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]

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]

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]

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]

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]

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]

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]

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.

 

[jIMOh]

Bumping this with a question.

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

My 401k IRR is -29.6%
According to my 401k provider my loss was twice that (-58.8%).

**edit** this 401k transferred custodians from Vanguard (old employer) to current employer (self maintained plan with institutional funds)- could this be causing the issue?

Thoughts?

 

[Alan]

Bumping this with a question.

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

My 401k IRR is -29.6%
According to my 401k provider my loss was twice that (-58.8%).

**edit** this 401k transferred custodians from Vanguard (old employer) to current employer (self maintained plan with institutional funds)- could this be causing the issue?

Thoughts?

I think your formula is wrong. I just tried your formula on my 401k data for the year and compared it with my 401k website and also my own IRR calculation (using the Excel function).

Using your calculation I get a number wildly different from mine.

Am I using your formula wrong?

Starting value = $373,467, Ending value = $287,890.
Total deposits = $25,383

your calculation gives 20% while website gives -29%

 

[FIREd]

Is your 401K provider quoting you an IRR?

As I understand it, the XIRR formula is based on cash flow, i.e. how much went into / out of the account and when did that transaction occur. XIRR calculations give you an annualized rate of return, so your account has to be opened at least 1 year for your results to be accurate.

So my guess is, if your transferred your 401K from one institution to another during the last 12 months, then the IRR quoted by the new institution is probably meaningless because they have less than 1 year worth of cash flow data to work with.

 

[jIMOh]

I think your formula is wrong. I just tried your formula on my 401k data for the year and compared it with my 401k website and also my own IRR calculation (using the Excel function).

Using your calculation I get a number wildly different from mine.

Am I using your formula wrong?

Starting value = $373,467, Ending value = $287,890.
Total deposits = $25,383

your calculation gives 20% while website gives -29%

Yeah I think my forumula is wrong too.

starting value 41202
ending value 33226
deposits 10741
I have the equation as [33226/ (41202+10741)]-1= -36.03%

or
starting value 167,685
ending value 120,496
desposits 27720

Which is [120496/ (167685+27720]-1= -36.29%

Do both equations look accurate now?

 

[Free To Canoe]

Here are some handy calculations and approximations that make sense to me.....

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

ExHermit

Thanks ExHermit,

I do the same except I just use G/S for the ROI.

Yours is better, of course.

Free

 

[Alan]

Yeah I think my forumula is wrong too.

starting value 41202
ending value 33226
deposits 10741
I have the equation as [33226/ (41202+10741)]-1= -36.03%

or
starting value 167,685
ending value 120,496
desposits 27720

Which is [120496/ (167685+27720]-1= -36.29%

Do both equations look accurate now?

I now get the same as you using your calculations but I think it is wrong.

I used the Excel IRR function with the 1st set of figures, assuming the $10741 deposit goes in 12 equal payments of $895 and I get -50.16%.

When I use my simple calculation I get -50.17%.

My simple calculation is as follows:

Gain = ending balance - starting balance - deposits
Avg balance = start +(end-start)/2
Return = Gain/Avg balance

Gain = 33266 - 41202 - 10741 = -18677
Avg = 41202 + (33266 - 41202)/2 = 37234
Return = -18677/37234 = -50.16%

 

[Frugality_of_Apathy]

Yeah I think my forumula is wrong too.

There is definitely something wrong with your formula.
If your starting value was 100,000 and you deposited 20,000 and at the end of the year you had 124,000 (matching inflation so no loss)

Your formula gives a -32% yield.

If you want one years return on investment and had a constant investment amount That number is simple enough to calculate. First of all to get how much you made vs. how much you should have made you need to have your ending value divided by what the ending value would have been with only inflationary growth.

Here's what you need (annual rate of inflation)/12=r This will be your expected monthly inflation rate. Normally annual inflation is 3% or 0.03.

Then you need to break up how much money was added assuming you added an equal amount each month (deposits)/12=D This is your monthly deposits.

S= starting balance

E= ending balance

IRR=investment rate of return

So now here's the equation:

IRR= E/(S*(1+r)^12+D((1+r^12)-1)/r)

To get IRR as a percentage subtract 1 and multiply by 100.

For the numbers you gave:starting value 41202
ending value 33226
deposits 10741

IRR =-37%

Alan: for your numbers

Starting value = $373,467, Ending value = $287,890.
Total deposits = $25,383

your calculation gives 20% while website gives -29%

I get -29.87% looks like the website is rounding up to make your returns look a little less terrible.

 

[Alan]

Alan: for your numbers

Starting value = $373,467, Ending value = $287,890.
Total deposits = $25,383

your calculation gives 20% while website gives -29%

I get -29.87% looks like the website is rounding up to make your returns look a little less terrible.

The Excel IRR calculation gives -33.44% for those figures, and my simple calculation gives -33.56%.

But I agree that your formula giving -29% taking into account inflation looks pretty good to me.

 

[Frugality_of_Apathy]

The Excel IRR calculation gives -33.44% for those figures, and my simple calculation gives -33.56%.

But I agree that your formula giving -29% taking into account inflation looks pretty good to me.

Yeah I have to use an 8.42% inflation to get your numbers.

I'm wondering how you are putting in your values for excels IRR. When I use your numbers in excel I get -23%

Why are you dividing your gain by the average (which is much easier to calculate as (33266 + 41202)/2= 37234 BTW) instead of the final value in your simple equation?

 

[jIMOh]

I am not using IRR within xcel.
I am trying to aproximate my IRR year over year, and also compare my IRR with the returns of the funds.
I will also soon do some 3 yr and 5 yr averaging once I have enough data.

I have seen the formula mentioned above

Gain = ending balance - starting balance - deposits
Avg balance = start +(end-start)/2
Return = Gain/Avg balance

but it was different than this (something like numerator is current value+1/2 deposits and denominator was previous balance-1/2 deposits).

In this equation (also mentioned above), what is r? INFLATION, just caught that. If I assume no inflation (because I don't measure that right now), is that 0 or 1? 1 is my SWAG. I need to take inflation out of this so I can compare the returns to the mutual funds actual return numbers.

IRR= E/(S*(1+r)^12+D((1+r^12)-1)/r)