While the idea that behavioral biases divert investors away from high-quality stocks provides a credible rationale for the excess return to high-quality companies, it flies in the face of notions of market efficiency. After all, if these biases are evident, why haven’t they been competed away by savvy arbitrageurs? An alternative perspective that coheres with behavioral explanations yet also aligns with notions of investor rationality is encapsulated by the low beta anomaly or beta puzzle. This refers to the empirical finding that low beta stocks (stocks that have lower sensitivity to overall index returns) on average tend to deliver higher risk-adjusted returns, in direct contradiction of what is predicted by the Capital Asset Pricing Model (CAPM).
High-quality companies, in addition to their strong fundamentals, typically have stocks with low betas. According to the CAPM, the expected return on a stock is directly related to its beta, which measures its sensitivity to market movements. Higher beta stocks are expected to have higher returns to compensate for their higher risk and vice versa. However, in practice the opposite holds true, with lower beta stocks on average yielding higher returns than would be expected and vice versa.
Higher beta stocks are expected to have higher returns to compensate for their higher risk and vice versa. However, in practice the opposite holds true, with lower beta stocks on average yielding higher returns than would be expected and vice versa.
Fisher Black, famously known for co-developing the Black-Scholes option pricing model, was among the first to spotlight the beta puzzle. In the early 1970s, Black posited that borrowing limitations might be a key factor behind the low beta anomaly. The CAPM presupposes that investors can freely borrow and lend at the risk-free rate, allowing them to adjust their leverage to meet their preferred risk levels. Black noted that in practice, investors faced restrictions on leverage, preventing them from achieving their desired beta through leverage adjustments alone. Consequently, they had to alter their portfolio composition to reach their beta objectives, resulting in the low beta anomaly.
Black’s theory was plausible at the time, considering the high trading costs and assorted frictions which made it hard for investors to access leverage. Yet, half a century later, after an explosion of innovation in financial derivatives and an extended period of ultra-easy borrowing conditions, the notion that investors are leverage-constrained seems almost quaint.
More likely the beta puzzle stems from the inherent limitations of the CAPM itself. As a static model that assumes market equilibrium and provides only a momentary glimpse of how a stock’s expected returns correlate with market returns, it fails to consider the evolution of this relationship over time.
This shortcoming of the CAPM is particularly acute in the model’s failure to account for the tendency of betas to converge during periods of market distress. The phrase “all betas go to one in a crisis” succinctly captures this phenomenon, where individual stock behaviors become increasingly synchronized under severe market conditions. This convergence is largely caused by a widespread rush for liquidity and a collective retreat from risk, as leveraged investors indiscriminately divest assets in their dash for cash. In such times, the unique attributes that typically differentiate stock performances become overshadowed by systemic risk, which exerts a uniform pressure across the market. Consequently, the usual factors that contribute to diverse performance fade into the background, and the collective retreat from risk catalyzes a comprehensive market downturn. This scenario sees individual stocks’ returns align closely with the market average, effectively normalizing betas to one, a shift that CAPM does not anticipate.
This dynamic has the effect of disadvantaging low-beta stocks while benefiting high-beta stocks during crises. High-beta portfolios, which are inherently riskier under normal conditions, experience a relative decline in beta during a crisis, providing a form of wealth protection not accounted for if beta remained unchanged. In contrast, investors with low-beta portfolios find themselves at a disadvantage as their stocks, previously less sensitive to market movements, start mirroring the broader market. Technically, the high-beta portfolio exhibits positive convexity, meaning that losses diminish in relative terms during a crisis, while the low-beta portfolio shows negative convexity, with losses accelerating. Positive convexity is desirable, something investors are willing to pay a premium for, whereas negative convexity, representing increased risk, is something investors expect compensation to endure. And, as market pricing incorporates the convexity associated with different portfolios, the premium attached to low-beta, or high-quality, stocks emerges as a form of compensation for the negative convexity they bear during times of crisis.
But while convexity may well be a piece of the quality puzzle, its impact is likely peripheral, affecting primarily those stocks where low beta coincides with high quality. Moreover, attributing all the excess return to convexity adjustments alone is hard to square with its overall magnitude, which typically ranges from 1% to 3% annually across global equity markets. Even staunch proponents of rational expectations struggle to justify such a rich premium for convexity alone, suggesting that additional drivers must be at play.