# Trading the Distribution of Market Returns

Below is a frequency distribution of a sample of S&P500 Daily returns which is compared to a normal distribution. A very large portion of the positive daily market returns lies within the normal distribution. A lesser portion of the positive returns lies outside it. This is symptomatic of a modern fairly efficient market. The more efficient it is, the more is characterises a normal distribution. There is only limited alpha available in a modern efficient market characterised by the positive portion that lies outside the normal distribution of returns.

The first thing to look at is the normal distribution curve. Any return that plots underneath that normal distribution curve is a potential random outcome. The normal distribution characterises the frequency distribution of an efficient market or during periods of time when markets are acting efficiently. You can be lucky and have a great profit or you can be unlucky and achieve a significant loss. This is allowed for by random outcomes.

Notice how you can have significant profits (to the right side of the normal distribution up to 4%) and significant loses to the left side of the normal distribution (down to -4%) but the vast majority of trades centre around the mean of 0. Now when including frictional costs of trading such as spread, SWAP, commissions etc. you can slightly adjust where your trading strategy performance plots with a bias towards a slightly negative result (being the impact of those frictional costs). So the profit distribution of a strategy with no edge is likely to plot somewhere under this normal distribution with a slight bias towards the left of the curve.

Now look at the chart again below.

Notice how I have highlighted two areas in red that lie outside the normal distribution of returns. These two areas represent where an edge resides in a market that can be capitalised on by a trading strategy. One class of strategy capitalises on the peak of the distribution that lies outside the normal distribution, and the other lies in the right hand tail. These two types of 'edge' coincide with our definition of how to distinguish between predictive and price following methods. Kurtosis (or peakedness) occurs during stable market conditions when markets are very predictive in nature. Fat tails (to the far left and far right) however are associated with unpredictable conditions when markets are in transition and trending between periods of stability (equilibrium).

Now the thing to remember is that dependent on the sample size, the market distribution of returns can plot in a vast array of different shapes from normal distributions, to distributions with high kurtosis, to distributions with large fat tails and is dependent on the prevailing market condition. Over the very large data set however you start to see how it all settles out in a distribution curve that is dominated by a normal distribution but with a small kurtosis and fairly high degree of fat tail. This more subdued distribution tells you where you need to plot to garner long term sustainable returns. The problem with the kurtosis is that it shuffles the peak and what was predictable in a previous market condition is now a different form of predictability with a new peak.

Successful predictive methods that rely on stable and predictable market conditions plot within the area of kurtosis of the distribution to the right of the 0 return line. Strategies that seek this available edge in stable market conditions with high kurtosis (predictability) have correspondingly high Pwin% (they are right in their prediction very often as markets behave) and the Pwin% increases as the profit targets get tighter.

To allow for this correct prediction in the future, they need to give room for this prediction to play out, so the lack of applied tight stop measures necessary to give the high Pwin% rate, makes them vulnerable to the negative fat tails that exist in the market from time to time (refer to the left hand fat tail that is slightly higher than the normal distribution plot). This is why....... despite the high Pwin% and only the occasional large loss, they are vulnerable to those times when the market behaves unpredictably and delivers consecutive large losses. Unsuccessful predictive methods can quickly plot on the far left of the distribution of market returns. Even worse if the applied strategy continues to warehouse risk and not release it through stop loss measures (such as grid trading and martingale methods).

Price following strategies simply capitalise on the far right side of the market distribution of returns where the positive outliers exist. The chances of an outlier are limited when not diversified...... but given that all losses are cut short, we restrict the ability of the trading strategy to encounter black swan events that exist on the left hand side of the distribution of returns. We therefore skew our trade results towards the right hand side of the distribution of market returns.

As speculators we need a non-efficient market. This therefore forces us towards a choice of prediction or price following. The vast number of traders prefer predictive methods as they like to feel in control and have many wins to make them feel good...however this is a market deception while they are stable and stationery. When unpredictable conditions occur from time to time....the predictors are left exposed with their pants down.

Trade the right hand side of the distribution of returns my friends. You will be wrong many more times than you are right, but at least you cover your risk exposure and from time to time with sufficient diversification you may be the beneficiary of a significant bonanza when you wake up one morning.

The market is always right...despite how clever you may think your prediction machine is..... for when you are wrong....there is a chance you could be dead wrong!!!!!

Cheers

C

Quidquid latine dictum, altum videtur

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