Index Investor Corner

Swedroe: Arbitrage Limits Cause Mispricing

February 03, 2016

Recent research on equities has found that, in contrast to classical economic theory, the term-structure of stock returns is downward-sloping. Stocks with low cash-flow duration earn higher returns than longer-duration stocks.

The duration of equities is defined as the weighted average time to maturity of cash flows. It comes from summing up discounted cash flows and comparing them to price. Stocks with a lot of cash flow in the near term have low duration, while stocks with low cash flow now, but that have a lot of prospective cash flow in the future, have high duration.

Michael Weber of the University of Chicago contributes to the literature with his October 2015 paper, “The Term Structure of Equity Returns: Risk or Mispricing?” In his study—which covers the period July 1963 to June 2014—Weber sorted stocks into deciles based on duration and rebalanced portfolios on an annual basis, weighting returns within portfolios equally.

Analysis Of Results

Following is a summary of his findings:

  • Duration is strongly positively related to CAPM betas. High-duration stocks have a CAPM beta of 1.41 (compared with low-duration stocks, which have an exposure to the market of only 1.05), yet they produce lower returns.
  • A strategy going long low-duration stocks and shorting high-duration stocks (the D1-D10 strategy) leads to a statistically significant CAPM excess return of 1.29% per month. Alphas are also positive using Fama-French three-, four- and five-factor models.
  • High-duration stocks tend to load more negatively on the value (HML, or high minus low), the profitability (RMW, or robust minus weak) and the investment (CWA, or conservative minus aggressive) factors. However, their exposure to these factors does not fully explain their lower returns compared with low-duration stocks. This finding is consistent with a mispricing explanation.
  • The difference in returns between low- and high-duration stocks is three times larger after periods of high investor sentiment (the propensity of individuals to trade on noise and emotions rather than facts), and excess returns of high-duration stocks load positively on changes in investor sentiment. (Investor sentiment has been shown to play a significant role in market volatility and is a contrarian predictor of returns. High investor sentiment predicts low future returns and vice versa.)
  • A strong negative relationship exists between duration and Fama-French-adjusted excess returns in high-sentiment months: The D1-D10 strategy earns a highly statistically significant abnormal return of 1.32% per month. However, almost 90% of this abnormal return is due to the large negative risk-adjusted return for the high-duration portfolio. The profitability of the D1-D10 strategy is reduced by a factor of 3% to 0.46% in low-sentiment months.
  • High-duration stocks earn negative risk-adjusted returns after periods of high sentiment. However, no abnormal returns occur in either direction for high-duration stocks following periods of low sentiment. This indicates that investors are prone to mispricing (overvaluing) high-durations stocks during periods of high sentiment.
  • Low-duration stocks grow on average by 7%, whereas high-duration stocks grow by 31%. Analysts expect stocks with high cash-flow duration to grow twice as fast over the next five years compared with low-duration stocks. However, the difference in growth rates disappears over the subsequent five years, in which both high- and low-duration stocks grow at an annual rate of roughly 10% per year. This finding hints at an extrapolation bias in analyst forecasts for the long-term growth prospects of high-duration firms and further indicates market participants are overly optimistic in their perception of the prospects of high-duration stocks. In addition, high-duration stocks have negative earnings surprises and seem to engage in earnings management.
  • High-duration stocks tend to have characteristics found to be associated with speculative, hard-to-value stocks prone to divergence of opinion. And with restraints on short-selling, the optimistic views are more easily expressed.
  • Impediments to short-selling can explain why rational arbitrageurs do not take sufficiently large short positions in possibly overpriced high-duration stocks. As one example, about 70% of mutual funds have charters restricting them from pursuing any short-selling activities, and only 2% actually do sell short. As institutions are the largest supplier of stocks available for lending, this supply is limited (which can lead to high borrowing costs, constraining short sales). Using institutional ownership (the fraction of shares held), the evidence is consistent with mispricing—the spread in excess returns is strongest among stocks that are potentially the most short-sale-constrained. Low-duration stocks outperform high-duration stocks on average by 1.32 percentage points per month in the lowest institutional ownership class. The difference in returns monotonically decreases in institutional ownership to a statistically insignificant 0.15% per month for potentially unconstrained stocks. Short-sale constraints only matter for high-duration stocks, which are potentially overpriced. They do not matter for short-duration stocks. On the other hand, if a stock is underpriced, sophisticated investors can take sufficiently large long positions to correct the mispricing because they are not constrained in the same way they are with short sales.


Weber found that mispricing only persists in the presence of limits to arbitrage. He provided evidence that the interplay between differences of opinion and short-sale constraints drives the results. He also demonstrated that investor sentiment plays a large role in mispricing, showing that there was no mispricing in periods of low investor sentiment. While he found that for short-sale-constrained stocks there was a statistically and economically large spread in excess returns between high- and low-duration stocks, no difference in returns occurs across duration categories for unconstrained stocks. In addition, he found that returns do not vary with short-sale constraints for short-duration stocks.

Weber’s paper adds to a substantial body of evidence showing that mispricings (anomalies) can persist when they are caused by limits to arbitrage, which in turn prevent sophisticated investors (institutions, for example) from correcting the pricing errors. The implication for retail investors is that they should avoid buying stocks where the evidence demonstrates that mispricings persist—such as high-duration stocks with low profitability and high investment. Other categories of stocks where mispricings have been shown to exist include “penny stocks,” stocks in bankruptcy and IPOs. They should also avoid mutual funds that fail to screen out these types of stocks.

Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.


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