Return rate

**ght02135** Mon Jun 11, 2007 10:21 am

Return rate
Blast and other fellow members,

I have a question about return rate calculation method for a fund with variable amount of principal.

For example, the fund started the year with a principal of $1 million, and the principal rose steadily because more investors bought in at a rate of, say, $20,000 per month. At the end of the 6th month, the principal was $1.12 million. In the 7th month, there was a major market correction so upon panic many investors redeemed their shares, and therefore the principal fell to $0.8 million. But since then the market recovered gradually and the principal pool grew again to $1.1 million by the end of the year. Note the numbers are all principal, not the size of the fund. In this case what is the right base number for return rate calculation? Thanks.

**blast_investor** Mon Jun 11, 2007 5:34 pm

Re: Return rate
ght02135 wrote: Blast and other fellow members,

I have a question about return rate calculation method for a fund with variable amount of principal.

Hi ght02135,

In mutual fund world or other similar fund world, usually funds calculated return based on NAV performance without consideration of tax. This is pre-tax return.

In other word, if an investor put in $5000 in a fund, no withdraw or increase, how much money the investor will get in pre-tax at time of checking? this is NAV.

Suppose, after 1 year, the investor get $7500 if he/she withdraw, $5000 -> $7500 is 50% return.

How much fund amount of dollar in and out is irrelevant. What matters is the NAV per unit performance.

Different fund, particularly hedge fund or other non-mutual fund may have different timeframe in calculating NAV, but the concept is same. Mutual fund NAV is calculated daily.

**clz2992** Tue Jun 12, 2007 1:45 pm

Re: Return rate
Hi ght02135,
ght02135 wrote: Blast and other fellow members,

I have a question about return rate calculation method for a fund with variable amount of principal.

For example, the fund started the year with a principal of $1 million, and the principal rose steadily because more investors bought in at a rate of, say, $20,000 per month. At the end of the 6th month, the principal was $1.12 million. In the 7th month, there was a major market correction so upon panic many investors redeemed their shares, and therefore the principal fell to $0.8 million. But since then the market recovered gradually and the principal pool grew again to $1.1 million by the end of the year. Note the numbers are all principal, not the size of the fund. In this case what is the right base number for return rate calculation? Thanks.

A fund's rate of return is usually time-weighted rate of return. Basically, the rate of return is calculated before any major principal contribution/distribution. For your case, the rate of return of each month for the first 6 month is calculated as

R_i = (EndValue-BeginValue+Div_received)/BeginValue i=1,...,6

where BeginValue is the value right after receiving/subtracting the monthly contribution/distribution and EndValue is the vlaue right before receiving/subtracting the monthly contribution/distribution.

if the value increase of principal is totally due to the contribution, you will have R_i=0 for i=1,...,6

R_12=( 1.1-0.8 )/0.8=37.5% for the months from 7 to 12 assuming no further major contribution and distribution, and 0.8 is the value right after the distribution, not because of the correction, ie, the distribution is 1.12-0.8=0.32

The total rate of return for the year is

R=(1+R_1)*(1+R_2)*...*(1+R_6)*(1+R_12)-1=37.5% per annum

If the portfolio's contribution/distribution is more frequent than once a month, you need to compute rate of return for each period more frequently and multiple them all together to get rate of return of the year.

If you have more than one year's data, you can annualize the total rate of return to get average annual rate of return using geometric average.

**clz2992** Tue Jun 12, 2007 2:21 pm

Re: Return rate
blast_investor wrote:

How much fund amount of dollar in and out is irrelevant. What matters is the NAV per unit performance.

Different fund, particularly hedge fund or other non-mutual fund may have different timeframe in calculating NAV, but the concept is same. Mutual fund NAV is calculated daily.

NAV per unit performance calculation is doable only for those funds like mutual funds, which have dividable unit measurement. For a portfolio or hedge fund, NAV is changeable with contribution/distribution, to eliminate any distortion from contribution and distribution, time-weighted rate of return is used.

**ght02135** Tue Jun 12, 2007 2:58 pm

Thanks guys. clz2992, to clarify, distribution in your term would include redemption, is it correct?

**clz2992** Tue Jun 12, 2007 3:08 pm

ght02135 wrote: Thanks guys. clz2992, to clarify, distribution in your term would include redemption, is it correct?
I think so. Any time cash inflows/outflows occur (except div, interest, etc from investment), you should calculate the rate of return for that period.