### CFA Practice Question

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

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.

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