Portfolio Optimization Presentation For Iacpm
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Portfolio Optimization Presentation For Iacpm

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Presentation on how to do optimize a bank\'s credit portfolio using Credit Default Swaps. This presentation was made at the IACPM conference in Toronto in 2008.

Presentation on how to do optimize a bank\'s credit portfolio using Credit Default Swaps. This presentation was made at the IACPM conference in Toronto in 2008.

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    Portfolio Optimization Presentation For Iacpm Portfolio Optimization Presentation For Iacpm Presentation Transcript

    • Vallabh MuralikrishnanDetermining the Efficient Frontier for Quantitative AnalystCDS Portfolios BMO Capital Markets Hans J.H. Tuenter Mathematical Finance Program, © 2008 IACPM University of Toronto NOVEMBER 2008 | ANNUAL FALL MEETING
    • Objectives• Positive EVA• Minimize Tail Risk• Maximize Expected Return• Manage Return on Capital© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • Optimization Strategy 4. Use optimization algorithm to improve 1. Identify acceptable trades 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© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • 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 2200 = 1.6 x 1060 portfolios!!!© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • Choose Risk-Return MeasuresSeveral options: RAROC, RORC, EVA, Historical MTM, VaRIn this study: • Risk: Conditional VaR (1 year horizon) • Return: Spread × Notional© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • Conditional Value-at-Risk Loss distribution generated by one-factor Gaussian copula model using correlation estimates from KMV CVaR calculated using Monte-Carlo simulation© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • 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 risk- return trade-off. INITIAL ESTIMATE© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • Improve the Frontier with Optimization RANDOM SEARCH OPTIMIZATION ALGORITHMStarting from the initial estimate, an optimization algorithm can identify more/betterportfolios than continuing a random search.© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • GeneralizationsThis optimization approach presented here can be customized in many waysChoice of trade universe • Longs only; shorts only; other assets;Choice of Risk-Return measures • VaR, Economic CapitalChange Optimization algorithm • Genetic SearchDiscussion PointsMathematical Optimization models can give you results that are only as good as the riskmeasures 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?© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING
    • Acknowledgements and ReferencesThe work presented here was developed jointly with prof. Hans J.H. Tuenter from theMathematical Finance Program at the University of Toronto.The authors would like to acknowledge Ulf Lagercrantz (VP, BMO Capital Markets) forhis 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 2008. • Hans J.H. Tuenter, “Minimum L1-distance Projection onto the Boundary of a Convex Set”, The Journal of Optimization Theory and Applications, 112(2):441 – 445, February 2002. • Gunter Löffler and Peter N. Posch, “Credit Risk Modeling using Excel and VBA”, Wiley Finance. pg 119 – 146, 2007.© 2008 IACPM NOVEMBER 2008 | ANNUAL FALL MEETING