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 (t1).
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
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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?
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