Final answer:
The equilibrium market risk premium based on a risk aversion coefficient of 2 and a standard deviation of 20% is 8%, resulting in an expected market return of 13%. If the risk aversion coefficient increases to 3, the market risk premium becomes 12%, leading to an expected market return of 17%.
Step-by-step explanation:
To determine the equilibrium value of the market risk premium and the expected return on the market based on an average investor's risk aversion coefficient (A) and the standard deviation of the market portfolio, we will use the Capital Asset Pricing Model (CAPM). The CAPM formula states:
Expected Return = Risk-Free Rate + (Market Risk Premium * Beta)
The market risk premium is the difference between the market's expected return and the risk-free rate. If investors have a risk aversion coefficient (A) of 2 and the standard deviation of the market portfolio is 20%, then their market risk premium would be 2 times the variance (0.22 or 0.04), which equals 8%. Thus, the expected return on the market would be the risk-free rate of 5% plus the market risk premium of 8%, totaling 13%.
If the average degree of risk aversion were 3, the market risk premium would be 3 times the variance (0.22) which equals 12%, and the expected market return would then be 5% (risk-free rate) plus 12% (market risk premium), equaling 17%.