Morningstar Advisor - August/September 2013 - (Page 63)

the effect of volatility, we sort stocks into starting quintiles based on the trailing, rolling 36-month volatility. Then, within each volatility-based quintile, we sort the stocks into five equally weighted composites (Q1, Q2, etc.) based on (k t–k t–1). Thus, we have 25 composites (five Q1 composites, five Q2 composites, etc). The past 12 months of growth rate changes (k t–k t–1) were used to form the 25 composites, and all of the composites were held for one month—the 13th month. At the end of the 13th month, we re-form the 25 composites using the same double-sorting algorithm on a monthly rolling basis. The 25 composites are rebalanced monthly from January 1964 to December 2011. The excess returns (over the T-bill) for each one of the 25 composites are averaged with equal weights. Finally, the five Q1 composites are averaged to derive the Q1 portfolio with equal weights, and the same procedure is repeated for the five Q2 through Q5 composites. Comparing the least-accelerated quintile (Q1) to the most-accelerated (Q5), we find that the annual geometric return was 7.21 percentage points higher (10.4% versus 3.19%), the standard deviation was 3.43% higher (20.54% versus 17.11%), and the Sharpe ratio was more than twice as high (0.62 versus 0.28). By construction, the Q1 portfolio most likely experienced a negative growth rate or a large price correction in the past six-month period (t). Q1 may carry a downside risk premium, which tends to be realized in the next period (t1). This can partly explain the outperformance of Q1, and it is also consistent with a contrarian strategy. On the other hand, the higher volatility for the Q1 portfolio is consistent with asymmetric volatility; stocks tend to be more volatile in negative-return periods. In contrast, the Q5 portfolio, by construction, experienced impressive faster-than-exponential growth over the last year. It is not surprising to observe its underperformance in the subsequent period because (k t–k t–1) has predictive power in identifying stock crashes. Exhibit 3 shows the growth of value for the five quintiles. Q1 and Q5 have ending values of $115.5 and $4.5, respectively, over the 48-year period. The most accelerated quintile (Q5) significantly underperformed the least accelerated quintile (Q1) by a factor of 25. As an important element in performance evaluation, we are interested in measuring the alphas of the five portfolios on a risk-adjusted basis. The alphas of the portfolios are measured against the Carhart (1997) four-factor model, the three Fama-French factors (Fama and French, 1993), plus momentum (Jegadeesh and Titman, 1993)1. The annualized alpha for the Q1 portfolio is quite large and statistically significant at 5.19%. In sharp contrast, the alpha for the Q5 portfolio is a significantly negative 3.28%. The skewness, ECVaR, and maximum drawdown are measured on the monthly return series over the entire period from January 1964 to December 2011 for the five portfolios. Skewness for Q1 and Q5 are 0.17 and negative 0.81, respectively. ECVaR for Q1 and Q5 are negative 1.25% and negative 2.22%, respectively. Maximum drawdown for Q1 and Q5 are negative 64.83% and negative 71.15%, respectively. All of these results are expected from previous cross-sectional regression results. They confirm that (k t–k t–1) has predictive power in identifying future stock crashes. For both skewness and ECVaR, the values decrease monotonically across the five portfolios. For maximum drawdown, the value is nearly monotonic except for Q1. One of the reasons for this is that the maximum drawdown measure is not adjusted for volatility. Because Q1 has the highest volatility among the five compos- ites, it tends to have a more negative value of maximum drawdown, all else the same. Forecasting Market Crashes Stocks that experienced the highest accelerated growth rates over the past year underperformed other stocks significantly. The annual geometric return for the highest accelerated growth quintile was reduced by 7 percentage points, and the Sharpe ratio was cut in half compared to the lowest growth quintile. Using these findings, investors have the ability to better forecast market crashes based on past accelerated growth rates. K James X. Xiong, Ph.D., CFA, is head of quantitative research with Morningstar Investment Management. References Abreu, D. and M. Brunnermeier, 2003, “Bubbles and Crashes,” Econometrica. Blanchard, O.J. and Watson, M.W., 1982, “Bubbles, Rational Expectations, and Financial Markets.” Crises in Economic and Financial Structure, Wachtel, P. (Ed.), Lexington Books, pp. 295–315. Carhart, M.M., 1997, “On Persistence in Mutual Fund Performance.” Journal of Finance 52, 57–82. Chen, J., Hong, H., and Stein, J. C., 2001, “Forecasting Crashes: Trading Volume, Past Returns and Conditional Skewness in Stock Returns,” Journal of Financial Economics 61, 345–381. Fama, Eugene F. and French, Kenneth R., 1993, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics 33 (1): 3–56 Jegadeesh, N. and S. Titman, 1993, “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency,” Journal of Finance, 48, 65–91. Shiller R.J. 2005. Irrational Exuberance (Second Edition), Princeton University Press. 1 The three Fama-French factors and momentum factor are used and downloaded from the Kenneth R. French Data Library. MorningstarAdvisor.com 63 http://www.MorningstarAdvisor.com

Table of Contents for the Digital Edition of Morningstar Advisor - August/September 2013

Morningstar Advisor - August/September 2013
Contents
Contributors
Letter From the Editor
Under Pressure
Has Your View of Bonds Recently Changed?
The Simple Life Cuts a Path to Prosperity
How Extended Is Your Bond Fund?
A Bond Contrarian Scours the Globe for Value
Investments á la Carte
Investment Briefs
Bond Market Behemoths
Shopping in the Digital Age
Shopping in the Digital Age
Diverse Crowd
Motor City Meltdown
Bond Convergence
Corporates Are Fairly Valued, but Opportunities Will Arise
A Legend Still Pines for the Good Fight
Greener Pastures
Forecasting Market Bubbles and Crashes
Forecasting Market Bubbles and Crashes
Home-Court Advantage
Overcoming Technophobia
These Funds Are Counting on Undervalued Sectors
Our Favorite Mutual Funds
50 Most-Popular Equity ETFs
Undervalued Stocks With Wide Moats
What Price Advice?

Morningstar Advisor - August/September 2013