Modern portfolio theory postulates that
the volatility and drawdowns associated with
investing in global capital markets is the
tradeoff an investor must accept to achieve corresponding
levels of return. However, what if
a passive investment in an asset class is not the
optimal way to gain exposure to that asset class?
This article examines a very simple
quantitative market-timing model. This trend
following model is examined in-sample on the
U.S. stock market since 1900 before out-ofsample
testing across more than twenty other
markets. The attempt is not to build an optimization
model (indeed, the chosen model is
decidedly sub-optimal, as evidenced later in
the article), but to build a simple trading model
that works in the vast majority of markets. The
results suggest that a market timing solution is
a risk-reduction technique rather than a
return-enhancing one. The approach is then
examined in an allocation framework since
1972, including such diverse asset classes as the
Standard and Poor’s 500 Index (S&P 500),
Morgan Stanley Capital International Developed
Markets Index (MSCI EAFE), Goldman
Sachs Commodity Index (GSCI), National
Association of Real Estate Investment Trusts
Index (NAREIT), and United States Government
10-Year Treasury Bonds.2 The empirical
results are equity-like returns with
bond-like volatility and drawdown, and over
thirty consecutive years of positive returns.
MARKET TIMING AND TREND
FOLLOWING
Two of the oldest and most discussed trend following
systems are Dow Theory, developed by Charles Dow, and
the Four Percent Model, developed by Ned Davis. “The
Research Driven Investor” by Timothy Hayes [2001], and
“Winning on Wall Street” by Martin Zweig [1986], present
good reviews of each system, respectively.
There have been many attempts to describe the success
of trend following and momentum trading systems.
They work, presumably, because the market exhibits
momentum (positive serial correlation) due to undereaction
and overreaction at different timescales. Kahneman
and Tversky [1979] provided a behavioral theory, entitled
prospect theory, which describes how humans have an
irrational tendency to be less willing to gamble with profits
than with losses. In short, investors tend to sell their winners
too early, and hold on to losers too long.
THE QUANTITATIVE SYSTEM
In deciding on what logic to base this system on,
there are a few criteria that are necessary to produce a
simple model that investors can follow yet is mechanical
enough to remove emotion and subjective decisionmaking.
They are:
1. Simple, purely mechanical logic.
2. The same model and parameters for every asset class.
3. Price-based only.
Moving average based trading systems are the simplest
and most popular trend following systems, according
to Taylor and Allen [1992] and Lui and Mole [1998]. The
most often cited long-term measure of trend in the technical
analysis community is the 200-Day Simple Moving
Average. In his book “Stocks for the Long Run,” Jeremy
Siegel [2002] investigates the use of the 200-day SMA in
timing the Dow Jones Industrial Average since 1900, and
he concludes that market timing improves the absolute
and risk-adjusted returns over a buy-and-hold of the DJIA.
Likewise, when all transaction costs are included (taxes,
bid-ask spread, commissions), the risk-adjusted return is
still higher when market timing, though timing falls short
on an absolute return measure. When applied to the
Nasdaq Composite since 1972, the market timing system
thoroughly out-performs the buy-and hold, both on an
absolute and risk-adjusted basis. (Note: Sigel’s system is
more active than the system presented in this article,
thus increasing the transaction costs). We will use the
monthly equivalent of Siegel’s 200-Day SMA—the 10-
Month SMA.
Because we are privy to Siegel’s results before conducting
the test, this query should be seen as in-sample.
It is possible that Siegel already optimized the moving
average by looking back over the period in which it is
then tested. To alleviate fears of datasnooping, the approach
will be applied out-of-sample to over twenty other markets
to test for validity.
The system is as follows:
BUY RULE
Buy when monthly price > 10-month SMA.
SELL RULE
Sell and move to cash when monthly price < 10-
month SMA.
1. All entry and exit prices are on the day of the signal
at the close.
2. All data series are total return series including
dividends, updated monthly.
3. Cash returns are estimated with 90-day commercial
paper, and margin rates (for leveraged models to be
discussed later) are estimated with the broker call rate.
4. Taxes, commissions, and slippage are excluded (see
“practical considerations” section later in the article).
S&P 500 FROM 1900–2005
To demonstrate the logic and characteristics of
the timing system, we test the S&P 500 back to 1900.
