The standard deviation of a stock\'s returns is 24% and the correlation of its r

Question

The standard deviation of a stock's returns is 24% and the correlation of its returns with the returns of the market portfolio is 0.4. The standard deviation of the returns of the market portfolio
is 16%. The expected return of the market portfolio is 11% and the risk-free rate of return is 3%. The stock is currently priced at $45 and you expect the price to be $50 in one year. The stock is not expected to pay any dividends during the year.
(a) What is the beta of the stock?
(b) What is the equilibrium expected return of the stock?
(c) What the expected return of the stock based on your information?
(d) Would you buy the stock?

Explanation / Answer

Beta = r * SD of Security / SD of Market Portfolio

= 0.4 * 24% / 16%

= 0.6

Expected Ret on stock = Rf + Beta ( Rm - Rf)

= 3% + 0.6 ( 11% - 3%)

= 3% + 0.6 ( 8%)

= 3% + 4.8%

= 7.8%

C. expected Return based on info:

= [ SP / pUrchase Price ] - 1

= [ 50 / 45 ] - 1

= 1.1111 - 1

= 0.1111 i.e 11.11%

D.

Expected Ret = 11.11%

Required Reurn = 7.8%

Stock is under priced, advicable to buy

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