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

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THE SOLUTION

If we think of each factor as an asset to own, we can frame the decision of how to weight the factors as an asset allocation problem. The objective is to own the portfolio of factors weighted to produce the highest Sharpe ratio. In this context, the uncertainty of future factor success is mitigated by taking advantage of the power of diversification defined by the historical factor returns. But that doesn't tell us how many factors to include in the portfolio. There are 45 factors in our database (described in Exhibit 15.1). Should all be used? Should we add to this list? While more factors could improve the Sharpe ratio by reducing risk, a diversified portfolio of many factors would likely produce lower returns than a concentrated portfolio of good factors.

Factor Competition

There is another consideration that suggests keeping the number of factors (assets) at a fixed small number. The goal of our approach is to provide a systematic framework that removes failed strategies from the playing field until they prove worthy, while providing an opportunity for new strategies to join the team. If we have a large pool of factors, that should be good enough to use for stock selection. And if we use a formal objective every month to decide which factors will be “on the team,” then we can have a systematic approach to weeding out poor “players” and allowing fresh talent to get into the game. The Sharpe ratio makes sense to use as the objective function in this process partly ...

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