Calculating Alpha as the Market Crashes

by: Christopher Holt

Investment consultant Hewitt Associates said last week that the majority of active long-only managers underperformed their passive benchmarks last year. This is particularly poor given that the cash holdings and inherent business caution of many mutual fund managers generally results in a lower volatility than the market (along with commensurately lower losses in bad years and lower gains in good years).

Hewitt blamed the usual culprits: management fees and trading costs. But the firm also pointed to an active bet that went sour for many of the world’s managers: an overweight position in financial right before the debacle known as Q4.

The result, says the firm, is that “some pension funds are already considering switching to passive management, as a way of generating growth through cutting costs.”

“Market Adjusted Alpha”

But the performance of some managers may have been even worse if you use a performance metric proposed by Al Ehrbar in this P&I article. Ehrbar is credited with popularizing Economic Value Added (EVA). So it may be prudent to check out what he has to say about measuring “alpha” in down markets. (We put alpha in quotes since he uses a simplified version of our favorite Greek letter - one that may be more commonly used in practice than, say, Jensen’s Alpha.)

Ehrbar writes that last year’s equities stinkfest has “exposed a fundamental flaw in the conventional method of calculating the alpha on relative-return strategies.”

According to Ehrbar, this flaw punishes managers who produced some alpha (i.e. benchmark out-performance) last year while unfairly benefiting managers who may have produced less alpha in up years for the markets.

The basic idea is that a manager who goes out on a limb in January and beats the index, then hugs the index for the rest of the year will benefit from the compounding effect on his one month wonder. Conversely, the manager who beats the index by the same amount, but in December instead, won’t have the advantage of watching his one good month compound further at the market rises.

Ehrbar essentially argues that any manager who produces one month of “alpha” in any period other than December will benefit in a rising market. But in a falling market, the manager who outperforms in January will only see their out-performance fall (in percentage-point terms) as the market contracts for 11 subsequent months.

He proposes a simple and intuitive adjustment to compare rising-market out-performance to falling market out-performance. Says Ehrbar:

Happily, there is a simple methodology to correct this distortion and compute what I call a “market-adjusted” alpha. Simply divide the conventionally calculated alpha for any period by one plus the percentage total return on the benchmark over the same period. The result always equals the manager’s percentage contribution to an investor’s wealth.

Aside from the inherent irony of the term “market adjusted alpha”, this makes sense. In more sane markets, a 5% market out-performance is essentially the same whether it happens in a down market (say, fund down 5%, market down 10%) or an up market (say, fund up 10%, market up 5%). But when an index takes an incredible shrinking pill and ends up 50% smaller, then a 5% YE out-performance can mean 5% if it happened in December or possibly 10% if it happened in January (and shrunk along with the markets for the rest of the year).

“Non-synchronous” Alpha

Ehrbar’s caveat is that his market adjusted alpha is designed for “relative return strategies.” But how about hedge performance last year? Dominic Clermont writes in Benefits Canada that

Many hedge fund strategies can have zero beta if properly managed. 2008 hedge fund returns were generally highly negative because greed led most hedge fund managers to have significant market exposure (beta) in their portfolios.

Clermont says that standard measures show that overall hedge fund beta was about 0.37 going into 2008. That suggests that hedge fund returns should have been around -13% last year (assuming no alpha). But a modification proposed in 2004 by Cliff Asness (for the “non-synchronous trading effect” on hedge fund returns) and cited in his article, says that the more appropriate hedge fund beta to use would be 0.84. That would mean that hedge funds should have produced -31% last year. Hedge funds, of course, produced about -18% last year. So using Asness’ metric, Clermont concludes that hedge funds actually produced a ton of alpha.

But in conclusion, Clermont laments that hedge funds were both successful and unsuccessful at the same time.

Since the aggregate hedge fund returns were much higher than that, it means that hedge fund managers may have delivered very significant alphas. Unfortunately, they lost it all, and more, due to their (beta) market exposure.