Question

Davita Spencer is a manager at Half Dome Asset Management. She can generate an alpha of 1.95 % per year on up to $ 144 million of assets. After that her skills are spread too​ thin, so she cannot add value and her alpha is zero on any additional money under management. Half Dome charges a fee of 1.24 % per year on the total amount of money under management​ (at the beginning of each​ year). Assume that there are always investors looking for positive alpha and no investor would invest in a fund with a negative alpha. In​ equilibrium, that​ is, when no investor either takes out money or wishes to invest new​ money,

a. What alpha do investors in​ Davita's fund expect to​ receive?

b. How much money will Davita have under​ management?

c. How much money will Half Dome generate in fee​ income?

Answer 1

a. At equilibrium, the alpha that investors in Davita's Fund would expect to receive is at least the amount of management fees that they would be paying i.e. 1.24% per year.

b. The amount of money that Davita would have under management can be calculated as below:

Amount upto which Davita generates an alpha of 1.95% = $ 144 million

Amount of alpha generated = $ 144 million x 1.95% = $ 2.81 million

Management fees charged by Half Dome = 1.24%

Thus, amount that Davita have under Management = $ 2.81 million / 1.24% = $ 226.45 million

c. Amount that Half Dome would generate as fee income = $ 226.45 million x 1.24% = $ 2.81 million.