CFAI Text, Book 3, Reading 26, P. 233 ________________________________________________________ “the criticism of pairwsie corrlations is that an asset class maybe highly correlated with some linear combination of other assets classes even when the pairwise correlations are not high”. I get the part above. The text then goes on to explain a method used by Kritzman (1999) that I don’t understand. “Kritzman proposed a criterion to assess a proposed assets class’s diversifiying qualities that is superior to relying on pairwise correlations: For each asset current asset class, find the linear combination of the other asset classes that minimizes tracking risk with the proposed asset class. (Tracking risk is defined as the square root of the average squared differences between the asset class’s returns and the combination’s returns.) Similarly find the minimum risk combination of the current asses classes for the proposed assets class and qualitatively judge whether it is sufficently high based on the current asset classes’ tacking risk levels. For example, if the tracking risks for existing assset classes are 18%, 12% and 8%, a proposed asset class with a 15 percent tracking risk should be diversifiying.” Can somebody help me out with the explanation here…
My understanding is as follows, but may be a little off… If we can construct a linear combination of existing asset classes that very closely mimics the returns of the proposed asset class, then we are not achieving anything by investing in that proposed class. So, we take all possible linear combinations of existing classes ( I suppose this would actually be an infinite number ), calculate the the tracking error for each class with the proposed class, and find the minimum. If the minimum error is very small, the combination closely tracks the proposed, and therefore it does not offer any diversification benefit. If we are not able to find a combination of existing classes that has a (apparently subjective) low enough tracking error, then the proposed class has a somewhat separate source of risk, and diversification benefits exist.
Thanks wyantjs. I think I am clear on this now.
…very good explanation. I haven’t read the section yet but I get it based on this response.