In a recent paper Lee et al. derive a pricing formula which is significantly different from that of Black and Scholes. Their derivation is inconsistent due to their failure to recognize that the rate of return of an option written on an asset whose rate of return is lognormally distributed will not be lognormally distributed.

This paper examines debt restructurings by financially distressed firms. We develop a model which predicts that, in public debt exchange offers, firms with unfavorable private information will offer equity claims to convince bondholders that the firm's prospects are poor. In contrast, offering equity to well-informed private lenders conveys favorable private information to outsiders. Consistent with our analysis, we find positive average abnormal returns around restructurings that offer equity to private lenders and senior debt to public debtholders, and we find significant negative average abnormal returns when private lenders are offered senior debt and public lenders are offered equity.

We consider a model of active asset management in which mutual fund managers exert unobservable effort to earn excess returns. Investors allocate capital to actively managed funds and passively managed products. In equilibrium, investors are indifferent between investing an additional dollar with an active manager or with a passively managed product. As passively managed products become more attractive to investors, active managers’ revenues from portfolio-management services fall, reducing their effort incentives. More-severe decreasing-returns-to-scale are also associated with reduced incentives and increased moral hazard. Performance-based fees and holdings-based data are all unlikely to mitigate moral hazard.

We investigate the optimal savings decisions for investors with access to pre-tax (traditional) and post-tax (Roth) versions of tax-advantaged retirement accounts. The model features a progressive tax schedule and uncertainty over future tax rates. Traditional accounts are valuable for hedging retirement account performance and managing current income near tax-bracket cutoffs, whereas Roth accounts allow investors to mitigate uncertainty over future tax schedules. The optimal asset location policy for most households involves diversifying between traditional and Roth vehicles. Contrary to conventional advice, the substantial economic benefits from Roth investments are not limited to investors with low current income.