Simulation is a rather large subject with a lot of very complex mathematics … well … it can be ;-). So over time I will do a set of articles covering a broad band of areas starting with the question of ‘What is Simulation ?’. Other areas I have interest in and touched my world in the past year include Predicting a sequence – some amazing papers on randomisation, using Brownian motion as a predictor and what trends are. Some ideas about introducing shocks to a prediction sequence (great for giving your forecast a stress-test), multiple running (such as Monte Carlo) and a bit about statistics (dull as dishwater really but just a few basics are needed).

I have had more fun playing around with simulation than I care to say in the past year. Mostly, as I started form a point of ‘I have absolutely no idea’…. but the engineer in me rather guided the approach I took. Yes, random, yes at times all over the place , but heck, I am retired and can go where any interest takes me.

## As a PI, why bother with Simulation ?

Its a good question. After all, we base our decisions on looking at data, like the financial reports of stocks, of funds, of anything we want to invest in ….. right ?

Well… yes if we want to ‘fire and forget’ … no if we actually want to take charge.

One of the great paradoxes causing much naval gazing and scratching of the head is the term ‘analysis’. Even the best experts get it wrong. A securities data is not always complete, does not always have the most up to date trading data, does not know that suddenly the market will change .. etc etc etc. The best we can do is understand what some of the terms mean, what is behind some of the maths and ratios, have a broad feel for whether there is a trend, an undervaluation or over-valuation. We can look at the management team and see what has changed and then start to delude ourselves into thinking nothing will change. Note I do not include broker recommendations. I simply have yet to see any that are accurate and the herd of brokers all coming up with different views rather suggests they don’t know any more than we do much of the time … use broker recommendations with a real pinch of salt is my advice.

I got very much into analysis early on. I bought books on it, looked at charting, brushed up on my financial training (years ago) and re-learned to read a balance sheet …. dull as watching paint dry. But if we have a handle (even a basic one) on past performance metric’s, we could make some educated estimation of what might happen in the future.

Enter stage left …. Simulation.

## Simulation is just another name for Forecasting … right ?

Wrong .. !

Forecasting (and this is my interpretation in financial planning), is essentially a linear prediction. For example, if inflation is 2% every year, I can forecast that my £1.00 is worth (in real terms) £0.98 next year, then £0.96, £0.94, £0.92, £0.90, £0.89 .. etc in subsequent years. We can make an assumption as to how a line item in our outgoings changes over time and simply compute an answer. Just using a simple substitution table of some variables we can map out boundaries of possible end points. Very useful and simple way of creating a big picture.

Simulation on the other hand is for me rather more about a level of variability in the parameters which means each ‘run’ could yield a different answer. In other words, there is an element of randomness to the computation. For example, if the function ‘RAND()’ returns a number between 0 and 1, we could say annual growth is a trend of 1.5% + a random element we could calculate as [(rand()-0.5)/10]. Run this and get a set of annual growth numbers. Plotted and a cumulative line shows a ‘sort’ of quasi-random movement.

If we run this a few times, we could get a set of possible outcomes. So each ‘run’ gives a different end point.

To be effective, simulation is likely to cover a number of variables. By mapping out a large number of possible outcomes, we can use statistics to help us quantify likely tolerance of outcomes.

Does this make simulation wrong ?

No ! Each answer is as valid as any other as a possibility.

So each ‘run’ gives a different end point. Later in the series I am going to delve into Monte Carlo and how that approach can give us a statistically valid picture of the possible outcomes… and that is something useful. Remember… Risk is a term we use to describe variability in the possible outcomes. Simply put, the higher the risk, the higher the spread of outcomes. Simulation gives us the chance to quantify in terms of probability – and that can give us an edge or at the very least help us see what is more (or less) likely to happen.

All dull mathematics … wish I had paid more attention at school and university !!

## Accuracy

How accurate do we need to be ?

Another really good question ? Do we need to be 99.9% accurate, 95%, 90% or just better than 50%. Later on, I want to discuss statistics and in particular look at what is termed ‘Confidence’ levels. In other words we can predict that (say) 9 times out of 10 the outcomes would be in range X, or 25% of the time in range Y. ‘Confidence’ is about narrowing the band of outcomes we might want or expect to get. In the end, they are just numbers, but numbers that help us paint and keep a view of the overall picture.

There is no system that can possible give a 100% answer. there are simply too many variables. It was only when I started looking at the problem of forecasting in terms of some basic simulation and statistics that I started to get a clearer idea of possible outcomes.

Frankly, if we are better than 95% right year on year we would be amazing stars snapped up by the big funds to manage them. In reality it is pretty hard to get numbers much better than 50% accurate. If you do not think that is true just consider how many fund managers actually beat the market year on year on year. The big classic in the UK is Woodford. Star over many years as a contrarian investor but when going alone and setting a very large fund up with vast numbers piling in (on past reputation), they find the last 2 years to have been rather negative. This does not mean long term success evades, but does remind us that if there was big crystal ball we would all win all the time.

Fortunately, there is a body of work that was published around 100 years ago following the great Wall Street Crash that sought to minimise errors and improve confidence of likely bands of prediction. This is loosely termed ‘Portfolio Management’ – a considerable future area of musing. This, along with some realistic and conservative simulation massaged with a bit of Statistics can, I think, help us manage our funds at least as well as the many champagne-guzzling city slickers.

## Boundaries

It is no good creating wild variables that give a massive spread in possible outcomes. Fundamentally, we should have a goal .. a trend in mind .. a target.

When I mused on how much we might need I came to a conclusion of the minimums as well as a sum to live very well. Note that I don’t call it ‘maximum’ … there is just no such thing and indeed, a short number of very positive yearly returns may well lead us to re-consider what is needed in light of greater funds and slightly shorter probable lifespan. A re-appraisal of Sequence Risks… more another time.

What Simulation helps provide is a picture of the possible boundaries of fund values and the boundaries of spending (remember, we may well want to simulate a level of variable outgoings as well).

The most important thing though is to use realistic variables and be conservative. It is possible to simulate variable returns, sector, market, country and global shocks, but having played about, the level of complexity is very high and I prefer a much simpler way to look at outcomes. A modest set of target growths, an appreciation of real volatility, a conservative view of likely headwinds a balanced approach is not going to give the most accurate answer … but the answer is likely to enable us to have far greater confidence of minimums and reduce the temptation to see an endless gravy train ahead: the so called ‘proximity mindset’.

Using simulation is a great way to help see a bigger picture involving a lot of independently moving variables. It is not a way to crystal ball the future, but much more a means to help us bound the possible and probably short, medium and long term returns and personal usage (remember… we spend differently as we get older and each outgoing stream should not be assumed to always increase).