Speaker:	Oleksandr Romanko
	Department of Computing and Software, McMaster University
	Quantitative Research Group, Algorithmics Inc.

Title: Constructing Sparse Replicating Portfolios for Insurance Liabilities by Regularized Optimization



Replicating portfolios are used by insurance companies to measure and manage risk. A replicating portfolio comprises a set of standard financial assets whose value closely matches that of a liability portfolio under current and future market conditions. If the replication is sufficiently precise and the assets can be priced faster than the liability then the replicating portfolio is a computationally efficient proxy for conducting risk analysis of the liability. Replicating portfolios are typically constructed by minimizing the difference between the cash flows of the liability and the replicating portfolio in a set of stochastic scenarios. For practical reasons it is desirable for the replicating portfolio to be sparse, i.e., to contain a relatively small number of assets. Sparse replicating portfolios perform better out-of-sample and can be priced faster.

Regularized optimization, by means of trading penalties or constraints, is an effective way to obtain sparse replicating portfolios. Previous studies considered only a simple type of trading constraint when an identical trading cost is assigned to all instruments. Studies of similar problems in regression analysis and signal processing indicate that more sophisticated costing schemes can yield better results. In this research we evaluate a number of alternative schemes for specifying trading costs based on their out-of-sample performance under different optimization models. The performance of trading cost restrictions is compared to that of cardinality-constraints, i.e., the portfolio is explicitly limited to contain at most a specified number of instruments. We find that trading costs based on simple statistics of the instrument and liability cash flows are an effective choice in practice.

Based on our experience at Algorithmics Inc., we discuss practical issues relevant to industrial-strength implementation of software for portfolio replication. Those issues, among others, include overcoming numerical difficulties occurring due to badly scaled financial data while solving large-scale portfolio optimization problems. We describe optimization techniques utilized for fast computing of efficient portfolio frontiers. Criteria for selecting a final replicating portfolio on the computed efficient frontier are discussed as well.

Joint work with Helmut Mausser and Curt Burmeister, Algorithmics Inc.