a new model for estimating risk premiums (along with some evidence of their decline)

Journal of Applied Corporate Finance S P R I N G 1 9 9 8 V O L U M E 1 1 . 1

A New Model for Estimating Risk Premiums (Along with Some Evidence of Their Decline)

by Laurence Booth, University of Toronto

109JOURNAL OF APPLIED CORPORATE FINANCE

A NEW MODEL FORESTIMATING RISKPREMIUMS (ALONGWITH SOME EVIDENCEOF THEIR DECLINE)

by Laurence Booth,University of Toronto

109BANK OF AMERICA JOURNAL OF APPLIED CORPORATE FINANCE

easuring the investor’s required rate ofreturn and the risk premium over de-fault-free securities is one of the criticalissues in finance. Corporate financing

bined with the yields on long Canada bonds, sug-gests how the risk premium for utilities has changedover time.

The stability of the risk premium is an importanttopic, since the CAPM is often implemented by firstestimating a long-run average historical excess re-turn and then assuming that this historical excessreturn is a good estimate of the future requiredexcess return, or risk premium. Unfortunately, sincelong time periods are needed to estimate an ex postexcess return with any degree of confidence, thisconventional approach precludes any attempt atincorporating time-varying risk premiums over shorterperiods of time.2

The major finding of this research is that theTelco risk premium has declined significantly overthe last 20 years. One of the main reasons for thisdecline has been the increase in interest rate risk,which has made the yield on long-term governmentbonds a very poor proxy for the risk-free rate. As aconsequence, the common practice of adding a“reasonable” risk premium to the the yield of anincreasingly risky long-term bond seriously over-states investors’ required returns. This result hasprofound implications for unregulated companies aswell as for utilities, where the “bond yield plus”method is even more common.

requires it to minimize the cost of capital, whilecapital budgeting requires it to determine whichprojects to invest in. Unfortunately, while there is alarge theoretical literature, as well as a large empiri-cal literature testing different models, there is alimited “estimation literature” to actually help do it.1

This paper will attempt to remedy part of this defi-ciency by estimating the required rate of return fora sample of Canadian Telecommunications (Telcos)companies and then analyzing the behavior of therisk premium for utilities.

The choice of Canadian Telcos was made forthree reasons. First, the estimates are directly usefulfor a significant regulated sector and, by inference,for the Canadian equity market as a whole. Second,and more substantially, there are significant institu-tional reasons to suspect that required rates of re-turn in Canada are different from those in the U.S.Hence, the analysis will reveal the effect of some ofthese institutional differences and provide a usefulcontrast for those familiar with the results of U.S.research. Third, the approach generates a time se-ries of required rates of return that, when com-

1. A notable exception is S. Godfrey and R. Espinosa, “A Practical Approachto Calculating Costs of Equity for Investments in Emerging Markets,” Journal ofApplied Corporate Finance 9-3, (Fall 1996).

2. Note that Clinebell et al (1994) had to use the relatively long periods 1926-58 and 1959-90 when estimating changing risk premiums from realized returns.

M

110VOLUME 11 NUMBER 1 SPRING 1998

THE GORDON MODEL

The basic model used in this paper is the familiarGordon growth model,3 sometimes referred to as the“constant growth” model, which expresses the valueof a share as follows:

P0 = D1/(K – g) (1)

where today’s price (P0) is determined by next

period’s dividend per share (D1) discounted by the

growth (g) adjusted required rate of return (K).Rearranging equation (1) gives,

K = D1/P0 + g (2)

where the discount rate, or cost of equity capital, isthe forecast dividend yield plus the forecast capitalgains or growth yield. The Gordon model assumesthat the dividend grows at the long-run averagegrowth rate forever, so that over the long run this isthe same as the average capital gain.

The assumptions of the Gordon model are notsatisfied for most firms, either because they don’t paydividends or because they are subject to periods ofgrowth that deviate from a long-run sustainableaverage. For regulated utilities, however, the as-sumptions of the Gordon model are satisfied verywell, in part because regulation removes the profit-ability “bubbles” that cause unregulated companies’growth rates to be difficult to predict. As a result, theFederal Energy Regulatory Commission (FERC) hassanctioned the use of the Gordon model as a basicmodel for estimating required rates of return for thecompanies that it regulates.

The difficulty in using equation (2) is in estimat-ing the growth rate, since it is a long-run averagegrowth rate. In practice, given the dividend-richnature of most utilities and the discounting involvedin the share price, the growth rates after about tenyears are of little importance.4 Hence the growth

rates used in practice are based on either averagegrowth rates achieved over the past five or ten yearsor analysts’ growth forecasts. Both of these methodshave some problems.

Historic growth rates follow the actual evolutionof the economy. For utilities this is a particularproblem since allowed and earned rates of return arevery closely related to interest rates and the rate ofinflation. When interest rates rise, so too do allowedreturns. In response, utilities increase their divi-dends—but only with a lag, thus causing theirretention rate to increase for a time. As a result,growth increases because of both a higher earnedreturn and a higher retention rate. Conversely, wheninterest rates and allowed returns fall, the desire toavoid a dividend cut causes the retention rate to fall.As a result, growth rates decline due to a drop in boththe earned return and the retention rate. The resultis that utilities’ historic growth rate of earnings anddividends does not meet the requirements of a trueexpectation, which is that the forecast error shouldhave a mean value of zero.

