# The Discount Rate Revisited

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.

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.

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]