# Fat Tail, Risk Budgeting, Factor Analysis & Stress Testing

### Fat Tail Analysis

1. VaR (Value at Risk) – The highest possible loss over a certain period of time at a given confidence level. A 99% Value at Risk is interpreted as the level at which the losses of an asset or a portfolio will not be exceeded with a probability of 99% (i.e. in 99 out of 100 cases the analyzed asset or portfolio return will be above the estimated VaR value). Calculating VaR can be done using the historical fund data or parametrically fitting the data to a distribution and simulating the risk variables of this fund to create potential outcomes that did not occur in the past. The traditional way of calculating VaR parametrically utilizes the Normal distribution which only accounts for 2 moments, mean and standard deviation. It also assumes that the return distribution of risk variables is normally distributed despite ample empirical evidence against this assumption. Utilizing Normal VaR underestimates downside risk and can overestimate upside potential because the tails of these fund risk drivers are completely ignored. In addition, if the right tail is longer, the normal distribution may underestimate the upside potential and you run the risk of leaving money on the table. The Fat Tailed distribution helps you avoid this by accurately capturing both the left and right tails. To solve this problem, “Fat-tailed” VaR utilizes the Skewed Student’s distribution which accounts for higher moments including skewness and degrees of freedom (tail fatness) allowing for a more accurate picture of tail activity and asymmetrical behavior.

Investors who are required to select and monitor investment managers should develop a basic understanding of investment statistics. Quantitative tools can provide you with good insight that you can use in your qualitative interviews with managers and when monitoring your investments.