A portfolio that combines the risk-free asset and the market portfolio has an ex

Question

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 7.5 percent and a standard deviation of 10.5 percent. The risk-free rate is 4.5 percent, and the expected return on the market portfolio is 12.5 percent. Assume the capital asset pricing model holds.

What expected rate of return would a security earn if it had a .50 correlation with the market portfolio and a standard deviation of 55.5 percent? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

Expected rate of return %

Explanation / Answer

Calculation of weights of portfolio- w(risk free)=wr w(market portfolio)=wm expected return of portfolio = wr x Rf + wm x Rm 7.5 = wr x 4.5 + wm x 12.5 also wm + wr = 1; wm=1-wr 7.5 = wr x 4.5 + (1-wr) x 12.5 solving above wr = 0.625 wm = 0.375 Variance of portfolio = wr^2xSDr^2 +wm^2xSDm^2+2 x wr x wm x COV(rm) as sd of risk free asset = 0 Variance of portfolio = wm^2xSDm^2 SD of portfolio = wm x SDm 10.5 = 0.375 x SDm SDm = 10.5/0.375 28.00 Corelation with market 0.5 SD of stock(Sdi) 55.50% SD of market portfolio 28.00% Beta of stock = r (im) x Sdi/SDm b= 0.5x28/55.5 0.252252 AS per CAPM = Re = Rf +(Rm-Rf)b Return = 4.5 + (12.5-4.5)0.25225 6.52% Please provide feedback… Thanks in Advance.. :-)

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