Question

You invest $1,700 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 18% and a standard deviation of 25% and a Treasury bill with a rate of return of 9%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 12%.

Answer #1

Standard Deviation of Portfolio =
** σ_{p}** = 12%

Standard Deviation of Stock = ** σ** =
18%

Standard Deviation of T-Bill = 0

Weightage of T-Bill = W_{1}

Weightage of Stock = 1 - W_{1}

Standard Deviation of Portfolio :

_{}

_{So,}

1 - W_{1} = 12% / 18% = 0.66667

W_{1} = 0.33333 = 33.33%

Amount Should Be Invested = Total Amount * Weightage = 17,000 * 0.33333 = 5,666.67

Ans : 33.33% of portfolio or 5,666.67 Amount should be invested in the risky portfolio.

2)
You invest $1,500 in a complete portfolio. The complete
portfolio is composed of a risky asset with an expected rate of
return of 16% and a standard deviation of 20% and a Treasury bill
with a rate of return of 7%. __________ of your complete portfolio
should be invested in the risky portfolio if you want your complete
portfolio to have a standard deviation of 10%.
Multiple Choice
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