Practical Applications from the Experts - September 2009

categories: Product Documentation, general

Incremental Standard Deviation and Incremental Expected Shortfall

Among the recent additions to RiskManager are two statistics: Incremental Standard Deviation and Incremental Expected Shortfall. This month’s note introduces our users to these statistics.

Standard Deviation is the most widely quoted risk statistic. While portfolio StdDev can give an initial understanding of risk, additional insight is gained by observing what happens to this number if a position size is increased. Incremental Standard Deviation (IStdDev) does just that. For example, a portfolio manager while rebalancing his portfolio will like to know how much each position contributes to the total standard deviation. In this sense IStdDev is similar to IVaR.

Recognizing that incremental statistics are a powerful tool, we have also added Incremental Expected Shortfall (IExpSF) as another statistic. As risk practitioners know, Expected Shortfall is the average P&L in the ‘tail’ for a given confidence level. Incremental Expected Shortfall shows the contribution of each position to portfolio’s total Expected Shortfall. Tail risk has gained importance since the financial Tsunami of last year, when markets experienced returns far in excess of the 3 standard deviation mark, so risk users will benefit from using IExpSF.

A few points to note regarding IStdDev and IExpSF:

• Both statistics can be calculated using the three methodologies: Parametric, Monte Carlo and Historical
• While the concepts of IStdDev and IVaR are closely linked, their calculation methodologies differ in RiskServer. Specifically for simulation methods, IStdDev makes use of the entire distribution of returns, while IVaR references scenarios close to the confidence level
• Monte Carlo IExpSF and IVaR are calculated using a similar approach. Details for this can be found in Chapter 6 of Return to RiskMetrics publication

Lastly, we look at a sample report. For the ‘CDS Itraxx’ position below, while standalone StdDev is 5.97% the position’s contribution to portfolio Standard Deviation (IStdDev) is only 0.30%. The difference comes from a diversification benefit. Similarly, while CDS Itraxx has the highest ExpSF (8.84%) it ranks much lower in IExpSF (0.99%). Also note the difference between the IStdDev and 0.8413 MC IVaR, which can be considered a proxy for IStdDev. The two numbers are considerably different (0.30% vs -2.40%), which can be due to the non-normality of returns distribution and/or the difference in calculation approach.

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