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Article

ДИНАМИЧЕСКИЕ СВОЙСТВА МОДЕЛИ ТРЕЙНОРА–БЛЭКА

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.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.