Measuring style tilting and decomposing style risk
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Theofanis Darsinos is an associate in the Global Markets Research Division of Deutsche Bank AG in London. He received his PhD in financial economics from the Faculty of Economics and Politics, University of Cambridge in 2002. He also holds an MPhil in Finance from Cambridge and a BSc in Mathematics from the University of London. During 2002-2003 he was an honorary research associate in the Department of Applied Economics, Cambridge University. His research interests are in financial econometrics and asset pricing.
Stephen Satchell* is a Fellow of Trinity College, a Reader in Financial Econometrics at the University of Cambridge and a visiting professor at Birkbeck College, Cass Business School and the University of Technology, Sydney (Australia). He provides consultancy for a range of city institutions in the broad area of quantitative finance. He has published papers in many journals and has a particular interest in risk. *Faculty of Economics and Politics, University of Cambridge, Austin Robinson Building, Sidgwick Avenue, Cambridge CB3 9DD, UK. e-mail: [email protected]
Abstract In this paper the authors examine the tendency of portfolio managers to under/over-weight portfolios with respect to a particular style such as book-to-price ratio, dividend yield, etc. The authors provide a test statistic for style tilting and a decomposition of ‘active’ risk for large cross-sectional portfolios with respect to exposures of a given attribute. The decomposition classifies risk into three categories — symmetric covariation, asymmetric covariation and variation — and allows the investment style to be identified and quantified. Keywords: style tilting, risk decomposition, investment style, portfolio construction
Introduction The purpose of this paper is to investigate style tilting, by which is meant the tendency of portfolio managers to under/over-weight their portfolio with respect to a particular style such as book-to-price ratio, dividend yield, earnings yield, cash flow yield, sales to price ratio, EBITDA, etc. To formalise this, a metric or measure of tilt is required. A single metric to capture a manager’s different style strategies probably does not exist. For example, a manager can pick ‘style’ stocks or take a general tilt across many stocks. It is possible, however, to develop a simple test-statistic that uses firm-specific
64
Journal of Asset Management
Vol. 5, 1, 64–71
attributes (for example dividend yield, book-to-price ratio, etc.). The structure of this paper is as follows. The next section contains details of a testing procedure, then a discussion of the validity of the procedure is presented, followed by a new approach to risk-decomposition and a conclusion.
The test-statistic Given a universe of n assets (stocks): i ⫽ 1, 2, . . ., n, let be a (n ⫻ 1) vector of active portfolio weights: n ⫽ (1, . . ., n)⬘; with 冱i⫽1 i ⫽ 1. Also let p be a (n ⫻ 1) vector of alternative portfolio weights: p ⫽ (p1, . . ., pn)⬘; with
䉷 Henry Stewart Publications 1479-179X (2004)
Measuring style tilting an
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