Exhibit 1 presents the yearly returns for the S&P 500 and
the timing method for the past 100+ years. A cursory
glance at the results reveals that the timing solution
improved return (CAGR), while reducing risk (standard
deviation, drawdown, worst year, Ulcer Index4), all while
being invested in the market approximately 70% of the
time and making less than one round trip trade per year.
The timing system achieves these superior results while
under-performing the index in roughly 40% of the years
since 1900. One of the reasons for the overall out-performance
is the lower volatility of the timing system, due to
high volatility diminishing compound returns. This fact can
be illustrated by comparing average returns with compounded
returns (the returns an investor would actually
realize.) The average return for the S&P 500 since 1900 was
11.66%, while timing the S&P 500 returned 11.72%. However,
the compounded returns for the two are 9.75% and
10.66%, respectively. Notice that the buy-and-hold crowd
takes a 191 basis point hit from the effects of volatility, while
timing suffers a smaller, 106 basis point decline. Ed
Easterling [2006] has a good discussion of these “volatility
gremlins” in John Mauldin’s book, “Just One Thing.”
It should be apparent from looking at Exibit 1 that
timing is superior over the past century, largely avoiding
the significant bear markets of the 1930s and 2000s. Timing
would not have left the investor completely unscathed
from the late 1920s to early 1930s bear market, but it
would have reduced the drawdown from a catastrophic
–83.66% to –42.24%.
A trend following model will underperform
buy-and-hold during a roaring bull market similar
to the U.S. equity markets in the 1990s. The ability
of the timing model to add value needs to be recognized
over the course of an entire business cycle, however. The
second feature is that the timing model will not participate
in a lengthy and protracted bear market. The timing
model exits the long investment in October of 2000, thus
avoiding two of the three consecutive years of losses, and
the –44.73% drawdown that buy-and-hold investors experienced,
with a more mild –16.52%.
E X H I B I T 1 (availalbe on request for free)
S&P 500 Total Returns and Timing Total Returns,
1900–2005
A glance at Exhibit 2 presents the ten worst years
for the S&P 500 for the past century and the corresponding
returns for the timing system. It is immediately
obvious that the two do not move in lockstep. In fact,
the correlation between negative years on the S&P 500
and the timing model is approximately –0.37, while the
correlation for all years is approximately 0.82.
It is possible that Siegel (or others) have optimized
the moving average by looking back over the period tested.
As a check against optimization, and to show that using
the 10-month SMA is not a unique solution, Exhibit 3
presents the stability of using various parameters. Calculation
periods will perform differently in the future as
cyclical and secular forces drive the return series, but all
of the parameters below seem to work similarly for a longterm
trend following application.
The grey boxes highlight the best performing moving
average length for each return and risk statistic. The
10-month SMA is not the optimum parameter for any of
the statistics, but it is evident that there is very broad parameter
stability across the five moving average lengths.
E X H I B I T 2 (available on request for free)
S&P 500 10 Worst Years vs. Timing
E X H I B I T 3 (availalbe on request for free)
S&P 500 vs. Various Moving Average Timing Lengths
OUT OF SAMPLE TESTING AND SYSTEMATIC
TACTICAL ASSET ALLOCATION
To address the possibility of data snooping, the
quantitative model is tested out-of-sample on over twenty
additional markets. The results of a stable model should
translate to all asset classes. The results are confirmatory,
and in approximately 70% of markets the absolute returns
were improved. In over 90% of the market’s risk-adjusted
return, Ulcer Index, and maximum drawdown were
improved upon. Exhibit 8 conveys the results.
King, Silver, and Guo [2002] described the effectiveness
of a one-year lookback momentum based asset
allocation strategy that improved absolute and risk-adjusted
returns. Here we examine the results of a simple trend
following asset allocation model that follows the same
timing system presented earlier. In addition to the
S&P 500, four diverse asset classes were chosen including
foreign stocks (MSCI EAFE), U.S. bonds (10 Year Treasuries),
commodities (GSCI), and real estate (NAREIT).
Exhibit 4 presents the results for each asset class and the
respective timing results.
While timing model returns are approximately the
same as each asset class (although higher in four of the five),
risk was reduced in every case across every measure —
standard deviation, maximum drawdown, Ulcer Index,
and worst year. Better yet, the results and trading statistics
were consistent across the five asset classes.
