# Covariance

An analyst is examining the relationship between the returns of two hedge funds, Hedge Fund 1 and Hedge Fund 2. Hedge Fund 1 was started in 1995 and Hedge Fund 2 was started in late 1997. The returns for both funds for the six full years between 1998 and 2003 are listed below. The variance of the returns of Hedge Fund 1 is 0.0625 and variance of the returns of Hedge Fund 2 is 0.2983. Also, the differences and the squared differences between the returns in each year and the average returns are listed in the table below: Year Differences between Differences between actual and average returns actual and average returns for Hedge Fund 1 for Hedge Fund 2 1998 0.35 0.75 1999 -0.35 -0.55 2000 -0.25 -0.10 2001 0.05 -0.05 2002 -0.05 -0.70 2003 0.25 0.65 Compute the covariance between the two funds. Covariance A) 0.1230 B) 0.1011 C) 0.1130 D) 0.0098 Your answer: C was correct! Cov1,2 = [(0.35 × 0.75) + (-0.35 × -0.55) + (-0.25 × -0.10) + (0.05 × -0.05) + (-0.05 × -0.70) + (0.25 × 0.65)]/6 = 0.113 Can someone pls explain why they are dividing the sum by 6? shouldn’t it be 5?

6 years.

Well… two things, because the size of the samples are built in to those variances. AND because you are given actual variances from the company. these arent sample statistics, its from the actual population that you are studying… TWO hedge funds… you got TWO variances… and you observed SIX years… you looked at 6 years, because you wanted to know those SIX years. you have the size youre working with. youre not trying to make a general statement of the 6 years using 5 because you have all 6 right there. god i suck at explanations… emra32

ditchdigger2CFA Wrote: ------------------------------------------------------- > 6 years. Yes what he said. damn it… took me 5 minutes to formulate that previus post, probably took u less than 5 seconds. cheers mate!

You make a good point though. Since this is a population you use N years. Had it been a sample, you would use N-1 years.

You should use 5 for the unbiased estimator. There is just no sense in which you have a population here. Honest to god, it would be nice if these study providers employed somebody who knew something about statistics.

Agree with Joey… there was another similar question and they used N-1 in that case…

Fund 2 was started in late 1997 … so this is a population and not a sample

Sure. Good thing you cleared that up for me. I’ll have to turn in my Stat. Ph.D.

where did you get your phd from :P?

Im just going with the fact that in all examples on the CFAI text they used N. I always thought it would be N-1 from all my stats courses i took. But i THINK its because theyre to find a relationship in those 6 years alone, and not make a general statement of other years using a sample of 6.

I think it’s because they are trying not to make an issue about unbiased estimation. That’s fine but they should do the same thing with the sample standard deviation then. The way they have things now, you could have complete data and estimate a var/covariance matrix that was not positive definite. That is very bad, and causes your risk management software to crash.

Hey im just glad you didint yell at me.

I never yell. Get sarcastic, sometimes. Get snippy, sometimes.