Skip to content

FRM Part I · FRM Exam Part I · Multivariate Random Variables

Two return series X and Y have standard deviations of 2% and 3% respectively. The cross central moment E[(X - mu_X)^2 (Y - mu_Y)] equals -12 (in %^3). What is the standardized coskewness S(X,X,Y)?

The standardized coskewness S(X,X,Y) divides the cross moment by sigma_X squared times sigma_Y. That is -12 divided by (4 x 3), giving -1.0. The negative value means Y tends to be low when X's deviations are large in magnitude.

  1. A-1.000Correct
  2. B-2.000
  3. C-0.667
  4. D-0.333

Explanation

Standardized coskewness S(X,X,Y) = E[(X-mu_X)^2 (Y-mu_Y)] / (sigma_X^2 sigma_Y) = -12 / (4 x 3) = -1. Dividing by sigma_X x sigma_Y gives -2, dividing by sigma_X x sigma_Y^2 gives -0.667, and dividing by sigma_X^2 x sigma_Y^2 gives -0.333; each uses the wrong scaling.

Did you get it right without looking?

One question tells you little. A timed set on Multivariate Random Variables shows your real accuracy, how long you take and where you lose marks.

Practise Multivariate Random VariablesFree diagnostic mock

More Multivariate Random Variables questions