Is faster-than-exponential asset price growth (acceleration of price increase) inherently unsustainable and therefore predictive of an eventual crash? In his June 2013 paper entitled, “Stock Crashes Led by Accelerated Price Growth”, James Xiong applies both regressions and rankings to test whether faster-than-exponential growth over the last two or three years predicts stock price crashes. Each month, he measures past price returns in non-overlapping six-month intervals to determine whether a stock’s price is accelerating. He consider three crash risk indicators: (1) skewness, with negative skewness indicating a tendency for large negative returns; (2) excess conditional value-at-risk, a normalized version of value-at-risk that controls for volatility; and, (3) maximum drawdown, cumulative loss from the peak to the trough over a specified interval. He computes these indicators monthly based on six months of daily returns. He then relates each crash indicator to stock price acceleration over the last two six-month intervals. In a separate test, he calculates returns from equally weighted portfolios reformed monthly by sorting stocks into fifths (quintiles) based on stock price acceleration over that last two six-month intervals. Using daily returns in excess of the contemporaneous U.S. Treasury bill yield for a broad sample of U.S. common stocks (those in the top 80% of market capitalizations if priced above $2) during January 1960 through December 2011, and for the S&P 500 Index during January 1950 to December 2012, he finds that:
- Over the entire sample period, the correlation between skewness and excess conditional value-at-risk is 0.78, indicating that these two indicators capture similar information. However, maximum drawdown has relatively low correlations with these metrics (0.22 and 0.34, respectively), indicating distinct information.
- Based on regressions, faster-than-exponential asset price growth relates to elevated crash risk for all three indicators.
- The equally weighted quintile of stocks with the highest price acceleration over the past year (as specified above), reformed monthly, significantly underperforms other stocks on average. Controlling for either volatility or momentum, the difference in gross annualized returns between the quintiles with the lowest and highest price acceleration is 6%-7%. The Sharpe ratio for high-acceleration stocks is about half that for low-acceleration stocks.
- Though results for the aggregate market are weaker than those for individual stocks, S&P 500 Index crash risk is elevated after intervals of faster-than-exponential increase.
In summary, evidence indicates that one to a few years of accelerating equity price appreciation indicates an elevated crash risk.
Cautions regarding findings include:
- Returns in the study are gross, not net. Accounting for reasonable trading frictions (which vary considerably over the sample period) due to turnover of price acceleration quintiles would reduce reported hedge returns. Hedging by shorting high-acceleration stocks may have been costly or unfeasible.
- It appears that the methodology assumes no lag between past and future calculation intervals (portfolio changes occur at the same close as some past return calculations). This assumption may be problematic for large portfolios, especially early in the sample period.
- The study does not test any strategies for exploiting market-level crash detection.
