Baker and Haugen explain that, in an environment where investors are leverage-constrained, and are unable to borrow money, and in which asset-class return expectations are positive, investors will bid up the riskiest stocks because that is the perceived route to outperformance.26 A more sophisticated version, by Antii Ilmanen, states that investors prefer positive skewness, and are willing to overpay for positive upside surprises and for protection from extreme downside events.27
Baker and Haugen state, “agency issues create demand by professional investors and their clients for highly volatile stocks. This demand overvalues the prices of volatile stocks and suppresses their future expected returns.” And later: “We find that (a) financial institutions hold more volatile stocks, (b) analysts’ coverage is significantly greater for more volatile stocks, and (c) news coverage is more intense for more volatile stocks.” They support their argument by explaining that managers who are judged by the simple metric of excess return versus a benchmark may have incentives to take excess risk or to bid up high-beta stocks. In many cases, portfolio managers can expect a performance bonus for generating excess returns above a certain level, but will not be fired for average performance or moderate underperformance. They have much to gain by increasing the risk of their portfolios, especially in a risk-on market environment.
The mismatched incentives explanation is more interesting. Baker, Bradley and Wurgler investigated the consequences of using the information ratio as performance metric.28 The information ratio compares the holding period returns in excess of the benchmark with the standard deviation of the difference in returns of the portfolio versus the benchmark. The information ratio’s numerator has much in common with that of the Sharpe ratio. Both measure excess returns—one in relation to the risk-free rate, the other in relation to the benchmark. The denominators appear similar too—one evaluates a security’s standard deviation on its own, whereas the other measures the variance of returns above or below a benchmark’s returns.
These similarities are deceptive, though, because of the function of the denominator. This happens because a low-beta stock can be expected to return less than the benchmark and simultaneously increase tracking risk. Consider the math for a security with a beta of 0.8. On a day when the benchmark is up 1 percent, the 0.8 beta stock will be up 0.8 percent. It will underperform the benchmark by 0.2 percent. Its one-day tracking risk is 0.2 percent. On a day when the benchmark is down 1 percent, the 0.8 beta stock will outperform the benchmark by 0.2 percent, with 0.2 percent contribution to tracking risk. Netted out over two days, the return versus the benchmark will be zero, but the tracking error will be close to 0.2 percent. Put another way, a stock with a beta of 0.8 has to present an ex-ante alpha that is high enough to outweigh its expected contribution to tracking error, at least in the math of the information ratio. Conversely, a stock with a beta of 1.2 can present negative ex-ante alpha up to the tracking error threshold, and still make a positive contribution to the information ratio.
The information ratio can be in conflict with the Sharpe ratio. Managers whose continued employment depends on producing a healthy information ratio have incentives to pick high-beta or high-volatility securities with inferior expected Sharpe ratios.
Still, not all managers are judged by the same metrics, and not all market participants have to answer to consultants. Indeed, many are benchmarked incorrectly, if at all. If poorly incentivized managers ignore low-risk stocks and bid up high-risk ones, should not some savvy investors come in and buy up the wallflowers? What about arbitrageurs, who are best positioned to ride valuation corrections?
It turns out that taking advantage of the low-beta/low-volatility wallflowers requires leverage, which is unpopular and generally believed to be very risky. Here is why: Imagine you are trying to build a market-neutral portfolio that buys low-beta stocks and sells short high-beta ones. You will have to buy more of the low-beta securities than you will be able to sell of the low-beta ones to achieve a beta-neutral portfolio. You will have to lay out cash, or borrow money, to achieve this. At a minimum, then, this portfolio will have to have an expected return that is greater than the cost of capital, or nobody will enter into it. In practice, however, many market participants are leverage-constrained, generally by dictate of the investment policy statement. Others are prohibited from selling short, or face stiff margin requirements. Those wishing to arbitrage away the low-volatility anomaly have hit a brick wall.
The low-volatility anomaly might be not so much a risk premium as a response to market structure and to the compensation and evaluation practices for agents.