An alternative—first proposed by John Craggand Burton Malkiel5—is to use analysts’ forecasts ofearnings. These forecasts are now available from avariety of sources (for example, Cragg and Malkieluse Value Line’s expected five-year earnings growthforecast). Others6 have used the estimates summa-rized by the Institutional Brokers Estimate System(IBES), which compiles estimates from a variety ofanalysts. However, the validity of such estimatesremains subject to debate, since prior research hasshown that analysts forecasts can be improved upon7

and that they are biased high.8 In addition to theseproblems, analyst forecasts are only available for asubset of firms and for relatively recent periods—andthey are not widely available for Canadian utilities.

As an alternative to the use of analyst forecasts,this paper uses some results that are suggested by themethod of regulating natural monopolies. As mo-nopolists, regulated firms have their allowed return

3. M. J. Gordon, The Investment, Financing and Valuation of the Corporation(R. Irwin, Homewood Ill, 1962).

4. For example, assume that a stock pays a $1 dividend and grows at 4%forever. With a discount rate of 10% the stock is worth $16.66. However, if thegrowth rate is underestimated by 1% after year 10 the impact on the price is only6%.

5. J. Cragg and B. Malkiel, Expectations and the Structure of Share Prices(Chicago, University of Chicago Press, 1982).

6. See, for example, E. Brigham, D. Shome and S. Vinson, “The Risk PremiumApproach to Measuring a Utility’s Cost of Equity,” Financial Management (Spring1985), R. Harris “Using Analysts Growth Forecasts to Estimate ShareholderRequired Rates of Return,” Financial Management (Spring 1986) and M. Gordon,

“The Pricing of Risk in Common Shares,” International Review of FinancialAnalysis 2 (Spring 1993).

7. See S. Timme and P. Eisemann, “On the Use of Consensus Forecasts ofGrowth in the Constant Growth Model: The Case of Electric Utilities,” FinancialManagement (Winter 1989) and C. Lee and C. Chen “Structural Change and theForecasting of Quarterly Accounting Earnings in the Utility Industry,” Journal ofAccounting and Economics 13 (1990).

8. See Ali et al., “Analyst’s Use of Information About Permanent and TransitoryEarnings Components in Forecasting Annual EPS,” Accounting Review 67-1(January 1992); and L. Ackert and G. Athanassakos, “Prior Uncertainty, Analyst Biasand Subsequent Abnormal Returns,” Journal of Financial Research 20-2 (Summer1997).


determined as a “fair” rate. In Canada the legalrequirement flows from the Northwestern Utilities(1929) decision of the Supreme Court of Canada thatspecifically determined a fair rate of return as beingthe investor’s opportunity cost. Moreover, this returnshould take into account “changed conditions in themoney market.” As a result, every rate hearingincludes significant testimony on the state of theeconomy and financial markets. Forecasts of GDPand the inflation rate, for example, are integral todetermining the risk of the enterprise, while interestrate forecasts are needed to determine conditions inthe money market. It is to be expected, therefore,that these broad macroeconomic factors should bemore influential for regulated utilities than for com-petitive firms, since their allowed rate of return isdirectly determined from them. Since regulated firmsinvariably earn their allowed return, thesemacroeconomic factors in turn affect earned returnsand growth rates in earnings and dividends.

This paper therefore tests the factors that de-termine the dividend growth rates for a sample ofCanadian regulated utilities. The specific model isas follows:

divgro = α0 + α

1 × yield + α

2 × Inflation + α

3 × GDP + ε (3)

where divgro is the dividend growth rate, yield is thelong Canada yield, inflation is the CPI inflation rate,GDP is the growth rate in real GDP, and epsilon isthe residual error term. These three macroeconomicvariables were chosen since they are the ones thatare most prominent in rate hearings and as a resultshould be related most closely to their subsequentperformance.

Estimating equation (3) is of little value unlessit can help to form better expectational data. Other-wise it suffers from the same problem as the CAPM,where beta can be estimated but there are stillformidable problems in estimating the expectedreturn on the market. The advantage of usingequation (3), however, is that, unlike corporateearnings, forecasts of broad macroeconomic vari-ables are available. Data Resources Incorporated

(DRI) Canada and its predecessors has forecastsgoing back to 1975.9 It is thus possible to substitutethe DRI forecasts for the inflation rate, GDP growthrate, and the interest rate in the empirical estimate ofequation (3) to obtain what I will call “quasi-expectational” growth rates.

An additional advantage in using equation (3)with expectational data is that a time series of equityrisk premiums can be obtained by subtracting thecontemporaneous long Canada yield. This in turnallows us to analyze the temporal variation in theutility risk premium and, in the process, to deter-mine whether or not it varies with the level ofinterest rates. It has been suggested that the uncer-tainty in the rate of inflation tends to increase withits level, causing bond yields to increase faster thanthe required equity return.10 Consequently, to theextent this is so, the risk premium would declinewith the bond yield. Other factors such as theincidence of tax on the inflationary component ofthe bond yield could also cause the same phenom-ena. Several studies have found that risk premiumsin the U.S. do indeed vary inversely with the level ofbond yields, particularly during the highly volatileperiod from 1978-1983.11

A complicating factor in Canada, however, isthat unlike the U.S., there are very significant taxdifferences between interest income and dividendincome. Interest income is fully taxed as ordinaryincome. However, since 1948, dividend income hasattracted a tax credit to compensate for the doubletaxation of equity income at both the corporate andpersonal level. Until 1972, there was a flat 20%dividend tax credit; since that time the dividend taxcredit has fluctuated to equalize the tax burden forsmall business income paid out as interest, dividendsor salary.12 Also unlike the U.S., there is no tax inCanada on intercorporate dividend flows, whichmakes preferred shares an attractive short-terminvestment for companies. It follows that the re-quired return on a dividend-rich investment likeutility shares would be more closely correlated withthe yield on preferred shares than the yield on longCanada bonds.

