## Do Monte Carlo worst case scenarios apply to portfolios?

In some of my past posts we have looked into ways in which we can evaluate and stop trading strategies that fail under some statistically defined worst case scenarios within a given confidence interval. However I have hardly ever spoken about applying this same logic to trading portfolios because of some important differences between single systems and trading system ensembles. Today I want to talk further about these differences and why it is so difficult to create Monte Carlo simulations for portfolios. I will also talk about whether these simulations are worth doing – is portfolio failure really a thing – and whether or not we should concern ourselves with the question of portfolio failure and performance boundary evaluations.

When we use single trading system statistical failure detection can be done in many ways. One of the most common we use is Monte Carlo simulations which allow us to draw some “lines in the sand” for systems provided that they comply with the key assumptions required for these simulations to yield adequate results. These simulations allow us to draw limits at any desired confidence interval – usually 99% – for statistics such as the CAGR or Sharpe for the current drawdown period based on all the previous trading system history we have gathered through back-testing. Since we can tell when we should stop trading a system, then it is only fair to ask if this same logic could be applied to portfolios. Can we draw statistical limits for portfolios using Monte Carlo simulations?

The problem is that Monte Carlo simulations of portfolios violate some key assumptions required for the Monte Carlo process to give adequate results because not all trades within a portfolio are bound to be taken with the same likelihood and with the same correlation. Suppose you have a portfolio that has 4 strategies, 2 of them trade only when there are strong trends in the 1H chart (say RSI30 > 80 or RSI30 < 20) and the two others trade when there are ranges (say RSI30 < 60 or RSI30 > 40). It is evident from this that the trades of the two trending systems will form a trade cluster while the ranging systems will form another cluster. These clusters will never overlap because they are logically exclusive, you cannot have ranging and trending conditions at the same time if you define trends and ranges as the systems are attempting to measure them. If you do a Monte Carlo simulation where you simply randomly pick from the distribution of trade returns you will heavily intermix both system types, something that will never happen in real life.

This issue with logical exclusiveness is something that automatically forbids Monte Carlo simulations for portfolios because there are only some types of signal mixing that can happen per the exclusive characteristics inherent to the relationships between strategies. Making such simulations would imply making some assumptions about these conditions, something which will introduce an inherent bias to the simulations that will also greatly diminish their usefulness. When there is more than one logic set present within a key assumption related to the independence of different signals becomes violated because some signals may never happen at the same time as others. The signals may also always happen in some sequence that is not included within the simulations (for example if one system always trades on Thursdays and another on Fridays).

Furthermore it is also worth asking ourselves what we could find out if such a simulation was possible. Is it even worth trying to get one? In the case of a single system a statistical failure implies that the system is no longer behaving as it is expected to behave from the system back-testing results. That is, the system can be said to no longer be what we thought it was from simulations at some given confidence interval. In the case of portfolios – even if we could get this data – this would mean that the portfolio is not behaving as it is expected to behave from back-testing results. But what does this mean? If all the systems are behaving within their predicted statistical characteristics then has the portfolio failed in some obscure way that is independent of its components?

Portfolios are always expected to under-perform their back-tests. We know from the get-go that the statistical characteristics derived from portfolio back-tests are not a good proxy for risk because we know that the historical correlations between trading strategies will change. A “statistical failure” for a portfolio while all single components remain within their predicted behavior would merely mean that the historical correlations have changed. But we knew that precisely from the start. All portfolios are bound to fail from this perspective – even rather quickly – when confronted with such statistically defined worst cases because they are by definition dependent on a very easily-changing component – especially in the short term – which is the correlation between their components. This does not mean that you should stop trading the portfolio – all individual components could be working – it is just a consequence of having unknown variability within component correlations, which you should expect.

The above is precisely the reason why portfolio worst cases shouldn’t be an issue, the important thing is to focus on the worst case scenarios of portfolio components and ensure that all systems are within their expected statistical behavior. If you would like to learn more about single system worst cases and how you too can create and monitor systems to see when they fail please consider joining Asirikuy.com, a website filled with educational videos, trading systems, development and a sound, honest and transparent approach towards automated trading.