This paper considers efficient set mathematics for the case where the covariance matrix of asset returns is assumed known but ex ante the vector of expected returns is replaced by an estimated or forecast value. It is shown that the ex post mean and variance differ from the standard results. Consequently the maximum Sharpe ratio portfolio also differs from the standard result. However, even wit...

We propose to train trading systems by optimizing financial objective functions via reinforcement learning. The performance functions that we consider are profit or wealth, the Sharpe ratio and our recently proposed differential Sharpe ratio for online learning. In Moody & Wu (1997), we presented empirical results that demonstrate the advantages of reinforcement learning relative to supervised ...

We provide a new theory for nodewise regression when the residuals from fitted factor model are used. apply our results to analysis of consistency Sharpe Ratio estimators there many assets in portfolio. allow an increasing number as well time observations Since is not feasible due unknown nature idiosyncratic errors, we feasible-residual-based estimate precision matrix errors which consistent e...

Performance measurement is an integral part of investment analysis and risk management. The goal of performance measurement is to build a ranking of different investments on the basis of risk-adjusted returns in order to evaluate the relative success of these investments. The Sharpe Ratio is the best-known measure of this type. It considers the first two moments of the return distribution (expe...

Traditional risk-adjusted performance measures, such as the Sharpe ratio, the Treynor index or Jensen’s alpha, based on the mean-variance framework, are widely used to rank mutual funds. However, performance measures that consider risk by taking into account only losses, such as Value-at-Risk (VaR), would be more appropriate. Standard VaR assumes that returns are normally distributed, though th...

We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic and frictionless market setting. First, we demonstrate that with such a performance measure, the manager’s focus on the short horizon performance is detrimental to the investor’s long horizon performance. Numerical experiments illustrate that when returns are iid, the performance loss is...