Negatively Skewed Distribution in Trading Strategies? – (Definition, Example and Histogram) – Fat Tail

Last Updated on June 19, 2022 by Quantified Trading

What is negatively skewed distribution in trading strategies? Negatively skewed trading strategies are “accidents waiting to happen”: You have many small winners and rare big losers. Unfortunately, the big losers can put you out of business.

This is what a negatively skewed distribution in trading strategy is – you need to understand the profit distribution of the strategy. Unfortunately, most traders don’t know that they are trading negatively skewed strategies until they blow up. We provide an example of a negatively skewed distribution (of a trading strategy).

Some years ago I traded proprietary with Echotrade. I remember what one of its principals said about new pair traders that started trading with them: oh no, he’ll make a lot of steady money, but ultimately he’ll lose it all, and perhaps even more. His experience was based on the objective numbers from the firm: pair traders did not last long. Why is that? It’s because of a negatively skewed trading strategy.

The majority of pair traders play the Martingale strategy*: they add to losers. Problem is, you get away with this most of the time.

However, once in a while you get stuck into a pair that does not mean reverse. The loss simply gets bigger and bigger until the account is wiped out or you are being asked for more margin.

When I started trading in 2001, I remember one trader doing merger arbitrage. The spread grew bigger and bigger but he kept on adding new positions. Later the deal was called off. In the end, he lost five years of profit and gave up trading.

What is a negatively skewed distribution in trading?

Skewness has a probability distribution that is not normally distributed.

Distribution refers to the profit and loss distribution of a strategy. When it’s negatively distributed, or skewed, there are more observations on the right side of the y-axis, but the left side of the y-axis is longer and thus contains many more big losers than comparatively winners on the right side.

Negatively skewed trading distribution in strategies have fat tails

A fat tail implies a profit distribution that has skewness. This could be on the left or right side. Obviously, if it’s on the right side the trading strategy has positive skewness.

Opposite, if it’s on the left side the fat tail has negative skewness. Below is an example of a trading strategy that is negatively skewed and thus has a left fat tail:

What does a negatively skewed histogram look like? An example

The chart below is a good example of how such a negatively distributed/skewed profit distribution trading strategy:

Negatively Skewed Distribution
Mean-reversion strategies have negatively skewed distribution: they have thin right tails and fat left tails.

The example shows many winners, but it has only 19 winners of more than 10% compared to 46 losers bigger than 10%.

Such a distribution is quite common in mean-revertive strategies. It doesn’t let the profits run and stop-losses don’t tend to work. The price you pay for this is many winners, but also few really big winners.

Opposite we have trend-following strategies that fewer winners, but they tend to be big.

Is negative skewness good?

As you could imagine, it’s not good. You trade happily for a long time until you have a rare, but big loser that wipes out many months, or years, of trading profits.

Moreover, it’s also problematic psychologically. After a big loss, you are more likely to commit behavioral mistakes. Perhaps you stop trading the strategy completely, or the effects might spill over to other parts of your trading.

Another problem with negative skewness and distribution is that most of the time we feel good. Most behavioral tests confirm that we continue hopeless strategies as long as we win frequently. We ignore the fat left tails, unfortunately.

Long-term Capital Management

Even “geniuses” don’t understand fat and long left tails. Perhaps the best example in financial history is the demise of Long-Term Capital Management:

Beginners luck (in trading)

The worst that can happen to a new trader, is to make much money from the start. The chances are that he’s just being lucky. It will feed his ego and increase his risk. He’ll not learn. I have yet to see a trader that does not experience significant losses from time to time. The more you learn, the better you can handle those losses.

A personal anecdote:

Some of my strategies are automated. And I know for sure: sometimes a fat finger or a program error will come and hit me like a boomerang. However, unlike most other traders I’m aware of the skewness and have it in the back of my head all the time. I make sure that my losses are limited in case it happens. Because I know it will happen.

 

*If it’s part of the strategy I see nothing wrong Martingale. However, that is only to add small units to get a full unit. For example, if you want to build a position of 100 000 USD as a part of a larger portfolio, you can add three units of 33 333 each. There is no way you can pick tops and bottoms, therefore I see nothing wrong with adding to losers if done this way.

Conclusion: what is negatively skewed distribution in trading strategies?

Negatively skewed distribution in trading strategies is difficult to spot, but certain trading styles and strategies are a disaster waiting to happen.

Strategies like statistical arbitrage, convergence trades, risk arbitrage, pairs trading are often negatively skewed. I recommend thinking about the possible worst things that can happen to a strategy before you count your winning chips.

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    • Hi, I only trade the pair ETF I wrote about in another article, and another one which I just started testing. I use time stop on all of them, to me that seems the best.

  • I agree with the fear of the unknown territory of the lower end of distributions (and adjusting for observed(!) skewness may not be sufficient either). Traders increasing their bets hoping for mean reverting while a correlated storm sets in can be in a situation (modelled) infinitely unlikely, but this is of little comfort when it very much is ongoing! A current example was the unlikeliness of the past 8-day positive streak in the S&P.

    Rules as you describe, dependent heavily on time-stops and other fixed/rigid external (perhaps anti-martingale) rules, may save many, as the process involved in the fat tails of a market, is perhaps governed by much “worse” characteristics than what is deterministic for a roulette player surviving (for a while) using martingale-like strategies.

    Strategies that on average profit from more or less “normal” market movements, may overcome the dangerous unknown extreme value distributions of the skewed left side, by having fixed rules such as time-stops (or other fixed rules) profiting from “normal” mean reverting processes etc, and staying AWAY from the markets when the extreme sets in. In the 8-day streak example, this could mean, profiting on average from mean reverting after a 3-4 streak, and if continued beyond this, the trader stays away while the violence increases.

  • If you want to see the beauty of a negatively skewed daytrading strategy, look at:
    http://stockhorizon.com/performance/
    85% of the signals generated a potential intraday return of +2%. That’s huge!
    But when you backtest the strategy using data provided by the website, the average trade makes less than +0.04% before commissions and slippage. Slippage should be large because the strategy is based on breakouts on small cap stocks.
    The website is transparent and honest: it’s not a fraud. But actually, it is just an alert service for experienced daytraders, not an automated trading system.