- CFA Exams
- CFA Level I Exam
- Topic 9. Portfolio Management
- Learning Module 45. Analysis of Active Portfolio Management
- Subject 2. Comparing Risk and Return

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**CFA Practice Question**

The risk-free rate is 1.8%. You have a choice of investing in two funds:

You want to accept a maximum volatility of 17.4% only. Assume you cannot borrow. What is the maximum expected return you can possibly get?

A. 12.5%

B. 12.64%

C. 12.78%

**Explanation:**If you invest 80% in Fund B and 20% in cash, the expected volatility of your portfolio will be 21.8% x 80% = 17.4%. Your expected return will be 15.8% x 80% + 1.8% x 20% = 12.64%, which is higher than investing in Fund A alone (with the same risk).

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**User Contributed Comments**
9

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

morel-san |
Numbers don't add up |

ange |
yes they do. remember to deduct 1.8% from the expected returns. |

tr4nceur |
how do the numbers add up |

tr4nceur |
wait nevermind - return from investing is cash is known with certainty hence needs no expectation |

truss88 |
they should clarify the question as it is possible for the correlation to be -1 between A and B, in which case investing .7962 in B and the rest in A gets you a return of 15.1%. |

gkbarr88 |
Why not invest 20% into fund A instead of cash? |

gkbarr88 |
Bunk question. Sharpe ratios don't tie out either. |

stefalf |
Investing 80% in Fund B and 20% in the risk free will indeed give you the 12.64% return. It will however also leave you with a volatility of 17.44% which is higher than the 17.4% stated. The solution should be investing 17.4/21.8= 0.7982 in Fund B, which is 0.7982*15.8 = 12.61, and investing the remaining 0.2018 in the risk-free asset (not Fund A as it will increase your volatility), which is 0.2018*1.8=0.3633. Total return: 12.6110 + 0.3633 = 12.97 |

JNW1980 |
I think the problem solution assumes you just leave the excess 20% in cash wheras if you invested in the RF rate then you would get the 12.97% You can figure this out by reworking the formulas and actually solving for the RF rate using the sharpe ratios. .64*.218 = Ra - Rf Therefore Rf = .158 - .64*.218 = 1.848 (close to the 1.8% given). Reworking the sharpe equation with the required 17.4% expected volatility in the denominator will yield you either 12.97 or 12.98 expected return assuming you invested the remainder in the Rf rate |