Year: 2008

Winter 2008 issue of the Expert Witness newsletter (volume 13, issue 2)

Posted on By economica

Contents:

  • Premiums, Profits, and Costs of Business in Alberta’s Automobile Insurance Industry, 1996-2006
    • by Christopher Bruce and Jason Strauss
    • In February 2008, Economica was retained by the Canadian Bar Association to prepare a series of reports on automobile insurance premiums in five provinces: Alberta, Ontario, New Brunswick, Prince Edward Island, and Nova Scotia. We have now completed this work, having prepared two reports on Alberta and one on each of the other four provinces. The first article in this newsletter summarises the main findings of the first of these reports, Alberta’s Minor Injury Regulation: Automobile Insurance Profits, Premium Rates, and Costs.
  • Examination of Expert Witnesses
    • by Christopher Bruce and Derek Aldridge
    • This article is based on Chris Bruce and Derek Aldridge’s experience as panelists at a Legal Education Society of Alberta seminar on examination of expert witnesses. The article offers some recommendations regarding the examination of expert economists.

Examination of Expert Witnesses

Posted on By economica

by Christopher Bruce and Derek Aldridge

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

On October 28 in Edmonton and October 29 in Calgary, Chris Bruce and Derek Aldridge were participants in a Legal Education Society of Alberta panel on examination of expert witnesses. In this note, we offer some recommendations regarding the examination of expert economists. These recommendations are based on our comments during the panel, and the feedback we received.

We divide our advice into pre-testimony and during-testimony periods.

Pre-Testimony

An effective examination is not created days, weeks, or even months before trial, but years. That is because an effective examination begins with a well-constructed expert’s report. In our experience, at least half of the judge’s impression of your expert’s opinion is going to be based on his or her reading of that expert’s report. Our advice, therefore, is that as soon as you receive the first report from your expert, you should try to read it from the perspective of the judge. If you cannot follow the report easily, despite having been immersed in the case, it is not likely that the judge will be able to follow it either.

This is not to say that you should attempt to influence what your expert is going to say. You do, however, have the right to ask your expert to improve how that opinion has been expressed. At this stage, you should particularly be looking for a clear, logical, methodical development of the expert’s argument. Are the facts and assumptions, upon which the opinion has been based, stated clearly? Is there a clear progression from the facts and assumptions to the conclusions? Does the expert employ clear, simple terminology and arguments? Does he or she “tell the reader what he/she is going to say, say it, then tell the reader what has been said?” Too often, we are sent opposing experts’ reports with a request that we please explain what that expert has said. If the lawyer we are working for cannot understand the opposing expert’s report, it is unlikely that the lawyer for whom the report was prepared could understand it either ? and it is also highly unlikely that the judge will understand it.

Be cautious when asking your economist to present scenarios that may not be supportable. For example, suppose your plaintiff had a well-established career and earned a steady income averaging $75,000 per year. Your economist will likely include a scenario in which it is assumed that the $75,000 annual income would have continued, but for the accident. However, your plaintiff might have advised you that earnings of $100,000 would have been available, due to a likely promotion, and you may decide to ask your economist to include such a scenario, with the understanding that supporting evidence (say, from the employer) will be forthcoming. If it turns out that no evidence will be offered in court to support the more-optimistic scenario, it will reflect badly on your expert (and your case) if the judge is unimpressed with scenarios that are presented as “illustrative only” or “at the request of counsel.”

We strongly recommend that you have a meeting with your expert some time in the two or three weeks preceding a trial: to clarify what the expert’s opinion is in detail and to prepare the most effective method of presenting that opinion in court. We feel that there are at least four major advantages to this pre-trial meeting. (i) As most experts are involved in hundreds of actions and may have written the report in this case months, if not years, ago, a pre-trial meeting can ensure that the expert is fully familiar with his/her own report. (ii) As it is common that new information becomes available in the last month or two before the trial, it is important that the expert is made aware of this information. (iii) You and the expert should discuss the most effective techniques for presenting his/her evidence. Are you, for example, going to follow the expert’s report page-by-page? At this stage, it is often useful to try some practice questions on the expert as experts can sometimes find the wording of questions to be confusing. If there are certain points that you especially want your expert to make during his/her testimony, make sure that your expert knows this, and knows what type of question you will ask in order to obtain the desired response. (iv) A review of the file with your expert may provide you with a clearer assessment of the strengths and weaknesses of both your expert’s report and that of the opposing experts, thereby creating a firmer basis on which to negotiate a settlement.

