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Over the past decade, expected returns on US equities have been higher and the risk of outright losses lower when investors were at their most pessimistic. During 2002-12, a contrarian, market timing strategy aimed at making alpha out of this seeming paradox could have by far outperformed the alternative of straight buy-and-hold. Even if real time (i.e. out of sample) results were less impressive, contrarian market timing may well remain an attractive option - at least for more risk tolerant investors, since the exceptional returns are partly compensation for higher risk. A careful analysis suggests the optimal strategy is to get in and out of the market quickly after a buy signal, with a holding period of 6 weeks as a rule of thumb. Since episodes of low investor confidence are relatively few and far between, other approaches to asset management would be needed the rest of the time.

Contrarian investors believe they can make money betting against the crowd. Recently, Jeffrey Dow Jones argued here in Seeking Alpha that low readings of the American Association of Individual Investors (AAII) Bullish Sentiment Index are a useful buy signal. The index is published weekly and measures the percentage of AAII members who self-report feeling bullish. Since 1987 it has averaged 39% with a standard deviation of 10.6%. Last week's reading was 23.6%, around 1.5 standard deviations below the mean. According to Jeffrey Dow Jones, the last time bullish sentiment dropped below 25% was August 26, 2010 and over the next 9 months the market gained 28%. The time before that was November 5, 2009, which was followed by a market rally of 15%.

The problem with such anecdotal evidence is that it risks cherry picking to support one's prior beliefs. Figure 1 shows the two episodes mentioned in the last paragraph along with a couple of others that ended less happily. In each case the S&P 500 (as proxied by SPY) is normalized to 1 at the outset and tracked over the next three months. That is, the graph shows the value of a dollar invested in the market on the day the Bullish Index was published. While there was a solid rally after August 26, 2010 and to a lesser extent after November 5 2009, returns in the other two periods were disappointing. For instance, after a Bullish Sentiment Index of 24.2% on June 9, 2010, SPY stayed basically flat for two months and then declined sharply by nearly 15%.

Figure 1 - SPY price following selected low readings of the AAII Bullish Sentiment index

(click to enlarge)

However, a more systematic look at the evidence does seem to support the contrarian point of view. In total, there have been 25 episodes of Bullish Index < 25% over the past 10 years. In Figure 2, the red line shows a simple average of these, once again normalized to one at the start. The figure tracks performance for a year, and for comparison purposes it also shows the unconditional expected average (i.e. regardless of the Bullish Index reading) performance of SPY. Note that both lines incorporate continuous dividend reinvestment, with the dividend yield assumed to be a constant 2.5%.

Figure 2 - Expected value of $1 invested in SPY after all 25 instances of Bullish index <25%, 2002-12

(click to enlarge)

Clearly, expected returns are higher following a low reading of Bullish Sentiment. Interestingly, almost all of the extra rewards can be harvested within the first 2-3 months, after which the two curves follow similar trends. Also noteworthy is the greater volatility of the red curve which is partly due to a smaller sample size (25 episodes compared to 480 for the blue line), but also reflects more market volatility following low readings of the index. In other words, the superior returns to contrarian market timing are partly compensation for higher risk.

This last point is important and Figure 3 examines it further. The first two sets of bars compare the contrarian and buy-and-hold portfolios (using these terms as a shorthand to refer to the red and blue lines in Figure 2) during the first 13 weeks of a one year holding period, and the second two sets compare quarterly averages over the next 39 weeks. Each set of bars shows the expected excess return and standard deviation (quarterly, in percent), together with the Sharpe ratio. As noted, in the first 13 weeks after a low value of the Bullish index, SPY averages an excess return of 5.6% compared to an unconditional average for SPY of just 1.2%. But volatility is also substantially higher, with a standard deviation of 12.6% compared to 9.3%. On balance, contrarian market timing delivers a Sharpe ratio more than three times higher, 0.44 compared to 0.13, though the difference in risk is not negligible. Over the next three quarters the differences are smaller, though the contrarian strategy continues to enjoy a small edge. Note: excess returns are calculated with reference to the yield on 1-month US Treasury bills.

Figure 3 - Risk and return in contrarian and buy-and-hold investing

A contrarian investment strategy

To see the practical value of a contrarian approach, we need an explicit asset allocation rule that can be formally tested and evaluated. Here, I'll consider a simple one: allocate 100% of the portfolio to SPY whenever the Bullish Index falls below 25%, hold it for a fixed period, then sell it and allocate 100% of the proceeds to 1 month Treasury bills until the next time the index falls below 25%. Thus, the portfolio is either fully in the market or fully out of it, dependent on receiving a buy signal within a fixed period. Of course, a better strategy might invest partially, incorporate sector rotations, utilize other information, employ futures and options, etc. But, even this very simple example turns out to be highly profitable. Moreover, with only one parameter, the length of the holding period, it's easy to implement.