9. For the period 1975-1978 these forecasts are from a University of Torontomacroeconomic model that the subsequent DRI model was built on. No othersource of macroeconomic forecasts is available in Canada. My thanks to PeterDungan of the University of Toronto and DRI Canada for making the basic sourcematerial available to me. All errors in interpreting and collating the data are mine.

10. See M. Gordon and P. Halpern, “Bond Share Yield Spreads UnderUncertain Inflation,” American Economic Review (September 1976).

11. See Brigham et al (1985) and other studies cited in footnote 6.12. See L. Booth and D. Johnstone “The Ex-dividend Day Behaviour of

Canadian Stock Prices: Tax Changes and Clientele Effects,” Journal of Finance(June 1984) and B. Amoako Adu et al., “Capital Gains Tax and Equity Values:Empirical Tests of Stock Price Reaction to the Introduction and Reduction of CapitalGains Tax Exemptions,” Journal of Banking and Finance 16 (1992) for discussionsof tax effects in the Canadian capital market.

For regulated utilities, the assumptions of the Gordon model are satisfied very well,in part because regulation removes the profitability “bubbles” that cause unregulated

companies’ growth rates to be difficult to predict.


An additional problem for Canada is that theCanada bond market has been very heavily affectedby the persistent budget problems of the federalgovernment. After the post-war recovery period,from 1964-1974 the federal government ran a surplusaveraging 0.64% of gross domestic product (GDP).From 1975-1995 the federal government ran a deficitaveraging 4.36% of GDP, reaching a peace-time highof 7.39%—one of the highest deficits in the industri-alized world. As a consequence, the bond marketwas flooded with Canada bonds, forcing bond yieldsup relative to required returns in the equity mar-kets.13 For both these reasons, it makes sense toestimate the risk premium over the yield on tradi-tional fixed-rate preferred shares, which are taxedsimilarly to utilities, and which have not beenaffected to the same degree by the structural changesin the Canada bond market.

I estimated equations (2) and (3) for a sampleof six Canadian telecommunications (Telcos) com-panies from 1966-1995. All estimates are made fromsimple arithmetic averages of these underlying sixcompanies. This was done for two reasons: first itreduces estimation risk attached to individual esti-mates; and second, the use of macroeconomicforecasts means that the resulting estimates will bedominated by general, rather than individual, ef-fects. The choice of Telcos was made simply becauseit is the only regulated sector that has a large enoughsample of privately owned, publicly traded compa-nies to make estimation feasible. Unlike the U.S., theCanadian Radio and Telecommunications Commis-sion (CRTC) has not required the divestment of longdistance from local carriers. Until a major decision in1992 (CRTC 92-12), there were prohibitive barriers toentry into the long distance market and a completemonopoly in local service.

The estimation period was chosen to maintaina large enough sample with reasonably completedata. The data consists of annual data on dividendsper share and stock prices from the Financial Post,yield to maturity data on the over ten-year longCanada series from Statistics Canada, and yield dataon an index of conventional preferred shares devel-oped from indexes maintained by Moss-Lawson andNesbitt Burns. The DRI data consist of reasonablyconsistent forecast data for short-term forecastsdeveloped quarterly (sometimes monthly) and a

bond markets are at least partially integrated. However, one indication is whetherrisk premiums are stable across Canada bonds and preferred shares.

13. It is still somewhat controversial as to whether the increase in the total valueof Canada bonds outstanding has affected market yields, since the Canada and U.S.

semi-annual long-term forecast, normally with a ten-year horizon. The basis of the DRI forecast has variedover time; for example, the long-term forecast wassometimes made in early summer and sometimesspring. However, this research uses annual averageestimates, and for this purpose the forecast used isthe one closest to the middle of the year. For the long-term forecast, the estimates are for a term closest toten years; and for the short-term forecast it is for thecurrent year and the next two years (and so forapproximately two and a half years).

EMPIRICAL RESULTS

The top panel of Table 1 provides the resultsfrom a series of ordinary least squares (OLS) regres-sions of the annual dividend growth rate against theactual values for the three macroeconomic series.Note that the coefficient on the CPI inflation rate ishighly significant, while that on the long Canadayield is less so, and that on the GDP real growth isnot significant at all. In the multi-variate model thatincludes all three variables, the CPI inflation rateagain provides most of the explanatory power andhas almost the same sign as in the uni-variateregression. This indicates a stable relationship be-tween the realized growth rate and the realizedinflation rate. In contrast, while the coefficients onthe long Canada yield and the real growth rateremain positive, their values and t statistics change,indicating multicollinearity between the two.

But if annual relationships are of interest, theyare less useful for forecasting since the Gordon modelneeds long-run relationships. Figure 1 is a graph ofthe ten-year average values for the threemacroeconomic series and the Telco dividend growthrate. In each case, the ten-year average is a simplearithmetic average of each year’s annual value. Clearly,the dominant influence on Telco dividend growthrates continues to be the CPI inflation rate. Althoughthe Telco growth rate seems to peak in 1981-82before the inflation peak, the increasing growth ratebefore then and its subsequent decline follows theprevailing inflation rate very closely. In contrast, theaverage real GDP growth rate seems to be on anunrelated secular decline, while average bond yieldscontinued to increase after the fall in inflation andpeaked a good five years after the Telco growth rate.


