Portfolio Optimization Presentation For Iacpm

NOVEMBER 2008 | ANNUAL FALL MEETING© 2008 IACPM

Determining the Efficient Frontier for

CDS Portfolios

Vallabh Muralikrishnan

Quantitative Analyst

BMO Capital Markets

Hans J.H. Tuenter

Mathematical Finance

Program,

University of Toronto

Objectives

• Positive EVA

• Minimize Tail Risk

• Maximize Expected Return

• Manage Return on Capital


Optimization Strategy

1. Identify acceptable trades

2. Choose risk-return measures

4. Use optimization algorithm to improve

the efficient frontier

5. Select desired level of risk and return


3. Estimate the efficient frontier 6. Back Test performance of portfolio

Identify Universe of Trades

LONGS SHORTS

Acceptable Credits

Liquid Notional and Tenors

Best EVA Trade per Credit

Acceptable Credits

Liquid Notional and Tenors

Best EVA Trade per Credit


Using only 200 swaps, one can create 2200 = 1.6 x 1060 portfolios!!!

Choose Risk-Return Measures

Several options: RAROC, RORC, EVA, Historical MTM, VaR

In this study:

• Risk: Conditional VaR (1 year horizon)

• Return: Spread × Notional


Conditional Value-at-Risk


� Loss distribution generated by one-factor Gaussian copula model using

correlation estimates from KMV

� CVaR calculated using Monte-Carlo simulation

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


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

Improve the Frontier with Optimization


RANDOM SEARCHOPTIMIZATION ALGORITHM

Starting from the initial estimate, an optimization algorithm can identify more/better

portfolios than continuing a random search.

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


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?

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 2008.

Acknowledgements and References

• 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.


Economy & Finance

Portfolio Optimization Presentation For Iacpm