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**CFA Practice Question**

Which of the following is incorrect?

A. Portfolio A has a higher Sharpe Ratio than portfolio B. Risk-averse individuals are given the choice of investing their total wealth in either portfolio A or investing their total wealth in portfolio B. All will choose Portfolio A.

B. For stock returns that are normally distributed, the Sharpe Ratio is the negative of the Z-stat with the risk-free rate as the cutoff.

C. Well diversified portfolios A and B have the same Sharpe Ratio and same beta. This implies that they have the same expected returns.

**Explanation:**Higher Sharpe Ratio is not enough for an individual to invest in a portfolio. If A has a very high risk, then very risk-averse individuals may select B over A for total wealth investment. However, all risk-averse individuals will choose a combination of the risk-free asset + portfolio A over a combination of the risk-free asset + portfolio B.

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**User Contributed Comments**
4

User |
Comment |
---|---|

Clude |
why? |

jingie |
A high sharp ratio simply means that the risk that an investor takes in an asset is well compensated for. A very risky asset can have a high sharp ratio if its expected returns are high enough but that does not mean that its a good investment for the risk averse. |

chandsingh |
can anyone explain what answer B is about? what do they mean by z stat |

ConnerVP1 |
Not sure why the sharpe ratio is the negative of the z-statistic, shouldn't the sharpe ratio equal the z-statistic if the null was that returns were the same as the risk free rate? |