# joint probability function and covariance calc.

Hey folks, The joint probability of returns, for securities A and B, are as follows: Return on Security B=30% Return on Security B=20% Return on Security A=25% 0.60 0 Return on Security A=20% 0 0.40 The covariance of the returns between securities A and B is CLOSEST to: The answer is B. I guessed it correctly on the CFA practice exam 1, but have no idea how they figured out covariance. I know the formula for covariance, but not sure how they got the return-expected return on the stock within the formula. Any ideas?

use this formula… it’s easier: E(XY) - E(X)E(Y) E(XY) = .6 * 25%*30% + .4 * 20% * 20% E(X) = .6*25% + .4*20% E(Y) = .6*30% + .4*20%

Interpret the above to mean the following Prob********A****** B 0.60*******25******30 0.40*******20******20 Then calculate the E(RA), E(RB) E(RA) = .6 * 25 + 0.4 * 20 = 23 E(RB) = .6 * 30 + 0.4 * 20 = 26 Calculate the Covariance now… pi*(E(Ra)-Ra) * (E(Rb)-Rb)

damn, wtf? are there other ways of solving this? i was thinking, maybe using your calculator… as in, enter (25,30) 6 times… and enter (20,20) 4 times… then let it solve it for you… thats the only way i know how

.6 * (25-23) * ( 30-26) = 4.8 .4 * (20-23) * (20-26) = 7.2 Sum = 12 = Covariance

ahhh thanks cpk, taht makes more sense to me…