The principal-agent problem, tracking error, and the optimal investment portfolio

The principal seeks a portfolio manager to manage funds. The principal uses a tracking-error constraint that restricts the portfolio's volatility. Without the constraint, the manager may increase the portfolio return by adding high-variance assets. Tests assume that the benchmark is the value-weighted market portfolio less the risk-free rate (MKT). Tests then add the Fama and French four long-short portfolios to test if they can increase return without a large increase in the portfolio variance. SMB (Small Minus Big) is long in small stocks and short in big stocks and picks up the small-firm premium. HML (High Minus Low) is long in high book-to-market stocks and short in low book-to-market stocks and picks up the value premium. WML (Winners Minus Losers) is long in past winners and short in past losers and picks up the momentum premium. Tests find that SMB adds tracking error and small returns, HML adds tracking error and large returns, and WML adds modest tracking error and large returns. WML requires heavy trading. Net of trade costs, the WML gain disappears. However, the trade execution costs to hold HML are modest. Net of trade costs, we see a gain from adding HML to MKT.