Approximating the Confidence Intervals for Sharpe Style Weights

• Published in: Financial analysts journal Vol. 53; no. 4; pp. 80 - 85
• Main Authors: Lobosco, Angelo, DiBartolomeo, Dan
• Format: Journal Article
• Language: English
• Published: Charlottesville The Association for Investment Management and Research 01.07.1997; Taylor & Francis Ltd
• Subjects: Analytical estimating; Coefficients; Confidence interval; Confidence intervals; Effectiveness; Estimates; Estimating techniques; Financial investments; Independent variables; Index numbers; Indexation; Investment policy; Investment portfolios; Investments; Monte Carlo simulation; Periodical indexing; Portfolio management; Portfolio performance; Rates of return; Regression analysis; Securities analysis; Standard deviation; Standard error; Stock exchanges; Stock returns; Studies; Time series; Variables; United States > US
• ISSN: 0015-198X; 1938-3312
• DOI: 10.2469/faj.v53.n4.2103

Style analysis is a form of constrained regression that uses a weighted combination of market indexes to replicate, as closely as possible, the historical return pattern of an investment portfolio. The resulting coefficients, called Sharpe style weights, are used to form inferences about a portfolio's behavior and composition. This technique has been widely adopted in the investment industry, despite the fact that no explicit confidence interval measures have been available to describe the results. We derive an approximation for the confidence intervals of these weights and, using Monte Carlo simulation, verify its efficacy. The estimation of these confidence intervals can help practitioners assess the statistical significance of their results and aids in determining which indexes to include in the analysis. It may also encourage the use of daily return data to meaningfully reduce the size of the confidence intervals.