The SA Equity Market
Risk Premium
By Christo Luüs  Absa Group Economic Research
hen evaluating the past relative performance of bonds versus
equities, reference is often made to the equity market risk
premium which essentially measures the average return that
investors would expect over and above the “riskfree”
rate of return.
Various methods exist to calculate the
equity market risk premium, although shortcomings are associated
with basically all approaches. Estimating the South African
historical risk premium, modified historical risk premium,
and implied risk premium, will briefly be discussed.
Historical
risk premiums
The historical risk premium remains the standard approach
to estimating equity risk premiums (ERPs). The actual returns
earned on equity over a long time period is calculated and
compared with the actual returns earned on a defaultfree
security (usually a government benchmark bond or bond index).
Depending on the time period used, the
choice of the riskfree security, and whether arithmetic
or geometric averages are used when calculating returns,
the estimate of the risk premium can vary significantly.
For a country such as the USA, equity risk premium (ERP)
estimates invariably range between and 4% and 6% –
even when using the same data sets.
Usually it is argued that the longer the
time period, the better (and more stable) the riskpremium
estimate. Such a period is often regarded to be 50 years
or longer. Other analysts argue that shorter (more recent)
periods yield better estimates because the risk aversion
of investors may change over time. However, the “cost”
associated with choosing a shorter time period, is that
the noise (as measured by the standard error) increases.
This implies that the probability of one over or underestimating
the risk premium also increases (see table 1).
Table 1:
Equity and Bond Standard Deviations and Standard Error
Estimate of SA ERP 
Estimation Period 
Equity Standard Deviation 
Bond Standard Deviation 
ERP Standard Deviation 
Standard Error 
75 years
50 years
25 years
20 years
15 years
10 years
5 years 
23.6%
23.8%
22.6%
24.0%
22.2%
21.8%
16.6% 
10.2%
11.5%
12.7%
10.8%
11.1%
9.0%
3.0% 
21.85%
22.42%
22.62%
23.06%
22.57%
20.52%
17.50% 
2.5%
3.2%
4.5%
5.2%
5.8%
6.5%
7.8% 
Source of basic data: Carsons;
JSE; BESA; INet; Barra 
The choice of the riskfree rate is also
important – especially when steep upward or downward
sloping yield curves often prevail. Usually a longterm
government bond is used. The additional question that needs
to be addressed is whether the yieldtomaturity, running
yield or total return is to be used. Since total returns
(capital appreciation plus dividend yield) are normally
used for equity, the best argument could probably be made
for using total bond returns as well.
Using geometric averages – which
incorporate compounding effects – is the preferred
method to calculate historical returns on bonds and equities.
The problem of lack of data usually associated
with emerging markets is less of a problem in South Africa.
In fact, data had already been compiled for capital market
returns going back to 1925 . Using the monthly annualised
returns for data until the end of December 2004, table 2
shows the historical ERPs for different periods.
Table 2:
Historical SA Equity Risk Premium (Period to end 2004) 
Period 
Equity Returns 
Bond Returns 
Risk Premium 
75 years
50 years
25 years
20 years
15 years
10 years
5 years 
13.7%
16.2%
19.0%
17.1%
13.7%
11.3%
14.4% 
7.4%
9.7%
14.8%
17.4%
17.7%
18.3%
17.9% 
6.3%
6.5%
4.2%
0.3%
3.9%
7.0%
3.6% 
Source of basic data: Carsons;
JSE; BESA; INet; Barra 
Modified
historical risk premium
Problems such as high market concentration, low liquidity
and high volatility often occur in emerging markets –
including South Africa. These factors add to the unreliability
of historical risk premiums as described above.
A modified historical risk premium that
can be used in a market such as South Africa’s, is
the following:
ERP = Base premium for mature equity
market + Country premium
The US equity market can be regarded as
a mature market. Over the period 19302004, the ERP in the
US was around 4,6% (see table 3).
Table 3:
Historical USA Equity Risk Premium (Period to end 2004) 
Period 
Equity Returns 
Bond Returns 
Risk Premium 
75 years
50 years
25 years
20 years
15 years
10 years
5 years 
9.7%
10.7%
13.1%
12.9%
10.7%
11.8%
2.2% 
5.0%
6.1%
9.4%
9.3%
7.8%
8.0%
7.8% 
4.6%
4.7%
3.8%
3.6%
2.9%
3.9%
10.1% 
The country risk premium for SA can in turn
be defined as follows:
Country risk premium 
= 
Country default spread x (Equity std dev/Bond std
dev) 

= 
1,2% x (21,7% / 9,1%) 

