How far are you on the road to Monte Carlo?

In the midst of a sustained market downturn, one that has its roots in the late 1990s, I thought it would be interesting to touch base with modern portfolio theory’s Monte Carlo risk simulations. 

The question is, how far along the original probability distributions are today’s investors?  

Monte Carlo simulations assume that the starting point is an equilibrium point, and that each of the many outcomes comprising the distribution of future outcomes, is a possible outcome with a given probability.  The expected or average outcome is only the average of all future scenarios and not the expected value of the unfolding present per se: it is only the expected outcome if you were to personally repeat the time frame a few hundred to a thousand times.

Since 2000, most developed financial markets have fallen.   If you rerun the Monte Carlo simulation with the new portfolio value, but with the same return assumptions, you will end up with a new “end of scenario” expected or average value.  In other words, the probability distribution of outcomes from all “the time sequenced” Monte Carlo simulations, if you mapped them together, would result in a skewed distribution – in this case the distribution is skewed towards negative returns and higher probabilities for those negative returns. 

One of the big problems with a Monte Carlo simulation is that it does not allow you to assume that you are indeed out of equilibrium – if you are out of equilibrium then future returns are not going to be random, but driven partly by the deviation from equilibrium.   Yes, there are developments to MC modelling which allow for regime switches and mean reversion, but these are still random processes and bounded by equilibrium assumptions. 

The mean return, risk and correlation inputs of a mean variance optimiser are meant to represent the sensitivities and characteristics of the economic and financial universe in question – a positive mean return implies that the universe, even though price movements are random, is a potentially expanding universe (sufficient energy to maintain the expected average rate of return without becoming unstable (oscillating wildly) or losing momentum).  

So what if we adjust the return on the Monte Carlo simulation downward to adjust for the often ridiculous return assumptions that were at one time put into these models?  Well, this further skews the distribution into negative territory, switches one universe for another midstream, and further highlights the dangers of Monte Carlo simulation for risk management during periods of financial, economic and market excess.

In truth, when modelling forward you should be aiming to build into your model systematic risks and financial, economic and market excess: in other words, this is not the return we expect, but the return we expect to receive after we have hit markets and economies with significant risk.  Acknowledging that mean returns will fall as market rise and economic cycles lengthen and that returns will rise in the reverse scenario creates a  more stable investment planning horizon.   This highlights another problem with the MC construct – its aim is precision over the range of outcomes, when in reality the aim of modelling is to acknowledge the fuzziness of outcomes while focussing on the range of outcomes most likely to cause problems – inflation, untimely death/longevity, changes in size and timing of planned financial needs and significant financial, market and economic risks all need to be built into modelling.  A significant risk scenario may only represent a small portion of the MC universe of outcomes, but it is precisely this area that needs to be managed.

It is most unfortunate that Monte Carlo’s raison d’etre has been predicated on the easiest of “straw men” to knock down.  This is the simple deterministic planning projection where an often high and positive constant annual average return is applied to a portfolio of assets while ignoring the uncertainties and risk of investment and the impact of large, sustained negative price movements on the ability of assets to fund liabilities. 

So, just how has your path evolved along your original Monte Carlo simulation?  

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