Treynor–Black model

In finance the Treynor–Black model is a mathematical model for security selection published by Fischer Black and Jack Treynor in 1973. The model assumes an investor who considers that most securities are priced efficiently, but who believes they have information that can be used to predict the abnormal performance (Alpha) of a few of them; the model finds the optimum portfolio to hold under such conditions.

In essence the optimal portfolio consists of two parts: a passively invested index fund containing all securities in proportion to their market value and an 'active portfolio' containing the securities for which the investor has made a prediction about alpha. In the active portfolio the weight of each stock is proportional to the alpha value divided by the variance of the residual risk.

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