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There are three portfolios and a risk-free asset (i.e., T-bill). A: E()=4% p.a.,STD=10% p.a. B: E(r)=6% p.a., STD=15% p.a. C: E()=8% p.a.,STD=20% p.a. T-bill: E()=1%p.a.STD=0% p.a. rho(AB) = 1.0: ho(AC) = 0.2 rho(B,C) =0.2, in which rho is the correlation coefficient between two return series. Whichportfolio (A, B, or C) yields the highest ratio of risk-premium/standard deviation (i.e., the reward-to-volatility ratio)?Select one:

Question

There are three portfolios and a risk-free asset (i.e., T-bill). A: E()=4% p.a.,STD=10% p.a. B: E(r)=6% p.a., STD=15% p.a. C: E()=8% p.a.,STD=20% p.a. T-bill: E()=1%p.a.STD=0% p.a. rho(AB) = 1.0: ho(AC) = 0.2 rho(B,C) =0.2, in which rho is the correlation coefficient between two return series. Whichportfolio (A, B, or C) yields the highest ratio of risk-premium/standard deviation (i.e., the reward-to-volatility ratio)?Select one:

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Solution

The reward-to-volatility ratio, also known as the Sharpe ratio, is calculated by subtracting the risk-free rate from the expected return of the portfolio and then dividing by the standard deviation of the portfolio.

Let's calculate this for each portfolio:

Portfolio A: Risk premium = E(r) - Risk-free rate = 4% - 1% = 3% Sharpe ratio = Risk premium / STD = 3% / 10% = 0.3

Portfolio B: Risk premium = E(r) - Risk-free rate = 6% - 1% = 5% Sharpe ratio = Risk premium / STD = 5% / 15% = 0.33

Portfolio C: Risk premium = E(r) - Risk-free rate = 8% - 1% = 7% Sharpe ratio = Risk premium / STD = 7% / 20% = 0.35

So, Portfolio C yields the highest ratio of risk-premium/standard deviation.

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