You are putting together a portfolio made up of four different stocks, however,

Question

You are putting together a portfolio made up of four different stocks, however, you are considering two possible weightings

1.What is the beta on each portfolio?

2. which portfolio is riskier?

a. the first portfilio because the beta is larger

b. the second portfolio because the beta is smaller

c. the second portfolio because the beta is larger

d. the first portfolio because th beta is smaller

3. If the risk free rate of interest were 5% and the market risk premium were 6% than the rate of return on the first portfolio is?

If the risk free rate of interest were 5% and the market risk premium were 6% than the rate of return on the second portfolio is?

Portfolio Weightings Asset Beta First Portfolio Second Portfolio A 2.20 8% 42% B 1.05 8% 42% C 0.60 42% 8% D -1.70 42% 8%

Explanation / Answer

1.

Beta of first portfolio = Beta of asset A * Weightage of asset A in first portfolio + Beta of asset B * Weightage of asset B in first portfolio + Beta of asset C * Weightage of asset C in first portfolio + Beta of asset D * Weightage of asset D in first portfolio

=> Beta of first portfolio = 2.20 * 8% + 1.05 * 8% + 0.60 * 42% + (-1.70) * 42%

=> Beta of first portfolio = -0.20

Beta of second portfolio = Beta of asset A * Weightage of asset A in second portfolio + Beta of asset B * Weightage of asset B in second portfolio + Beta of asset C * Weightage of asset C in second portfolio + Beta of asset D * Weightage of asset D in second portfolio

=> Beta of first portfolio = 2.20 * 42% + 1.05 * 42% + 0.60 * 8% + (-1.70) * 8%

=> Beta of first portfolio = 1.28

Therefore, Beta of first portfolio = -0.20 and Beta of second portfolio = 1.28

2. c. the second portfolio because the beta is larger.

3.

Rate of return of first portfolio = Risk free rate + Beta of first portfolio * Market risk premium

=> Rate of return of first portfolio = 5% + (-0.20) * 6%

=> Rate of return of first portfolio = 3.80%

Rate of return of second portfolio = Risk free rate + Beta of second portfolio * Market risk premium

=> Rate of return of second portfolio = 5% + 1.28 * 6%

=> Rate of return of second portfolio = 12.66%

Therefore, Rate of return of first portfolio = 3.80% and Rate of return of second portfolio = 12.66%

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