Estimation of Cost of Capital 91Some theorists argue that arithmetic mean is consistent with the mean—variance framework of CAPM.
There are some pitfalls in using arithmetic mean. Suppose the price of an asset increases from Rs 100 to
Rs 200 and then falls to Rs 100. Holding period returns are 100 percent and –50 percent. The arithmetic
mean is 25 percent. Clearly, the return is zero.
The geometric mean = [(1 + 1)(1 – 0.5) – 1]½ = 0Consequently some suggest that the geometric mean of returns be used. Exhibit 4.3 presents the mean and
standard deviation of returns of some popular indices in India.
Exhibit 4.3 Mean and standard deviation of return on indices
Mean return (percent) Standard deviation (percent)
Weekly Monthly Quarterly Weekly Monthly QuarterlyBSE 200 0.29 0.94 4.46 4.17 11.01 25.68
Sensex 0.39 1.23 4.92 4.47 10.25 22.44
NIFTY 0.34 1.88 3.87 4.22 9.9 17.33
Exhibit 4.4 shows the arithmetic and geometric mean returns in stock markets around the world.Exhibit 4.4 Returns around the world
Monthly
G.M. Std.
Country Mkt. cap A.M. Returns Returns
deviation Source Sample start ($ in million) (percent) (percent) (percent)
Argentina IFC Oct 1979 17,939 42.0 7.9 93.1
Brazil IFC — 81,800 33.1 14.0 64.0
India IFC — 71,904 17.4 14.1 29.5
Indonesia IFC Oct 1990 21,841 3.3 –1.4 30.8
Mexico IFC Oct 1979 47,962 20.8 9.1 46.5
Taiwan IFC Oct 1985 147,472 35.8 25.9 51.3
Thailand IFC Oct 1979 90,882 22.1 20.1 27.1
Venezuela IFC Oct 1985 2,992 21.7 11.5 46.1
Source: Erb et al. (1996).
The actual returns earned by stocks (i.e., index) over a long period of time over and above the actual re-
turn earned on a default free security is the market premium, Rm – Rf. The arithmetic average of returns on
government bonds is deducted from the average returns from stocks. This historical premium is used as
proxy for future risk premium. The choice of index, obviously, affects the market premium estimate. In India
five indices are available: Sensex, BSE Natex, BSE 200, NSE 50, CRISIL 500. Sensex is popular because it
has the longest history. Sensex data is available for 18 years whereas other indices have a shorter history.
A study by ICICI Securities and Finance suggests that the market premium for 1980–96 is 10 percent. This
could be used as the market premium. Another study by CS First Boston indicates that the market premium
is 8 percent. The premium in the case of the US and UK are 5.5 percent, and 8–9 percent respectively. The
risk premia for some Asian countries and the US are presented in Exhibits 4.5 and 4.6.
Risk premium as measured by the historical difference between stocks and bonds usually suffers from
statistical noise. Further, risk premiums may change over time. So adding a constant risk premium to the
T-bond rate might be inappropriate.