Calculating profits for a private fund

Question

I'm running a small private mini-fund with and for a small group of friends. We pool the money and I use it to trade securities on all our behalf.

Profits/losses are realised both from capital gains and from trading.

People may enter the fund at different times and invest any amount.

I am having a very hard time working out the math to answer the following scenario: if we were all to exit right this moment, how should the profits be divvied out equitably (bearing in mind that there are differing investment amounts and people entered at different times).

Take for example this scenario:

Person  Buy In  Amount  X Price  Qty X Bought  |  Current X Price  Current X Total
A       1 Jan   $100    $1.00    100           |  $2.00            $200
B       1 Feb   $200    $0.90    180           |  $2.00            $360
C       1 Mar   $250    $1.10    275           |  $2.00            $550

Current Date: 1 April
Total Buy In: $550
Current Fund Value: $1500 (after capital gains and trading profits)

It records a buy in for three different people in the fund at different times and at different amounts. Total invested was $550, and after three months we find ourselves with $1500 worth of stock X. We want to liquidate everything and divvy out profits.

How do I figure out an equitable profit distribution for each player? Is it even possible with this data?

Answer 1

Thanks for the answer/comments!

The time-based method was something we mooted and something I almost went with.

But just to wrap this up, the method we settled on was this:

Every time there is an entry or exit into the fund, we divvy out any unrealised market profits/losses according to each person's profit share (based on % of the asset purchased at buy-in) JUST BEFORE the entry/exit.

These realised profits are then locked in for those particpants, and then the unrealised profits/loss counter starts at zero, we do a fresh recalculation of shareholding after the entry/exit, and then we start again.

Hope this helps anyone with the same issue!

Answer 2

The total number of shares on April 1st is 100 + 180 + 275 = 555. The price on April 1st is required. The current price is stated as $2, but $2 * 555 = $1110 and the current fund values is stated as $1500. Opting to take the current value as $1500, the price on April 1st can be calculated as $1500/555 = $2.7027.

The amounts invested as number of shares x share price are:

invA = 100*1.0 = $100
invB = 180*0.9 = $162
invC = 275*1.1 = $302.5

(Note these investment amounts do not match the example scenario's investment amounts, presumably because the example numbers are just made up.)

The monthly returns can be calculated:

retFeb = 0.9/1.0 - 1 = -10%
retMar = 1.1/0.9 - 1 = 22.2222%
retApr = (1500/555)/1.1 - 1 = 145.7%

The current values for each investor as invested amount x returns are:

valA = (100*1.0)*(0.9/1)*(1.1/0.9)*((1500/555)/1.1) = $270.27
valB = (180*0.9)*(1.1/0.9)*((1500/555)/1.1) = $486.486
valC = (275*1.1)*((1500/555)/1.1) = $743.243

Checking the total:

valA + valB + valC = $1500

Answer 3

One way I heard of, from a friend who ran a similar fund as yours, is to calculate $days of investment and divide the investment as accordingly.

For example, If I invested 10$ for 10 days and you have invested 20$ for 5 days. At the end of the 10th day my $day = 10*10=100, while your $day=20*5=100. If the investement has grown to 100$, the I should get $100/(100+100)*100=$50, you also should get the same. This I guess is equitable, you could try dividing the corpus with above method. It consideres the amount invested as well as the time invested for.

I think by the above method, you could also handle the inbetween withdrawals.