a) What is the market risk premium? Explain the meaning of market risk
The market risk premium is the difference between the expected return
on a market portfolio and the risk-free rate. That is, for example,
the difference between the return rate of a market benchmark, like the
S&P 500, and the 10-year government bond yield.
In this case the risk free rate is the treasury bill rate, equal to
3%, and the market portfolio return is expected to be 12.5%; then:
Market Risk Premium = 12.5% - 3% = 9.5%
See for references:
"History Yields AEX Index":
"Y-aex is the weighted average of the future returns (Yields) of the
24 stocks in the Dutch AEX index."
"Market Risk Premium":
"The Market Risk Premium is the reward-premium that investors
implicitly require for investing in a diversified portfolio of stocks
instead of risk free bonds. It is computed as the difference between
Y-aex and the yields on 10 year Dutch Treasury bonds."
b) What is required rate of return on an investment which has a beta of 1.8%?
According to CAPM:
r = Rf + Beta * (Rm ? Rf)
r = the expected return on the investment
Rf = the risk-free rate
Rm = the expected return on the market portfolio
Beta = investment's beta
r = 3% + 1.8 * (12.5%-3%) = 20.1%
c) If the required rate of return on stock X is 12%, what is its beta?
According to the problem statement you know r, Rf, and Rm; so you only
need to isolate Beta:
Beta = (r - Rf) / (Rm ? Rf) =
= (12% - 3%) / (12.5% - 3%) =
= 9% / 9.5% =
d) If an investment with a beta of 1.2 were expected to give a return
of 14%, would you accept it?
Required rate of return = r = Rf + Beta * (Rm ? Rf) =
= 3% + 1.2 * (12.5% - 3%) =
In this case the investment return is less than the required rate of
return. Hence, its NPV will be negative. You must REJECT.
I hope this helps you. Feel free to request for a clarification if you need it.