Jul 23 2015

What is Monte Carlo Simulation?

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What is Monte Carlo Simulation?

The Monte Carlo Simulation (MCS) is a set of computational algorithms that rely on random sampling. It is used to try to predict the likelihood of an outcome. We often talk about MCS in financial circles as if it is specific to our area of work but in fact it is also used in other areas too and originated in the project to design the atomic bomb.

In financial services MCS is used to predict risk; perhaps the risk of a business failing or, in more familiar territory, the risk of an investment or a portfolio not achieving a target value at a particular date. MCS thus gives us a probability that a particular return can be achieved. In order to do that the system needs to compute a large volume of data. Some of this data will be known. For example the client’s current age and the current value of the portfolio. Other data (those which look into the future) must be assumed, whether by using historic data or some other basis.

Limiting the range

Given the large number of unknown variables, such as life expectancy, inflation, expenditure, investment returns, costs and taxation – all of which must be assumed and all of which are therefore likely to be wrong – it is necessary to limit the range of possible outcomes in order to produce anything useful at all. The usual approach is therefore to set a number of variables to fixed values (such as life expectancy, costs, taxation and expenditure) and then leave investment returns to float subject to the MCS process.

To run the simulation, it is necessary to have assumptions for the mean and standard deviation of each data series and also values for the correlations between each of the series being used. More sophisticated tools may allow further assumptions to be made about the degree of ‘skewness’ (how symmetrical the distribution curve is) and ‘kurtosis’ (how flat it is) of the distribution range of each variable but the easiest is to assume a normally distributed series. Inevitably, such assumptions introduce further uncertainty to the outputs and the more uncertainties there are at the input stage, the less reliable the outputs.

The simulation is then run by setting each floating variable to a random value limited by the mean, standard deviation and correlations that have been loaded. The outcome is recorded as either success or failure (in this instance, does the portfolio last the required term or not?) and then the process is repeated. Since the random values will be different each time, after being run hundreds or thousands of times with each run representing a possible future, eventually the tool will generate a figure for the likelihood of success or failure which will change very little from one run to the next. Of course it is possible that among the multiple scenarios that are run, one will closely match the actual future experience; the challenge lies in identifying which of them it will be.

One of the problems with MCS is that it appears extremely precise; outputs may be given to numerous decimal places. This precision can lead advisers to believe that the result is what will happen and not just what is likely given all the assumptions they have made.

Clients themselves will have risks with which they are uncomfortable and others they find are easier to bear to achieve their goals – discussion of capital loss often brings these issues to the fore. However, MCS does not know how a client feels about something. It can not; it is just running repeated scenarios and enabling an estimate to be made of the probability of an outcome arising.

We need to recognise the difference between risks that are too severe for the client to weather and those which are manageable. The data’s start and end points will also make a difference to the outcomes, especially if we use historic average returns. This needs to be borne in mind when looking at the outputs. In many financial plans I see advisers use phrases such as, “despite this I am erring on the side of caution and hence reducing my assumptions for this investment return.” This suggests they have reviewed historic performance but, for various reasons, they feel such a return is not realistic moving forward and so they reduce the assumption in that area. The problem with doing that – not just in MCS, but at any time – is that it leads to a higher return required to meet a future goal so the client would need to take on more risk or cut back in other areas to invest greater sums.

Helping the clients?

How is MCS useful in daily dealings with clients? It can help when talking to them and educating them about the risks of different asset classes and markets. In my experience many people do not really understand basic economics and therefore lack the understanding of the interaction of stockmarkets and various other aspects of the financial world, for example the relationship between interest rates and gilt returns, or how other asset classes are more or less correlated with each other.

US adviser Michael Kitces takes the view that, where dealing with an uncertain future, using an approach which implicitly assumes that (for example) MCS is likely to give rise to better outcomes in terms of understanding than one which does not allow for such uncertainty.

However, he suggests that rather than use the phrases ‘probability of success’ or ‘probability of failure’, advisers use ‘probability of adjustment’ when speaking to investors as the advantage of projections is that course corrections can be made before it is too late.

It is also important to understand the difference between correlation and causation: Correlation is the extent to which two or more variables fluctuate together. A positive correlation indicates that they increase or decrease in parallel; a negative correlation indicates that one variable increases as the other decreases.

Causation is often confused with correlation. However, correlation by itself does not imply causation. There may be a third factor, for example, that is responsible for the fluctuations in both variables; or they may both be random.

As an example, imagine that a class of students take a test. The results are analysed and it is found that those students with long hair performed best. That could lead us to deduce that there is a correlation between the length of a student’s hair and their ability to do well in the test.

However, if we looked deeper we would see that all those students with long hair were female. So although there is a correlation between the length of hair and success in the test, it is just as possible that the actual causation is that those with long hair were female.