Using the Treynor Black Model in Active Portfolio Management

6935 Words Mar 22nd, 2013 28 Pages
Treynor-Black Model

Using the Treynor-Black Model in Active Portfolio Management

Aruna Eluri, David S. Price, Kelly Walker

Course Project for IE590 Financial Engineering Purdue University, West Lafayette, IN 47907-2023 August 1, 2011

Abstract In 1973, Jack Treynor and Fischer Black published a mathematical model for security selection called the Treynor-Black model. The model finds the optimum portfolio to hold in the situation where an investor considers that most securities are priced effectively, but believes he has information that can be used to predict an abnormal performance of a few of them. The theory behind the model is presented, along with numerical examples to highlight specific realistic investment scenarios and how the
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By blending a portfolio of these assets with an index fund, the investment manager can produce a portfolio that can outperform the benchmark while also keeping risk at a relatively low level. [1] 2 2.1 Theory Assumptions

In using the Treynor-Black model, the following assumptions are made. [11] 1. Analysts have a limited ability to find a select number of undervalued securities while the rest are assumed to be fairly priced (i.e. the security markets are nearly efficient). 2. There is a high degree of co-movement among security prices. 3. The “independent” returns of different securities are almost, but not quite, statistically independent. 4. The costs of buying and selling are ignored in order to treat the portfolio problem as a single period problem. 5. Individual Portfolio managers can estimate the future performance of certain securities that is not reflected in the current price or projected market return of the asset.

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Treynor-Black Model 6. Individual Portfolio managers can estimate the expected risk and return parameters for a broad market (passively managed) portfolio. 7. The quantitative performance measure for a single asset is alpha, which is determined in a subjective manner. 8. All returns are
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