APPENDIX F
US MARKET RISK PREMIUM ESTIMATES
1
The main source of data on the U.S. market risk premium comes from the seminal work of
2
Ibbotson and Sinqufield, who calculated holding period return data from December 1925 for
3
common equities, long term government bonds, treasury bills, and the consumer price index. For
4
our purposes we will calculate the risk premium of equities over long bonds in the same way as
5
in Appendix E. For comparison purposes, we will also present the equivalent Canadian
6
estimates. These estimates differ from those in Appendix E, since the time periods differ slightly.
7
Schedule 1 gives the estimates of the average realized excess return of equities over long bonds
8
for the overall period 1926-2006.1
9
10
The central message from the data in Schedule 1 seems to be straightforward, US common
11
equities have on average earned between 10.42-12.34% and long Treasuries 4.92-5.79%,
12
depending on the estimation method. The excess return of common stocks over long term
13
government bonds has been in the range 6.27-6.55% for annual holding periods (OLS & AM),
14
declining to 5.00% as the holding period is lengthened (GM). For Canada, the results are almost
15
identical to those in Appendix E, with the excess return of Canadian equities over long Canadas
16
in the 4.86-5.16% range for annual holding periods declining to 3.92% as the holding period
17
lengthens.
18
19
Note that based on annual holding periods the US realised equity risk premium is higher than the
20
Canadian equivalent. Given the "higher" quality of the US data as well as the volatility of the
21
estimates, many put greater faith in the US estimates, even for the Canadian market. This is also
22
frequently justified by the doubt expressed at the “higher risk”2 Canadian market having a lower
1
Data for 1926-1995 are the Ibbotson and Sinquefield data from the CRSP data files with 1996-2006 data updated
from S&P and the FRED.
2
Note, however, that the standard deviation or variability of the S&P500 equity returns was 20.07% or 1.60% higher
1
1
realized market risk premium, as well as the increasing integration between the two capital
2
markets, which “presumably” will move Canada closer to the US experience.
3
4
However, the difference between the US and Canadian arithmetic mean risk premiums for the
5
overall period of 1.36% (6.55%-5.16%) is split between a difference in the average equity return
6
of 0.67% and a difference in the average government bond return of 0.72%, that is approximately
7
equally between the equity and bond markets. The difference between the equity market returns
8
can partly be explained by the previous effects of Canadian government policy to deliberately
9
segment the Canadian equity market from that in the US,3 as well as by the historically lower risk
10
of the Canadian market. The difference in the returns on Canadian and US government bonds in
11
turn reflects the pivotal role of the US government bond market in the world capital market and
12
the observation that the Canadian market has had to react to that in the US during an era of
13
significant government financing problems.
14
15
The difference in the average realised returns between the US and Canada is consistent with
16
known institutional differences, which are unlikely to completely disappear. The data does,
17
however, emphasise that the realised risk premium is just the difference between the realised
18
return on equities minus that on bonds. However, from Appendix E we know that a "break"
19
occurred in the capital markets in the mid 1950's. Although the exact dates are somewhat
20
arbitrary, there are good reasons for putting the split at 1956/7. First, changes in monetary policy
21
freeing up interest rates to reflect market movements started around then; second, at least in
22
Canada the availability of quality data begins in 1956 and finally the incidence of personal taxes
23
on investment income became much more important in the post war period.
24
25
Schedule 2 gives the estimates for both the US and Canada for the two sub periods 1926-1956
26
and 1957-2006. For the earlier period the realised return on equities is around 9.0-13.0% in both
than that for the Canadian market. Over this whole period US equities were more risky than Canadian equities.
3
The dividend tax credit only applies to dividends from Canadian corporations; foreign withholding taxes apply to
foreign source income, while portfolio restrictions have existed in tax-preferred plans.
2
1
the US and Canada with the lower estimate coming from the least squares regression estimate
2
that takes into account the massive volatility in the equity market at the time of the Great Crash.
3
US equity returns were then largely the same in the latter period at 10.61-11.89% range.
