# What expected rate of return would a security earn if it had a 0.5 correlation with the market portfolio and a standard deviation of 2 percent?

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A portfolio that combines the risk-free asset and the market portfolio has an expected return of 25 percent and a standard deviation of 4 percent. The risk-free rate is 5 percent, and the expected return on the market portfolio is 20 percent. Assume the capital-asset-pricing model holds. What expected rate of return would a security earn if it had a 0.5 correlation with the market portfolio and a standard deviation of 2 percent?

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#### Solution Preview

Rp = 25%

Sp = 0.04

Rf = 5%

Rm = 20%

correlation coefficient is r = 0.5

Std. dev. of security is Ss = ...

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