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Reversion to Mean

Many short-term trading systems are designed to exploit mean reversion patterns and benefit from it

One of the most powerful ideas in investment theory is that of mean-reversion. The hypothesis of mean-reversion suggests that stock prices and corporate profit margins will tend to move back towards an average level. Many investment systems and many trading systems as well, are based upon this assumption.

For example, mean reversion underlies the concept of valuation. If a stock happens to be valued lower than its historical average, it is generally considered attractively priced. This is because investors assume it will rise and approach closer to the average again. Conversely if a stock is valued above its average, it may be over-valued and due for a decline as it will tend to drop back towards its average.

A value investor buys stocks when they are low-valued. Conversely, a growth-investor looks for the rarer cases when a stock trends into a boom period where it will consistently receive high valuations.

A number of short-term trading systems are also designed to exploit mean reversion patterns. The trader assumes that a stock or some other financial asset will trade within a certain range. That is, it will tend to move fairly close to an average price. When it gets far above the mean or drops far below the mean, it will show its mean-reversion tendency and reverse direction.

Such range-trading systems are vulnerable to the occasional trending breakout or breakdown caused by some new information that alters range-trading behaviour. In the most extreme cases of breakouts and breakdowns, the business may go bankrupt, or it may suddenly double or treble in price. Momentum traders chase such breakdowns and breakouts because they can be very lucrative when they do occur. But even dedicated momentum chasers concede that range trading is much more common behaviour than trending breakouts.

Mean reversion is also a key assumption that leads logically to passive index investing. At any given time, some sectors will be performing above their average and others will be performing below their average.

If you buy only the high-performers, you risk losing money if the behaviour reverts to mean. If you buy only the poor performers, you risk losing money if there are extraordinary circumstances such as bankruptcies in the offing. If you buy and hold a well-diversified index, with both high and low performers, you are more or less guaranteed an averaged return.

The useful thing about mean-reversion behaviour is that we have a fairly good statistical understanding of how normally distributed data behaves. If a stock does display mean reverting behaviour, its price movements will be broadly predictable. This makes both investment and trading models a little less risky.

Most stock market prices, and many other financial assets as well, do fall into roughly normal distributions. This means the frequency distribution of the prices looks somewhat like the famous bell curve. A large number of prices will be clustered in a central area, close to the average, creating a shape somewhat like a bell with a few prices scattered to the left and the right of the bell.

There are mathematical laws that govern this sort of centralised distribution. For example, around 68 per cent of all values will fall within one standard deviation (or 1 Sigma) from the average and around 95 per cent of values will fall within two standard deviations and about 99 per cent of values will fall within three standard deviations.

However, stock prices don't conform perfectly to normal distributions. For one thing, they tend to have long tails. A larger number of values tend to fall outside the third standard deviation. Also, in any market that reflects a growing economy, prices tend to move up over the long-term. As the chart of the Nifty over 15 years shows, both the index itself and its own 10 month (200 Day) Moving average have shifted in values. The prices swung roughly between 850 and 6400 - a swing of 8x - and an average across this period would be meaningless.

So the bell curve for prices won't hold over long periods. But there is a way to use mean-reversion behaviour to predict the behaviour of even high-growth stocks in growth economies. This is by using balance sheet ratios instead of price.

Balance sheet valuation ratios tend to be mean-reverting in a stable fashion over very long periods. If earnings goes up, prices go up. But the PE ratio tends to remain within a range. Similarly book value to price ratios also tend to be distributed within ranges. Once in a while, there will be a boom or bust where the ratio goes to an extreme value. But the ratios will tend to follow a more or less normal distribution. Take a look at the PE ratio of the Nifty over the same period. The minimum value is 10.7 and the maximum value is 28.5 -a spread of less than 3x. An average is meaningful since the values are tightly ranged.

The frequency distribution is more or less a bell curve. In statistical terms, it conforms reasonably well to a classic normal distribution.

The dispersion beyond the first standard deviation (14.86-21.76) and second standard deviation (11.4- 25.22) is slightly more than the classic normal. But the entire set of values falls within the third standard deviation. The current value of the Nifty PE is 17.3, which is below the average. The Nifty trades below the average about 51 per cent of the time. The median (where exactly 50 per cent of values are above and 50 per cent are below) is at 18.26. Can we use this data to modify our investment patterns? I believe it's possible. This is a very long-term range of values and the range trading patterns appear to be stable. A passive index investor could use these signals to modify his investment methods.

Given the distribution, I would suggest that a passive index investor just maintains a Systematic Investment Plan when the Nifty is within one standard deviation (14.86-21.76) - this is the case here. If the Nifty drops below 14.86, the investor should look to increase the SIP commitment. He should definitely increase the SIP (maybe double or treble it) if the Nifty drops to the lower end of two sigma (11.4) or below. Conversely, the index investor should look to decrease his commitments if the Nifty PE rises beyond the top end of the first sigma (21.76). He should consider selling some of his holdings if the PE approaches or crosses the top end of the second sigma (25.22).

Back testing suggests that a strategy like this could boost overall returns. If the overall economy goes into a prolonged growth phase (2004-2007) or a prolonged recession (2011-present), the average PE will rise or fall. But GDP growth also has a trend or average rates and is likely to revert towards the average levels eventually.

The writer is an independent financial analyst.

This story appeared in the April 2014 Issue of Wealth Insight.