4
However, the substantial decrease in equity market risk from 25% to 17.0% has caused the
5
arithmetic return in the US to decline, even though the compound return has increased. This is
6
because from the discussion in Appendix E, the arithmetic return is approximately the compound
7
return plus half the variance. So even with a similar compound return the arithmetic return has
8
fallen since 1956 in the US.
9
10
Also it is not frequently recognised that the reason the US data starts in 1926, rather than 1924 in
11
Canada, is simply that the original authors of the data wanted a complete business cycle prior to
12
the great stock market crash of 1929. As a result, the start date for the data is inherently biased,
13
both in terms of volatility and the average realised return estimates.4 Note also that similar to
14
Canada, the realised return on the long US treasury bond more than doubled from around 3.5% to
15
around 7.00% while the standard deviation (variability) of the annual bond returns more than
16
doubled, from 4.93% to 10.81%. Again changes in the bond market have had a direct impact on
17
the risk premium of equities over bonds.
18
19
For Canada equity market returns were also essentially unchanged between the two periods. The
20
arithmetic return declined from 12.55% to 11.12%; but unlike the US the compound rate of
21
return declined marginally from 10.30 to 9.93%. Similar to the US, equity market, risk declined
22
from 22% to 16.25%. In looking at equity market returns, the major differences are that in the
23
earlier period the US equity markets was riskier than in Canada whereas more recently this
24
difference has narrowed, while Canadian equity returns have been lower probably due to the
25
impact of government policy. Similar to the US, long Canada bond returns almost doubled from
26
about 4.0% to 8.0%, as the variability in the long Canada bond return also almost doubled from
27
5.41% to 10.40%
4
This is discussed in more detail in Laurence Booth, AEstimating the Equity Risk Premium and Equity Costs: New
Ways of Looking at Old Data,@ Journal of Applied Corporate Finance, Spring 1999.
3
1
2
The data in Schedule 2 is very important. First, it highlights the fact that the main reason for the
3
decline in the equity market risk premium is not to be found in the equity market. Equity market
4
risk in both the U.S. and Canada has been less since 1956 than it was in the earlier period.
5
This is what we would expect given the greater diversification opportunities available in modern
6
capital markets. Second, it points out that it is changes in the bond market that have caused the
7
equity market risk premium to decline. In both the U.S. and Canada bond market risk has
8
essentially doubled over these two long time periods. At the same time average bond market
9
returns have also doubled. This has significantly reduced the market risk premium, when
10
measured as the excess of the equity market return over the bond market return. Moreover it
11
points to the fact that the same factors have been at work in the US as in Canada.
12
13
Another way of looking at the data is in Schedule 3, which looks at what has caused the decline
14
in the market risk premium. In the U.S. the market risk premium has declined by 1.88-5.06%,
15
whereas in Canada the decline has been 3.06-5.49%. It is clear that while equity market returns
16
have remained quite similar between the two periods, for both the US and Canada average bond
17
market returns have increased significantly. As is to be expected, bond market returns have
18
increased marginally more in Canada as judged by all three estimation techniques. The upshot
19
from this analysis is that even if the equity market had performed the same between these two
20
periods the equity market risk premium would have fallen by about 4.0% due to the increase in
21
bond market returns and risk. To understand this we can look at the risk faced by a bond market
22
investor.
23
24
The graph in Schedule 4 gives the relative uncertainty of the equity market to the bond market for
25
both the US and Canada. In both cases uncertainty is measured by the standard deviation of
26
annual returns over the prior ten years. As is very clear, like Canada, the US equity market was
27
much more volatile than the bond market until the mid1950s. Until then equity markets were
28
about four times as volatile as the bond market and frequently more. After the mid 1950's,
29
however, the increasing uncertainty in the bond market caused the differences in risk to become
4
1
less pronounced. For the last twenty years, since the early 1980s, the bond market has been
2
almost as risky as the equity market, but in both the US and Canada recent bond market stability
3
has caused the relative riskiness of the equity market to increase marginally.
