# Covariance

An analyst gathered the following data for Stock A and Stock B: Time Period Stock A Returns Stock B Returns 1 10% 15% 2 6% 9% 3 8% 12% cov1,2 = {Σ[(Rstock A - Mean RA)(Rstock B - Mean RB)]}/(n - 1) = 6 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? Covariance = (1/n) * [Summation over t=1 of (ReturnX– MeanX) * (ReturnY – MeanY)] =2.25 Does anyone know why in the first question, the formula they used had a denominator of (n-1) whilst in the second one, they simply divided it by n??? Thanks

The formulas are different. The first one is using the expected value of the product of the differences, then dividing by n-1 because it is a sample. The second one is using the SUM of the products of the differences, then dividing by n, which produces the expected value of the product.

Huh? Because they do random things - it should be (n-1) for both.

JoeyDVivre Wrote: ------------------------------------------------------- > Huh? > > Because they do random things - it should be (n-1) > for both. absolutely…n-1 for both

mib20 Wrote: ------------------------------------------------------- > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > Huh? > > > > Because they do random things - it should be > (n-1) > > for both. > > > absolutely…n-1 for both do we use “n-1” even when it is a population?

nop.

reg Wrote: ------------------------------------------------------- > mib20 Wrote: > -------------------------------------------------- > ----- > > JoeyDVivre Wrote: > > > -------------------------------------------------- > > > ----- > > > Huh? > > > > > > Because they do random things - it should be > > (n-1) > > > for both. > > > > > > absolutely…n-1 for both > > do we use “n-1” even when it is a population? nope…you would use n as the denominator. however, unless they explicity mention that the data set is the population data set, we will use n-1.