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Equity Valuation and Portfolio Management by Harry M. Markowitz, Frank J. Fabozzi

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METHODS OF ACTIVE MANAGEMENT

The goal of all forms of active portfolio management is to produce a return in excess of a benchmark without incurring an excessive degree of risk. Traditional portfolio managers endeavor to achieve excess return by weighting the securities in their portfolio differently from the weightings of the securities in the benchmark. However, these weights are determined and whatever their values may be, one can generally think of any portfolio as a linear combination of the benchmark-replicating portfolio and a pure active portfolio:

image

where rt is the portfolio return, λ is a weighting parameter, image is the return of the benchmark-replicating portfolio, and image is the return of the active portfolio. Although many active managers might argue that the weighting parameter λ is equal to zero—that is, they provide purely an active return, most actually provide some blend of benchmark exposure and active exposure. Without loss of generality, one can view all active portfolio management strategies relative to some benchmark, and thus any portfolio can be decomposed into an active and passive component.8 Regardless of the particular value of the parameter λ or the process employed ...

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