Abstract
Many strategies for asset allocation involve the computation of the expected value and the covariance matrix of the returns of financial instruments. How much of each instrument to own is determined by an attempt to minimize risk — the variance of linear combinations of investments in these financial assets — subject to various constraints such as a given level of return, concentration limits, etc. The covariance matrix contains many parameters to estimate and two main problems arise. First, the data will very likely have outliers that will seriously affect the covariance matrix. Second, with so many parameters to estimate, a large number of return observations are required and the nature of markets may change substantially over such a long period. In this paper we discuss using robust covariance procedures, FAST-MCD, Iterated Bivariate Winsorization and Fast 2-D Winsorization, to address the first problem and penalization methods for the second. When back-tested on market data, these methods are shown to be effective in improving portfolio performance. Robust asset allocation methods have great potential to improve risk-adjusted portfolio returns and therefore deserve further exploration in investment management research.
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References
1986Generalized autoregressive conditional heteroskedasticity1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1990Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized Arch Model1988A Capital Asset Pricing Model with Time-Varying Covariances1963A Simplified Model for Portfolio Analysis1992Global Portfolio Optimization2001Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH1989The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?