Question

Suppose the risk-free rate is 3% and the average investor has a risk-aversion coefficient of 1.4. Further, assume that the standard deviation for the market portfolio is 14%.

1. What is the equilibrium value of the market risk premium?

2. What is the expected rate of return on the market?

3. What is the equilibrium value of the market risk premium if the average investor had a risk aversion coefficient of 1.1 instead of 1.4?

d. Why does the answer in part c go up or down?

Please show work! Thanks

Answer 1

Expected market risk premium can be solved by the following insights,

Optimal allocation in a risky asset is given by,

weight = (Em - Rf) / A*variance

Em = Expected return on market

Rf = risk free rate

variance = variance of the market returns

Let us assume weight in the market portfolio is 1 ,

Hence , Em - Rf = A*variance

= 1.4 * 0.14^2

= 2.744%

Equilibrium value of the market risk premium = 2.744%

expected rate of return on the market = Em - Rf + Rf

= 2.744 + 3

= 5.744 %

equilibrium value of the market risk premium if the average investor had a risk aversion coefficient of 1.1 = 1.1* 0.14^2

= 2.156%

The answers are going up or down due to the risk aversion of the investor. If the investor is risk averse they will ask for more compensation and higher market risk premium and vice versa.