A brief examination of methods of representing Financial Risk and Returns: from Ibbotson cones in a Gaussian environment to Monte Carlo simulations.
When designing pension products, as with any financial product, we need to make assumptions about the potential returns from specific securities and the associated risks.These can be broadly classified into hypotheses about the security’s risk/return distribution curve and those regarding the quantitative/qualitative nature of the returns and risks themselves. In discussing this topic it is worth noting from the outset that every financial instrument is subject to its own specific sources of risk; therefore detailed statistical analysis of the proprieties of returns is crucial in determining our choice of one model over another. Analysis of historical equity returns, especially using low frequency samples such as monthly price series, suggests they have a Gaussian or Normal distribution, though such normality tends to be less evident when we take daily series. This property of some types of returns plays an important role in supporting certain very popular modeling assumptions, as we shall see below.