In: Finance
. Can someone explain this in depth with step by step solutions? How does one calculate equilibrium expected return and how is it different from regular? Thanks in advance.
Suppose the market portfolio's volatility is 16% and expected market return is 10%. Sup-
pose that a stock has correlation of 0.70 with the market and volatility of 20%. Suppose
the risk-free rate is 2%. The equilibrium expected return of the stock is:
(A) 6.48%
(B) 7.00%
(C) 9.00%
(D) 10.72%
Equilibrium expected return of a stock is computed using the CAPM approach as follows:
Expected return= Risk free return + Beta of the stock*(Market return - Risk free return).
The regular return from a stock is compured as follows:
Regular return= Dividend yield + Growth rate.
Investors generally employ the regular return model to calculate the expected return from any stock whereas the CAPM is used to calculate the required return. For instance, if it is anticipated that the price, dividends, and earnings of stock Y would grow at a rate of 5% and if the current dividend of the stock is $2 with a current market price of $20, the dividend from the stock one year hence would be calculated as follows:
Dividend a year hence= $2*105%= $2.1.
General investors would tend to compute its expected return through the employment of regular return model as follows:
Regular return= Dividend yield + Growth rate= $2/$20 + 5%= 15%.
Given, risk free rate= 2%,
Expected market return= 10%,
Volatility of market portfolio= 16%,
Correlation coefficient between returns of stock and that of market portfolio= 0.70,
Volatility of stock= 20%.
To compute the equilibrium expected return of stock, we have to compute the beta of the stock first as follows:
Beta of stock= (Correlation coefficient * Volatlity of stock)/ Volatility of market portfolio
= (0.70*20%)/ 16%= 0.875.
Therefore, equilibrium expected return of stock= Risk free return + Beta of the stock*(Market return - Risk free return)
= 2% + 0.875*(10% - 2%)= 9%.
Hence, option C is the correct option.