It is often also important to meet with your expert during the trial, a day or two before his/her testimony. As the lay witnesses appear before the experts, it is important that your expert be informed about any new information that has been presented during the lay testimony. Also, since the economist typically follows most (if not all) of the other experts, your economist can be advised of what evidence was ultimately offered by some of the other experts who prepared reports that were used as a foundation for the economist’s evidence. For example, if the vocational expert’s evidence has changed slightly from that offered in his 218 report (based on new information offered by lay witnesses during trial perhaps), it is important for your economist to know about this. Finally, the expert can be informed concerning the general approach that has been taken by both the opposing counsel and by the judge.

In the weeks or days before testimony, it is important to discuss with your expert the counter-arguments that you and he/she expect will be raised by the other side. While rebuttal reports may been prepared already, it is useful to try to identify what will be the most contentious economic issues, and what your expert’s response will be. Discuss any weaknesses in your expert’s report, and how they might be dealt with in court.

During-Testimony

Unless you have a particularly poorly-qualified expert, you should always begin the expert’s testimony by reviewing his/her qualifications, to impress the judge with the expertise of your witness. If you have a particularly well-qualified expert, opposing counsel may attempt to preclude you from introducing these qualifications by announcing that he/she will accept the expert’s qualifications without a review of the c.v. It is not advisable, of course, to succumb to this tactic.

Before beginning a review of the expert’s qualifications, it is advisable to inform the judge what that individual’s area of expertise is, so the judge can contrast the expert’s qualifications with the expertise that you are claiming.

Do not simply ask the expert to describe his/her c.v. Some experts will be too modest to provide a full description ? and some will be too boastful. Rather, ask them a series of questions about specific aspects of their expertise ? for example, about their most important educational attainments, their professional experience, their most important publications, and their experience testifying.

Enter the expert’s report and base your examination on the report. As the judge will not have expertise in the expert’s area, it will be useful for the judge to have the report before him/her as an aid to understanding the testimony. Also, as the judge will need to read the report later, when preparing a decision, it will be useful to be able to relate the recorded testimony to the report.

Follow the report page-by-page, if not paragraph-by-paragraph or line-by-line in your questioning of the expert. Our experience is that judges find it useful to follow the report during the testimony. If you start jumping around from page to page, the judge will become frustrated.

Ask questions that require only short answers. The court’s attention is held better that way than by allowing the expert to ramble on, perhaps becoming embroiled in the language of his/her discipline.

If you are representing the plaintiff and you think opposing counsel is going to introduce his/her own expert to counter yours, it may be advisable to ask your expert to comment on the opposing expert’s arguments. Your expert may be in a better position to expose the weaknesses of those arguments than you will be in cross-examination.

Similarly, you should also attempt to anticipate the tack that opposing counsel will use in cross-examination of your witness and ask your expert to comment on the anticipated arguments. Your expert will be much more comfortable “arguing” with you than with your opponent, both because cross-examiners will often severely curtail any attempt by experts to raise counter-arguments and because most experts will be reluctant to appear argumentative (with cross-examiners) as it makes them appear biased.

Sometimes during cross-examination, your expert may concede a weakness or error in his/her report. If the other lawyer does not allow your expert ample opportunity to discuss the significance of this weakness/error, then it may be helpful for you to raise the issue during redirect. This will provide your expert with additional time to think about the issue, and to provide a more in-depth response, if one is required.

Conclusion

In summary, a successful examination of your expert economist begins with a well-written report, containing scenarios and assumptions that match the evidence that will ultimately be offered in court. Regardless of your expert’s prior trial experience, it is always useful to meet with him or her before trial to discuss the economic evidence that will be offered, prepare for the other side’s arguments, and advise him/her of relevant testimony by other witnesses. With a suitable foundation and preparation before trial, your expert will have the best opportunity to perform well during trial.

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Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary.

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

Premiums, Profits, and Costs of Business in Alberta’s Automobile Insurance Industry, 1996-2006

Posted on By economica

by Christopher Bruce and Jason Strauss

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

Introduction

In February, 2008, Economica Ltd. was retained by the Canadian Bar Association to prepare a series of reports on automobile insurance premiums in five provinces: Alberta, Ontario, New Brunswick, Prince Edward Island, and Nova Scotia. We have now completed this work, having prepared two reports on Alberta and one on each of the other four provinces.

