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**CFA Practice Question**

You are a risk-averse investor. You currently are invested in a portfolio of the riskless asset and stock A. The correlations between stocks A, B and C are given below.

B and C: 0.

A and C: -0.5.

A and B: 0.5

B and C: 0.

A and C: -0.5.

All three stocks A, B and C have an expected return of 8%. Which of the following is incorrect?

A. If there were no restrictions on your investments, your portfolio would have all three stocks A, B, and C.

B. To your existing portfolio of stock A and the riskless asset, if you have to choose an additional investment in either stock B or stock C, you will choose to invest in stock B.

C. The expected return to the portfolio does not change, but the portfolio std dev changes, as stocks A, B or C are substituted for each other.

**Explanation:**Stock C (negative correlation with stock A) would be chosen as it will reduce std dev of portfolio more than stock B. As A, B and C all have expected returns of 8%, substituting one for the other will not change expected returns. As the stocks are not perfectly correlated with each other, substituting one for the other will change portfolio std dev. In a situation where the portfolio has only two of the 3 stocks, reducing the weights of the existing two and adding the third stock will always reduce portfolio variance, this follows from straightforward algebra.

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**User Contributed Comments**
1

User |
Comment |
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Sunmeet23 |
I think the answer is wrong here....C should be chosen no? |