I The Sharpe Ratio
1. The Sharpe Ratio and the Signal-Noise Ratio
2. The Sharpe Ratio for Gaussian Returns
3. The Sharpe Ratio for Other Returns
4. Overoptimism

II Maximizing the Signal-Noise Ratio
5. Maximizing the Sharpe Ratio
6. Portfolio Inference for Gaussian Returns
7. Portfolio Inference for Other Returns
8. Overoptimism and Overfitting
9. Market Timing
10. Backtesting
Appendix A Prerequisites

The Sharpe ratio is the most widely used metric for comparing the performance of financial assets. The Markowitz portfolio is the portfolio with the highest Sharpe ratio. The Sharpe Ratio: Statistics and Applications examines the statistical properties of the Sharpe ratio and Markowitz portfolio, both under the simplifying assumption of Gaussian returns and asymptotically. Connections are drawn between the financial measures and classical statistics including Student's t, Hotelling's T^2, and the Hotelling-Lawley trace. The robustness of these statistics to heteroskedasticity, autocorrelation, fat tails, and skew of returns are considered. The construction of portfolios to maximize the Sharpe is expanded from the usual static unconditional model to include subspace constraints, heding out assets, and the use of conditioning information on both expected returns and risk. {book title} is the most comprehensive treatment of the statistical properties of the Sharpe ratio and Markowitz portfolio ever published. Features: * Material on single asset problems, market timing, unconditional and conditional portfolio problems, hedged portfolios.* Inference via both Frequentist and Bayesian paradigms.*A comprehensive treatment of overoptimism and overfitting of trading strategies.*Advice on backtesting strategies.*Dozens of examples and hundreds of exercises for self study. This book is an essential reference for the practicing quant strategist and the researcher alike, and an invaluable textbook for the student. Steven E. Pav holds a PhD in mathematics from Carnegie Mellon University, and degrees in mathematics and ceramic engineering science from Indiana University, Bloomington and Alfred University. He was formerly a quantitative strategist at Convex us Advisors and Cerebellum Capital, and a quantitative analyst at Bank of America. He is the author of a dozen R packages, including those for analyzing the significance of the Sharpe ratio and Markowitz portfolio.