For a portfolio of 20 stocks, How many covariances you to be able to calculate to find the std dev of the portfolio. a) 20 b) 360 c) 380 d) 400 e) 420
C. 380 ?
20…I think Think about the formula for a three stock portfolio…you only need three covariances w1^2*stddev1^2 + w2^2*stddev2^2 +w3^2*stddev3^2 +2w1w2Cov1,2 + 2w1w3Cov1,3 + 2w2w3Cov2,3
It’s not 20…it’ll be a huge number but I can’t remember how you figure it out
I woulda guessed half of 380 (so 190) if it was in the answers, since although you might have 380 different covariances by notation (cov i,j), half of them are duplicates (cov j,i) = (cov i,j)
but for a 4 stock portfolio, you’ll need 6 covariances: 2w1w2Cov1,2+2w1w3Cov1,3+2w1w4Cov1,4+2w2w3Cov2,3+2w2w4Cov2,4+2w3w4Cov3,4
I agree with grimer, it should be 190. I just said 380 because 190 wasn’t on the list…
That would be combination of 20, taken by 2 = 20!/(2!*18!)=190.
I get 20 Choose 2, 190 Do you like this problem? if yes, then thank me for making it up! lolol.
map1 Wrote: ------------------------------------------------------- > That would be combination of 20, taken by 2 = > 20!/(2!*18!)=190. DAMN! you are good.
This problem is totally wrong pepp, the answer is 190, not 380.
Good question, but the answer should be 190. You need to use the combination formula, because order doesn’t matter. The covariance (x,y) is the same as covariance (y,x). map and grimer are both right.
map1 Wrote: ------------------------------------------------------- > This problem is totally wrong pepp, the answer is > 190, not 380. Answer is 190 according to my understanding. Feel free to prove me wrong yet again 
I think we just did, didn’t we? 
On the TI… 20 [2nd] [nCr] 2 = 190
It’s 190. Order doesn’t matter, thats why the extended format of the equation reduces to the format where the Cov of a variable to itself becomes the variance i.e. Cov(a,b)=Cov(b,a) and Cov(a,a)=Var(a). Your a jerk for not putting 190 in the answer column. I almost convinced myself 380 was the right answer before I broke down the equation and thought about the labels.
Relax man, I wasn’t sure what the answer was, when I was composing the question, but figure it was important for me to know the concept. By the time I figured out the answer, I realized its not in the choices. hehe
You need 190 DISTINCT covariances. simple formula is n(n-1)/2. Where n is no of stocks. However you need 190*2 (380) covariance terms to calculate portfolio std deviation.
A more interesting question is how close could you come with 189? 188? 50?
JoeyDVivre Wrote: ------------------------------------------------------- > A more interesting question is how close could you > come with 189? 188? 50? how would you know which 50 or so to use?