- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 7. Expected Value, Variance, Standard Deviation, Covariances, and Correlations of Portfolio Returns
CFA Practice Question
Suppose that the future short-term outlook for the economy is favorable, with probability 0.6, and unfavorable with probability 0.4. For two stocks, F and G, the return is 0.25 and 0.2, respectively, in favorable conditions, and 0.01 and 0.02 in unfavorable conditions. Calculate cov(Rf,Rg).
A. 0.0041472
B. 0.0062208
C. 0.010368
Explanation: E[Rf] = 0.6*0.25 + 0.4*0.01= 0.154
E[Rg] = 0.6*0.2 + 0.4*0.02 = 0.128
Cov(Rf,Rg) = E[{Rf - E(Rf)}*{Rg - E(Rg)}] = 0.6 * [{0.25-0.154}*{0.2-0.128}] + 0.4 * [{0.01 - 0.154}*{0.02-0.128}] = 0.010368
E[Rg] = 0.6*0.2 + 0.4*0.02 = 0.128
Cov(Rf,Rg) = E[{Rf - E(Rf)}*{Rg - E(Rg)}] = 0.6 * [{0.25-0.154}*{0.2-0.128}] + 0.4 * [{0.01 - 0.154}*{0.02-0.128}] = 0.010368
User Contributed Comments 8
User | Comment |
---|---|
eddeb | computing exactly the explanation given, i get 0.00628 ?? |
bj90392 | There are a lot of calculations to this. In the end I got .010348 so I think C is right |
RichWang | Can BA II Plus Professional calculate COV(X,Y)? |
riouxcf | RichWang, nope. |
jpducros | Already explained in a previous question, use here the shortcut : cov (xy) = E (xy)-E(x)E(y) It is less confusing. I think that this is the type of question that you can make the difference with other CFA candidates...it is not that complex...and cov calculations scares a bit at first sight. |
cleopatraliao | The use of the short cut here requires one to know E(xy) which is impossible to compute here so the short cut is not an option here. |
PeterL | thank you, short cut is worthless |
elmagico10 | Like jpducros explain, use the shortcut formula: COV (FG)=E(FG)-E(F)E(G) E(FG)=0,6*0,25*0,2+0,4*0,01*0,02 E(F)=0,6*0,25+0,4*0,01 E(G)=0,6*0,2+0,4*0,02 |