The anti-benchmark

Market-cap weighting is the most efficient and cheapest way to tap an economy’s growth has long been under attack.

First, it was in the seminar rooms of business schools, where persistent anomalies — the value, small-cap and momentum effects — defied the so-called market portfolio. Then it hit opposition on the ground, at least for index investors, when tech stocks inflated and burst at the beginning of the decade. It turned out that market-cap indexes chase returns just as much as the next investor.

There are alternatives to market-cap weighting, among them equal weighting, and more recently, fundamental weighting developed by Rob Arnott. Each tries to strip out the momentum effects — the buy-high sell-low dynamic inherent in market-cap weighting.

Both approaches seem to be less risky than market-cap weighting. But the fundamental flaw with market-cap weighting is that it isn’t diversified, suggests Yves Choueifaty, president of Paris-based TOBAM. Risk reduction is the product of diversification. But no one has defined diversification. Now he has a patent pending on it.

He’s developed what he calls “the real neutral risk allocation.” To illustrate the meaning of neutrality, he points to the recent history of the S&P 500. In the 1960s, it overweighted consumer stocks — GM in particular — just as the oil crisis was brewing. Similarly, in the 1970s it overweighted energy stocks — just as oil was about to bust. And then there were technology, media and telecom stocks—all received their highest weightings when those sectors were about to crash.

“Clearly the benchmark is biased,” Choueifaty says. “It is not diversified. The bias of the benchmark changes over time,” meaning that the benchmark is a “dynamic risk allocator.”

To correct for risk, Choueifaty has built an “anti-benchmark” based on two factors: volatility and correlation. It’s a purely mathematical exercise that eschews views on stock fundamentals or market trends. Instead, it starts from the observation that stocks having varying volatilities. As a result, he equal weights the volatility of the stocks in portfolio. Volatility is the first moment. Then he applies correlation analysis. In this second moment, stocks with similar volatility are again equalized, this time according to their correlation. This, he says, is the neutral risk allocation.

“If you have a value portfolio or a growth portfolio, you are biased,” he notes. “Why? Because some risk factors are contributing more than others to your own risks, typically the value risk factors. So when you are building a diversified portfolio, what you are trying to do is build a portfolio [where] volatility is evenly contributed by all the risk factors available in the market.”

The intent of the exercise is not to maximize returns. Indeed, Choueifaty’s portfolios are agnostic about expected returns. The goal is to earn a true equity premium by diversifying risk until one gets to the ultimate ratio — the point where a portfolio is no longer diversifiable by idiosyncratic or stock-specific factors. The return on that portfolio — arguably the true market portfolio — earns solely the equity risk premium. And on this, Choueifaty is quite emphatic. He is not an alpha provider. He seeks to avoid the negative alpha of market-cap indexes — by not taking sector or company bets that are implicit in cap-weighted indexes.

“Not only do we believe that you will systematically reduce risk, we believe that you will systematically increase the return. Why? In fact it is not us who will increase the return, it is the benchmark that destroys a large part of the equity risk premium. So when compared to the benchmark, of course, we will be look much more profitable.”

He finds that his anti-benchmark has a lower risk than market-cap portfolios, but also higher returns. It has higher returns than equal-weighted and minimum-variance portfolios, but the evidence on risk is mixed. Still the risk reduction is significant.

“The anti-benchmark seems to reduce the volatility by about 25%, which is enormous because when you reduce the risk by 25% it means that you can increase your allocation by 30% without increasing the risk your allocation to equities.

“In terms of return now, the second very important thing that you should have in mind is that we have a very large tracking error, not because we are implementing a very risky strategy but because the benchmarks are concentrated.”

By contrast, the anti-benchmark has the highest diversification ratio, a term Choueifaty defines as the weighted average volatility of assets divided by the portfolio volatility. Right now, Chaoueifaty notes, the benchmark is 31% financials — which may not be the kind of risk diversified investors want to assume. More particularly, the MSCI sports a diversification ratio of 3. The anti-benchmark has a ratio of 9.

As a result, the anti-benchmark is the most diversified portfolio — but it uses few stocks: 50 to 70 out of the MSCI universe of 600 for the U.S. “It’s a result of the math,” he says. “It could be counterintuitive that I am the most diversified but I have only 62 stocks. The way to make that intuitive is to think about the definition of those 62 stocks.” It’s the correlations that tip the scales. “Those 62 stocks are exactly the least correlated stocks to what? To one another. Which means that they are the stocks least correlated to the anti-benchmark.”

He offers this example: “If I hold Intel but don’t hold Boeing, it is exactly because I am already more correlated to Boeing than I am to Intel, otherwise I would have Boeing.”

That formula has won praise from Rob Arnott, among others. “I am so diversified that I am even less correlated to any of my holdings than I am to any other stocks I am not holding. I am not holding them because I am already more correlated to them than to the stocks that I am already holding.”

Still, Arnott’s fundamental indexes have been accused of tapping the value and small-cap premiums.

Does Choueifaty think there’s an economic bias in his purely mathematical exercise? Perhaps.

“If you have a corporation that is a leader, a leader is always a diversifier because it is introducing something new. So I don’t have a value bias, I don’t have a small-cap bias, I have no bias. But if you need to describe some kind of the behaviour of the anti-benchmark, it will be to buy Yahoo at its early stage because it was introducing new risk factors, something that is diversifying. When will the benchmark notice Yahoo? When Yahoo has already grown a lot. So when compared to the benchmark, I will overweight Yahoo when Yahoo goes from $1 to $100 and the benchmark will overweight Yahoo against me when Yahoo will go from $100 to $120, which means I will take advantage of everything that is interesting, I will abandon something — I will always leave $5 to the casino” — or money on the table, lest the anti-benchmark make its own bets.

This article originally appeared on InvestmentReview.ca

(10/18/10)