Anatomy of a Hedge Fund

Last year, John Paulson, a hedge fund manager, made $5 billion dollars. There was a great deal of damage control on this news, including by Business Insider, explaining that $4 billion of that amount was gains from his own investment in his fund.

That lead me to the following analysis:

A typical hedge fund manager gets a 20%/2% to run the fund, which means 20% of the annual profit, and 2% of the value of the fund.

Assume no tax dodges, so that the investors (including the manager) pay 15% Capital Gains tax on the annual gains (directly from the fund).

Being confident in his own abilities, the manager invests his after-tax income in the fund.

At the start of a year, the investors have $M_old in the fund, the manager has $m_old, and the fund gains r%.

Capital Gains tax on the investor money is $0.15*r*M_old, 20% of the after-tax gain goes to the manager, and remainder gets rolled into the investor funds. The manager then gets 2% of the total.

For the manager, his share of the fund increases by $r*m_old, of which $0.15*r*m is Capital Gains tax. He also gains the 20% of the after-tax investor gains, and 2% of the fund, on which he pays a 35% tax rate.

Thus, we have

M_new = (0.98)*(1+(0.8)*(0.85)*r)*M_old

m_new = (1+(0.85)*r)*m_old+(0.2)*(0.85)*r*M_old+(0.65)*(0.02)*(1+(0.8)*(0.85)*r)*M_old

What is the result?

If the fund gains 20% per year, it only takes 16 years for more than half of the money in the fund to belong to the manager. At 10%, it takes 23 years.