Figure 1 provides a good example of why theuse of historic growth rates is frequently biased. Itwould be difficult, for example, to justify the use ofa ten-year realized Telco growth rate as a proxy forthe ten-year forecast dividend growth rate, when itis clearly influenced by the prevailing rate of infla-tion. Throughout the 1980s, for example, as both theinflation and dividend growth rates fell, the historicdividend growth rate seriously overpredicted actualgrowth rates. Put another way, the use of the currentforecast inflation rate should significantly improvethe use of any historic dividend growth rate as aforecast of the future dividend growth rate.

In the lower panel of Table 1 are the results ofa series of regression models of the historic ten-

year average growth rate. The individual regres-sions have a correction for first order serial correla-tion, since there is built-in autocorrelation in theuse of a ten-year moving average. However, theresults parallel those based on annual data. Theaverage inflation rate has an almost one-to-onerelationship with the average dividend growth rate,while the coefficient on the long Canada yield isalso significant. Once again, the GDP growth rate isnot significant.

For the multi-variate model a variety of differentspecifications all yield essentially the same results.The two that are reported in Table 1 include just theinflation rate and long Canada yield as independentvariables estimated with and without the serial

TABLE 1 REGRESSION ANALYSIS OF GROWTH RATES*

Intercept Inflation Canada GDP Adj R2 DW

ANNUAL GROWTH RATE MODELSOLS 0.9671 0.7028 (3.728) 0.3078OLS 1.0528 0.4639 (1.471) 0.0389OLS 4.551 0.2539 (0.8549) –0.0094OLS –1.500 0.6919 (3.1626) 0.1526 (0.4523) 0.4338 (1.6155) 0.3238

TEN YEAR AVERAGE GROWTH RATE MODELSAR1 0.773 0.909 (6.999) 0.937 1.86AR1 6.755 .785 (2.471) 0.926 1.49AR1 0.9077 0.214 (0.397) 0.886 1.07AR1 3.398 1.007 (22.682) –0.385 (–6.168) 0.964 1.77OLS 2.787 1.011 (20.709) –0.331 (–5.274) 0.955 1.79OLS (’75-’92) 3.001 0.985 (13.83) –0.332 (–4.946) 0.919 1.83

*Numbers in brackets are the T statistics, OLS is ordinary least squares regression and AR1 is after the Cochrane Orcutt correction for serial correlation in the error term.

FIGURE 1TELCO GROWTH RATESAND THE ECONOMY

Fully 95% of the variation of ten-year Telco dividend growth rates can be explainedby the average rate of inflation and the yield on long Canada bonds.


correlation correction.14 Note that in the multi-variateresults the direct impact of the long Canada yield ispositive, while its marginal impact when the inflationrate is included is negative. When viewed together,these two findings suggest that the inflationarycomponent of the nominal interest rate has a positiveimpact on dividend growth, whereas the real interestrate component has a negative impact.

The implication of the empirical evidence inTable 1, then, is that fully 95% of the variation inrealized ten-year growth rates can be explained bythe average rate of inflation and the yield on longCanada bonds. It is also difficult not to escape theconclusion that the relationship between growthrates and inflation is one to one, since none of thecoefficients on the realized inflation rate is statisti-cally different from one. Further, the dividend growthrate has declined during similar inflationary peri-ods, when by implication real interest rates havebeen high.

In one sense, the evidence in Table 1 should be“obvious,” since the driving force behind mostnominal growth rates is the rate of inflation. How-ever, this then implies that the Telco dividend yieldis close to the real rate of return, and that Telco stockscan be viewed as inflation hedges; and, as we will seelater, this could have an impact on investor percep-tions of risk. Finally, what is somewhat surprising isthe strength of the relationship with inflation and thelimited impact of GDP growth rates.

One final concern is whether or not the resultsare contaminated by the introduction of competi-tion into the Telco long distance market by CRTC92-12. Because the effects of competition would befelt in the period 1993-95, the two-variable model(whose results are shown in the bottom line ofTable 1) was re-estimated over the period 1975-1992. As expected, the results are substantially thesame, except that the growth rate is marginally lesssensitive to the inflation rate and the intercept islarger. These findings together suggest that thegrowth rates realized from 1993-1995 were lowerthan would have been expected without the intro-duction of long-distance competition. This in turnimplies that recent growth estimates are probablymildly understated.

Table 2 presents the average telco dividendyield over the period 1975-1995, along with theshort-term and long-term (ten-year) DRI forecastdata for the CPI inflation rate, the yield on the (over-ten-year) long Canada bond, and the forecast GDPgrowth rate. The data for the long-term forecasts forthe period 1975-1977 was not actual but “fitted” databecause long-term forecasts were not made. Never-theless, a regression on the 17 years of data thatincluded both the short- and long-term forecastsindicates that the short-term forecast explained 90%of the variability of the long-term inflation forecast,87% of that in the interest rate forecast and 16% ofthat in the GDP forecast. Clearly, the long-terminflation rate, in particular, is driven by the currentand immediately expected inflation rate. In contrast,the long-term GDP growth rate forecast is much lessdependent on the short-term forecast.

