We divide hedging methods between single-period and multi-period. After reviewing some well-known hedging algorithms, two new procedures are introduced, called Dickey-Fuller Optimal (DFO), Mini-Max Subset Correlation (MMSC). The former is a multi-period, cointegration-based hedging method that...

Most papers in the financial literature estimate the p-value associated with an investment strategy, without reporting the power of the test used to make that discovery. In this paper we provide analytic estimates to Type I and Type II errors for the Sharpe ratios of investments, and derive...

Convex optimization solutions tend to be unstable, to the point of entirely offsetting the benefits of optimization. For example, in the context of financial applications, it is known that portfolios optimized in-sample often underperform the naïve (equal weights) allocation out-of-sample. This...

Correlation matrices are ubiquitous in finance. Some key applications include portfolio construction, risk management, and factor/style analysis. Correlation matrices are usually estimated from historical empirical observations or derived from historically estimated factors. It is widely...

We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) has a number of important applications: First, it allows us to...