This study uses the Bayesian approach to examine the incremental contribution of stock characteristics to the investment opportunity set in U.K. stock returns. The paper finds that size, book-to-market (BM) ratio, and momentum characteristics all make a significant incremental contribution to the investment opportunity set when there is unrestricted short selling. However, no short selling constraints eliminate the incremental contribution of the size and BM characteristics, but not the momentum characteristic. The use of additional stock characteristics such as stock issues, accruals, profitability, and asset growth leads to a significant incremental contribution beyond the size, BM, and momentum characteristics when there is unrestricted short selling, but no short selling constraints largely eliminates the incremental contribution of the additional characteristics.