Investments, tenth edition

   The BL Model as Icing on the TB Cake 

 The Treynor-Black (TB) model is really oriented to individual security analysis. This can 

be seen from the way the active portfolio is constructed. The alpha values assigned to 

securities must be determined relative to the passive portfolio. This portfolio is the one that 

would be held if all alpha values turned out to be zero. Now suppose an investment com-

pany prospectus mandates a portfolio invested 70% in a U.S. universe of large stocks, say, 

the S&P 500, and 30% in a well-defined universe of large European stocks. In that case, 

the macro analysis of the organization would have to be split, and the TB model would 

have to be run as two separate divisions. In each division, security analysts would compile 

values of alpha relative to their own passive portfolio. The product of this organization 

would thus include four portfolios, two passive and two active. This scheme is workable 

only when the portfolios are optimized separately. That is, the parameters (alpha, beta, and 

residual variance) of U.S. securities are estimated relative to the U.S. benchmark, while the 

parameters of European stocks are estimated relative to the European benchmark. Then the 

final portfolio would be constructed as a standard problem in asset allocation. 

 The resulting portfolio could be improved using the BL approach. First, views about the 

relative performance of the U.S. and European markets can be expected to add informa-

tion to the independent macro forecasts for the two economies. For reasons of specializa-

tion, the U.S. and European macro analysts must focus on their respective economies. 

Obviously, when more country or regional portfolios are added to the company’s universe, 

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  The Theory of Active Portfolio Management 

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the need for decentralization becomes more compelling, and the potential of applying the 

BL model to the TB product greater. Moreover, the foreign-stock portfolios will result in 

various positions in local currencies. This is a clear area of international finance and the 

only way to import forecasts from this analysis is with the BL technique.  

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