observes how individuals actually behave when they have to commit large sums of money to their decisions.

Similarly, economists who are asked to forecast long-term interest rates recognise that little is at stake should those forecasts be in error. Whereas those who are involved in purchasing long-term bonds recognise that the smallest error can result in losses of tens of thousands, even millions of dollars. For this reason, Economica prefers to rely on the interest rates observed in the money market, rather than on surveys of economic consultants, to determine the long-run discount rate.

The following table summarises money market estimates of the long-run real rate of interest for three series: the rate of return on trust company five year guaranteed investment certificates, the interest rate on Government of Canada 10-year bonds, and the rate of return on RRBs. In each case, the figure represents the average of the rates reported in the second quarter (April-June) of 1996, net of the forecast rate of inflation. Two alternative real rates have been calculated for the GICs and the 10-year bonds: the first uses a forecasted rate of inflation of 2 percent and the second a rate of 3 percent. (The figure for RRBs is the same in both scenarios as the observed, market rate is already net of the rate of inflation.)

Real Rates of Return on Selected Long-term Investments: Canada 1996
Investment 2% Rate of Inflation 3% Rate of Inflation
Trust Company 5-year GICs 4.5% 3.5%
Government of Canada 10-year bonds 5.6 4.6
Real rate of return bonds 4.7 4.7

The figures in this table suggest that investors currently anticipate that the real rate of interest will fall somewhere between 3.5 and 5.0 percent. At Economica, we employ the mid-point of this range: 4.25 percent.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).

What is a “Discount Rate”?

by Christopher Bruce

This article first appeared in the spring 1996 issue of the Expert Witness.

Alberta is one of only four provinces in which the discount rate is not mandated. As I argued in Ontario’s 2 1/2% Solution (Canadian Bar Review, December 1982) this means that we are able to react much more flexibly to changes in the economic situation than are the six provinces whose rates are set by a central authority. Indeed, the superiority of Alberta’s approach is seen in the fact that whereas interest rates have varied significantly over the last 15 years, not one of the provinces with mandated rates has adjusted that rate.

Nevertheless, the lack of a mandated rate does carry the drawback that an onus is placed both on financial expert witnesses and on counsel to understand how the discount rate is determined and to identify whether economic forces have changed in such a way as to make previous assumptions about that rate obsolete. The purpose of this article will be to provide a basic explanation of what the discount rate is and of how it works. In a second article, I identify a number of alternative methods of forecasting the discount rate and use what is generally considered to be the preferred method to identify such a rate for Alberta.

Assume that a plaintiff will require dental work one year from now. If that work was carried out today, it would cost $1,040. The question which faces the legal system is: “How much does the plaintiff have to be compensated today, in order to ensure that he/she will have enough money to pay for this procedure one year from now?” The answer to this question depends, first, upon the effect of the rate of inflation on the cost of the procedure; and, second, upon the rate of interest at which the plaintiff can invest his/her award.

The effect of the rate of inflation is relatively straight forward. If, for example, the cost of dental procedures is expected to increase by 2.5 percent in the next year, this plaintiff will need $1,040 increased by 2.5 percent one year from now. That is, the amount required will be:

$1,040 + (2.5% x $1,040)
= (1.00 x $1,040) + (0.025 x $1,040)
= (1.00 + 0.025) x $1,040
= 1.025 x $1,040
= $1,066

In short, to find the inflated value one year from now, the current value (here, $1,040) is multiplied by 1 plus the rate of inflation (here, 1.025).

The second step is to determine how much has to be paid to the plaintiff today in order to ensure that he /she will have $1,066 one year from now. Assume for this purpose that the rate of interest which plaintiffs can expect to receive on secure investments is 6.6 percent per annum. It is intuitively clear that $1,000 invested at this rate will yield $1,066 (the desired amount) one year from now. Formally, this $1,000 figure, which is called the present discounted value or commuted value of $1,066, can be derived in the following way: Call the present discounted value $P. When $P is invested at 6.6 percent interest, we want it to yield $1,066. Hence,

$P + (6.6% x $P) = (1.00 x $P) + (0.066 x $P)
= (1.00 + 0.066) x $P
= 1.066 x $P
= $1,066

That is, we know that

1.066 x $P = $1,066

Therefore, to find $P, we need only divide both sides of this equation by 1.066, to obtain

$P = ($1,066 / 1.066)
= $1,000

Remembering that the $1,066 figure in this equation was found by increasing the current cost of the dental procedure, $1,040, by the rate of inflation, 2.5 percent, it is now seen that amount which must be paid to the plaintiff today, $P, may be obtained from the formula:

$P = $1040 x (1.025 / 1.066)
= $1,040 x (1.00 / 1.04)
= $1,000

What this set of calculations is intended to show is, first, that $P can be found by multiplying the current cost of the expense to be compensated, here $1,040, by (1 + inflation), here 1.025, divided by (1 + interest), here 1.066. Second, (1.025 divided by 1.066) can be replaced by (1.00 divided by 1.04). This 1.04 figure is known by economists as the real rate of interest or the discount rate. This is the figure which expert witnesses use to determine the present, or lump sum value of a future cost. It is called the real rate of interest because it was calculated by dividing 1.066 by 1.025; that is, (1.025/1.066) = 1.00/(1.066/1.025) = (1.00/1.04). Dividing (1 + interest) by (1 + inflation) in this way has the effect of “netting out” the impact of inflation from the observed, or nominal, interest rate, leaving only that element of interest payments which is independent of inflation – the “real” rate of interest.

Economists and other financial experts have used the real rate of interest to discount future losses because it has been less volatile than the nominal rate of interest. (The nominal rate increases and decreases with the rate of inflation while the underlying real rate remains stable.) Recently, however, the real rate has been almost as variable as the nominal rate. Nevertheless, because the courts have become accustomed to the use of the real rate, the Expert Witness will follow that convention.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).