Numbers don’t lie, but they may not tell investors what they need to know. In the early years of the Vietnam War, U.S. Secretary of State Robert McNamara, a whiz kid recruited from Ford Motor Co., famously proclaimed, “Every quantitative measurement we have shows that we’re winning this war.”

The numbers said one thing; reality said something else.

For most investors, beta is the number they want to beat—or buy. It’s provided by an index. But beta is much richer and more complex. It’s not simply the number given by an index; and it can be deceptive.

So what is beta? In his 1955 doctoral dissertation, Harry Markowitz established the notion that a diversified portfolio of stocks could smooth out fluctuations among individual stocks, providing those stocks weren’t closely correlated. Markowitz’s three principal achievements were correlation analysis, diversification as a risk-dampening measure, and the definition of risk as volatility. Those achievements are summarized in the notion that there’s an efficient frontier beyond which diversification adds no boost to returns.

That was step one in modern portfolio theory. Step two was the articulation of beta. That goes back to the work of William Sharpe, among others. His Capital Asset Pricing Model established the market portfolio as the sum of all risky assets. And instead of analyzing the correlation of individual stocks to each other, his model looked at their correlation to the market portfolio.

Beta, said Sharpe, is the variability of an individual security’s returns against the market return—usually a benchmark such as the S&P 500. But in popular parlance, it’s come to stand in for the market return itself. CAPM involves more than that. Securities have to be evaluated against a risk-free asset like a treasury bill. The result is the capital markets line, which tracks a portfolio starting with a risk-free asset and slopes upward as riskier assets are introduced until it reaches a portfolio of risky assets only. The higher the risk, the higher the reward.

Simple theory; the reality is less so. “There are a few different ways to define beta, but really, it’s a description of the risk/return characteristics of a particular asset class,” says Michael Cooke, head of distribution, PowerShares Canada.

“It captures the performance characteristics of a particular market or asset class, for example equities or fixed income, and it is representative of the total invested capital in that particular market. So in theory it’s reflective of the beliefs and expectations of every market participant about the future prospects of individual securities, and in aggregate it reflects the market portfolio.”

Adds Rotman School of Finance professor Eric Kirzner, “A high-beta stock is expected to be more volatile than the market. When the market is strong, a high-beta stock [tends to] go up more than the market; and when the market is weak, a high-beta stock [tends to] go down more than the market.”

But, he notes, in practice, betas are not the best way to pick individual stocks.

“Beta is not a terrific measure for individual stocks. Although the Capital Asset Pricing Model shows that there is a strong relationship between return and volatility, betas are quite unstable for individual stocks. So using beta for individual stocks is probably not a very powerful tool.”

Kirzner says it works much better on a portfolio level when the beta of that portfolio can be benchmarked against a relevant index.

Built-in unpredictability

All the same, Tyler Mordy, director of research and co-CIO at HAHN Investment Stewards, comments, “I love what Andrew Lo at MIT says—that finance suffers from physics envy. We would like our models to be as predictive as they are in physics. You labour in this business for a while and you realize that humans run financial markets. So things aren’t as predictive.”

He finds price variability too restrictive a definition of risk. “If you think about short-term variability and you look back, even if you took a broad-based volatility measure five years ago […] volatility was heading lower right into the financial crisis.”

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