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**CFA Practice Question**

Which of the following is incorrect?

A. If an investor is invested in a portfolio that lies within the efficient frontier, she can change her investments to have both higher expected returns and lower risk.

B. CAPM implies that the only reason for differences in expected returns should be only systematic risk. Other characteristics like firm size or book to market should not matter.

C. If two assets are positively correlated, combining them into a portfolio cannot result in the portfolio standard deviation being less than the standard deviations of both assets.

**Explanation:**Variance for a portfolio of assets A and B = Var(w1*A + w2*B) = w1^2 * Var (A) + w2^2 * Var (B) + 2 * w1 * w2 * cov(A, B)

Due to the 2nd powers of weights, the portfolio std dev can be lower than individual std devs. Note that in comparison, the weights for expected return are only 1st power.

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**User Contributed Comments**
3

User |
Comment |
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7Ricky |
A is in correct The efficient frontier is on a graph with a x axis of deviation and y axis of return. Any point on the graph whether it is on the EF or not can either move left and have less risk or up and have higher return. It cannot get more of one without sacrificing the other. So it is wrong to say she can have both higher return and lower risk. Even a point above it would on the CAL(P) would only have higher risk. I think C is wrong: portfolio can have lower variance but not with positive correlation. |

chandsingh |
I think for A they are saying that the security is below the efficient frontier so if it is moved onto the line it can have better returns without additional risk. For c, they may be positively correlated but by different degrees allowing some diversification. |

GBolt93 |
A is a little confusing. I thought it might be talking about the botton half where you do get more return with less risk. Remember the EF is shaped like a C where there are 2 Y outputs (returns) for 1 X input (risk). |