MARKET-TIMING STRATEGIES THAT WORKED
Pu Shen
MAY 2002
RWP 02-01
Research Division
Federal Reserve Bank of Kansas City
Pu Shen is an economist at the Federal Reserve Bank of Kansas City. Douglas Rolph
co-authored an earlier draft of this work entitled “Do the Spreads between the E/P Ratio and Interest
Rates Contain Information on Future Equity Market Movements?” (RWP 99-03), which can be found at
www.kc.frb.org/publicat/reswkpap/rwp99.htm. The author is grateful for the excellent research assis-
tance provided by Jonathan Corning, a research associate at the Federal Reserve Bank of Kansas City.
The views expressed in this paper are solely those of the author and do not necessarily reflect the views
of the Federal Reserve Bank of Kansas City or the Federal Reserve System.
Shen email: pu.shen@kc.frb.org

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Abstract
In this paper, we present a few simple market-timing strategies that appear to outperform the
“buy-and-hold” strategy, with real-time data from 1970 to 2000. Our focus is on spreads between the E/P
ratio of the S&P 500 index and interest rates. Extremely low spreads, as compared to their historical
ranges, appear to predict higher frequencies of subsequent market downturns in monthly data. We
construct “horse races” between switching strategies based on extremely low spreads and the market
index. Switching strategies call for investing in the stock market index unless spreads are lower than
predefined thresholds. We find that switching strategies outperformed the market index in the sense that
they provide higher mean returns and lower variances. In particular, the strategy based on the spread
between the E/P ratio and a short-term interest rate comfortably and robustly beat the market index even
when transaction costs are incorporated.
JEL classification: G10, G11, G14
Keywords: Investment, stock market, earning yields

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Market-Timing Strategies That Worked
May 2002
Few investment strategies have a worse reputation than market timing. Investors are told that their
best strategy in stock investing is a simple “buy-and-hold” strategy: buy a diversified stock market index and
hold it. Yet most investment literature assumes that investors will hold a security if and only if its expected
return at the market price provides an adequate tradeoff with the risk exposure the security brings. In other
words, investors are assumed to make their own judgment on whether a security is worth holding. Saying
that investors should not “time the market” is equivalent to saying that consumers should not maximize
utility when making consumption decisions.1 The standard reply to this criticism is that because the stock
market is fairly efficient, accurate market timing is very difficult. In fact, it is said to be so difficult that
investors are better off not trying.2
In this paper, we present a few simple market-timing strategies that would have worked well over
the past three decades, using real-time data. The simplicity and effectiveness of these strategies challenge
the notion that market timing is inherently difficult. We investigate strategies that focus on spreads
between the E/P ratio of the S&P 500 index and interest rates. As most media attention to these spreads
occurs when they are extremely high (such as in the 1970s) or extremely low (such as in 1999 and 2000),
we consider whether extreme values of the spreads contain useful information for timing the market. In
particular, we focus on periods when the spreads were extremely low relative to their historical values,
and examine whether such low spreads are associated with market downturns in the following month.
We also investigate whether extreme values of the components of the spreads predict market downturns.
These strategies are, in a sense, modifications of the “buy-and-hold” strategy, rather than active
market timing strategies. They are consistent with the belief that, on average, stock prices generally
reflect fundamentals, but there are times, although rare, when even aggregate market prices may deviate

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widely from fundamentals. Further, such rare times may be hinted at by extreme values of the spreads.
For example, when the market is dominated by overly optimistic sentiment, the E/P ratio of the market
index is more likely to be extremely low relative to yields of alternative investments, such as debt
instruments. Therefore, extremely low values of the spreads may indicate that most stock prices are too
high to be justified by fundamentals, thus it may be a good time to alter the usual “buy-and-hold” strategy
and exit the stock market temporarily. Using data from 1962 to 2000, we find that the frequencies of
negative monthly returns in the S&P 500 index are significantly higher when spreads at the end of the
prior month were at extremely low levels.
We also construct “horse races” to examine the profitability of trading on spreads. We compare a
benchmark strategy, which is a buy-and-hold strategy that invests in the stock market index all the time,
with alternative strategies that invest in the stock market most of the time, but switch to cash investment
when the spreads are at unusually low levels. If information in the spreads is economically important, we
will expect the alternative strategies to have higher risk-adjusted returns. We find that the alternative
strategies indeed have better Sharpe ratios than the benchmark buy-and-hold strategy.