With the forecast macroeconomic variables, it isnow possible to substitute these long-term expecta-tions into the structural model from Table 1 andestimate “quasi-expectational” growth rates. Then,by using equation (1) with the dividend yield, we canestimate the required rate of return. The estimates ofrequired rates of return (calculated using the two-variable OLS model from Table 1)15 are presented inTable 3 together with the associated risk premiumsover the contemporaneous long Canada and pre-ferred stock yields.

Several important observations can be madefrom these data. First, the size of the risk premiumis obviously affected by the tax treatment of theunderlying base instrument. Because of Canada’stax preference at the investor level for dividendincome, the risk premium over Canadas is affectedby both the differential risk and the differential taxtreatment. As a result, both the size of the riskpremium and its behavior over time can easily bemisinterpreted.

For example, the risk premium over Canadashas been very low over the last ten-year period, andappears to be an “anomaly.” However, some of thisis due to the above tax reasons, which caused longCanada yields to be higher than the yields onpreferred shares, even though the bonds are unam-biguously less risky. Second, even when measured

14. Including the GDP growth rate left the coefficients on inflation and the(lagged) long Canada yield virtually unchanged and had no impact on the R square.

15. The two variable OLS model was chosen for two reasons: first, althoughthe models are all very similar, this model is the simplest to implement; and, second,

it provides the most forecasts. Both the AR1 and lagged variable models produceone less estimate.


against a similarly taxed security, i.e., such as pre-ferred shares,16 the risk premium has declined froman average of 4.0-6.0% in the period 1975-1985 to1.24-3.01% in the period 1985-1995.

There are a variety of possible reasons for thisdecline:

One explanation would start by noting thatduring the 1970s the regulatory system was underconsiderable strain. Most companies were on anhistoric test-year basis that meant that their revenueswere determined by their existing costs and materialchanges that were clearly anticipated. This left manyregulated companies exposed to unanticipated infla-tion.17 The adoption of a forward test year withextensive use of deferral accounts to pass these costs

onto customers dramatically lowered the risk of theaverage regulated utility by the early 1980s.

A second explanation would note a significantchange in the state of financial markets. Real interestrates have been higher since the change in U.S.monetary policy in 1979-81. As shown in Table 4, thereal interest rate in Canada was generally in the rangeof 2.0-3.0% during the 1970s, prior to the turbulenceintroduced by the change in monetary policy in1979; since then, it has been much higher. It appearsthat the decrease in the utility risk premium hascoincided with the increase in the real interest rate.18

One explanation for this is that, unlike fixed incomeinvestors, the utility investor is protected from changesin interest rates, since if rates go higher the utility’s

TABLE 2 FORECAST MACROECONOMIC DATA

Short Term Long Term

Dividend Yield Inflation Canada Yield GDP Growth Inflation Canada Yield GDP Growth

1975 8.63 8.40 10.70 6.03 7.49a 9.86a 4.14a

1976 8.84 7.07 10.11 4.73 6.56a 9.45a 4.97a

1977 7.99 6.57 8.42 4.20 6.22a 8.29a 3.67a

1978 7.19 7.03 9.33 4.73 5.82 9.19 4.601979 7.27 7.33 9.86 4.30 6.67 9.05 4.471980 8.13 9.73 12.51 1.83 8.20 10.94 4.001981 9.93 11.07 12.86 3.30 9.00 12.19 3.801982 10.43 9.13 13.46 2.33 8.09 11.89 3.631983 8.19 5.80 10.41 3.07 6.56 9.79 3.411984 7.68 5.07 12.10 3.53 5.67 9.85 3.221985 6.79 4.20 13.23 3.20 5.61 11.21 3.111986 6.37 3.73 9.67 3.63 5.54 9.99 3.141987 6.60 4.57 9.07 2.63 5.12 9.54 2.891988 6.74 4.80 9.79 2.37 5.20 9.59 3.321989 6.48 4.47 10.27 2.77 4.74 9.75 3.201990 6.88 4.93 10.53 2.23 4.77 9.69 3.091991 6.41 4.17 10.29 2.33 3.75 9.31 2.801992 6.27 2.67 9.21 3.57 3.42 8.52 2.921993 5.86 1.87 7.86 4.03 2.49 7.60 3.191994 5.47 1.30 7.27 3.63 2.00 7.50 3.371995 6.02 2.06 8.17 3.83 2.40 7.53 3.35

Source: Data from DRI Canada.a. Fitted econometrically from the short term forecast.

16. Note that comparison of utility shares with preferred shares is strengthenedby the fact that many Canadian investment banks have set up secondary markettrusts to buy utility shares and then repackage the income stream into traditionalpreferred shares and “capital shares,” which are essentially deep in the money longterm options. The value is usually split 80% preferreds and 20% instalment receiptsso that utility shares can be viewed as 80% preferred shares.

17. Brigham et al (1985) also found that U.S. utility risk premiums increasedsignificantly during this period.

18. The statement is qualified, since the real interest rate is the market yieldminus the inflation expectation, and the Gordon DCF cost is dependent on the sameinflation expectation. As a result, the correlation could be due to measurement errorin the inflation expectation.

The Telco risk premium has declined significantly over the last 20 years, from anaverage of 4.0-6.0% in the period 1975-1985 to 3.0% or less in the period 1985-1995.One of the main reasons for this decline has been the increase in interest rate risk,

which has made the yield on long-term government bonds a very poor proxy for therisk-free rate.


allowed return is raised commensurately in thefollowing year’s rate case. As a result, utility investorsare not exposed to the interest rate risk faced byinvestors in holding long-term fixed-rate instru-ments. Moreover, since utility commissions havemoved to a forward test year and changed allowedreturns on an ongoing basis, an investment in utilityshares has become similar to an investment infloating-rate preferred shares, where the dividend isreset periodically in line with market interest rates.

