Required rate of return

CFA Level II Equities
#1

Hi,

So when calculating required rates of return with average systematic risk (i.e. beta) are we supposed to use the geometric mean return relative to 10-year govt. bond returns over 10 years or yields of 10-year govt. bonds. Why do we use it (whichever it is)?

Also does average systematic risk means a beta of 1? and why?

Thanks.

#2

The geometric mean is for ascertaining what the equity risk premium is (ie do you use the geometric mean or arithmetic mean when averaging years of equity returns data, assuming a historical estimate), not what the risk-free rate is.

Yes, average systematic risk just means market risk, which is defined to have beta = 1. If a stock has average systematic risk, it has the same volatility as the market. If a stock has beta > 1, it means it has more than average systematic risk, and is more volatile than the market, which means we want additional compensation for this risk (assuming risk-averse investors), hence beta is the slope which reflects this.

#3

But in the question they have used the yield of a 10-year bond for the risk-free rate not the geometric mean

#4

The sentence: “geometric mean return relative to 10-year government bond returns over 10 years is 2 percent per year” refers to the equity risk premium. For the risk-free rate, you have 7%, which is the yield for the 10-year maturity. Hence, you have a required return of 9% using those two figures (assuming beta = 1).

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