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What the Beta Puzzle Tells Us about Investing
By David Cowan and Sam Wilderman
November 18, 2011

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What the Beta Puzzle Tells Us about Investing

David Cowan, Sam Wilderman



One cornerstone of finance theory is that investors demand return in exchange for assuming risk. As a consequence, the long-term returns of an investment strategy should be commensurate with the risks the strategy takes. This proposition sounds reasonable and intuitive, but it remains controversial. As both academics and practitioners have noted, there appear to be some anomalies, i.e., investment strategies that generate returns greater than expected in light of their perceived risks. One example that has generated considerable discussion recently in both academic and practitioner circles is what one might call the “beta puzzle”: portfolios of low beta stocks have historically matched or beaten broader equity market returns, and have done so with significantly lower volatility. At the same time, high beta stocks have significantly underperformed, exhibiting lower returns while appearing to take much more risk.(note 1)


A number of strategies have been proposed to take advantage of this perceived inefficiency, from risk parity to minimum-variance portfolios. In each case, the investment thesis hinges on the belief that the counterintuitive performance of high and low beta stocks is an exploitable anomaly.(note 2) In this paper we argue that this puzzling phenomenon is not an anomaly at all, but, more simply, stems from a misunderstanding of risk. In examining the beta puzzle and what lies behind it, we provide a framework for thinking about risk and return that can offer insight into a wide variety of investment strategies, from low-beta equity portfolios to levered ETFs and hedge funds.


The Puzzle


Let’s begin by taking a look at the empirical data behind the beta puzzle. Exhibit 1 shows the performance of portfolios of high and low beta large-cap U.S. stocks.


As Exhibit 1 shows, the portfolio of low beta stocks has outperformed the broader market, with substantially lower realized volatility and smaller drawdown. The high beta portfolio has underperformed the market, and done so with substantially higher volatility and larger drawdown. This is the essence of the beta puzzle: why should the low-risk asset have no compensating reduction in performance, while the high-risk asset (which should be compensated for its additional risk) underperforms?





This phenomenon is not limited to the U.S.; the same pattern can be seen for global equities (Exhibit 2). As in the U.S., the global low beta portfolio provides a much better return than high beta despite appearing to carry much lower risk.


Proposed Explanation(s)


This puzzle has been widely discussed, and several explanations have been offered. To us, the most interesting of them theorizes that high beta assets trade at a premium because they provide implicit leverage to investors who are not able to get it explicitly. (note 3) High beta stocks, the theory goes, provide exposure similar to borrowing money to lever a market position—but the mandates of some investors prohibit them from borrowing money (or they may simply prefer to avoid it), and these investors might turn to high beta stocks to get their additional market exposure. This extra demand drives up the price of high beta stocks, driving down their long-term returns.


In our view, leverage is an important part of the explanation, but the offered theory misses a critical element. It is not the implicit nature of the leverage that is at the heart of the matter, but rather the fact that the leverage high beta provides comes with an additional benefit: it is leverage with protection.


Let's look at a stylized example to understand this feature a little more fully.





To illustrate the desirability of protected leverage, Exhibit 3 contrasts how we might expect two forms of leverage to behave. Compare, for example, the fate of two investors, each starting with $100: one invests $100 in a portfolio of beta-2 stocks, while the other borrows an additional $100 from his prime broker and buys $200 of the market. The first is using implicit leverage, while the second levers the portfolio explicitly. While the investors earn similar returns in a market advance, each gaining twice what the market does, their outcomes should differ when the market falls. When the market declines 50% or more, the investor who borrowed money explicitly has no capital left from his investment (and could potentially lose even more). The owner of the high beta portfolio, however, will have some value left in his portfolio, as the prices of the equities in the beta-2 portfolio will most likely remain above zero in a down 50% market (and they certainly cannot go down 120% in a down 60% market).


The point here is that the form of leverage offered by high beta is different in an important way from explicit borrowing. Investors should prefer this kind of leverage, and, in an efficiently priced market, they will accept a lower return for it. As we will show, the performance of high beta is not a product of excessive demand, but rather a reasonable and rational consequence of the fact that it provides a convex payoff to the market.


To continue reading, go here.


1 Here and throughout this paper we use beta in the usual way: as a measure of the sensitivity of an asset’s return to the contemporaneous return of the market. We measure this using 250-day returns of each stock, regressed against 250-day returns of the relevant universe, weighted by market capitalization.

2 In some cases the focus is more on volatility than beta, but in general the dynamics are similar. Beta is an important contributor to a stock’s total volatility, and becomes an even more central factor in contexts like minimum-variance portfolios, where the strategy is focused on low portfolio-level volatility.

3 Andrea Frazzini and Lasse Pedersen, “Betting Against Beta,” NBER Working Paper No. w16601, December 2010.














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