The portfolio Alpha has an expected return of 18.50% and risk of 60%. The portfo

Question

The portfolio Alpha has an expected return of 18.50% and risk of 60%. The portfolio Gamma has an expected return of 11.75% and risk of 30%. The risk of market portfolio is 40%. Ms. Investor would like to create the portfolio Delta by utilizing the risk free rate and the market portfolio. However, she is interested in earning higher return than the one given by the market portfolio. She has her own wealth of $10,000 for the investment purpose. From her broker, she can borrow additional $4,000 at the risk free rate. Assume that the Capital Asset Pricing Model holds and Ms. Investor utilizes her maximum borrowing capacity, what are the expected return and risk of the portfolio Delta?

Explanation / Answer

The equation for Capital allocation line is,(These portfolios lies on the line)

E(Rp)-0.1175=((.1175-.1850)/(0.30-0.60))*(p-0.30)

E(Rp)-0.1175=((-0.0675)/(-0.30))*(p-0.30)

E(Rp)-0.1175=0.225*(p-0.30)

E(Rp)=0.1175-0.225*0.30+0.225*p

E(Rp)=0.05+0.225*p ...1)

CAL is also given as E(Rp)=Rf+slope of CAL*p ...2)

comparing equations 1 and 2 gives,

Rf=Risk free rate=0.05=5%

The E(Rm)=expected return on market portfolio=0.05+0.225*0.40( p=0.40 for market)

E(Rm)=0.14=14%

The expected return on Delta=1.4* E(Rm)-0.4*Rf (weight of market portfolio=(10,000+4,000)/10,000,weight of risk free=-4,000/10,000=-0.4 since he is borrowing and investing in market portfolio)

The expected return on Delta=1.4* 0.14-0.4*0.05

The expected return on Delta=0.176=17.6%

risk of the portfolio Delta=1.4*risk of market portfolio

risk of the portfolio Delta=1.4*40%

risk of the portfolio Delta=56%

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