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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 “risk-free” 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 default-free security (usually a government benchmark bond or bond index).

Depending on the time period used, the choice of the risk-free 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 risk-premium 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; I-Net; Barra

The choice of the risk-free rate is also important – especially when steep upward or downward sloping yield curves often prevail. Usually a long-term government bond is used. The additional question that needs to be addressed is whether the yield-to-maturity, 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; I-Net; 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 1930-2004, 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 foreign-currency 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 long-term 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%    
Long-term 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/(r-g)]/(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 long-term (risk-free) 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 long-term 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 long-term (risk-free) 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

  1. Brigham, E.F., and Gapenski, L.C., Financial Management – Theory and Practice, Orlando: Dryden Press, 6th ed, 1991
  2. Damodaran A, Estimating Equity Risk Premiums, Stern School of Business: New York, 1998
  3. 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.

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