COV

CFA Level I
#1

An analyst observes the following return behavior between stocks X and Y. Time Period X’s Return Y’s Return 1 7 5 2 9 8 3 10 11 4 10 8 What is the covariance of returns between stocks X and Y? A) -3.0. B) +3.0. C) -1.5. D) +1.5.

#2

B.

#3

I’ll go with B. I always mess up though if its based off sample or population.

#4

I am trying to do this in BA II PLUS PRO and I’m getting it wrong ? Any help with that ?

#5

input DATA X and Y Goto STAT R = Correlation Sx - Sample Standard Dev. Sy - Sample Standard Dev. R=COVx,y/ (SX)(SY) Comes outo like 2.9 something

#6

Thanks, bud.

#7

What is sigma x on the calculator? population standard deviation? Would that be divided by 4 instead of divided by 3?

#8

Because I have Sx, sample std deviation of 1.414 and sigma, population std deviation of 1.225, hmm…

#9

Sx = Sample STD of variable Y SigmaX = Population STD Of variable Y

#10

sample std dev = sum((X - Xbar)^2)/ (n-1) pop. std dev = sum((X-Xbar)^2)/(n) So can’t I just take 1.414 * 3 / 4? I get 1.0605 not 1.225

#11

Notice the DEGREES OF FREEDOM. That’s very important to differentiate b/w Sample & Population.

#12

For the manual calculation, I’m not sure what I am doing wrong. Covariance = Sum of [x - E(x)]*[y-E(y)] So the mean of X = 9, mean of Y = 8 [(7-9)*(5-8)] + [(9-9)*(8-8)] + [(10-9)*(11-8)] + [(10-9)*(8-8)] = [-2*-3]+[0]+[1*3]+[0] = 6 + 3 = 9 Not 3. What’s wrong with this?

#13

When I type it into excel and use the Covar function, ti comes up with 2.25, which is the 9 I got in the last post divided by 4 (I forgot that step) How do you get to 3 manually?

#14

boost: divide by n-1

#15

Can someone please show how it is done manually. I can’t get the accura result…

#16

are we sure that 3 is correct? i’ll share how i did it, but want to be sure its right first : )

#17

E[Rx] = (7 + 9 + 10 + 10) / 4 = 9 E[Ry] = (5 + 8 + 11 + 8) / 4 = 8 Cov[Rx,Ry] = [(7 - 9)(5 - 8) + (9 - 9)(8 - 8) + (10 - 9)(11 - 8) + (10 - 9)(8 - 8)] / (4 - 1) = 3 I saw a problem with the exact same numbers but with different answers, and the correct one was 2.25. So either divide by n = 4 or n - 1 = 3 and you’re fine. Pray 2.25 and 3 are not both possible answers.

#18

Great. Thanks!