4
5
The graph in Schedule 5 gives the beta for the US and Canadian bond markets. In both cases the
6
betas are estimated using annual holding periods over the prior ten-year period, so that 1935
7
measures the bond beta from 1926-1935. Since interest rate risk has recently been much more
8
pronounced we would expect that the long-term bond market would begin to show some of the
9
same risk characteristics as the equity market, which it does. Note that until the 1970's bond
10
market betas could be safely ignored, since interest rate risk had little impact on the equity
11
market. This means that there should have been no or very a very small risk premium attached to
12
investing in bonds. However, bond market betas started to dramatically increase in the mid
13
1980's, reaching a recent peak of about 0.57 for Canada and 0.70 for the US. Recently bond
14
market betas5 have declined significantly in both the US and Canada so that there is currently
15
little evidence of significant systematic risk premiums in bond returns.
16
17
In Schedule 6 is the Canadian equity market beta from the point of view of a US investor both
18
with and without foreign exchange (FX) risk. This estimate of risk is that of a US investor adding
19
Canadian securities to a diversified US portfolio. The estimate without foreign exchange risk
20
assumes that the investor can somehow remove all the foreign exchange risk whereas that with
21
FX risk converts both return series to a common currency and involves changes in the FX rate.
22
Note that the Canadian equity market beta was generally around 0.80 until the late 1980's when it
23
briefly increased to above 1.0, since then it has been declining. This has primarily been due to the
24
different growth paths of the US market during the tech boom, the performance of the Canadian
25
market around NAFTA inspired restructuring post 1989 and the recent effect of commodity
26
prices on the TSX. What this data indicates is that if capital markets have become more
5
The bond market betas are based on a simple regression of the bond market return against the equity market return.
Estimating the betas over five years of monthly data produces the same types of estimates, see J. Petit ACorporate
Capital Costs, Journal of Applied Corporate Finance, Spring 1999 Figure 4.
5
1
integrated then the Canadian market would be seen as a lower risk market from the point of a US
2
investor thereby justifying a lower risk premium than would be required of a US investor
3
investing in the US, where the beta by definition is 1.0. With recent betas for the Canadian
4
market of 0.50 or lower this would put the Canadian market risk premium from a US perspective
5
at less than half the US market risk premium.
6
7
The conclusion from examining US equity market data is that US equity returns continue to
8
marginally exceed those in Canada, with the recent excess probably reflecting Canadian tax
9
preferences and the lower risk nature of many Canadian companies. In contrast, Canadian bond
10
returns have exceeded those in the US as public sector borrowing has persistently forced
11
Canadian governments into the capital market. In both countries, realised market risk premiums
12
have declined significantly due to the large increase in bond market risk and bond returns.
13
14
However, the US equity market risk premium has behaved much the same as the Canadian one.
15
Due to the increasing bond market risk, relative to the declining equity market risk, realised
16
equity risk premiums have shrunk dramatically. Even if equity market risk is assumed to be
17
constant, the increasing bond market risk will have reduced the equity risk premium by about
18
4.0%. When the marginal reduction in equity market risk is considered it is easy to see why
19
equities have earned less since 1956 than before.
20
21
Finally in Schedule 7 is the yield on the real return bond in both the US and Canada. This data is
22
only available in the US since July 2004. However, it clearly shows that US real interest rates
23
have recently been above those in Canada, probably because of the budget problems at the
24
Federal level in the US. However, it indicates that the historically larger market risk premium in
25
the US due to lower interest rates has probably now been partially reversed.
