Multi Target Risk Measurement & Portfolio Optimization

Abstract

Multiple investment targets naturally arise in portfolio management when investments are subject to performance benchmarks such as a stock/bond reference portfolio and absolute drawdown limits. Additional layers of investment targets like inflation outperformance or liability coverage ratios further complicate risk management and portfolio optimization. This paper illustrates a comprehensive approach for managing a portfolio against multiple random or deterministic investment targets concurrently in a single period setting. The approach expands from the well-established body of academic and practical research on downside measures, and in particular the mean-below target (MBT) measure, also known as target shortfall (TS), first lower partial moment (LPM1), put premium (PP) risk measure or mean excess loss (MEL) and stop loss premium (SLP) in actuarial sciences. Despite embedding multiple targets the new approach reduces the mathematical complexity to a single dimension allowing to apply well-known results. Even though targets are co-dependent, the multi-target MBT measure allows for explicit decomposition into marginal single target MBT measures. Besides exploring the properties of such risk measure the paper covers all aspects of performance measurement, cost of capital allocation as well as portfolio optimization with multiple targets. Here, the portfolio optimization of the multi target MBT measure remains of linear programming complexity. The resulting comprehensive portfolio management framework is appealing for its simplicity in application, implementation and communication.