Faculty Bibliography

We present examples that show how the delta-based test of Prop. Reg. 1.871-15 can hinge upon superficial labeling of instruments rather than their underlying economics. We propose an alternative approach that eliminates the concept of a referenced number of shares and accurately reflects economic reality, but we also show how even an economically accurate test can be gamed because of administrative necessities, such as requiring that instruments be evaluated at only a single point in time.

This review illustrates the interaction between law and finance in the particular case of the taxation of constructive sales. The focus is on the treatment of variable prepaid forward contracts and the rules regarding these instruments articulated by Revenue Ruling 2003-7 and the recent case involving Philip Anschutz (Anschutz Co. et al. v. Commissioner of Internal Revenue 2011). Simple models are used to show how the tests established by the law fail to reflect important financial considerations, such as the volatility of asset returns and the riskiness of dividend payments. These models provide examples that form the basis for a critique of the current rules and also indicate a possible path for future reform and improvement of the law, namely the addition of a delta-based test to the existing rules. The analysis presented here aims to encourage future work that applies financial theory to critique and improve legal rules in a wide range of other situations.

A key result of the capital asset pricing model (CAPM) is that the market portfolio—the portfolio of all assets in which each asset's weight is proportional to its total market capitalization—lies on the mean-variance-efficient frontier, the set of portfolios having mean-variance characteristics that cannot be improved upon. Therefore, the CAPM cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position. We call such efficient frontiers “impossible,” and show that impossible frontiers are difficult to avoid. In particular, as the number of assets, n, grows, we prove that the probability that a generically chosen frontier is impossible tends to one at a geometric rate. In fact, for one natural class of distributions, nearly one-eighth of all assets on a frontier is expected to have negative weights for every portfolio on the frontier. We also show that the expected minimum amount of short selling across frontier portfolios grows linearly with n, and even when short sales are constrained to some finite level, an impossible frontier remains impossible. Using daily and monthly U.S. stock returns, we document the impossibility of efficient frontiers in the data.