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Robust Equity Portfolio Management. Fabozzi Frank J.

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      where

is the target level of portfolio return. By substituting the formulas from sections 2.1 and 2.2, the portfolio problem is written as

      where

in the first line is added for calculation convenience, and the last line guarantees full allocation of investment principal. Conventionally, the optimization problem is written in matrix form:

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      1

      Harry M. Markowitz, “Portfolio Selection,” Journal of Finance 7, 1 (1952), pp. 77–91.

      2

      An example of improving the robustness of inputs is to use shrinkage estimators, intr

1

Harry M. Markowitz, “Portfolio Selection,” Journal of Finance 7, 1 (1952), pp. 77–91.

2

An example of improving the robustness of inputs is to use shrinkage estimators, introduced in Philippe Jorion, “Bayes-Stein Estimation for Portfolio Analysis,” Journal of Financial and Quantitative Analysis 21, 3 (1986), pp. 279–292. Using simulation to gain robustness is illustrated in Richard Michaud and Robert Michaud, “Estimation Error and Portfolio Optimization: A Resampling Solution,” Journal of Investment Management 6, 1 (2008), pp. 8–28. The Black–Litterman model is an equilibrium-based approach that incorporates an investor's views; it was proposed in Fischer Black and Robert Litterman, “Asset Allocation: Combining Investor Views with Market Equilibrium,” Goldman, Sachs & Co., Fixed Income Research (1990). Various robust approaches including the ones mentioned here are detailed in Chapter 4.

3

MATLAB documentations and a list of functions with examples are available at http://www.mathworks.com/products/matlab/

4

A CVX user's guide and download details can be found at http://cvxr.com/cvx/

5

The approach was first introduced in Harry M. Markowitz, “Portfolio Selection,” Journal of Finance 7, 1 (1952), pp. 77–91; and also in Harry M. Markowitz, Portfolio Selection: Efficient Diversification of Investments (New Haven, CT: Yale University Press, 1959).

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