Computing Returns on a fund

FuturesTrader71

FuturesTrader71

Hi guys,

I'm running a small fund of investments and doing well. I am computing the return of the fund based on the initial balance at the beginning of the measuring period (say Jan 1, 2006).

Let's say the fund is returning 16% so far this year. A client wants to add funds to the fund. I'm a bit uncertain as to how to integrate that new amount without making the fund look like its performance is deteriorating.

For example, the return is 160k on 1MM so far. The client adds 500k. I don't want to report 180k on 1.5MM at the end of the following month after the deposit.

I know this is a novice question, but I haven't been able to find a discussion on this elsewhere.

Thanks.
 
Quote from FuturesTrader71:

Hi guys,

I'm running a small fund of investments and doing well. I am computing the return of the fund based on the initial balance at the beginning of the measuring period (say Jan 1, 2006).

Let's say the fund is returning 16% so far this year. A client wants to add funds to the fund. I'm a bit uncertain as to how to integrate that new amount without making the fund look like its performance is deteriorating.

For example, the return is 160k on 1MM so far. The client adds 500k. I don't want to report 180k on 1.5MM at the end of the following month after the deposit.

I know this is a novice question, but I haven't been able to find a discussion on this elsewhere.

Thanks.
More...

Like a mutual fund, convert everyone's interest in the group to a unit asset value (UAV). The return will be the percentage change of the UAV regardless of how many shares are outstanding or who owns them.
 
You can also use an NPV calculation. You got Starting capital, interim cash flows and future value. The IRR is your rate of return.
 
Hi FT71,
The trick here is that you need to track the HWM for each invesment independently. This is why most hedge funds have a monthly "dealing window", as opposed to say daily.

The way funds and fund administrators solve this porblem is by treating each new investment in a given month as a seperate "share class". Then you calculate an NAV independently for each share class, track NAV, calculate fees etc.

Wait until you've got multiple investors and you need to start explaining tracking error - then the fun really begins.

Good luck.
 
FT71, in this particular case, what you want is to follow the standard developed by the CFA Institute, a geometric (mean) return. Feel free to google that. The basic idea is fairly intuitive: whenever there is a significant incoming or outgoing cash flow (deposit or withdrawal), you compute and record performance for the period since the last cash flow (possibly since inception), then reset your beginning / base NAV, going forward. Then you link those periodic returns geometrically, using the multiplication operator (as opposed to arithmetically, with the addition operator). That's really all there's to it, for this purpose.

An example using some of your numbers and dates:

Jan. 1, 2006 fund inception - initial deposit $1,000,000
May 4 NAV of the fund $1,160,000
(say) May 5 - additional deposit $500,000
May 31 NAV of the fund $1,680,000

Then we have:

Period 1: 1/1/06 through 5/4/06
Beginning NAV = 1,000,000
Ending NAV = 1,160,000
R1 (return for period 1) = 16.00%, of course.

Period 2: 5/5/06 through (e.g.) 5/31/06
Beg. NAV = 1,660,000
Ending NAV = 1,680,000
R2 = (1,680,000 - 1,660,000) / 1,660,000 = 1.20%.

Combined Periods 1 and 2: 1/1/06 through (e.g.) 5/31/06
Cumulative Return = (1.1600 x 1.0120) - 1 = 1.1740 - 1 = 0.1740 = 17.40%.

If you wanted to compute annualized return since inception, as of May 31st:
1.1740 ^ (12 / 5) - 1 = 1.1740 ^ 2.4 - 1 = 1.4695 - 1 = 0.4695 = 46.95%.

Or, slightly more precisely, using each month's actual day count instead of months:
1.1740 ^ (365 / (31+28+31+30+31)) - 1 = 1.1740 ^ 2.4172 - 1 = 47.36%.

We can see that the geometric (mean) return algorithm for performance measurement has a desirable characteristic of not being affected either way by any deposits into or withdrawals out of the fund. In other words, it is designed to measure the fund manager's performance, independent of both 1) magnitude and 2) timing of external, client-driven cash inflows or outflows, if any.
 
Quote from late apex:


An example using some of your numbers and dates:

Jan. 1, 2006 fund inception - initial deposit $1,000,000
May 4 NAV of the fund $1,160,000
(say) May 5 - additional deposit $500,000
May 31 NAV of the fund $1,680,000

Then we have:

Period 1: 1/1/06 through 5/4/06
Beginning NAV = 1,000,000
Ending NAV = 1,160,000
R1 (return for period 1) = 16.00%, of course.

Period 2: 5/5/06 through (e.g.) 5/31/06
Beg. NAV = 1,660,000
Ending NAV = 1,680,000
R2 = (1,680,000 - 1,660,000) / 1,660,000 = 1.20%.

Combined Periods 1 and 2: 1/1/06 through (e.g.) 5/31/06
Cumulative Return = (1.1600 x 1.0120) - 1 = 1.1740 - 1 = 0.1740 = 17.40%.

If you wanted to compute annualized return since inception, as of May 31st:
1.1740 ^ (12 / 5) - 1 = 1.1740 ^ 2.4 - 1 = 1.4695 - 1 = 0.4695 = 46.95%.

Or, slightly more precisely, using each month's actual day count instead of months:
1.1740 ^ (365 / (31+28+31+30+31)) - 1 = 1.1740 ^ 2.4172 - 1 = 47.36%.
More...

what if my numbers were as follows.

Jan. 1, 2006 fund inception - initial deposit $1,000,000
(say) March 13 - additional deposit $160,000
May 4 NAV of the fund $1,160,000
(say) May 5 - additional deposit $500,000
May 31 NAV of the fund $1,680,000

if I left the funds in cash and never invested, can I still claim a the same results you posted?
 
You've got an extra $20K at the end there, so I think you meant $1,660,000 for May 31 NAV. If so (and also assuming that the NAV on March 12 was still unchanged from Jan. 1 at $1M), then no, you couldn't make such a claim. Well, you could, but you'd be doing Enron math...

In your example, there was a 0% return in each of the 3 consecutive sub-periods, defined by the timing of external cash flows: Jan. 1 - Mar. 12, Mar. 13 - May 4, May 5 - May 31. Linking a number of 0 returns, by any method, will still produce 0% cumulative return since inception.
 
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