In this article, we summarise the main findings of the first of these reports, Alberta’s Minor Injury Regulation: Automobile Insurance Profits, Premium Rates, and Costs, prepared by Christopher Bruce, of Economica, and Jason Strauss, a Ph.D. student in the department of Risk Management and Insurance at Georgia State University. (The full text of this report can be found at: www.cba-alberta.org)

Our Report had three purposes:

  • to provide a measure of the profitability of automobile insurance in Alberta in the period 1996-2006, (that is, immediately preceding and immediately following the introduction of Alberta’s Minor Injury Regulation, the MIR, in the Fall of 2004);
  • to determine whether the observed changes in profits and premiums in the years prior to the introduction of the MIR had been caused by changes in costs; and
  • to identify what the effects on profits and premiums would be if the MIR was removed.

We summarise the results of our analyses in the three following sections of this article.

1. Profitability of Basic Coverage

As the MIR applied primarily to Basic Coverage, we focus in this section on that line of insurance. The methodology we use to estimate profits is based on the approach developed by the Insurance Bureau’s actuary, Mr. Joe Cheng, for his testimony in the case of Morrow v. Zhang (2008). (It was in Morrow that the constitutionality of Alberta’s Minor Injury Regulation was challenged.)

The most common measure of industry profitability (and the measure used in the Cheng Report), is after-tax “return on equity” (ROE) – that is, the industry’s after-tax profits divided by the value of the investments made in the industry. In Table 1 and Figure 1 (taken from our Report), we show that, prior to 2003, Basic Coverage was not profitable in Alberta, with an ROE ranging from -5.6 to +2.1 percent. In 2003, however, the return on Basic Coverage increased dramatically, to 19.1 percent, and rose above 20 percent in each of 2004, 2005, and 2006.

Table 1

Figure 1

1.1 Claims costs relative to total costs

It is possible that the sudden increase in ROE in 2003 could have arisen from a dramatic change in the costs of claims. The data in Table 2, however, indicate that these costs remained a relatively constant portion of insurance companies’ total costs throughout the entire period 1996 to 2006. That is, the rate at which the costs of claims were rising was not appreciably different from the rate at which insurance companies’ other costs – primarily the costs of administration – were increasing.

Table 2

1.2 Claims costs relative to premiums

Alternatively, profits may have risen in the 2003/2004 period because claims costs fell relative to premiums. We investigate this possibility in Table 3, which reports changes in claims costs per motorist, relative to average premiums. What this table indicates is that, until 2002, premiums tracked claims costs fairly closely. That is, each increase in claims costs per motorist was matched by a similar increase in insurance premiums, resulting in a ratio of costs to premiums that varied only slightly. For example, while the average claim for Basic Coverage was 99.0 percent of the average premium in 1996, that ratio was 92.9 percent in 2002 – because premiums rose by 39.1 percent over that period, while average claims rose by a similar amount, 30.3 percent.

Table 3

In 2003 and 2004, however, premiums rose much more quickly than did claims costs, driving down the claims ratio. Between 2002 and 2004, for example, the average premium rose by 19.3 percent, while average claims actually fell by 21.9 percent. Thus, it appears that the dramatic increase in profit rates over the 2003-2004 period was driven, in large part, by a sudden change in the relationship between the costs of Basic Coverage and the premiums that were charged for that coverage. In the following section, we investigate a number of factors that might have led to this change.

2. Changes in Costs per Vehicle

The price of automobile insurance – the premium – is affected by four components. First, there are the average costs of claims (including adjustment expenses) per vehicle that were discussed in the preceding section. Second, allowance must be made for administration expenses (broker’s commissions, overhead, etc.). Third, insurers earn income from the investment of equity and reserves (premium revenue that will eventually be used to pay claims). Finally, a reasonable rate of profit must be added to net costs.

The question we address in this section is whether the increases in premiums between 1996 and 2004 can be attributed to changes in any of these components.

2.1 Average claims per vehicle

In Table 3, we showed that the cost of claims rose at approximately the same rate as the price of premiums over the period 1996 to 2002. Thus, if there was a need for increased premiums in 2003 and 2004, it was not because the ratio of claims costs to premiums had changed over the preceding six years.