While E/P ratios of individual stocks or portfolios are regularly used to explain the returns of the
stocks or stock portfolios,3 few papers use the spreads between E/P ratios and interest rates to forecast
movements of broad stock market indices. Campbell and Shiller [1998] show that the E/P ratio at the
beginning of a 10-year period is negatively correlated with stock returns for the 10-year period. Lander,
Orphanides, and Douvogiannis [1997] use various linear combinations of the E/P ratio and bond yields to
predict returns on the S&P 500 index in a regression framework.4 Finally, Pesaran and Timmermann
[1995] include both interest rates and E/P ratios as possible explanatory variables of stock market
movements. None of these papers, however, has directly evaluated the usefulness of the spreads between
E/P ratios and interest rates as indicators for future equity market movements.5
Many academics have tested various strategies that may be useful in timing the market.6 For
example, Lander, Orphanides, and Douvogiannis [1997] tested their models’ ability to time the market.
Fuller and Kling [1990, 1994] studied regression-based market-timing strategies using dividend yields.
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Grauer and Hakansson [1987, 1998] and Grauer, Hakansson, and Shen [1990] studied market-timing
strategies that rotate among different portfolios based on a non-linear algorithm that weighs both
investors’ risk attitudes and past empirical distributions of portfolios.7 The current study differs from
most of the past work in that the strategy does not rely on sophisticated statistical models to explore every
return advantage. As discussed earlier, the strategy is based on the belief that it is usually “good enough”
to follow the buy-and-hold strategy. The strategy is simple and crude and only meant to identify the very
rare times when the stock market seems so pricey that investors may be better off to avoid it.8
The rest of the paper is organized as follows. The first section examines the signaling quality of the
spreads: when the spreads are below certain historical thresholds, they are interpreted as giving signals that
market downturns are likely to happen in the following month. We examine the stock market performance
during those months to measure the quality of the spread signals and find that extremely low spreads indeed
signal a higher occurrence of imminent market downturns. The second section describes three portfolios in
“horse races”. One is the benchmark buy-and-hold portfolio. Another is a portfolio that switches between
stock market index and cash investment using the spread between the E/P ratio and the short-term interest
rate for the signal. And the third is the switching portfolio using the spread between the E/P ratio and the
long-term interest rate for the signal. We then show that, generally, the portfolios based on switching
strategies outperformed the benchmark portfolio. We also discuss the impact of transaction costs and the
robustness of the results. The third section describes three additional “horse races” between the same
benchmark buy-and-hold portfolio and portfolios that switch between stock market index and cash
investment using just components of the spreads. The last section concludes the paper.
Do Spreads Provide Useful Signals?
In this section, we examine whether very low spreads between the E/P ratio and interest rates, i.e.
a very high P/E ratio relative to interest rates, are associated with a higher occurrence of subsequent
market downturns. In other words, we use spreads as signaling devices: when the spreads are lower than
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some pre-specified thresholds, to be defined shortly, we consider them to be signals that market
downturns are imminent. In this context, we can evaluate the quality of the signals by comparing the
percentage of times the spreads give the correct signal versus the percentage of times the spreads do not
give the correct signal.9
We use two spreads corresponding to two interest rates: one is the yield of 3-month Treasury
bills, and the other is the yield of 10-year Treasury notes. For simplicity, when the yields of 3-month
Treasury bills are used in calculating the spreads, we call them short spreads; and when the yields of
10-year Treasury notes are used, we call them long spreads.
We are interested in short spreads because short-term interest rates are closely related to the
returns on alternative “safe” investments, which is an important factor in evaluating the stock market. In
addition, short-term interest rates are highly influenced by the Federal Open Market Committee. Thus,
short spreads may reflect contemporaneous monetary policy better than the long spreads. Many analysts
consider the current stance of monetary policy to be an important predictor of short-term stock market
movements. For example, Conover et al [1999] find that both US and international security returns are
much higher during periods of expansionary monetary policy, and much lower during periods of restrictive
monetary policy. We investigate long spreads because many practitioners have focused on them.10
Our sample covers the time period from January 1962 to December 2000. Spreads are calculated
as follows. The E/P ratio is the reciprocal of the P/E ratio of the S&P 500 index. The earnings are the
total earnings of all companies in the S&P 500 index for the previous four-quarters11 and the price is the
current monthly average of the S&P 500 index.12 The short spread is the difference between the E/P ratio
and the yield of 3-month Treasury bills; and the long spread is the difference between the E/P ratio and
the yield of 10-year Treasury notes. Both yields are the most recent weekly averages as of the last
Monday of the current month. We purposely restrict the spreads to include only past information and
make no attempts to forecast either future interest rates or future earnings. This way, the signaling power
of the spreads (if there is any) will not be confused as the consequence of superior forecasts of future
interest rate movements or earnings growth.
