# Risk modelling in the 21st century – part II

29 June 2015

Jason Baran – Insight Analyst (Investments)

In our previous Multi-Asset Funds Newsletter we reviewed some of the developments in measuring risk over the past few decades, beginning with the notion of volatility providing a measure of risk within Markowitz’s work in the 1950s. So let's explore this topic further.

### Conditional value at risk (VaR)

The notion of VaR is now commonplace in the investment industry. Less known, but also in widespread use, is the concept of conditional VaR. This represents an improvement in VaR in that not only do we consider the investment loss that can occur at a set probability level, but also estimate the expected losses that would occur beyond this probability (and this is why conditional VaR can also be referred to as ‘expected shortfall’ or ‘expected tail loss’).

In other words, we can better consider the full amount of tail risk and not just the loss at a set level.

### Factor modelling

Another area now gaining widespread use in risk management is the use of factor models to more accurately represent risk.

The original CAPM, or Capital Asset Pricing Model, can be thought of as a single factor model, one where our factor is the β and represents how a portfolio or stock is influenced by the market. From here Fama-French proposed a three-factor model whereby stock returns could be explained by a stock’s price-to-book value and market cap (particularly small caps stocks) in addition to the original CAPM market factor.

This has further led to other factors being considered and the establishment of the returns-based style analysis (RBSA). This work on factors is now the underlying principle behind the use of smart beta funds, which aim for an active level of investment returns but a level of expenses similar to a passive tracker fund.

### Monte Carlo Simulations

Additionally, with the increase in computing power available, more complex simulations can be made involving complex probability distributions and weight for outlier events. For example, Monte Carlo Simulations can now be run by an adviser on their desktop as part of their suitability assessment. This wouldn’t have been possible 15 or 20 years ago.

### Conditional/Bayesian Statistics

Increases in computing power are also enabling the development of Bayesian Statistics in risk modelling.

With Bayesian Statistics we can set a probability for the distribution used to model data, and then using an iterative process as we observe more data, improve our estimation of the distribution behind these returns.

Bayesian Statistics are also flexible enough to allow subjective input from risk management, allowing us to implement an assumption of ‘fat tails’ to our risk model in a more measured manner. This compares with the traditional ‘frequentist’ statistics where we assume a specific distribution and assess if new data fits appropriately, but without any improvement in our original distribution assumption.

Despite all these refinements and continuing improvement, one should be aware of the limits to a model as nothing is ever perfect, and to keep risks in mind before making investment decisions. Remember, there's a difference between the 'known unknowns' and the 'unknown unknowns'!