Rates of return calculation

[jIMOh]

I am working on 2007 IRR.

The equation I have (from other forums, similar to this) is

([starting value-.5*deposits]/[ending value+.5*desposits])-1

is this the formula you use?

[LOL!]

You gotta use the XIRR() function of excel.
XIRR stuff

[jIMOh]

Originally Posted by LOL!

You gotta use the XIRR() function of excel.
XIRR stuff

my function wizard does not have XIRR

running excel 2003.

the link does not show the math behind the calculation, can you display it here? thx

[LOL!]

I don't know the math. I'm sure you can find out how to download/install the XIRR() function with a little typing

[audreyh1]

For ROI (that's not the same as IRR, but it's what I use when looking at my YTD performance), Quicken does the calculation like this:

[Ending Value + all withdrawals]/[Starting Value + all deposits] - 1

This is a somewhat conservative approach, as if you made some deposits late in the year, the remainder of the portfolio would have supplied most of the return (assuming a linearly positive year), but it's good enough for me!

Audrey

[SecondCor521]

Originally Posted by jIMOh

my function wizard does not have XIRR

running excel 2003.

the link does not show the math behind the calculation, can you display it here? thx

I'm pretty sure the math for XIRR is not a simple equation. I believe Excel starts with a guess (of 10%, unless you give it a different guess) and tweaks it slightly up or down until it gets the correct answer.

2Cor521

[Rustic23]

From Microsoft:
Excel uses an iterative technique for calculating XIRR. Using a changing rate (starting with guess), XIRR cycles through the calculation until the result is accurate within 0.000001 percent. If XIRR can't find a result that works after 100 tries, the #NUM! error value is returned. The rate is changed until:
where:
di = the ith, or last, payment date.
d1 = the 0th payment date.
Pi = the ith, or last, payment.

Good Luck! I use an HP calculator.

[podey]

Originally Posted by audreyh1

For ROI (that's not the same as IRR, but it's what I use when looking at my YTD performance), Quicken does the calculation like this:

[Ending Value + all withdrawals]/[Starting Value + all deposits] - 1

This is a somewhat conservative approach, as if you made some deposits late in the year, the remainder of the portfolio would have supplied most of the return (assuming a linearly positive year), but it's good enough for me!

Audrey

Audrey - Is it ending value PLUS or MINUS all withdrawals. I have been staring at this and its starting to go fuzzy. In other words, does my ending balance go up or down after I factor in withdrawals?

[audreyh1]

PLUS (ending balance goes up).

You have to give yourself credit for withdrawals, otherwise your ROI is artificially lowered.

Audrey

[ExHermit]

Here are some handy calculations and approximations that make sense to me. Maybe someone else will find them useful. Or maybe not. DW claims that I do everything backward.

S = Starting portfolio value.
E = Ending portfolio value
F = net cash Flow = deposits - withdrawals

F must include all money moving in or out of the portfolio. I need to track this anyway, since this is the Withdrawal part of Safe Withdrawal Rate.

G = Gain = E-S-F (Will be negative in the case of a loss.)

If you made all deposits or withdrawals at the end of the period, your percentage gain or loss, also called Return On Investment (ROI), would be G / S. If you made all deposits or withdrawals at the start of the period ROI would be G / (S+F). If your deposits and/or withdrawals are made evenly over the period, a reasonable approximation is

ROI = G / (S+(F/2)).

To obtain an annualized rate of return (IRR) from ROI the formula is

IRR = ((1+ROI)^(d/365)) - 1

Where d = number of days between the start date and the end date and "^" is used as in spread sheet functions to mean "to the power of".

ExHermit

[saluki9]

The most common method of performance calculation used in the investment industry is the Modified Dietz Method

Modified-Dietz Method

r(T) = {MV(T)-MV(0)-sum[C(t)]}/{MV(0)+sum[w(t)*C(t)]}

r(T)... Modified Dietz Return
MV(T)... Ending market value
MV(0)... Beginning market value
C(t)... Net contribution occurring on day t
w(t)... weight of the net contribution on day t...

w(i) = {T - t} / T

T... Total number of days
t... day the net contribution occurs
The Modified Dietz method assumes that net contributions are invested at the end of the respective day they occur.

