A stock has a beta of 1.55 and an expected return of 15 percent. A risk-free ass

Question

A stock has a beta of 1.55 and an expected return of 15 percent. A risk-free asset currently earns 2.2 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16)) Expected return % b. If a portfolio of the two assets has a beta of 0.93, what are the portfolio weights? (Round your answer to 4 decimal places. (e.g., 32.1616)) Weight of stock Risk-free weight c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161)) Beta d. If a portfolio of the two assets has a beta of 3.10, what are the portfolio weights? (Negative amount should be indicated by a minus sign.) Weight of stock Risk-free weight

Explanation / Answer

Details Stock Risk free asset Beta                       1.55                         -   Expected rate of return 15% 2.20% a When portfolio invests equal amounts: Expected return =0.5*15%+0.5*2.2%= 8.60% So Expected return =8.6% b Given Portfolio beta =0.93 Suppose weight of stock =w so weight of risk free asset=(1-w) w*1.55+w*0=0.93 w=60% Stock Risk free asset So weights of assets 60% 40% c Given portfolio expected return =8% Suppose weight of stock =w so weight of risk free asset=(1-w) w*0.15+(1-w)*0.022=0.08 0.15w+0.022-0.022w=0.08 0.128w=0.058 w=45.31% Stock Risk free asset So weights of assets 45.31% 54.69% Portfolio beta=0.4531*1.55+0.5469*0=                     0.702 d Given portfolio beta =3.1 Suppose weight of stock =w so weight of risk free asset=(1-w) w*1.55+(1-w)*0=3.1 w=200% So weight of Stock =200% It indicates short selling risk free asset

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