Injudicious use of Monte Carlo simulations could overestimate individual asset risks by two thirds if strict normality is assumed and the shape of the underlying distributions is ignored. Similarly total returns and Sharpe Ratios could be overstated by 20% or more when assuming strict normality. Individual assets that have positively skewed distributions may have their returns under estimated by 13% or more.

Most investors and software do not consider the asymmetry of returns and risks when conducting Monte Carlo simulations of future portfolio returns and simply rely on the central limit theorem to assume normality. Whilst the CLT certainly holds, it does so only over the long-term. In the short run, things may be very different indeed.

This month we look at the three main methods of generating correlated random deviates for the purposes of performing Monte Carlo simulations, namely;

• The Cholesky Method,

• The Spectral ( SVD ) Method and,

• The Inverse method

As you may know, Monte Carlo simulations were invented by Stanislaw Ulam and John von Neumann during their work on the Manhattan project. The requirement for significant computing power meant that the method remained the preserve of think tanks, large universities and corporations until around the the 1980s and the advent of the Personal Computer. Since then, the use of the method has exploded and it has become ubiquitous in finance and financial planning even to the detriment of stopping people from trying to find closed form solutions for some problems which may have them.

Thanks to Moore’s law, most of us now have sufficient computing pow......................

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This article was published in Opalesque's New Managers a top-down monthly analysis, news and research publication on the global emerging manager space.