Dr. O’Neal and attorney/author Dan Solin today released a statistical analysis of the results of the mandatory arbitration process during the 1995 – 2004 period. They assessed almost 14,000 NASD and NYSE arbitration cases and found that Claimant win rates and recovery amounts have declined significantly over time. Moreover, claimants fare more poorly in large cases and in cases against larger brokerage firms. Dr. O’Neal and Mr. Solin estimate that the expected recovery before legal fees and expenses in a large case against a top brokerage firm is only 12% of the amount claimed.

Stock trading models are used by economists to estimate damages in securities class action lawsuits. In this note, we explain the three types of models used by plaintiffs’ and defendants’ experts.

Published in the Journal of Risk, Vol. 16, No. 6.

The presence of options in a portfolio fundamentally alters the portfolio’s risk and return profiles when compared to an all equity portfolio. In this paper, we advocate modeling a risk-based criterion for optioned portfolio selection and rebalancing problems. The criterion is inspired by Chicago Mercantile Exchange’s risk-based margining system which sets the collateralization requirements on margin accounts. The margin criterion computes the losses expected at the portfolio level using expected stock price and volatility variations, and is itself an optimization problem. Our contribution is to remodel the criterion as a quadratic programming subproblem of the main portfolio optimization problem using option Greeks. We also extend the margin subproblem to a continuous domain. The quadratic programming problems thus designed can be solved numerically or in closed-form with high efficiency, greatly facilitating the main portfolio selection problem. We present two extended practical examples of the application of our approach to obtain optimal portfolios with options. These examples include a study of liquidity effects (bid/ask spreads and limited order sizes) and sensitivity to changing market conditions. Our analysis shows that the approach advocated here is more stable and more efficient than discrete approaches to portfolio selection.