26
27
My conclusion from examining US data is that Canada and the US have marched to different
28
drummers over this very long period, but in both cases the market risk premium has declined due
29
to increased returns in the bond market. What this means is that estimates of the market risk
6
1
premium using long data periods from the US are as biased as they are from Canadian data
2
unless adjustment is made for known risk factors. In my judgment recent estimates post 1956
3
from the US of 3.63-4.61% and from Canada of 1.86-3.06% are both biased low. In both cases
4
they reflect bond market risk that has now largely dissipated, particularly in Canada. In my
5
judgment a reasonable current estimate of the market risk premium is 5.0%. This is significantly
6
higher than the evidence of realised risk premiums in the US and Canada since 1956, but reflects
7
the diminished risk in the bond market as reflected in current yields. A 5.0% market risk
8
premium on top of the current level of long Canada bond yields would place the equity market
9
return at just over 9.0%, which is consistent with long run historic evidence.
7
SCHEDULE 1
Annual Rate of Return Estimates 1926-2006
U.S.
CANADA
S&P
Long US
Excess
TSE
Long
Excess
Equities
Treasury
Return
Equities
Canadas
Return
AM
12.34
5.79
6.55
11.67
6.51
5.16
GM
10.41
5.41
5.00
10.07
6.16
3.92
OLS
11.19
4.92
6.27
10.47
5.60
4.86
Volatility1
20.07
9.24
18.47
8.91
1. Volatility is the standard deviation of the returns over the whole period.
SCHEDULE 2
Equities Over Long Term Bonds in the U.S. & Canada
S&P500
U.S.
Excess
TSE
Long
Excess
Equities
Treasuries
Return
Equities
Canadas
Return
AM
13.05
3.38
9.67
12.55
4.00
8.55
GM
10.11
3.27
6.84
10.30
3.87
6.42
OLS
8.98
3.46
5.52
8.90
3.99
4.91
Volatility1
24.88
4.93
22.09
5.41
AM
11.89
7.28
4.61
11.12
8.06
3.06
GM
10.61
6.77
3.84
9.93
7.60
2.34
OLS
11.31
7.68
3.63
10.40
8.55
1.86
Volatility
16.69
10.81
16.25
10.40
1926-1956
1957-2006
1. Volatility is the standard deviation of the returns over the whole period.
SCHEDULE 3
Factors Determining the Decline in the Market Risk Premium
(Between 1926-56 & 1957-2006)
Decline in
Equity
Bond
Decline in
Equity
Bond
U.S. Risk
Returns
Returns
Canadian
Returns
Returns
Premium
Risk
Premium
AM
5.06
1.16
3.90
5.49
1.43
4.06
GM
3.00
-0.50
3.50
4.09
0.36
3.74
OLS
1.88
-2.33
4.22
3.06
-1.50
4.56
A positive value for the equity or bond returns would indicate an increase in return which for
equities means an increase in the market risk premium and for bonds a decrease. In both the US
and Canada the decline in the realised risk premium has largely been due to much larger bond
returns. The evidence in the equity market returns have been mixed due to differences across the
estimation methods.
SCHEDULE 4
Relat ive U ncer t aint y: Equit y ver sus Bond M ar k et
Risk (1935-2006)
12.00
10.00
8.00
6.00
4.00
2.00
0.00
1935
1945
1955
1965
US
1975
Canada
1985
1995
2005
-0.2
US
-0.4
Canada
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
1963
1961
1959
1957
1955
1953
1951
1949
1947
1945
1943
1941
1939
1937
1935
SCHEDULE 5
Bond Betas
0.8
0.6
0.4
0.2
0
No FX risk
With FX risk
20
20
20
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
05
03
01
99
97
95
93
91
89
87
85
83
81
79
77
75
73
71
69
67
65
63
61
59
57
55
53
51
49
47
-0.20
19
SCHEDULE 6
Canadian Equity Market Beta
1.20
1.00
0.80
0.60
0.40
0.20
0.00
US
Can
30/11/ 2006
30/09/ 2006
30/07/ 2006
30/05/ 2006
30/03/ 2006
30/01/ 2006
30/11/ 2005
30/09/ 2005
30/07/ 2005
30/05/ 2005
30/03/ 2005
30/01/ 2005
30/11/ 2004
30/09/ 2004
30/07/ 2004
SCHEDULE 7
Canadian and US real rates
3.00
2.50
2.00
1.50
1.00
0.50
0.00