Investments, tenth edition

   A Model for the Estimation of Potential Fees 

 The value of market timing was derived from the value of an equivalent number of call 

options that mimic the return to the timer’s portfolio. Thus, we were able to derive an 

unambiguous market value to timing ability, that is, we could price the implicit call in the 

timer’s services. We cannot get quite that far with valuation of active portfolio manage-

ment, but we can do the next best thing, namely, we can calculate what a representative 

investor would pay for such services. 

 Kane, Marcus, and Trippi  

12

   derive an annuitized value of portfolio performance mea-

sured as a percentage of funds under management. The percentage fee,  f,  that investors 

would be willing to pay for active services can be related to the difference between the 

square of the portfolio Sharpe ratio and that of the passive portfolio as 

 

   f

5 (S

P

2

2 S

M

2

)/2A 

 (27.16)   

 where   A  is the coefficient of the investor’s risk aversion. 

 The source of the power of the active portfolio is the additive value of the squared    infor-

mation ratios       

¢

a

i

s(e

i

)

≤  and precision of individual analysts. Recall the expression for the 

square of the Sharpe ratio of the optimized risky portfolio:

   S

P

2

5 S

M

2

1 a

n

i

51

B

a

i

s(e

i

)

R

2

  

 Therefore,

 

   f

5

1

2A a

n

i

51

B

a

i

s(e

i

)

R

2

 

 (27.17)   

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7/31/13   7:25 PM

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  C H A P T E R  

2 7

  The Theory of Active Portfolio Management

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 Thus, the fee that can be charged,  f,  depends on three factors: (1) the coefficient of risk 

aversion, (2) the distribution of the squared information ratio in the universe of securities, 

and (3) the precision of the security analysts. Notice that this fee is in excess of what an 

index fund would charge. If an index fund charges about 20 basis points, the active manager 

could charge incremental fees above that level by the percentage given in Equation 27.17.