[Alan]

Originally Posted by ExHermit

Here are some handy calculations and approximations that make sense to me. Maybe someone else will find them useful. Or maybe not. DW claims that I do everything backward.

S = Starting portfolio value.
E = Ending portfolio value
F = net cash Flow = deposits - withdrawals

F must include all money moving in or out of the portfolio. I need to track this anyway, since this is the Withdrawal part of Safe Withdrawal Rate.

G = Gain = E-S-F (Will be negative in the case of a loss.)

If you made all deposits or withdrawals at the end of the period, your percentage gain or loss, also called Return On Investment (ROI), would be G / S. If you made all deposits or withdrawals at the start of the period ROI would be G / (S+F). If your deposits and/or withdrawals are made evenly over the period, a reasonable approximation is

ROI = G / (S+(F/2)).

To obtain an annualized rate of return (IRR) from ROI the formula is

IRR = ((1+ROI)^(d/365)) - 1

Where d = number of days between the start date and the end date and "^" is used as in spread sheet functions to mean "to the power of".

ExHermit

This is similar to what I use except I estimate avg monthly balance.
G = Gain = E-S-F (Will be negative in the case of a loss.)
AvgBal = S+(E-F)/2

ROI = G/AvgBal

[ExHermit]

Originally Posted by saluki9

The most common method of performance calculation used in the investment industry is the Modified Dietz Method

Modified-Dietz Method

r(T) = {MV(T)-MV(0)-sum[C(t)]}/{MV(0)+sum[w(t)*C(t)]}

r(T)... Modified Dietz Return
MV(T)... Ending market value
MV(0)... Beginning market value
C(t)... Net contribution occurring on day t
w(t)... weight of the net contribution on day t...

w(i) = {T - t} / T

T... Total number of days
t... day the net contribution occurs
The Modified Dietz method assumes that net contributions are invested at the end of the respective day they occur.

We are on the same page here. If it is assumed that all deposits and withdrawals are made in one lump sum in the middle of the period then the formula I posted is numerically identical to the Modified Dietz Return formula you posted

Clearly, the Modified Dietz Return is more accurate if this is not a reasonable assumption. The more the cash flow is skewed toward one end or the other of the period, the more error my simplifying assumption introduces.

Even the Modified Dietz Return is slightly off, in that it does not quite account correctly for compounding effects. I don't think that there is a closed function that is 100% accurate, hence the use of XIRR iterative numerical approximation.

[ExHermit]

Originally Posted by Alan

This is similar to what I use except I estimate avg monthly balance.
G = Gain = E-S-F (Will be negative in the case of a loss.)
AvgBal = S+(E-F)/2

ROI = G/AvgBal

I'm not sure that I follow your computations, Alan.

Let's take an example:

Starting value = S = $100
Ending value = E = $125
$10 was deposited half way through the period, F =10$

You, I and saluki9 all agree on the numerator, G = E - S - F = $15

Using your formula, the denominator would be
AvgBal = S+(E-F)/2 = 100+(125-10)/2 = 100+(115)/2 = 100+57.5 =157.5

and ROI would be G/AvgBal = 15/157.5 = 9.52%

I would use a denominator of S+(F/2) = 100+(10/2) = 105

giving a ROI of 15/105 = 14.29%

We have made $15, having put in a total of $110, $100 at the start plus $10 halfway through. I would think that the rate of return would be at least 15/110 = 13.64%. Allowing some credit for the fact the the $10 deposit was only earning returns for half the period, 14.29% seems to me more reasonable than 9.25% as an estimated rate of return.

Am I missing something?

[kaneohe]

Originally Posted by jIMOh

my function wizard does not have XIRR

running excel 2003.

the link does not show the math behind the calculation, can you display it here? thx

Perhaps your software has the IRR function?
ExcelTips: Using the IRR Function

I guess you'd set up the time scale as months and the IRR would be the
monthly return so probably not as accurate as XIRR. I'm assuming the annual return would be the monthly return compounded for 12 mos and you could set up the spreadsheet to calculate that.