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An investor decides to diversify her favorite stock holding(expected return 25%, standard deviation 50%) with a...

An investor decides to diversify her favorite stock holding(expected return 25%, standard deviation 50%) with a nearly riskless governmental bond( risk-free rate 4%) What risk( standard deviation, in %) does the investor have to accept in order to receive an expected return of 20% ?

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Expert Solution

  

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Let the weight of Risky Asset is X

weight of Risk free Asset will be 1-X

Expected return = Return of risky Asets * Weight of Risky assets + Return of risk free Asets * Weight of Risk free assets

20% = 25% * X + 4% * (1-X)

20% = 25% * X + 4% - 4%*X

20% = 21% * X + 4%

X = 20% - 4% / 21%

X = 76.19% OR 0.7619

Standard Deviation of the portfolio = Standard Deviation of Risky assets * Weight of Risky Assets

= 50% * 0.7619

= 65.63%

jeff jeffy answered 2 years ago
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