1.a.6 Practice Bag (covariance calculation)

[hsuwang]

Hello David,

In the Foundations practice bag 1.a.6, in the "SML" and "CAPM" tab, I am really having a hard time figuring out the formula you used to calculate the Covariance (port, market). Is that formula covered anywhere in the BT course? Thanks.

 

[David Harper CFA FRM]

That formula is not really covered in FRM/BT program; although, in Stulz Chapter 4, during the tedious calculation on the impact of a small project on VaR, it is used in a footnote (which gives confusion to careful readers). Here I merely employ as a means to setup the SML under the ridiculous assumption that the entire market portfolio is only the two assets. So, the covariance property (not given in Gujarati) is:

http://learn.bionicturtle.com/images/forum/covar_expanded.png
source: http://en.wikipedia.org/wiki/Covariance

where a = portfolio weight in asset A, b = portfolio weight in asset B, c = weight in asset A for the MARKET portfolio (i.e., portfolio with highest sharpe ratio), d = weight in asset B for MARKET portfolio. Then note that COV(X,W) = Covariance(return asset A, return asset A) = Variance(return asset A).

Hope that explains...David