6. Asset 1 has an expected mean return of µ1 = 9%, standard deviation of its return is σ1 = 6%. Asset 2 has an expected mean return of µ2 = 14%, with a standard deviation of σ2 = 11%. The correlation coefficient between returns on these two assets is rho1,2 = - 1. If you invest all your financial wealth on a portfolio holding only these two assets such that w1 + w2 = 1. How should you choose weights w1and w2 such that the portfolio is risk free (i. e., σp = 0) ? In that scenario, what is your expected return on that portfolio, E (rp) ?

Question

Jensen Sparks

Business

13 August, 11:59

6. Asset 1 has an expected mean return of µ1 = 9%, standard deviation of its return is σ1 = 6%. Asset 2 has an expected mean return of µ2 = 14%, with a standard deviation of σ2 = 11%. The correlation coefficient between returns on these two assets is rho1,2 = - 1. If you invest all your financial wealth on a portfolio holding only these two assets such that w1 + w2 = 1. How should you choose weights w1and w2 such that the portfolio is risk free (i. e., σp = 0) ? In that scenario, what is your expected return on that portfolio, E (rp) ?

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Blake Martin · Answer 1

Weight w1 = 0.65

Weight w2 = 0.35

Expected return = 10.75%

Explanation:

w1 + w2 = 1 ... (1)

w1 = SD of asset 2 / (SD of asset 1 + SD of asset 2)

w1 = 11 : (6 + 11) ⇒ 0.65

∴ w2 = 1 - w1 ⇒ 1 - 0.65

w2 = 0.35

Expected return = Weighted average

[0.65 * 9] + [0.35 * 14] ⇒ 10.75%