Interpreting a covariance computation question....

[sridhar]

"You observe the following pairs of annual returns on two stocks: [(0.03, 0.01), (0.06, 0.06), (0.02, 0.05), (0.13, 0.08)]. Assuming that each pair of observations is equally likely, the covariance of the returns on the two stocks is closest to:

....."

When you see a question like this, (in the absence of any further clarification) do you interpret this as "population covariance" or "sample covariance?"

In other words, should the denominator be 4 or 4 - 1?

Of course, if the answer choices do not include both computations, then, of course, we could wing it

--sridhar

 

[David Harper CFA FRM]

sridhar,

I have no doubt it is a sample covariance; the population covariance of a series of stock returns might be unknowable (or at very least, it will be based on a much larger dataset).

But, here is a great illustration of the challenge with old (prior) questions: only this year, with Gujarati readings, did the FRM distinguish between sample and population covariance. It would not surprise me if the answer is incorrectly based on a population covary as only the population covary was previously in the cirriculum.

An actual question, IMO, ought to specify "sample covariance" in the query to eliminate doubt. Lacking that, here is my suggestion:

assume it is a sample statistic unless they say population or unless it's obvious it's an entire population
(in practice, that is to say in reality, it is typically a sample!)
So, if a guess must be ventured, i'd always guess sample.

...thanks for raising a great point!

David

 

[sridhar]

David,

Yes it was an old question and they (incorrectly in my view as well) compute the population covariance...

--sridhar