The risk management techniques in common use for equity portfolio management include Nobel prize winning concepts like the capital asset pricing model, arbitrage pricing theory, and the efficient frontier concept. The list of researchers behind these concepts reads like a who's who of finance: William Sharpe, Harry Markowitz, John V. Lintner, Jr., Jan Mossin, Steven Ross, and many other key contributors. Like any theory, however, the CAPM, APT and efficient portfolio concept are based on the same flaw that has doomed simple implementations of value at risk (see the April 6 blog entry) and the copula approach for CDO valuation: a normal distribution of equity returns is at the heart of CAPM, APT, and the efficient frontier. Default risk is ignored. The current credit crisis makes a more sophisticated and realistic assessment of risk in equity portfolios a mission critical function. We talk about how to do that in this post.
In yesterday's post, we observed that the assumption that equity returns are normally distributed with their historical mean and standard deviation is so highly stylized that it makes default disappear like magic. In Bear Stearns' case, for example, the historical mean and variance of monthly returns from January 1990 onward implied that the probability of a -100% return in a given month was 0 to six decimal places. The fact that this -100% return did occur is not a "Black Swan" a la Nassim Taleb, it's a very predictable result that is a measurable probability for any public firm. The decision to ignore default in measuring risk and return in equities is a simplification that has proven extraordinarily costly to many in the current crisis. Still we hear things like this all the time from equity portfolio managers:
"Why do I need default probabilities? I manage an equity portfolio, not a fixed income portfolio."
On hearing this, Professor John Y. Campbell at Harvard University laughingly responded, "Don't they know that equity is the most highly subordinated liability on the balance sheet of a public firm?" He's exactly right. A more subtle argument for ignoring default in equity portfolio management is embedded in this comment:
"I don't need default probabilities to manage my equity portfolio. My benchmark is the S&P 500 and no firm in the S&P 500 has ever defaulted."
It turns out, thanks to the web site of Standard & Poor's, that this comment is dramatically untrue. Remember Dana Corporation? Calpine? Delphi? Winn-Dixie? All of these firms failed while they were a component of the S&P 500. There is a more important phenomenon, however, that is very much credit driven that affects equity managers. Consider firms like Washington Mutual, Wachovia, Merrill Lynch, General Growth Properties and Lehman Brothers. All of them were thrown out of the S&P 500 as their credit quality deteriorated. These changes in the composition in the index happen "after hours." The stock price of the firm dropped from the index will be down 10-20% at the next day's open, and the stock price of the firm replacing them in the index will be up 10-15% on the open. Even if the equity portfolio manager is running a perfect replica of the S&P 500, the manager will lose the equivalent of 20% (best case) to 35% on one of the 500 elements of the index because of this phenomenon. This is a serious "negative alpha" phenomenon. Changes in index composition are similar to what the always insightful Michael Lewis pointed out in his baseball book Money Ball: walking is a skill, not an accident. Similarly, changes in index composition are not accidents either. They are highly predictable, and the default probabilities of the companies in the index have a very high degree of correlation with their probability of being dropped from the index.
Just as important to equity managers is the disconnect between the credit default swap market and equity returns. The CDS market is focused on senior unsecured debt. What if Citigroup is bailed out continuously but not nationalized? Most observers expect that equity holders will lose everything (by being completely diluted) and debt holders will lose nothing. Only default probabilities that predict the probability of the company failing (i.e. the shareholders being wiped out) capture this impact correctly. The CDS quotes for this example, Citi, would be much lower than the correct default probabilities because they reflect anticipation of 100% recovery like that which has accompanied the creeping nationalization of AIG.
This is the reason that the most aggressive users of Kamakura Risk Information Services default probabilities include some of the most famous equity fund managers in the world. For more on this topic, please contact us for a private research note at info@kamakuraco.com and mention this blog post.
Donald R. van Deventer
Kamakura Corporation
Honolulu, April 7, 2009