What happens to the price of a put in a period during which the stock price stays constant? The hedging strategy implicit in the Black-Scholes model would seem to imply that the put goes up in value. Pure arbitrage arguments imply the opposite result. This paper resolves the paradox and uses it to explore the restrictions inherent in the diffusion processes assumed for all option pricing models.

To price assets with a parsimonious set of factor-mimicking portfolios, one typically identifies and weights well-diversified basis portfolios. Traditional weightings lead to factor-mimicking portfolios that are unlikely to price even the basis portfolios from which they are formed. We offer a method to combine basis portfolios into a single factor-mimicking portfolio that is closely linked to the optimal portfolio. In practice, this method improves the pricing accuracy of parsimonious factor models, even for anomaly portfolios formed from characteristics that are distinct from those underlying the basis portfolios.

Mark Grinblatt, Sheridan Titman, A Study of Monthly Mutual Fund Returns and Performance Evaluation Techniques, The Journal of Financial and Quantitative Analysis, Vol. 29, No. 3 (Sep., 1994), pp. 419-444

Corporate bonds’ book-to-market ratios predict returns computed from transaction prices. Senior bonds (even investment grade) with the 20% highest ratios outperform the 20% lowest by 3%–4% annually after non-parametrically controlling for numerous liquidity, default, microstructure, and priced-risk attributes: yield-to-maturity, bid–ask spread, duration/maturity, credit spread/rating, past returns, coupon, size, age, industry, and structural model equity hedges. Spreads for all-bond samples are larger. An efficient bond market would not exhibit the observed decay in the ratio’s predictive efficacy with implementation delays, small yield-to-maturity spreads, or similar-sized spreads across bonds with differing risks. A methodological innovation avoids liquidity filters and censorship that bias returns.