Performance Measures

"Future returns may vary."

In fact, they may vary so hugely and in such disturbingly structural ways that one may worry at times if it is a fool's errand even to try to measure the performance of a fund, a manager, an asset class, or --- perhaps especially --- a strategy.

Nevertheless, the job will done ---for better or worse --- in Singapore or in New York.

However skeptical we may be about one measurement or another, we may be reassured that banks, brokerages, hedge funds, and central banks around the globe have very few secrets.

Their tools and our tools may differ in a few details --- but, just as likely, they will not differ at all.

It is intuitive to most people that a proper analysis of returns should somehow account for risk. Unfortunately, there is no clear-cut prescription for doing this, even though there are some widely reported measure such as "beta" and "VAR." We have already seen some of the limitations of these measures.

The Usual Suspects

You can find expositions of these measures in many places. The Wikipedia is starting to get these right, but the Wiki articles were wildly inaccurate for several years.

One source that I like is given in the thesis of Venkat Chandramouli, in section 4.2 (beginning on the pdf page 47, thesis page 39).

The "Tap Root" Criticism

The most fundamental criticism of all of these measures is that they incorporate only the historical risk.

This limitation can be serious. For example, for many years the return on unhedged deposits in Mexican banks would have had an infinite Sharpe ratio for US investors. This was in fact a reasonable and well-performing investment if held during certain periods of time. Not unexpectedly, was not a strong investment for those Jonny-come-latelies who piled on when it looked the juiciest.

Investments that face real but unobserved risks are said to suffer from the Peso Problem.

The sad fact is that every investment suffers from the Peso Problem to some extent. In particular, the issue of unobserved risks has been used to explain almost everything that does not have a less global explanation . For example, one can argue that it explains the "equity premium" ---the fact that over long periods of time equities have provided greater returns than bonds even when both asset classes are adjusted for observed volatilities.