Calculating return

by NOSMO_KING58_@_YAHOO.COM (NOSMO KING) on 2006-06-03 14:05:56

What is the method for calculating annual return for an investment where
additional contributions are made throughout the year ? For example, assume I
have an account with a starting balance of $10,000. On the first of each
month, I contribute $1000. At the end of the year, the account is worth
$25,000. I would think the return would be 13.6%, calculated as $3000
(ending balance - starting balance - contributions) divided by $22,000
(starting balance + contributions).

If I had the same values, except I made contributions on the last day of the
month, would the return be the same ? It seems that last $1000 contribution
made on December 31 would not have time to affect the return and would only
skew the calculation. If that last contribution was not made, the return
would have been 14.3% ($3000/$21,000).

Calculating return

by JOETAXPAYER on 2006-06-03 15:33:07

Nosmo King wrote:


My 'back of envelope' calculation says the rate of return (to be clear,
I understood the you started on 1/1 with 10K, but added 1K each month,
including 1/1, 2/1, etc) is 18.18%.
Here's the math;
You start with 11K really on 1/1, and have deposited a total of $22K, so
the average amount invested is (11+22)/2 = 16.5K. The return of 3/16.5
is 18.18%.

I then ran a spreadsheet where I used 12 seperate calculations and added
them up. I used successive approximation (that is I lowered or raised
the rate) until the sum of returns was exactly $3000. Result was 18.17%.
I trust the difference was due to the different number of days in given
months.

Using end of month jumps to 19.3% return.

BTW, I used balance on 1/1/06 to 1/1/07, so even the 12/31 deposit has
about 50 cents interest.

JOE

Calculating return

by RICH CARREIRO on 2006-06-03 15:52:48

Nosmo_King58_@_yahoo.com (Nosmo King) writes:


The most proper way would be the Internal Rate of Return (IRR) method.
To calculate the IRR, you compute the net present value of the cash
flows (taking the starting balance and all deposits as positive cash
flows and the ending balance and all withdrawals as negative cash
flows) and find the discount rate that makes the NPV identically zero.
That rate is your rate of return. Many spreadsheets and financial
calculators have this function. In MS Excel, read the documentation
for the IRR() and XIRR() functions.

An approximation to IRR would be to divide the investment gain (or loss)
by the average amount invested. The gain over the period is simply:
gain = end balance - start balance + withdrawals - deposits

The average amount invested weights the contributions by how long
they've been in the account and withdrawals by how long they've been
out of the account. Let c[i] be the amount of the i-th contribution
(c[i] will be negative for a withdrawal) and let t[i] be the number
of months from the *start* of the year that the contribution was made,
and the average amount invested is:
avg amt invested = start balance + Sum (c[i] * t[i]/12)

Once you have that, the approx rate of return is gain divided
by average amount invested.

But if you're going to go through that much effort, you may as
well use the proper IRR algorithm, because by the time you've
set up the c[i] and t[i], you have everything you need to plug
into the IRR algorithm.

There is one gotcha with IRR -- if the simple "running balance" formed
by starting with the initial balance and adding/subtracting the
contributions and withdrawals ever switches sign, the IRR calculation
can give multiple return values. Those of you who remember more about
the theory of polymonials than I do can explain why :-)

--
Rich Carreiro rlcarr@animato.arlington.ma.us

Calculating return

by RICH CARREIRO on 2006-06-03 16:24:00

Rich Carreiro writes:


Duhhhhh....

Make that:
...let t[i] be the number of months from the *end* of
the year that contribution c[i] was made...

--
Rich Carreiro rlcarr@animato.arlington.ma.us

Calculating return

by GREG HENNESSY on 2006-06-03 17:12:35

On 2006-06-03, Nosmo King wrote:

I opened a spreadsheet, a few minutes of playing around with the
future value function I obtained an average return of 18.0146 percent
for the first one, and 16.982 percent for the second case. I am sure
that there are other values which solve the problem, although those
values may not be realistic (i.e. they may be imaginary).

You underestimate the return because you overestimate the money
available. In January you only have 10K or 10K available in the two
choices that need to earn interest.

I did my calculation assuming monthly compounding, I'm sure there is a
different way to calculate it with continiuous compounding.

Calculating return

by JOHN GUNN on 2006-06-03 20:08:38

Greg Hennessy wrote in
news:slrne83se7.klj.greg.hennessy@localhost.localdomain:


The AIMR is responsible for the standards in this area. It is essentialy
the IRR, but check their information for the autoritative answer.