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Amplitude and Frequency in Bull and Bear Markets

August 3, 2009

This is a subject that is very important to understand when you attempt to use oscillators. The whole concept behind most indicators of central tendency is that prices will stay contained within certain limits (such as in bollinger bands), and will oscillate with a regular tendency above and below the mean. One of the reasons the DV2 and the RSI2 work so well is that they capture the most regular oscillating frequency in stocks across all conditions, which happens to be roughly two days.

However, there are important differences between bull and bear markets that makes a big difference in how all oscillators, channels or bands perform. First, amplitude is higher in bear markets than in bull markets. The definition of amplitude is that it represents the magnitude of change. Moves are much larger both up and down in bear markets than in bull markets, and this has been documented by academia and noted by several market practitioners. Furthermore, frequency is also higher in bear markets than in bull markets—there can be numerous swings from corrections to rallies within a given year. In bull markets, moves take much longer to develop, and only on rare occasions do they achieve significant magnitude in both directions (such as the Nasdaq in the late 90’s).

Before i get into oscillators, i will give you a practical example of how this knowledge can be used to improve performance. Most of the research done at CSS is on stock ranking, and for this type of research you need far more historical data. In many cases, our studies go as far back as the 1950’s. One of the most important variables in our models is momentum– we look at the relative strength of both industries and stocks within our rankings. The momentum effect is well documented as the most powerful anomaly in all of the academic literature. Even the high priest and promoter of the EMH (efficient markets hypothesis)- Eugene Fama concedes that this is a persistent and robust anomaly. The question is, what is the best way to use momentum? One combination stands out in the finance literature that works across ALL asset classes– a ranking of 12 month price returns. Our own research shows that this in fact is also useful to rank stocks and industries.

One dirty secret about relative strength is that it does NOT work well in bear markets. I often read that this was the case, and unsuprisingly our results showed the same effect. But the concept of relative strength should be valid regardless of whether you are in a bull or bear market…..after all, some stocks outperform and other stocks underperform. They don’t arrive at those points instantaneously. The problem therefore, must be in the length of period used to measure relative strength. It dawned on me after considerable testing that the confounding difference lay in the increased amplitude and frequency in bear markets. Buying the biggest winners over the last 12 months greatly obscured the sector rotation that occured in the most recent period. As the bear market started, you would be long the biggest winners of the previous bull market. The result was that they would tank the most, because more people owned them. As the bear market dragged on, you would be long defensive stocks–which held up the best– only to watch them severely undperform when a major rally set in, lifting the worst stocks the fastest. Lastly, you would be long the biggest winners at the tail end of the rally (the laggards), only to be brutalized by a sudden correction.

The intial solution it turned out, was to have variable weightings on 12 month and 1 month price performance. This way, repsonsiveness could be drastically improved. By performing a mathematical learning procedure, the new rankings learned from past data. Most importantly, they were only allowed to learn from bear markets, when the 12 month average was falling, and only from bull markets when the 12 month average was rising. The difference in the weights was signficant, with the 12-month return receiving far less weight in bear markets than in bull markets.

I will present the results of different weighting schemes for the recent bull and bear market in the next post. Meanwhile, lets return to talking about how we can apply that to oscillators like the DVO as well as the DVI. Because these oscillators were designed to be flexible and adaptive (unlike the DV2), they can be improved without overfitting by allowing them to learn differently from bull and bear markets. The training procedure i like to use involves distingushing between bull and bear markets using a rising 252-day (1-year) average since we are daily data.
Again this procedure results in different weights, as well as different optimal entry/exit criteria. This results in a robust, and substantial improvement in the raw returns, as well as sharpe ratio of using either indicator. Taking a look at shorter term trend indicators like the ADX, fractal efficiency, R-squared, and the Hurst statistic  also provided valuable information for a separate training procedure. But it is important not to overdo things, otherwise we will lose degrees of freedom in our testing. This imposes a practical limit on the usefulness of new factors.

To do this on your own, you don’t need to get that fancy. All you need to do is to use either common optimization, or brute force experimentation on both weighting schemes, lookback period, and entry/exit criteria. Of course, the only problem is that you may foolishly apply the absolute optimal settings, when broad generalization is most appropriate. To prevent this, I suggest you use deciles or quartiles instead of continous weights or entry/exit criteria. Furthmore, i suggest you test this across more than one index and ideally more than one asset class. More on this to come.
First we will revisit the “Market Grid” and the integration of the DV2 with the DVS.

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