# In this case we cant simply turn to the sharpe ratio

• Notes
• shi1hong
• 18

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In this case, we can’t simply turn to the Sharpe Ratio, because there are two risk-free rates.

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Different Borrowing and Lending Rates 5 To find a portfolio with same total risk, use stat rule 2: 0.2625=w(.16) w=1.64 (1-w)=-0.64 Expected return Which risk free rate do you use? Since my weight in Vanguard is above 1, this means I am borrowing . E[r]=1.64*0.12-0.64*0.11 = 0.1264 < 0.14 p s w σ σ =
Different Borrowing and Lending Rates 6 Now, if we switch to Vanguard we are worse off if we create a portfolio with same total risk as the client’s current portfolio. Your client is better of sticking with her Mosaic fund.

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Different Borrowing and Lending Rates 7 Question 3 - Assuming now that borrowing and lending rates differ: Can you find a portfolio with same expected return but lower total risk? In this case, we can’t simply turn to the Sharpe Ratio, because there are two risk-free rates.
Different Borrowing and Lending Rates 8 To find a portfolio with same E[r], use stat rule 1: Which risk free rate do you use?

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• Fall '10
• BrianBoyer
• Interest, different borrowing, Financial Markets

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