Let A, B, and C be three portfolios of securities available in the market. Their

Question

Let A, B, and C be three portfolios of securities available in the market. Their expected rates of return are: E(RA) = .10, E(RB) = .15, E(RC) = .20 The standard deviation of their rates of return are ?A= .20, ?B = .30, ?C = .35. Statement: At least one of these portfolios is not an efficient portfolio. Is this statement True, False, or uncertain? Explain your answer (assume there are no risk-free borrowing or lending opportunities). (Hint: plot the three portfolios on a mean-variance graph and look at the shape).

Explanation / Answer

True. As you can see the portfolios are not arrayed along a straight line, but rather if you connect them there is a kink and it is facing the wrong way. Even if A and C were perfectly correlated, leaving no room for diversification, a portfolio could be constructed which was half A and half C which would offer the same return as B with a lower standard deviation.

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