Financial investors frequently confront factors such as financial regulations that prevent them from attaining a first-best solution to the optimal asset allocation problem. For example, they may be required to implement a mean-variance efficient portfolio, or they may be constrained to invest in a non-well-diversified choice of assets, such as holding stocks only or bonds only, or they may be constrained from short-selling. Such constraints imply the imposition of a welfare loss on the investor. That a welfare loss is inevitable is well known, but the portfolio choice literature thus far has offered little guidance on how to measure the loss, and how various factors will influence the amount of the loss. This volume tackles the welfare loss problem in a comprehensive and rigorous manner. Using a combination of mathematical analysis and computer simulation, deep insight is achieved into a variety of constrained portfolio choice problems. The book will be found highly illuminating to portfolio choice theorists as well as to students and practitioners of investment analysis.