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 = W₁

Weightage of Stock = 1 - W₁

Standard Deviation of Portfolio :

_So,

1 - W₁ = 12% / 18% = 0.66667

W₁ = 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.