CFA Practice Question

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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

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
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