Investments, tenth edition

 Example  10.3 

Exploiting Alpha 

bound. Similarly, when the residual risk of an asset in the active T-B portfolio is zero, it 

will displace all other assets from that portfolio, and thus the residual risk of the active 

portfolio will be zero and elicit the same extreme portfolio response. 

 When residual risks are nonzero, the T-B procedure produces the optimal risky port-

folio, which is a compromise between seeking alpha and shunning potentially diversifi-

able risk. The APT ignores residual risk altogether, assuming it has been diversified away. 

Obviously, we have no use for the APT in this context. When residual risk can be made 

small through diversification, the T-B model prescribes very aggressive (large) positions 

in mispriced securities that exert great pressure on equilibrium risk premiums to eliminate 

nonzero alpha values. The T-B model does what the APT is meant to do but with more 

flexibility in terms of accommodating the practical limits to diversification. In this sense, 

Treynor and Black anticipated the development of the APT. 

 

   

 Index Risk Premium  5  7  

Index SD  5  20  

Index Sharpe Ratio  5  0.35