DYNAMIC FEATURES OF THE TREYNOR–BLACK MODEL

Sergey Kurochkin

The Treynor–Black (TB) model seems to be the first active portfolio managenent model to give the direct answer to the problem of how a portfolio manager should incorporate analysts’ estimates in her/his portfolio structure. Concerning the assets’ returns probabilities distributions W. Sharpe Diagonal Model was taken here as an assumption. In this article I analyze the qualitative dynamics of the stock market under the dynamic version of the TB model, assuming all the investors apply the TB model to their portfolios. A similar assumption is made in CAPM, where market stability and pricing relations are deduced supposing all investors have equal access to information and use Modern Portfolio Theory in their portfolio decisions. I also show, how one should recalculate analysts’ target prices to alphas in TB model. The study of the related dynamic system reveals that the TB model produces stable pricing only for the big companies: about 10% market capitalization and more. These findings are then compared to the empirical data on market/target (the latter according to analysts’ consensus forecasts) prices for the Russian Blue Chips. It turns out that actual price dynamics usually shows steady gaps between target and market price while the model price should increasingly oscillate around the target. The likely interpretation is: the market does not trust analysts’ forecasts.