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**CFA Practice Question**

The following is the return distribution for 2 stocks where the future consists of 3 discrete states.

1 | 0.35 | 4% | 6%

2 | 0.25 | 9% | 3%

3 | 0.4 | 10% | 5%

State | Probability | Return for Stock A | Return for Stock B

1 | 0.35 | 4% | 6%

2 | 0.25 | 9% | 3%

3 | 0.4 | 10% | 5%

The covariance of stock A and B is:

A. -0.0001953

B. 0.0007328

C. 0.0001328

**Explanation:**Calculate mean return of stock A and B, then subtract from returns for A and B respectively. Finally multiply the deviations and weight by probability.

Hint: Skip longer questions like this if you are short of time to finish the exam, and come back to it later if you have the time.

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**User Contributed Comments**
9

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

aashishb |
more explanation needed |

bd1984 |
Can anybody run the numbers line by line for us? I'm having such a hard time wrapping my head around these covariances with different probabilities. |

Mikehuynh |
No way I can finish this question in 1.5m. So better to skip it and return when finishing others. |

jann |
ER(A): 0.35*.04 + 0.25*.09 + 0.4*.1 = 0.0765 ER(B): 0.35*.06 + 0.25*.03 + 0.4*0.05 = 0.485 COVab = SUM [Prob1* (Ra1-ER(a))(Rb1-ER(b))] [prob2*(ra2-ER(a)(rb2-er(b)][prob 3 * (ra3-er(a))(rb3-er)b)] which is [0.35*(0.04-.0765) (0.06-0.485] + 0.25(0.09-.0765)(0.06-0.485) + 0.4(0.4-.0765)(0.05-0.485) and you will get the answer. no way we can do this in 1.5mins tho |

shawnpope |
A quick and dirty way I did it. If you notice that the 3 probability weights are close and the answer choices are reasonably apart, then you can use the data input function on the BA II. 2nd 7 (Data) Input X0,Y0, X1, Y1, X2, Y2 2nd 8 (Stat) then calculate sigma(x) * sigma(y) * r(correlation coefficient) = -0.000211 This puts you the closest to A. If the given answers are close together this method probably won't work well, but if you are short on time... |

tijean25 |
This will come as the second part of the exam. So at that time you would be around 30 minutes from the start and thus will think that you have a way to waste time. Just pick an answer and you would have 33% chance of getting it right in 15 seconds and save the rest of your time for better questions. I got it right by applying this method |

jjhigdon |
No calculation needed in this particular case, just casually looking at the different returns of A band B in each state, it should be obvious they are negatively correlated. A is the only negative number. |

birdperson |
jj for the win |

lynserious |
listen my friend, you can easily tell the CORRELATION is negative, that's how I solve this. Because I don't believe they will ask you to do a boring calculation |