= 
2,77% 
In the above equation the standard deviations
of SA equity and bond returns for the past 75 years were used
together with the spread (average 3rd quarter 2004) of SA
foreigncurrency denominated debt. This is done in order to
adjust the bond premium for the relative equity market volatility
in the specific country.
The equity risk premium in SA can therefore
be calculated as: 4,4% + 2,8% = 7,2%, using an equity risk
premium of 4,4% (past 75 years) for the USA. However, the
assumption of the risk premium in the USA at more than 4%
is a doubtful assumption as many analysts put the US ERP at
less than 2%, which could leave the SA ERP at anything between
2,8% and 4,8%, instead of 7,2%.
An additional problem with this method of
calculation is that some analysts would argue that country
risk is diversifiable and that there should be no country
risk premium. This would indeed have been the case if equity
returns across countries were uncorrelated. However, in recent
times equity markets across countries have become increasingly
more correlated. The fact that the SA market is still not
perfectly correlated with the US market, nevertheless justifies
some adjustment to be made to the above country risk premium.
When calculating the cost of capital for a firm, this method
of calculation will also have to be expanded to relate the
exposure of the specific company to the country risk.
Suggested approach:
Implied equity risk premium
Because of the various problems associated with calculating
historical risk premiums, another approach is suggested that
does not require historical data or corrections for country
risk. This method, based on the Gordon model, assumes that
the market, overall, is correctly priced:
Expected dividends next period
Value = (Required return on equity  Expected dividend growth
rate)
The above equation is applicable where the dividend growth
rate is kept constant but can be adjusted to make provision
for the view that the growth may be different in the first
few years before reverting to a longterm constant rate.
Consider the following historical and anticipated market
data for the JSE ALSI:
Average index level (Nov 2004): 
12202 
P0 


Average dividend yield (Nov 2004): 
2,66% 
DY0 


Expected dividend growth rates: 
year 1: 
19,1% 



year 2: 
10,7% 



year 3: 
12% 



year 4: 
10% 



year 5: 
9% 


Longterm dividend growth rate after 
year 5: 
8% 
g 

Therefore, the dividend level in : 
year 0 
325,6 
d0 
( = P0 x DY0) 

year 1: 
386,6 
d1 


year 2: 
427,9 
d2 


year 3: 
479,3 
d3 


year 4: 
527,2 
d4 


year 5: 
574,7 
d5 

after 
year 5: 
620,6 
dn 

By using the above historical figures and projections, the
following equation must be solved for r (the required rate
of return):
P0 
= 
d1/(1+r)+d2/(1+r)2+d3/(1+r)3+d4/(1+r)4+d5/(1+r)5+[dn/(rg)]/(1+r)5 

= 
386,6/(1+r) + 427,9/(1+r)2 + 479,3/(1+r)3 + 527,2/(1+r)4
+ 574,7/(1+r)5 + [620,6/(r 0,08)]/(1+r)5 
Solving for r, we get: r = 11,8%. This rate must be deducted
from the longterm (riskfree) bond yield which averaged 8,4%
during November 2004. This then gives an estimate of the equity
risk premium:
ERP = 11,8%  8,4% = 3,4 % (using current forecasts as
per scenario A, table 4).
Table 4: SA
Equity risk premium based on different dividend growth
scenarios 

A 
B 
C 
D 
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6 & Beyond 
19.1%
10.7%
12%
10%
9%
8% 
15%
10%
8%
7%
6%
5% 
4%
6%
8%
10%
12%
15% 
8%
8%
8%
8%
8%
8% 
Require return on equity
Yield on long bond rates 
11.8%
8.4% 
8.7%
8.4% 
17.5%
8.4% 
11.2%
6.0% 
Equity risk premium 
3.4% 
0.3% 
9.1% 
5.2% 
The higher the dividend (and earnings) growth
assumptions, the higher the equity risk premium becomes (see
table 4). If it is assumed that the government will succeed
in bringing down inflation to 3% over the longterm and that
real economic growth is optimistically projected at 5% p.a.,
dividend and earnings growth rates are unlikely to be much
higher than 8% in nominal terms. Under a scenario where the
inflation stabilises at around 3%, the longterm (riskfree)
interest rate can be expected to average around 6% p.a. A
constant 8% nominal growth rate in dividends will ensure a
risk premium of between 3% and 5% (see scenarios A and D).
A weaker equity market performance will of course imply a
much lower risk premium (scenario B), while the converse will
happen if future earnings and dividend growth rates are much
higher (scenario C).
References
 Brigham, E.F., and Gapenski, L.C., Financial Management
– Theory and Practice, Orlando: Dryden Press, 6th
ed, 1991
 Damodaran A, Estimating Equity Risk Premiums, Stern School
of Business: New York, 1998
 Falkena, Kok, Luüs & Morgenrood, The Equity Market,
Halfway House: Southern Book Publishers, 1993
1Carsons (later Ginsburg, Malan & Carson),
a frim of consulting actuaries, was the source for the original
data from 1925 to around 1960. 