Question

Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why.

(Hint: Beta of asset i (??)=???????, where ??,?? are standard deviations of asset i and market portfolio, ??? is the correlation between asset i and the market portfolio)

Answer 1

Given that,

Risk free rate Rf = 3%

Market return Rm = 15%

Standard deviation ?? = 20%

Expected return of asset A, Ra = 5%

Standard deviation ?A = 20%

Correlation with market ?AM = 0

Expected return of asset B, Rb = 8%

Standard deviation ?B = 20%

Correlation with market ?BM = 0.5

So, beta of stock A = Correlation with market*standard deviation of asset/standard deviation of market = 0

Beta of stock B = 0.5*20/20 = 0.5

Using beta, stock return can be calculated with CAPM. = Rf + beta*(Rm - Rf)

=> required return on stock A = Rf = 3%

and required return on stock B = 3 + 0.5*(15-3) = 9%

Since required return of stock A is less than its Expected return, so stock is overvalued. and it is drawn above SML line.

For asset B, required return is more than its expected return so this stock is undervalued and it is plotted below SML line.