Variance-Covariance VaR

CFA Level III Derivatives
#1

Variance-Covariance VaR cannot be used when the returns do not follow a normal distribution. Can someone give example of financial instruments that do not follow normal distribution other than options? Are the returns of future contracts normal for example?

Thanks.

#2

I’m pretty sure that no single security has returns that are normal, or even close to normal.

For giggles, take a look at the monthly returns of pretty much any US stock over, say, the last 10 years; you can get the monthly closing prices from Yahoo! Finance and download them to Excel, wherein you can compute the monthly returns. Create a histogram of those returns and see if it looks close to normal or not. You can also use the built-in SKEWness and KURTosis functions to see how close the returns are to being normally distributed.

I just tried this with GOOG:

  • Skewness = 0.4181
  • Kurtosis = 1.1779

Not remotely normal.

#3

Especially wouldn’t be a normal in cases of further stock issuing, dividend stocks and repurchasing.