Morningstar Advisor - August/September 2013 - (Page 62)

Gray Matters the five variables is measured for each stock, and then averaged over our stock universe from June 1960 to December 2011. Exhibit 2 Average Correlation Between Crash Metrics Growth Maximum Deviation Skewness Drawdown ECVaR 1.00 –0.13 0.72 0.33 0.42 1.00 –0.60 0.11 0.01 1.00 0.22 0.34 1.00 Growth Rate Standard Rate 0.78 Standard Deviation Maximum Drawdown Skewness ECVaR 1.00 Exhibit 3 Performance of Five Accelerated-Growth Quintiles of Stocks $ 1 1,000 2 3 Least Accelerated Quintile 4 5 Most Accelerated Quintile 100 10 The growth rate and maximum drawdown are correlated at a positive coefficient of 72% because a negative growth rate usually accompanies a more negative maximum drawdown in a given period. The correlation between skewness and ECVaR is 78%, indicating that they capture much of the same tail information of the return distribution even though they are constructed in very different ways. Both skewness and ECVaR have a relatively low correlation with maximum drawdown, so it is informative to include maximum drawdown as an alternative crash measure. The correlation between the value of maximum drawdown and standard deviation is negative 60% mainly because of asymmetric volatility (volatility is higher when drawdown is more severe). Impact of Fast Growth on Performance 1 12/1963 12/1969 12/1975 12/1981 2011. Daily returns, daily exchange-based trading volumes, daily number of shares outstanding, and monthly book-to-market ratios are collected from Morningstar’s equity database. We employ three stock-crash metrics: skewness, excess conditional value at risk (ECVaR), and maximum drawdown. Skewness is a measure of the asymmetry of the data around the sample mean. Negative skewness indicates that there is a greater probability to have large negative returns. In other words, skewness is a measure of crash expectations. ECVaR specifically measures the left tail risk, and it is based on conditional value-at-risk, or the expected tail loss. A stock’s ECVaR is a 62 Morningstar Advisor August/September 2013 12/1987 12/1993 12/1999 12/2005 12/2011 normalized version of conditional value-at-risk by controlling for the volatility of the stock. Maximum drawdown is the cumulative loss from the peak to the trough over a given time period. It quantifies the worst-case scenario of an investor buying high and selling low. Maximum drawdown is a popular downside risk measure. By definition, it will have a negative value unless the price never declines, in which case it has a maximum value of zero. Exhibit 2 shows the average correlation among the five variables that we studied in this paper: growth rate (k), standard deviation, maximum drawdown, skewness, and ECVaR. All five variables are computed over a six-month period using daily returns. The correlation matrix of Our cross-sectional regression results provide strong evidence that faster-than-exponential growth rates can lead to stock crashes. Here, we investigate the impact of accelerated growth on portfolio performance. We form portfolios by sorting stocks into quintiles based on their changing growth rates over the past two six-month periods ((k t–k t–1). Our thesis suggests that the portfolio of stocks that have experienced higher increased growth rates will suffer a higher probability of a crash. While a single sorting on (k t–k t–1) will provide useful information, the performance will be coupled with other factors, such as stock volatility. We are more interested in performance evaluation by controlling the volatility. In other words, we perform double sorting, with first sorting on volatility and then on (k t–k t–1). Using 12 months of returns, we compute the increased growth rate or change in growth rate from the first six-month period to the second six-month period (k t–k t–1). To control for

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