Both of these changes coincided with thedecline in the utility risk premium that set in after1981. One corroborating piece of information iscontained in Figure 2, which charts the Telcodividend yield as a percentage of the long Canadaand preferred stock yields. This data has the advan-

tage of using directly observable market yields, thusavoiding most estimation problems (as well as goingback to 1966, well before expectational data wasavailable). Note that the Telco dividend yield wentas high as 95% of the prevailing long Canada andpreferred stock yield in the mid to late 1970s beforedeclining to the “normal” 70% range by the mid1990s. The changed ratio of the Telco dividend yieldto the preferred stock yield has important implica-tions for the utility risk premium. With a ratio of 95%in the 1970s, it took a Telco growth rate of only 0.6%for an investment in Telco common stock to “breakeven” with the preferreds. With 10% prevailinginflation during that period, it is easy to justify adividend growth expectation consistent with a utilityrisk premium of 6%. In the 1980s, by contrast, a 70%

TABLE 3GORDON DCF ESTIMATESAND ASSOCIATED RISKPREMIUMS

Premium Premium RealDCF Estimates Over Preferreds over Canadas Interest Rate

1975 16.34 6.86 7.35 1.391976 15.70 6.42 6.47 2.501977 14.83 6.44 6.14 2.331978 13.23 4.88 3.99 3.231979 14.28 5.64 4.10 3.291980 16.19 6.31 3.85 3.821981 18.56 6.54 3.57 5.491982 18.19 4.41 3.81 5.821983 14.88 4.72 3.11 4.881984 13.35 3.46 0.61 6.691985 11.86 2.60 0.75 5.211986 11.78 2.86 2.23 3.791987 11.73 3.21 1.80 4.571988 11.93 3.56 1.71 4.781989 11.12 2.65 1.20 4.951990 11.59 2.38 0.77 5.771991 10.13 1.58 0.32 5.841992 9.91 1.71 1.14 5.171993 8.81 1.08 0.93 5.261994 7.92 -0.04 -0.66 6.451995 8.91 1.15 0.55 5.82

TABLE 4AVERAGE RISK PREMIUMS

Premium over Premium Real Telco Canada/ CanadaPreferreds over Canadas Interest Rate Beta Market Riska Bond beta

1976-80 5.94 4.91 3.03 .29 .39 .221980-85 4.35 2.37 5.62 .41 .66 .151986-90 2.93 1.54 4.77 .43 .64 .331990-95 1.10 0.46 5.71 .52 .72 .51

a. Risk as measured by the standard deviation of the prior sixty months returns.


ratio of dividend to preferred yields meant that thebreakeven dividend growth rate increased to 2%;and, with ongoing inflation also dropping to 2%, itbecame difficult to justify the dividend growthexpectations of about 8% that would be necessary fora constant 6% utility risk premium. The implicationis therefore inescapable that there has been asizeable drop in the Telco risk premium.

Finally, note again that the dividend yield as apercentage of the preferred stock yield has been morestable than that for the long Canada yield, and did notsuffer the same precipitous decline in the mid 1980s.This indicates yet again the importance of estimatingrisk premiums over similarly taxed instruments.

A final comment on the data in Table 3 is thatthere is little to suggest a stable relationship betweenutility risk premiums and interest rates in Canada.One older study of U.S. utilities found a positiverelationship for electric utility risk premiums for 1966-1979 and then a negative relationship for 1980-8419—and a more recent study of U.S. utilities reported thatthis negative relationship continued through to the1990s.20 With annual data, the estimates are not fineenough to statistically examine subperiods. But con-sistent with the U.S. findings just cited, Telco riskpremiums were very high in the mid 1970s and thendeclined as long bond yields increased from 1979-81. However, as happened in the U.S., in Canadaduring the ’80s and ’90s this once negative relation-ship between risk premiums and interest rates hasinverted, as Canadian utility risk premiums have fallentogether with the decline in long Canada yields.

Further, the risk premium over preferred yieldsalso implies there is no inverse relationship betweenrisk premiums and the level of interest rates, evenduring the highly volatile 1979-84 period that pro-duced the U.S. results cited above.21 Indeed duringthis period it appears that the risk premium overpreferred shares varied directly with the level ofpreferred stock yields, a relationship that has seemedto continue since then.

IMPLICATIONS FOR UNREGULATEDCOMPANIES

While certainly useful for utilities, the behaviorof utility risk premiums may have little application tounregulated companies. For example, the decline inthe utility risk premium just discussed may beattributable entirely to utility-specific factors thathave lowered their relative risks leaving the risk ofthe broader market unchanged. It is thus importantto “back up” and consider whether the above resultshave broader import.

To do this, let’s begin by looking at how therequired return is determined in the capital assetpricing model (CAPM),

Ku = Rf + MRP × β

where the required return for a utility (u) is equal tothe risk-free rate (R

f) plus the risk premium, which

is the product of the market risk premium (MRP) andthe security’s systematic risk, or beta coefficient.

19. Brigham et al. (1985), cited earlier.20. R. Harris and F. Marston, “Estimating Shareholder Risk Premia Using

Analyst’s Growth Forecasts,” Financial Management (Summer 1992).21. Regression analysis of the risk premium over long Canadas produced no

significant coefficient on the long Canada yield. For the risk premium on preferreds

the sign on the preferred stock yield was significantly positive. These results wererobust even after a dummy variable was added for the change in real interest ratesafter the monetary policy changes of 1979-81.

