Oct 5

3:30 pm

## Tail Risk Budgeting

### R. Douglas Martin

Seminar

University of Washington - Department of Statistics

Risk budgeting is a methodology that has become increasingly popular over the last decade as a relatively transparent alternative to rebalancing portfolios via a black-box portfolio optimization method. We begin by briefly reviewing â€œclassicalâ€ risk budgeting methodology based on volatility (standard deviation) of returns as the risk measure. The basic elements of this approach are an additive decomposition of portfolio volatility in terms of easily computed marginal and percentage contributions to risk and the use of the expected returns implied by â€œreverse optimizationâ€, i.e., by computing the expected returns that one would have if the given portfolio were optimal according to the so-called â€œModern Portfolio Theoryâ€ mean-variance objective function. We then introduce â€œPost-Modernâ€ portfolio construction methods based on mean-risk objective functions using downside tail risk measures such as value-at-risk (VaR) and expected tail loss (ETL), and show how Eulerâ€™s theorem leads to an additive decomposition of portfolio risk based on downside risk measures that are positive homogeneous. In this approach one computes implied returns based on the assumption that the given portfolio is mean-risk optimal using a tail risk measure. The challenge in applying the method is the computation of the marginal contributions to tail risk, and we show how this can be done effectively for the VaR and ETL risk measures. Several graphical displays are useful for implementing tail risk budgeting and for comparing tail risk budgeting with classical volatility based risk budgeting. The efficacy of the approach is demonstrated by an out-of-sample test of portfolio rebalancing based on tail risk budgeting.

*Joint work with Stoyan Stoyanov and Svetoslav Delev at FinAnalytica, Inc.