. Suppose that there is a risky asset that provides you with an expected return

Question

. Suppose that there is a risky asset that provides you with an expected return of 8% per year and 16% standard deviation. Also, there is a risk-free asset that provides you with a 1% risk-free return.

a) If you have $1, 000 and invest 80% into the risky asset and 20% into the risk-free asset, what is the expected return and risk of your portfolio?

b) If you cannot borrow money, what is the maximum possible expected return of your portfolio?

c) If you are allowed to borrow money, how can you construct a portfolio with an 12% expected return and what is the risk of this portfolio?

Explanation / Answer

a) Expected Return = 80% x 8% + 20% x 1% = 6.60%

Standard Deviation (Risk) = 80% x 16% = 12.80%

b) The maximum expected return = 8%, when you invest 100% in the risky asset.

c) E(R) = w x R1 + (1 - w) x R2

where E(R) = 12%, w - investment in risky asset, R1 = 8%, R2 = 1%

=>12% = w x 8% + (1 - w) x 1%

=> w = (12 - 11) / (8 - 1) = 157% invest in risky asset

and borrow 57% at risk-free rate to generate a return of 12%

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.