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Suppose you are able to precisely identify the portfolio of risky assets with the highest Sharpe...

Suppose you are able to precisely identify the portfolio of risky assets with the highest Sharpe ratio (the "tangency portfolio"). The tangency portfolio has an expected return of 11% and a standard deviation of 15%. Risk-free treasuries return 3%. You are advising a client whose risk aversion is such that you would recommend they choose the "optimal" portfolio with an expected return of 7%. Which of the following portfolios does this description match?

Multiple portfolios would meet this criterion

50% tangency portfolio and 50% risk-free treasuries

The portfolio consisting of risky assets that minimizes risk for a return target of 7%

Not enough information

75% tangency portfolio and 25% risk-free treasuries

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Answer #1

Weight of Tangency Portfolio + Weight of Risk Free Treasuries = 1

Expected Return = Weight of Tangency Portfolio * Return from Tangency Portfolio + Weight of Risk Free Treasuries * Return from Risk Free Treasuries

0.07 = ( 1 - Weight of Risk Free Treasuries) * 11% + Weight of Risk Free Treasuries * 0.03

0.07 = 11% - Weight of Risk Free Treasuries) * 11% + Weight of Risk Free Treasuries * 3%

- 4% = - Weight of Risk Free Treasuries) * 8%

Weight of Risk Free Treasuries = 50%

Weight of Tangency Portfolio = 50% OptionA

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