Inside downside risk
MANAGING ASYMMETRIC RETURNS—INSIDE DOWNSIDE RISK
The measurement of downside risk can be a controversial area. Jim Bachman and Tobias Gummersbach explain how the use of variations of annual tail-value-at-risk (T-VaR) analysis can be used to gain a more accurate assessment.
M ean variance (MV) asset allocation methodologies are
criticised most often on two counts: first, the derivation of returns is predicated upon historic information; and second,
variance as a measure of risk fails to account adequately for the risk of loss, giving it the same relevance as the likelihood of upside gain. The validity of the first criticism depends upon practitioners’ return assumptions. The second criticism is valid. However, we believe it can be overcome by using enhanced metrics of downside risk in an MV framework to provide improved risk of loss estimates.
Our measure of downside risk is annual tail-value-at-risk (T-VaR). We
estimate T-VaR using three different methods: standard normal end-of- period (SNEOP); diffusion inter-period (DIP); and Levy inter-period (Levy).
In addition to mean and variance, the Levy method accounts for
skewness and kurtosis (tail behaviour statistics). These metrics yield significantly different asset allocations and enterprise solvency assessments when they replace the risk metric in an MV framework.
There are three sections in this article. In the first section, we show
estimates of T-VaR on the three different bases for several of the 140 asset class indices and product series used in the analysis. The second section contrasts asset allocation outcomes for each of the risk measures; and the third section provides a summary highlighting the potential impact upon Solvency II required capital levels.
T-VAR ESTIMATES OF DOWNSIDE RISK We use daily total return data to estimate each asset class’s annual T-VaR.
Chart 1 displays daily returns, rolling annual returns, descriptive statistics and fitted returns distributions for a representative property and casualty investment portfolio. The portfolio is a blend of the BoA Merrill Lynch PC01 Fixed Income Insurance Index (80 percent) and the S&P 500 (20 percent) from December 31, 1997 to December 31, 2010. The returns are asymmetric, i.e. negatively skewed and fat-tailed. The normal distribution will understate downside risk, or the likelihood of extreme adverse outcomes.
CHART 1. REPRESENTATIVE STATISTICS (80 PERCENT BOA ML PC01 AND 20 PERCENT S&P 500) DECEMBER 31, 1997 TO DECEMBER 31, 2010 DAILY TOTAL RETURNS
Dec-97 Jun-98 Dec-98 Jun-99 Dec-99 Jun-00 Dec-00 Jun-01 Dec-01 Jun-02 Dec-02 Jun-03 Dec-03 Jun-04 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Dec-08 Jun-09 Dec-09 Jun-10 Dec-10
3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5
Time frame scanned December 31, 1997
December 31, 2010
42 | INTELLIGENT INSURER | September 2011
% returns
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