For the sake of realism, I continue to assume SPY has a constant dividend yield of 2.5%, but now also add a transactions cost of 0.1% each time the portfolio moves in or out of the market. Tax considerations are ignored. With only 10 years of daily SPY data available, I begin by using the entire run to evaluate the outcome of different holding periods. For each one, performance is benchmarked according to three criteria: (1) average return, (2) Sharpe ratio, and (3) maximum dollar drawdown. Figure 4 plots these out for holding periods ranging from 1 to 104 weeks. Evidently, short holding periods deliver very good results, but performance drops off sharply at 10-15 weeks and then recovers slowly. For a risk averse investor, a holding period of 6 weeks would be a good choice, while a more risk tolerant one might prefer 48 weeks which delivers the maximum expected return (8.3%), though with a substantially lower Sharpe ratio (.42 v. .66) and higher maximum drawdown ($1.09 v. $0.47).

Figure 4 - Trading rule with different holding periods evaluated over 2002-2012

It's instructive to see what both these cases look like. In Figure 5, the implementation with a 6 week holding period grows each dollar invested into $2.05, compared to $1.54 for buy-and hold. The short holding period misses much of the turbulence in 2002-03 and 2007-08, which explains the higher Sharpe ratio and lower drawdown. But, it also largely misses the 2003-07 boom, during which the portfolio is invested in the market less than 8% of the time and returns a mere 23% while the market moves up 80%. Try explaining that to a client! In Figure 6, an initial dollar grows to $2.22. The longer holding period tracks the market more closely, both up and down, but gains ground against buy-and-hold on a couple of occasions, specifically in 2002-03 and during the initial stages of the 2007-08 downturn, before investor panic sets in and generates a buy signal.

Figure 5 -- Contrarian strategy with 6 week holding period compared to buy and hold

Figure 6 - Contrarian strategy with 48 week holding period compared to buy-and-hold

(click to enlarge)

Contrarians may feel vindicated by these results. But how robust are they? In-sample testing is notoriously unreliable and has been the downfall of many an investment scheme. To explore this question, I split the sample into two halves, then estimate an optimal holding period rule for each half and apply it to the other. In fact, this is a pretty demanding test, since market performance in the two halves of the sample is about as different as it could be - a strong upswing in one half and a highly volatile downturn and recovery in the other.

Recreating Figure 4 for each half of the sample by itself selects a relatively short holding period of 6 weeks for 2007-12 and a longer one of 53 weeks, or possibly 15 weeks for 2002-07. It's not surprising that the sustained market boom in 2002-07 would dictate a longer period, and hence more market exposure.

Without going into the details of the calculations, Table 1 summarizes how each of these choices performs both in- and out-of sample. Bolding indicates out of sample results, which are of primary interest. The 6 week holding period generates a stellar return of 9% in 2007-12 (for which it was optimally chosen), but only 5.9% in 2002-07 compared to 9.7% for buy-and-hold. In part, the lower return is compensated by a higher Sharpe ratio and lower drawdown, though in light of the relatively subdued market risk during this period, these considerations seem less compelling, at least in hindsight. Still, the outcome is by no means a disaster. The longer holding periods of 15 weeks and 53 weeks, optimally selected for 2002-07, give roughly comparable results to buy-and-hold in 2007-12, though are markedly inferior to the optimal 6 week holding period.

Table 1 - In- and out-of-sample performance of timing strategy with various holding periods

Arguably, the estimation risk highlighted by Table 1 favors choosing a relatively short holding period. Though this would have underperformed during the boom market in 2002-07, it still produced a respectable return and at least was somewhat less risky. Note also that it benefited from higher interest rates (the one month T-bill rate peaked at 5.3% in 2007) which would likely also accompany any strong, sustained market upswing. Meanwhile, during the turbulence of 2007-12, the short holding period performed brilliantly (9% compared to 0% for the market), and this at a time when investors - worried about job security and having their homes foreclosed - would have been especially appreciative. In other words, weighting bad market conditions more heavily may be appropriate for determining the optimal rule.

Conclusion

A contrarian market timing strategy potentially offers significant alpha, though actual results will depend, as usual, on luck or skill in anticipating broader market trends. More risk tolerant investors are especially likely to find the approach attractive, since it entails higher risk. Given model and market uncertainty a relatively short holding period seems advisable, with 6 weeks a good rule of thumb. Since contrarian buy signals are relatively few and far between, contrarian market timing will necessarily be only one element of a portfolio manager's toolkit, to be supplemented by other styles the rest of the time. For instance, with only 25 buy signals over the past decade, a six week holding period would have kept the portfolio out of the market 70% of the time.

Note, finally, that these should be considered preliminary results. Fine tuning and elaborating the strategic options would almost certainly enhance expected performance. Further research might be undertaken to identify buy and sell signals more precisely, investigate sector-and style-specific asset allocations, or endogenize the length of holding periods using probits or state space modeling.

Source: A Guide To Contrarian Market Timing