Nevertheless, Basic Coverage is composed of a number of sub-categories, including Third-Party-Liability and Accident Benefits. In turn, Third-Party-Liability (TPL) is composed of TPL-Property Damage and TPL-Bodily Injury, of which only the latter was affected by the Minor Injury Regulation (MIR). Thus, it is possible that even though claims costs for Basic Coverage as a whole did not increase in 2003 and 2004, there may yet have been an increase in the component that was affected by the MIR. To investigate this possibility, we report the data in Table 4.

Table 4

In this Table, it is seen that the claims for TPL-Bodily Injury increased at roughly the same rate as the other components of Basic Coverage prior to the MIR. For example, whereas claims for Bodily Injury increased by 32.5 percent between 1996 and 2002, claims for Property Damage increased by a similar percentage, 27.8.

We are led to ask, therefore, whether a change in some other element of the cost of insurance can explain the sudden increase in premiums that was observed in 2003 and 2004. In sections 2.2, 2.3, and 2.4 we analyze administrative expenses, investment income, and return on equity.

2.2 Administrative expenses

Table 5 reports that the ratio of administrative expenses to premiums (the expense ratio) decreased from 25.5 percent in 1996 to 23.8 percent in 2001. As average premiums increased only slightly over this period, the dollar value of expenses must have been decreasing or relatively stable. Furthermore, in the time period immediately prior to the introduction of the Minor Injury Regulation, 2002 and 2003, expense ratios fell further while premiums increased dramatically. It can be concluded, therefore, that changes in administrative expenses were not the source of the premium increases that occurred in 2002 and 2003.

Table 5

2.3 Return on investment

Insurance premiums are placed in a reserve until claims have to be paid. Those reserves are invested and the investment income generated thereby is credited against the cost of premiums. Hence, an increase (reduction) in the rate of return on investment, ROI, may lead to a decrease (increase) in premiums.

It is seen in Table 6 that the ROI insurers earned on their equity and reserves declined almost continuously over the period 1996 to 2001. Nevertheless, this decrease placed only limited upward pressure on premium rates. Specifically, we estimate that to compensate for the decrease in ROI from 9.0 percent in 2000 to 6.2 percent in 2003, insurers would have needed a $44 increase in the 2003 premiums on Basic Coverage. In fact, those premiums increased by $213, from $537 to $750. (See Table 3.) This confirms that decreasing ROI was not the primary impetus for the premium increases in 2002 and 2003.

Table 6

2.4 Return on equity

Once the net costs of insurance have been calculated, the premium is determined by adding a profit margin, or return on equity, ROE, to those costs. Thus, as the necessary ROE increases, premiums will also increase. We surveyed seven sources of expert opinion concerning the appropriate ROE target for the automobile insurance industry. We found:

  • Dr. Norma Nielson and Dr. Mary Kelly, in a presentation to the Alberta AIRB October 20, 2006, recommended an ROE in the range of 14.31 to 18.26 percent
  • NERA Consulting Economists, in a report for the Newfoundland & Labrador Board of Public Utilities, October 13, 2004, recommended an ROE in the range of 11 to 14 percent.
  • Based on NERA’s report, Dr. Ronald R. Miller of Exactor Insurance Services Inc. recommended an ROE of 12.5 percent.
  • Dr. Basil A. Kalymon, on behalf of the consumer advocate, recommended to the Newfoundland & Labrador Board of Public Utilities that the target return on equity for the setting of automobile insurance rates should be 9 to 10 percent.
  • The consumer representative to the Alberta AIRB, Ms. Merle Taylor, CMA, recommended that the ROE be higher than the allowable rate for utilities (at that time, 8.9 percent). She also stated that a 19.6 percent ROE would be “excessive.”
  • In his testimony in Morrow v. Zhang (2008), actuary Joe S. Cheng, F.C.I.A. stated that a 12.5% ROE was considered by many insurers to be in the low end of a reasonable range; and that the high end of a reasonable range might be 20%.

The Alberta Automobile Insurance Rate Board (AIRB) currently employs a formula that implies that an after-tax ROE of 9.5 percent would be appropriate.

Excluding the report by Merle Taylor, which did not give an exact range or recommendation, the average of the six remaining experts’ opinions concerning a reasonable ROE for automobile insurance is 12.76 percent. This figure is well above the rates earned on Basic Coverage in Alberta between 1996 and 2002, (see Table 1), but is well below the rates earned since then. Most importantly, Alberta insurance companies earned an ROE of 19.1 percent in 2003, the year before the introduction of the MIR.