The average winning trade was seven times larger
than the average losing trade, and the length in winners
was six times larger than the length of losing trades. Percent
winning trades across the five asset classes was at an
uncharacteristically high (for trend following systems)
54.8%.
E X H I B I T 4 (available on request for free)
Asset Class Total Returns vs. Timing Total Returns, 1972–2005
Given the ability of this very simplistic market timing
rule to add value to various asset classes, it is instructive
to examine how the returns would look in the context
of an investor’s portfolio. The returns for a buy-and-hold
allocation are referenced as asset allocation (AA) and are
equally weighted across the five asset classes. The timing
model treats each asset class independently—it is either
long the asset class or in cash with its 20% allocation of
the funds.
Exhibit 12 presents the results for the buy and hold
of the five asset classes equal-weighted (AA) vs. the timing
portfolio. The buy-and-hold returns are quite respectable
on a stand-alone basis and present evidence of the benefits
of diversification. The timing results in a reduction in
volatility to single-digit levels as well as single-digit drawdown.
The Ulcer Index gets cut in half, and the investor
would not have experienced a down year since inception
in 1972.
EXHIBIT 12 (available on request for free)
CONCLUSION
The intent of this article is to create a simple-tofollow
method for managing risk for an asset class, and
consequently, a portfolio of assets. A non-discretionary
trend following model acts as a risk-reduction technique
with limited to no impact on return. When tested on
over twenty markets, risk-adjusted returns were almost
universally improved. Utilizing a monthly system since
1972, an investor would have been able to increase his
risk-adjusted returns by diversifying his assets and
employing a market timing solution. In addition, the
investor would have been able to side-step many of the
protracted bear markets in various asset classes. Avoiding
these massive losses would have resulted in equity-like
returns with bond-like volatility and drawdown, and over
thirty consecutive years of positive performance.
In “Reminiscences of a Stock Operator,” Jessie Livermore
states, “A loss never bothers me after I take it. I
forget it overnight. But being wrong—not taking the loss—
that is what does damage to the pocketbook and to the soul.”
MEBANE T. FABER, author
is the managing director
and portfolio manager at
Cambria Investment
Management, Inc. in
Los Angeles, CA.
ENDNOTES
1Drawdown is the peak-to-trough decline an investor
would experience in an investment, and we calculate it here on
a monthly basis.
2All data are total return series, and are updated monthly.
S&P 500 Index—A capitalization-weighted index of 500
stocks that is designed to mirror the performance of the United
States economy. Total return series is provided by Global Financial
Data and results pre-1971 are constructed by GFD. Data from
1900–1971 uses the S&P Composite Price Index and dividend
yields supplied by Cowles Commission and from S&P itself.
MSCI Developed Market Index (EAFE)—A marketcapitalization-
weighted index that is comprised of 20 countries
outside of North America. Total return series is provided
by Morgan Stanley.
E X H I B I T 1 5
Trade Length Distribution for the Five Asset-Class Portfolio, 1972–2005
U.S. Government 10-Year Bonds—Total return series is
provided by Global Financial Data.
Goldman Sachs Commodity Index (GSCI)—Represents a
diversified basket of commodity futures that is unlevered and
long only. The returns include the collateral yield an investor
would receive if invested in the index. Total return series is
provided by Goldman Sachs.
National Association of Real Estate Investment Trusts
(NAREIT)—An index that reflects the performance of publicly
traded REITs. Total return series is provided by the
NAREIT.
All other data sources in the out-of-sample backtest are
provided by Global Financial Data.
3The S&P 500 Total Return Index is based upon calculations
by Global Financial Data before 1971.
4The Ulcer Index (UI) takes into account depth and duration
of drawdowns from recent peaks and is a measure of downside
volatility. A lower number is more desirable. The Ulcer
Index was developed by Peter G. Martin and Byron B. McCann
and is detailed in their book, “The Investor’s Guide To Fidelity
Funds” (1989).
UI = square root [the sum of all R^2 values/N)
Where: R = the percent a fund is below its highest previous value
N = the number of measurements (days, months) in the period.
Sharpe ratio is a measure of excess returns versus volatility
in general, and it uses yearly returns and 4% as the risk free
rate. CAGR—Compounded annual growth rate, Stdev—
Standard deviation, MaxDD—Maximum drawdown, Mar
Ratio—absolute value of (CAGR/MaxDD),
5 Margin rates are estimated with the broker call rate.
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