FIGURE 2DIVIDEND YIELDPERCENTAGE OF MARKETYIELDS

For the period 1975-80, Canada bonds were about 40% as risky as the Canadianequity market as a whole. Since the changes in monetary policy in 1979-81, interestrate risk has increased, and the long Canada bond market has increased in risk to

become about 65-70% as risky as the equity market.


The CAPM is an alternative to the Gordon DCFmodel for estimating the required rate of return. Itpoints out that the decline in the utility risk pre-mium could be attributed to two different causes:(1) a change in utility-specific factors captured bythe beta coefficient or (2) a general decline in themarket risk premium. As reported in Table 4, thebeta of the Telco subindex22 of the Toronto stockexchange has actually increased from the 1976-80average of 0.29 to the current level of 0.52. Taken atface value, a decline in the Telco risk premiumcombined with an increase in the Telco beta wouldsuggest that the risk premium of the broad markethas declined even more!

However, the above logic assumes that the riskpremium is measured over the risk-free rate. In prac-tice, risk premiums are measured over long-termbond yields. The reason for long-term rather thanshort-term rates is that short rates like the 90-dayTreasury bill rate reflect short-term monetary policy.For this reason, they are generally viewed as unre-liable for valuation or capital budgeting purposes—applications where the discount rate is used to dis-count cash flows many years into the future. For thesepurposes, as suggested, the risk premium is normallymeasured over longer-term yields that reflect longer-term inflation and interest rate expectations.23

But this practice raises the question of whetherthe riskiness of the long Canada bond yield haschanged. As reported in Table 4, For the period 1975-80 (which actually covers the period from 1971-5

through 1976-80), Canada bonds were about 40% asrisky as the Canadian equity market as a whole;conversely, the equity market was about 2.5 timesriskier than the bond market. Since the changes inmonetary policy in 1979-81, interest rate risk hasincreased, and the long Canada bond market hasincreased in risk to about 65-70% as risky as theequity market.24

Figure 3 graphs the ratio of the Canada bondmarket risk to equity market risk from the 1956-61period to the present. The graph indicates that theresults in Table 4 for the four subperiods are notanomalous. Prior to 1979 the bond market wasconsistently 40% as risky as the equity market; sincethen there has been a persistent increase in interestrate risk relative to equity market risk. Moreover, inabsolute terms (that is, in terms of the variance of thetotal return), the Canada bond market has recentlybeen almost as risky as the equity market!

The final part of the puzzle is the riskiness oflong Canada bonds themselves. Figure 3 showedthat the absolute riskiness of long Canada bonds hasincreased to close to that of the equity market as awhole. However, what it does not indicate is howmuch of that risk is diversifiable. In the final columnof Table 4 is the beta of the long Canada bond, whichhas increased from the 0.15 level to the current levelof 0.51. Figure 4 graphs the long Canada bond betafor the whole period. What is evident from Figure 4and the data in Table 4 is that the long Canada bondbeta was around 0.15 prior to 1979 and has subse-

22. Using the subindex has significant advantages over the individualcompany betas, since it allows for broader coverage than just these six companiesand is less sensitive to thin trading estimation problems.

23. In this paper we use the “over ten” year long Canada index, since this indexgoes back over the whole period, and the commonly forecast long Canada yield.

24. These risk estimates are “backward” estimates in recording the variabilityof the actual rates of return over the prior five-year period.

FIGURE 3LONG BOND VOLATILITY*

*Ratio of five-year standard deviations of returns on Canada bonds to that on the market.


quently increased “consistently”25 to the current levelof around 0.50.

As shown in Figures 3 and 4, then, since 1979the Canadian bond market has become much riskierboth in terms of absolute risk, as well as market risk.This increase in interest rate risk in turn explains whythe real interest rate on long Canada bonds hasincreased from the 2.0-3.0% level prior to 1979 to theplus 5.0% level since then.26 Clearly investors haverequired increasing yields on long Canada bonds inthe face of this significant increase in risk.

One way to see this is to recognize that theCAPM also applies to long Canada bonds. If themarket risk premium is assumed to be, say, 5%,27

then the recent long Canada bond beta of 0.50implies a 2.5% risk premium, which is broadlyconsistent with the increase in the long-term realrate. And once the long Canada bond is recognizedas being risky, the CAPM can no longer be appliedin the usual way by simply adding a risk premium tothe long Canada yield. Instead, more sophisticatedadjustments need to be made

One possible adjustment is to calculate “a risk-free” long Canada yield by subtracting this interestrate risk premium from the long Canada yield andthen applying the CAPM in the normal way. Forexample, if the long Canada yield is 7%, the 2.5%long Canada risk premium implies that the true risk-

free rate is 4.5%. A “normal” risk premium wouldthen be added to the 4.5% rate, not the actual yieldof 7.0%.

The problem with this adjustment, however, isthat the 4.5% “true” risk-free rate is an artificialconstruct; it is a yield for an instrument that does notexist. An alternative adjustment would be to measurethe Telco risk premium (TRP) as the broad marketrisk premium multiplied by the difference betweenthe Telco beta and the beta of the long Canada bond,as follows:

TRP = MRP (βu - βc) (4),

where the beta subscripts denote the utility and theCanada bond, respectively. This risk premium couldthen be added to the actual long Canada yield todetermine a Telco’s cost of equity. This way, insteadof reducing the long Canada yield, the risk premiumitself is reduced.