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Figures 1 and 2 show the historical short and long spreads from the beginning of 1970 to the
end of 2000, and their respective tenth percentiles. We start with the first eight years of data (January
1962 - December 1969) to calculate the initial value of the 10th percentile threshold for the beginning
of 1970. We use the tenth percentile of the historical range of a spread to define the threshold of the
extremely low range. That is, when a spread was below its historical tenth percentile level, we consider
the spread to be extremely low and thus interpreted as predicting a market downturn in the following
month.13 As the spread for a particular month is used to predict the market movement in the following
month, the plotted spread is shifted one month later for better visual alignment. For example, in Figure
1, at the end of 2000, the plotted short spread was –2.36%, which was based on the E/P ratio and yield
on the 3-month Treasury bill at the end of November.14 Similarly, the plotted tenth percentile of the
spread in December was –1.35%, which was based on all spreads from January 1962 to November
2000. The shaded areas in the figures represent low-spread months: those when the spread was below
the tenth-percentile threshold based on data at the end of the previous month.
Tables 1 and 2 tabulate the actual market downturns versus the predicted market downturns.
When the monthly return (including dividends) of the market index was negative, it is considered an
actual market downturn. We start at the beginning of 1970, as the first eight years of data are used to
calculate the initial value of the tenth percentile threshold. Every month, we add the new observation
and update the threshold. Thus the actual testing is from January 1970 to December 2000, with a total of
372 monthly observations. By our definition, a market downturn occurred roughly 39% of the months in
the sample period ( N = 144 ). By contrast, when the short spreads “predicted” a market downturn, 51%
2
of the time a market downturn occurred in the following month. Similarly, when the long spreads
“predicted” a market downturn, 45% of the time the prediction was correct. Therefore, it appears that
signals produced by the spreads indeed contained useful information on how vulnerable the overall
market was in the near term.
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We can also formally test the statistical significance of the signals. The null hypothesis is that the
spreads produced the correct signals by mere luck. Under this null hypothesis, the number of times that
the “prediction” of the spreads coincided with the actual market downturns is distributed as a hyper-
geometric distribution.15 Table 3 shows the test results. The first row shows the sum of the ratios that the
“signals” of the spread were correct. n / N is the ratio when the spread “predicted” that the next
1
1
monthly return of the market index would be positive and the realized return was indeed positive.
n / N is the ratio when the spread “predicted” the next monthly return of the market would be negative
2
2
and it was indeed negative. Under the null hypothesis that the spreads only got it right by luck, this sum is
expected to be unity. As shown in Table 3, both sums for short spreads and long spreads are bigger than
unity. Further, the p-value shows the probability of achieving this performance or better by mere luck is
only 1% for the short spreads, and under 9% for the long spreads.16 In other words, we can reject the null
hypotheses that the signals produced by the short spreads were correct by pure chance at the 1% level,
and reject the null hypothesis that signals produced by long spreads were correct by chance at the 9%
level.
Figures 3 and 4 show the log levels of the S&P 500 total index from January 1970 to December
2000 with shaded areas corresponding to the low-spread months. Visually, these figures suggest that the
S&P 500 index tended to perform worse in the low-spread months. They also suggest that not all major
market downturns were signaled by extremely low spreads. In particular, both spreads were well above
their thresholds in the 1974 market downturn.
