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Tail Risk as Stock Return Anomaly Driver

Posted in Size Effect, Value Premium, Volatility Effects

Do investors exploiting common stock return anomalies risk extraordinarily large drawdowns during market crashes? In their May 2016 paper entitled “Can Exposure to Aggregate Tail Risk Explain Size, Book-to-Market, and Idiosyncratic Volatility Anomalies?”, Sofiane Aboura and Eser Arisoy investigate whether portfolios based on the size, book-to-market ratio and idiosyncratic volatility effects bear elevated stock market tail risk. They measure market tail risk as change in VIX Tail Hedge Index (VXTH), which hedges extreme drops in the S&P 500 Index by holding the index and one-month far out-of-the-money (30-delta) call options on the CBOE Volatility Index (VIX). They test sensitivity of size and book-to-market factors to overall risk and tail risk by adding change in VIX (market volatility risk factor) and change in VXTH (market tail risk factor) to the Fama-French three-factor (market, size, book-to-market) model of stock returns. They consider two equal subperiods, one containing the 2008 financial crisis, to check robustness of findings. Using monthly values of VIX and VXTH, factor model returns and U.S. Treasury bill yields during January 2007 through February 2016 (110 months), they find that:

  • Over the full sample period, small stocks exhibit positive and statistically significant tail risk dependence, but big stocks exhibit negative (close to significant) dependence. In other words, small stocks and a small-minus-big hedge portfolio are particularly risky during market crashes. This finding is strong in the first half of the sample period, but disappears in the second half.
  • Over the full sample period, value stocks exhibit positive tail risk dependence, but growth stocks exhibit negative dependence. In other words, value stocks and a value-minus-growth hedge portfolio are particularly risky during market crashes. This finding is strong in the first half of the sample period, but is missing or weak in the second half.
  • Within small stocks, value stocks drive the positive tail risk dependence. Small growth stocks exhibit little tail risk dependence. Only big growth stocks hedge against tail risk. In contrast, value stocks of all sizes have positive tail risk dependence.
  • Over the full sample period, stocks with high idiosyncratic volatility exhibit positive tail risk dependence, but stocks with low idiosyncratic volatility exhibit negative dependence. In other words, high-volatility stocks and a high volatility-minus-low volatility hedge portfolio are particularly risky during market crashes. This finding is persistent through both halves of the sample period.

In summary, evidence indicates that small, value and high-idiosyncratic volatility stocks are riskier than big, growth and low-idiosyncratic volatility stocks because they are particularly poor performers during market crashes.

Cautions regarding findings include:

  • Contrary to the conclusions in the paper, while offering potential explanations of the size and value anomalies, tail risk dependence appears not to explain the idiosyncratic volatility anomaly. On average, high idiosyncratic volatility stocks underperform rather than outperform low-idiosyncratic volatility stocks, so there is no compensation for positive tail risk of the former.
  • Testing the tail risk factor model on multiple sets of portfolios introduces snooping bias, such that the strongest findings overstate expectations.
  • Inclusion of momentum factor tail dependence seems an obvious addition to the study.
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