This adjustment has the additional advantage ofexplaining directly why the Telco risk premium, asnormally measured as a risk premium over a longCanada bond yield, has recently been so small. Withrecent beta estimates on both the long Canada bondand the Telcos being about 0.50, they both shouldhave the same risk premium. As a result, regardlessof the size of the market risk premium, the Telco risk

25. The word “consistently” is used in full recognition of the fact that theestimated long Canada bond beta declined significantly from October 1987 untilSeptember 1992. The loosening of monetary policy by the Bank of Canada inresponse to the stock market crash of October 1987 led to significant gains in thebond market offsetting losses in the equity market (long Canadas recorded an 8.4%gain while the market index dropped 22.5% in Canada); and this negativecorrelation reduces the beta estimate for every estimate that includes October 1987.Absent this one month, the beta on the long Canada bond would have increasedthroughout the period.

This temporary negative correlation suggests that while the normal riskinvolving Canada bonds has increased, they probably remain a safe harbor in the

event of a “market break.” Similar comments apply to the Telcos, whose betas alsodrop during this period for the same reason.

26. The government of Canada has issued real return bonds where principaland interest payments are indexed to the rate of inflation. These bonds removeinflation uncertainty relative to traditional nominal bonds, but have still yielded4.50% over the period 1991-1995, so the real return estimates in Table 4 lookreasonable.

27. See L Booth, “On Shaky Ground,” Canadian Investment Review (Spring1995) for estimates of the long run market risk premium in Canada that supporta 5% estimate.

FIGURE 4LONG CANADA BONDBETA

If companies continue to estimate their equity cost as a risk premium over a long-term bond yield, then failure to take account of the increased riskiness of the long-

term bond will lead to serious overestimation of their equity costs.


premium as measured over the long Canada bondyield should be close to zero, which is exactly whatthe earlier estimates have shown.

The above discussion has implications for allcompanies, unregulated as well as regulated. Ifcompanies continue to estimate their equity cost asa risk premium over a long-term bond yield, thenfailure to take account of the increased riskiness ofthe long-term bond will lead to overestimation oftheir equity costs. When the beta of the long Canadabond was about 0.15, the resulting overestimationwould only have amounted to about 65 basis points(.15 x 5.0%), which could be forgiven as part of the“estimation error.” However, when the beta is about0.50, the overestimation can be as large as 2.50%!

The above situation is more severe in Canadathan in the U.S., both because Canada bonds are taxdisadvantaged relative to preferred stock and be-cause their risk has increased more. But the under-lying logic is the same. As long as monetary policyis the main macroeconomic tool to manage theeconomy, then interest rate risk is here to stay. As aresult, the yield on a long Government bond is notthe relevant base on which to add a risk premium tomeasure a company’s equity cost (unless significantadjustments are made). In my judgment, commonestimates of reasonable risk premiums are seriouslyoverstated.

CONCLUSIONS

This paper has focused on estimating risk pre-miums for a sample of Canadian Telcos to illustratethe potential for a new variant of the Gordon modeland to discuss broader issues involving the recentbehavior of risk premiums.

The main results are as follows:Macroeconomic variables can explain nearly all of

the realized long-term dividend growth rates for asample of Canadian telecommunications compa-nies. Of these variables, the realized inflation rate isthe most important, but the data also indicate that thereal interest rate is significant. Telco growth ratesincrease with the level of inflation and decrease withthe level of real interest rates. Both of these resultsare empirically robust.

When the empirical dividend growth rate modelis combined with macroeconomic forecast data, itis possible to come up with “quasi-expectational”dividend growth rates. These estimates have theadvantage of providing long-term growth rate fore-casts, since they feed off long-term macroeconomicforecasts. The data indicates that the long-termmacroeconomic forecasts are robust, since forthe inflation rate most of the variability comesfrom the variability in the short (2-3 year) infla-tion forecasts.

The derived risk premium series produce two newinsights: (1) The utility risk premium in Canadaseems to have been on a long-term secular decline(a decline that is even more pronounced whenmeasured over Canada yields, since these yieldsreflect tax changes not evident in the dividend-richpreferred share market); (2) Contrary to U.S. results,the utility risk premium in Canada does not seem tovary inversely with the level of market yields (ifanything they vary positively).

Evidence from the ratio of dividend to marketyields provides strong circumstantial evidence of thesecular decline in utility risk premiums (while alsobringing to light problems in defining a risk premiumover differentially taxed bond yields).

Long-term Canada bonds have become signifi-cantly riskier since 1979, both in absolute terms aswell as market risk. Relative to the equity market, thelong Canada bond market has gone from about 40%as risky to about 70-80% as risky over the last 20years, while the Canada bond beta has gone from0.15 up to about 0.50, or roughly the same as that forregulated utilities.

All companies should seriously reconsider thestandard practice of adding a “normal” risk premiumto the long bond yield to estimate their cost of equity.(Lower-risk companies like utilities may deserve norisk premium at all when using this method.) If thelong bond yield is used as the base for calculating afirm’s equity cost, the risk premium should bereduced to reflect the increased interest rate risk builtinto long bond yields.

Perhaps Warren Buffett has it right when hereportedly uses just the long-term U.S. treasury yieldto discount all corporate cash flows.

LAURENCE BOOTH

is Professor of Finance at the University of Toronto’s RotmanSchool of Management.

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a new model for estimating risk premiums (along with some evidence of their decline)

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