Table 4 provides some statistical evidence that the stock market performs very differently when
spreads are extremely low. The first column of the table shows that for the whole sample period of 372
months, the monthly total returns of the stock index averaged almost 1.1%.17 The next two columns
compare the stock index performance during low-spread months and other months, based on the short
spreads. For the 300 months when spread was not particularly low, the return to holding the stock market
index averaged 1.5%. For the 72 low-spread months, in contrast, the return averaged negative 0.4% per
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month. The difference in average returns is statistically significant at the 1% level. The final two
columns compare the stock index performance during low-spread months and non low-spread months,
defined by the long spread. It shows that, similarly, in the low-spread months, the average returns of the
stock index was lower than the average market returns of the stock index in other months, and such
difference is significant at the 4% level.
In addition to growing slower in low-spread months, the stock market index also tended to be
more volatile in these months. One measure of volatility is the standard deviation of the growth rate of
the index. As shown in Table 4, based on the short spreads, the standard deviation was 5.05% in low-
spread months but only 4.23% in other months. The difference is statistically significant at the 6% level.
Similarly, based on the long spreads, the standard deviation was 4.58% in low-spread months, but only
4.39% in other months, though the difference is not significant. Thus, it appears that on average the stock
market performed poorly during the months when the spreads were very low, both in terms of average
returns and volatility.
Portfolio Switching Strategies
The previous section showed that extremely low values of spreads tend to be followed by poor
performance of the overall stock market, and the relationship is statistically significant. A natural
question to ask is whether this information has any economic value. In this section, we construct two
simple portfolio-switching strategies, which use extreme values of the short or long spreads as signals to
exit the stock market temporarily. We use historical data to compare the performance of the switching
strategies with a benchmark strategy, which is to simply invest in the market index all of the time. This
way, our evaluation of the effectiveness of the market-timing strategies using spreads can be based on the
relative performance of the switching strategies to the benchmark strategy. The comparison between the
switching strategies and the “buy-and-hold” strategy suggests that the information contained in the
spreads is economically important.
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The switching strategy using short spreads as the switching signal proceeds as follows. The
portfolio starts with $1 in the market index at the end of January 1970. At the end of every month, we
look at the value of the short spread. If the spread is above the threshold level, which is the historical
tenth percentile of the short spread, the portfolio is invested in the market index for the next whole month.
If the spread is under the threshold level, the entire portfolio is liquidated at the end of month market price
and invested in 30-day Treasury-bills for the entire next month. At the end of the next month, if the
spread is still under the updated threshold level, the portfolio will again be 100% invested in the 30-day
Treasury-bills for the following month. If the spread is above the updated threshold level, the entire
portfolio will be moved into the stock index for the following month. We repeat this process at the end of
every month until the end of 2000. All dividends and interest income are reinvested in the portfolio. The
switching strategy using the long spread is similarly constructed except the switching signal is based on
long spreads, i.e., the portfolio stays in the stock market unless the long spread is under its tenth
percentile threshold.
The strategies are designed to be extremely simple and to be easily implemented with real-time
data. The timing of the spread variable is constructed such that the earnings are lagged one month more
than price, because market price data are available earlier than earnings data. For example, the P/E ratio
of the S&P 500 index for May is reported in the middle of June. To make sure that the switching
strategies are feasible in real time, we use the earnings data for May and the average stock market prices
for the month of June to calculate the spreads at the end of June and decide the portfolio allocation for the
month of July.18
Table 5 shows some statistics of the benchmark portfolio and the two switching portfolios. Both
switching portfolios did slightly better than the benchmark portfolio. The mean monthly return for
investing in the market all the time for the entire 31-year period was 1.1%. In contrast, the mean monthly
return for the switching portfolio using short spreads was 1.3%, and 1.2% for the switching portfolio
using long spreads. Given the volatility of stock prices, it is not surprising that the differences in the
mean returns are not statistically significant. The standard deviations of the mean returns of the switching
7

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Document Outline

• Market-Timing Strategies That Worked
  • • May 2002
  • Do Spreads Provide Useful Signals?
  • Portfolio Switching Strategies
  • The Impact of Interest Rates
  • Conclusion
• References
• T1.pdf
  • M = 300
  • N = 372
• T2.pdf
  • M = 284
  • N = 372
• T3.pdf
  • Table 3. Henriksson and Merton tests on the significance of the spread signals
    • Short spreads
• T4.pdf
  • Table 4. Performances of the S&P 500 Total Index in Different Periods
• T5.pdf
  • Table 5. Switching Strategies versus Benchmark.
• T6.pdf
  • Table 6. Switching Strategies Based on Components of the Spreads versus Benchmark.

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