Question

Question 3:

3. Assume that there is a risky portfolio with an expected rate of return of 12% and a standard deviation of 30%. The T-bill rate is 2%. If you have $100,000 and want to construct a complete portfolio that has an expected return of 8%, how much should you invest in the risky portfolio? Answer: $ Show your calculations here. & 10/ 11/1ot ic the eauivalent

Answer 1

The expected return of the portfolio = Weight of risky portfolio * return of risky portfolio + weight of t-bill * t-bill rate

0.08 = Wa * 0.12 + Wb * 0.02

We know that Wa + Wb = 1

Wb = 1 - Wa

0.08 = Wa * 0.12 + (1 - Wa) * 0.02

0.08 = Wa * 0.12 + 0.02 - 0.02 * Wa

0.08 = Wa * 0.10 + 0.02

Wa * 0.10 = 0.06

Wa = 0.06/0.1 = 0.6 = 6%

You should invest 60% in the risky portfolio to get 8% return on the combined portfolio.

That is 100,000 * 0.6 = $60,000

Let's verify if Wa = 0.6

The expected return of the portfolio = Weight of risky portfolio * return of risky portfolio + weight of t-bill * t-bill rate

The expected return of the portfolio = 0.6*0.12 + 0.4 * 0.02

The expected return of the portfolio = 0.08 = 8% (Verified)

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