2.5 Summary and conclusions

  • As indicated in the preceding sections, claims did not dramatically increase in the time period leading up to the Minor Injury Regulation.
  • As also shown above, administrative expenses did not increase but, rather, decreased in the time leading up to the Minor Injury Regulation.
  • Although investment returns decreased in the time leading up to the Minor Injury Regulation, their effect on the increase in premiums was minor.
  • ROE for Basic Coverage averaged -1 percent per year in the period 1996 to 2002 (7.4 percent for All Coverages). During this same period, average premiums for Basic Coverage only increased by 6 percent per year on average (4.5 percent per year on average for All Coverages). This premium deficiency (the difference between premium charged and premium required to reach a reasonable rate of return) appears to have been the primary impetus for the sharp increase in premiums that occurred in 2002/2003, as the “soft” market ended and a “hard” market began.
  • We estimate that without the premium increases in 2002 and 2003, ROE on Basic Coverage would have been -3.8 percent (in 2003).

 

3. Projected Effect of Removing the Minor Injury Regulation

Using the AIRB’s methodology, and controlling for other reforms beside the Minor Injury Regulation (i.e. controlling for the gross to net income reform and the collateral income reform), we estimate that the required average premium increase for Basic Coverage, if the Minor Injury Regulation had been removed, would have been $111.76/year if industry profits were to be maintained at their 2006 level, of 21.8 percent.

Alternatively, using the AIRB’s methodology, we estimate that insurer ROE for Basic Coverage would have been 12.2 percent in 2006 if the Minor Injury Regulation had been removed and premiums held constant. (Furthermore, in this case, the ROE would have been 16 percent for All Coverages.)

leaf

Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary.

Jason Strauss is a Ph.D. student in the department of Risk Management and Insurance at Georgia State University.

Spring 2008 issue of the Expert Witness newsletter (volume 13, issue 1)

Posted on By economica

Contents:

Mathematical Mistake: Averaging Multiple Statistical Sources Together to Form One “Overall” Average Income Figure

Posted on By economica

by Laura Weir

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

In estimating a plaintiff’s without- or with-incident income, there is a mathematical mistake that an economist can make that will potentially have a large impact on the resulting income path and, subsequently, on the plaintiff’s loss of income. This mistake is the practice of averaging multiple statistical sources together to obtain one “overall average”. It may seem reasonable, at first glance, to assume that averaging multiple sources of statistical data would result in an overall average which is superior to the quality of the individual averages. However, this is often not the case. This approach can lead to an incorrect and misleading estimate of a plaintiff’s income due to double-counting, a failure to take into account differing quality of each source (as measured by sample size), and the inclusion of important characteristics (such as age, education, and gender) that are not applicable to the plaintiff. This method also has the potential to provide misleading estimates simply based on the choice of the sources used in calculating this “average”.

To illustrate these effects, we have summarized in the table below, the average income for partsmen (as an example) obtained from a number of common statistical data sources.

Table 1

As shown in the table, if we were to “average” across all of the incomes then we would get an income figure of $44,567 (in 2008 dollars). However, this would be an incorrect and potentially misleading estimate of the average income of partsmen.

The first reason the above “average” figure is incorrect stems from a form of double-counting. Notice that sources one and three provide the average income of partsmen in Alberta, source two provides the average in the whole of Canada, and source four provides the average income of partsmen in Calgary. However, the Alberta data from source one are already included in the Canadian data from source two. Similarly, the Calgary data from source four are already included in the Alberta data from source three. Thus, the average incomes reported by sources one and four are based on data that were already present in sources two and three. Additionally, because the data from sources one and four are already included in sources two and three, these sources have been included in the overall average figure twice. This double-counting is mathematically incorrect and can lead to biased estimates of a plaintiff’s income (i.e. estimates which are either higher or lower than the actual average income). For example, if we were to use only the sources for Alberta overall (and exclude the sources for Calgary and for Canada overall), we would obtain an average income of $47,023 (or approximately $2,456 more than the “overall” average). Thus, taking an average across multiple sources of statistical data will lead to double-counting, and thus to biased estimates of a plaintiff’s income, due to this overlapping of data from a variety of sources (i.e. data from Canada includes data from Alberta, which in turn includes data from Calgary).

