An investor invests 65% of her wealth in a risky asset with an expected rate of return of 9.53% and a variance of 3.72%, and she puts 30% in a Treasury bill that pays 2.47%.

An investor invests 65% of her wealth in a risky asset with an expected rate of return of 9.53% and a variance of 3.72%, and she puts 30% in a Treasury bill that pays 2.47%. Her complete portfolio's expected rate of return and standard deviation are ________ and ________ respectively.

Solutions

Expert Solution

Weight of the risky asset is 65%
Expected return is 9.53%
Variance is 3.72%
Standard deviation is square root of variance, that is equal to 0.192873015

Weight of the Treasury bill is 30%
Expected return is 2.47%
Variance and standard is 0 as Treasury bill is a risk free asset.

Expected rate of return of the portfolio=(Weight of the risky asset)*(Expected return of the risky asset) + (Weight of Treasury bill in the portfolio)*(Expected return of Treasury bill)
=(65%)*(9.53%) + (30%)*(2.47%)
=0.061945 + 0.00741
=0.069355 or 6.94% (Rounded to 2 decimal places)

Standard deviation of the portfolio=(Weight of the risky asset)*(Standard deviation of the risky asset)
=65%*0.192873015
=0.12536746 or 12.54% (Rounded to 2 decimal places)

Answer:
Expected rate of return of the portfolio is 6.94%
Standard deviation of the portfolio is 12.54%

jeff jeffy answered 2 years ago

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