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Trading, Managing OPM and the Role of Luck

Trading strategies depend on objectives. It is maybe wrong to generalize as many authors do in books and papers. Retail traders have different objectives from funds: the former try to take advantage of luck, the latter strive to minimize risks.

If a fund managers mentions “luck” maybe it is better not to invest with them. Although luck is always welcome, it should not be a factor in managing OPM. One the other hand, many retail traders want to risk some fraction of their capital in hope they can harvest high returns. For a retail trader considering luck as part of the game is legitimate but for a fund it is not. But in the past there have been funds that implicitly relied on luck; I will mention LTCM for example. Why is this true? It is because the risk and money management they employed relied partly on luck. I will explain below with a few simple examples.

Furthermore, although it is true that a high percentage of retail traders hit uncle point – some claim over 85% – this is mostly attributed to risk and management tactics and to the fact that they rely on luck to make high returns. This failure rate is not due to technical or quant analysis as many without skin-in-the-game think, although these methods have problems that contribute to losses.

Below is a graph of 1000 simulations of 100 trades for a small edge of 5% (p = 0.55) with payoff (average win over average loss) equal 1, risk per trade equal to 2% of equity and $1 starting capital.

It may be seen that no equity line goes below 50% of initial equity. This is the conservative risk and management approach found in many articles and books. Potential is limited as the luckiest traders will only double their initial capital after 100 trades. Probably this is good risk and money management for a fund but retail traders want to make it big and this is nearly not good enough.

If we increase the risk to 5% of available equity, the result is as follows:

For 2.5× the risk we get a little more than triple the maximum return due to luck. In this case, 4% of traders lose more than 50% of initial capital on the way to 100 trades, which we consider the uncle point. Although profits more than doubled for luckiest ones, they are still not appealing to many retail traders.

Next, we consider Kelly fraction betting. For payoff equal to 1, the formula is as follows:

%K = 2p-1

and if p = 0.55 then %K = 0.1 or 10% of available equity.

Note that Kelly fraction betting is different from Kelly leverage but this will be maybe subject of another article. In essence Kelly fractional betting is the same as fixed factional but in this case at 10% level instead of the 2% or 5% considered before, assuming that the edge is constant, which is dubious assumption in reality.

The simulation of 1000 traders for a path of 100 trades for Kelly fraction betting is shown below:

Now, this looks like the way to riches! There is an order of magnitude increase in maximum profit for luckiest traders but this comes at a huge price: nearly 30% of traders lose more than 50% of initial equity of $1 on their way to 100 trades with Kelly betting.

Therefore, high returns, as we already know, come at high risks. This is not a good strategy for funds but LTCM for example traded like a retail speculator. They probably thought since they were lucky to receive a Nobel prize (another random process) they will also be lucky to hit high returns before ruin. But they were not.

In my opinion retail traders are justified to seek high returns since they also trade small capital and are not subject to liquidity constraints. But funds are not justified to do that and must concentrate on strict risk management as most do. This is one reason that CTA results have been dismal in the last 10 years. Managers due to competition and previous incidents focus on risk rather than reward. Retail trading ruin rate should not be attributed solely to lack of edge but also to focus on high reward and implementation of risky money management strategies. But retail traders are justified doing that, funds are not.

As you may have seen via the use of simple examples, high reward trading presupposes higher risks and the result at the end of the day relies also on luck. Anyone who thinks their realized high returns are solely due to skill is naive, to say the least. Luck is a significant factor in trading and investing.

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