The second reason that taking an average across all of the sources is incorrect is that we have not accounted for the “quality” of each source, measured in this case by the size of the sample upon which the average income from each source is based. For example, we have applied equal weight to source one, whose average income was obtained using data from a Statistics Canada survey of approximately 179 workers (about one-fifth of the reported “number of workers” figure), as to source two whose average income was obtained using data from about 843 workers (almost five times as many as source one). In addition, we have taken an average that includes sources whose sample size is unknown. As an example, and ignoring the “double-counting” problem for a moment, if we were to take a simple average of sources one and two, we would get an overall average of $49,635 (= [$53,960 + $45,309] ÷ 2). However, if we were to calculate a proper average that takes into account the different sample size of each source, we would get an average income of $46,824 (= $53,960 × 895 / 5,110 + $45,309 × 4,215 / 5,110), or approximately $2,810 less than the simple average. Thus, taking a simple average across multiple sources of statistical data will lead to biased estimates of the plaintiff’s income, due to a failure to account for varying sample sizes across the different statistical sources.

The third reason that taking an average across multiple sources of statistical data is incorrect is that this figure includes income data from partsmen of varying education levels and gender. That is, (setting aside the double-counting and sample size problems for a moment), sources one and two provide average incomes for males with a trade certificate/diploma, while sources three and four are comprised of data for partsmen of all education levels, as well as from data for both male and female partsmen. Essentially, each of these sources provides income data for individuals who are not comparable to each other (the “apples to oranges” problem).

For example, the “overall” average figure combines the average income of partsmen with trade certificates or diploma with partsmen of all education levels. The partsmen with formal post-secondary training  in their field will be expected to earn more than partsmen of all educations, since the latter group will include some workers without formal training. Thus, including the all-educations categories will bias the overall average downward if we are attempting to estimate the average income of partsmen with formal post-secondary training in their occupation. (And similarly, if we are attempting to estimate the average income of partsmen without formal post-secondary training, then including categories one and/or two will bias the average upwards.) Additionally, by including sources three and four, we have included data from female partsmen and from partsmen with varying levels of education. Thus, by taking an average across all sources, we have incorporated a variety of important characteristics (such as location, education, and gender) which may not be applicable to the plaintiff and which could significantly bias the resulting estimate of the plaintiff’s income.

Finally, the approach of taking an average across multiple sources of statistical data has the potential for allowing estimates to be biased upwards, or downwards, simply by choosing the sources that are included in the average. For example, we have included the 2001 Census and the 2007 Alberta Wage and Salary Survey in Table 1 and obtained an “overall” average of $44,567. Suppose we also found one survey that indicated an average income for partsmen of $60,000 and one survey that indicated an average income of $35,000. If both of these new sources were included in the “overall” average (and ignoring the double-counting, sample-size, and characteristic problems for the moment), we would calculate a new average of $45,545, which is close to our original average. However, if we chose to only include the $60,000 survey, our new average would be $47,653. Alternatively, we would obtain an average income of $42,653 by only including the $35,000 survey. In other words, one could potentially obtain an estimate of a plaintiff’s income which is biased upwards, or downwards, by simply altering the selection of sources. The fact that this method is open to this potential form of abuse suggests that this approach should not be used.

In summary, taking an average across multiple sources of statistical data can lead to biased estimates of a plaintiff’s income due to the double-counting of data, the failure to take into account differing sample sizes, and the inclusion of important characteristics (such as geography, age, education, and gender) that are not applicable to the plaintiff. In addition, this approach has the potential for abuse in that the estimate of a plaintiff’s income can be biased upwards or downwards by the selection of the statistical sources used in the calculations. Note that it may be difficult to detect these problems if the sources have not been adequately described or if the reader is not familiar with the sources or methodology used in calculating the average. A better approach would be to rely on one, high quality, well justified data source (such as the Canadian census). This avoids the many problems associated with combining multiple sources and does not open the door to using various sources to obtain a higher or lower estimate of a plaintiff’s income.

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Laura Weir has a Bachelor of Arts in economics (with a minor in actuarial science) and a Master of Arts degree from the University of Calgary. She has worked for Economica since 2006.

The Discount Rate Revisited (Spring 2008)

Posted on By economica

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.