Determining the Efficient Frontier for CDS Portfolios

Transcription

1 Determining the Efficient Frontier for CDS Portfolios Vallabh Muralikrishnan Quantitative Analyst BMO Capital Markets Hans J.H. Tuenter Mathematical Finance Program, University of Toronto

2 Objectives Positive EVA Minimize Tail Risk Maximize Expected Return Manage Return on Capital

3 Optimization Strategy 1. Identify acceptable trades 4. Use optimization algorithm to improve the efficient frontier 2. Choose risk-return measures 5. Select desired level of risk and return 3. Estimate the efficient frontier 6. Back Test performance of portfolio

4 Identify Universe of Trades LONGS SHORTS Acceptable Credits Acceptable Credits Liquid Notional and Tenors Liquid Notional and Tenors Best EVA Trade per Credit Best EVA Trade per Credit Using only 200 swaps, one can create = 1.6 x portfolios!!!

5 Choose Risk-Return Measures Several options: RAROC, RORC, EVA, Historical MTM, VaR In this study: Risk: Conditional VaR (1 year horizon) Return: Spread Notional

6 Conditional Value-at-Risk Loss distribution generated by one-factor Gaussian copula model using correlation estimates from KMV CVaR calculated using Monte-Carlo simulation

7 Estimate the Efficient Frontier The efficient frontier of CDS portfolios is discrete because it is difficult to meaningfully interpolate between portfolios. A random search of several thousand portfolios can provide an estimate of the efficient frontier. The green line represents the non-dominated portfolios from this search. It represents the portfolios with the best riskreturn trade-off. INITIAL ESTIMATE

8 Improve the Frontier with Optimization OPTIMIZATION ALGORITHM RANDOM SEARCH Starting from the initial estimate, an optimization algorithm can identify more/better portfolios than continuing a random search.

9 Generalizations This optimization approach presented here can be customized in many ways Choice of trade universe Longs only; shorts only; other assets; Choice of Risk-Return measures VaR, Economic Capital Change Optimization algorithm Genetic Search Discussion Points Mathematical Optimization models can give you results that are only as good as the risk measures used. There are a lot more long positions than short positions in the CDS universe identified in this study. Does this mean that the capital measure to calculate EVA is wrong? Portfolio risk measures depend on estimates of PD, LGD, and asset value correlations. If the measures are not accurate, your portfolios will be suboptimal. For example, consider PD estimates of Lehman Brothers, one month before they defaulted. Does this mean the PD estimate was wrong or that we were just unlucky?

10 Acknowledgements and References The work presented here was developed jointly with prof. Hans J.H. Tuenter from the Mathematical Finance Program at the University of Toronto. The authors would like to acknowledge Ulf Lagercrantz (VP, BMO Capital Markets) for his help in developing the algorithm to identify the list of potential longs and shorts. Further Reading: Vallabh Muralikrishnan, Optimization by Simulated Annealing, GARP Risk Review, 42:45 48, June/July Hans J.H. Tuenter, Minimum L 1 -distance Projection onto the Boundary of a Convex Set, The Journal of Optimization Theory and Applications, 112(2): , February Gunter Löffler and Peter N. Posch, Credit Risk Modeling using Excel and VBA, Wiley Finance. pg , 2007.