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Best Investment Risk-Return Measure?

| | Posted in: Volatility Effects

In their September 2011 paper entitled “The Impact of Asymmetry on Expected Stock Returns: An Investigation of Alternative Risk Measures”. Stephen Huffman and Cliff Moll investigate the relation between various measures of lagged total, downside and upside risk and future daily stock returns. Specifically, they consider the following 12 alternative risk measured over rolling intervals of the past 100 trading days: standard deviation, semi-variance, semi-deviation, skewness, kurtosis, downside risk below zero, upside risk above zero, mean absolute deviation and lower partial moments for four investor types (extremely risk averse, risk averse, risk neutral and risk seeking). Using daily returns and quarterly market valuation and firm accounting data for a broad sample of U.S. stocks over the period 1988 through 2009, they find that:

  • Based on raw returns, most alternative risk measures are statistically significant predictors of future daily returns (only skewness and kurtosis are not).
  • Based on returns adjusted for book-to-market ratio, size and debt leverage, all alternative risk measures (including skewness and kurtosis) are statistically significant predictors of future daily returns. It appears that firm size is a proxy for downside risk.
  • The most useful measure of total risk is mean absolute deviation, not standard deviation.
  • While total risk has some power to predict future stock returns, measures of downside risk (such as lower partial moment) work better.
  • Models that simultaneously address downside and upside risks indicate that investors care only about downside risk.

In summary, evidence suggests that investors are only averse to the left tail (downside) of return distributions for individual stocks.

The paper provide mathematical definitions for each risk measure.

Cautions regarding findings include:

  • Returns used are frictionless. A trading strategy designed to exploit daily return predictability is likely to involve frequent trading and therefore material trading frictions.
  • Testing of multiple models on the same data set introduces data snooping bias, suggesting that findings for the best risk-based predictor of future returns are overstated (include luck).
  • Subsample tests would confirm consistency of conclusions over time (in different market environments).
  • The study focuses on a linear relationship between risk and future returns. There may be important non-linear interactions.
  • While the statistical significance test employed accounts for return autocorrelation and some distribution wildness, it may not account for the degree of wildness found in actual daily stock returns. 
  • As noted, findings are for individual stocks and may not translate to stock indexes.
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