# Calculating Portfolio Return - my spreadsheet

Hello,

I’ve tried to follow Saul’s explanation on “Calculating Portfolio Returns” in the knowledgebase and used it on my portfolio using monthly snapshots. My version is here in google spreadsheet:

I have changed the amounts here and there to not share everything outright, however the logic should work.

Would anyone check the few formulas whether the approach is correct? Can I say that for these numbers I was +14.59% in 2017, 3.71% in 2018 and 16.87% in first 3 months of 2019?

Note that you can easily make copy of this spreadsheet if you find it useful or want to fix my mistakes.

Thank you,

Tomas

7 Likes

Hi Tomas,

The idea of calculating portfolio returns is to determine how your investment decisions, by themselves, are working out. In order to do this, you need to remove the influence of any external cash flows in or out, as Saul rightly pointed out.

The way this works is having the portfolio balance at the beginning and end of a period. The return, if there is no cash flow event, is simply (End balance / Begin balance) - 1. So, if you have \$110,000 at the end and you started with \$100,000, then the return is 10%.

The cash flow in or out cannot be used in calculating the return, because then it makes a deposit look like an investment return. So that needs to be corrected for. Note, however, that internal cash flows like interest paid or received, dividends received, proceeds from investment sales, and so on are not counted or corrected for. These are part of the portfolio return itself. That is, a dividend is counted as part of the return on a stock, and is therefore not a cash flow added to the portfolio.

I haven’t worked through the math and the correction methodology Saul provided, so I’ll show you what I do and what all professional shops do (e.g. mutual funds).

For any given period, they break down the long period into a bunch of shorter ones, with a border between successive periods whenever a cash flow happens. They then calculate the return over that period, and then add / subtract the cash (external) to have a new cash-flow-adjusted beginning value at the start of the next period. The periods themselves can be any length in time.

For example, if at the end of the first period add \$15,000, you add that to the \$110,000 ending balance (from above) to use this as the starting point for the next period, or \$125,000. Suppose you end with \$135,000 at the end of the next period. That would be an 8% return: (\$135,000 / \$125,000) - 1. If you didn’t add the \$15,000 to create a new starting point, then you’d assume you had a 22.7% return, instead: (\$135,000 / \$110,000) - 1, but a bunch of that came from the cash deposited, so shouldn’t be counted.

``````
**Date    \$\$ Before CF    CF In      CF Out    \$\$ After CF**
2/28/17   \$    ---      \$85,883.97 \$   ---    \$ 85,883.97  <-- you don't have any data earlier, thus CF In
3/31/17   \$ 85,883.97   \$27,000    \$   ---    \$112,883.97
4/30/17   \$112,179.88   \$   ---    \$   ---    \$112,179.88
5/31/17   \$114,196.59   \$   ---    \$   ---    \$114,196.59
6/30/17   \$112,749.98   \$   ---    \$   ---    \$112,749.98
7/31/17   \$116,716.72   \$   ---    \$   ---    \$116,716.72
8/31/17   \$121,033.60   \$   ---    \$   ---    \$121,033.60
9/30/17   \$121,500.33   \$26,000    \$   ---    \$147,500.33
10/31/17   \$150,798.43   \$   ---    \$   ---    \$150,798.43
11/30/17   \$151,475.20   \$15,000    \$  (980)   \$165,495.20
12/31/17   \$168,205.79   \$   ---    \$   ---    \$168,205.79
``````

Now, with that, we can calculate the holding period return (HPR). Each period can be arbitrarily every month, or they can just go between cash flows – the end result will be the same.

The calculation is: (\$\$ Before CF end current month) / (\$\$ After CF end previous month) - 1.

Here are the Holding Period Returns for each month, assuming the cash flow happens at market close on the last day of each month:

``````
**Date    \$\$ before CF    CF In      CF Out    \$\$ after CF    HPR**
2/28/17   \$    ---      \$85,883.97 \$   ---    \$ 85,883.97    N/A
3/31/17   \$ 85,883.97   \$27,000    \$   ---    \$112,883.97   0.00%
4/30/17   \$112,179.88   \$   ---    \$   ---    \$112,179.88  (0.62%)
5/31/17   \$114,196.59   \$   ---    \$   ---    \$114,196.59   1.80%
6/30/17   \$112,749.98   \$   ---    \$   ---    \$112,749.98  (1.27%)
7/31/17   \$116,716.72   \$   ---    \$   ---    \$116,716.72   3.52%
8/31/17   \$121,033.60   \$   ---    \$   ---    \$121,033.60   3.70%
9/30/17   \$121,500.33   \$26,000    \$   ---    \$147,500.33   0.39%
10/31/17   \$150,798.43   \$   ---    \$   ---    \$150,798.43   2.24%
11/30/17   \$151,475.20   \$15,000    \$  (980)   \$165,495.20   0.45%
12/31/17   \$168,205.79   \$   ---    \$   ---    \$168,205.79   1.64%
``````

Those HPRs are the monthly returns correcting for all the cash flows in/out and show what the portfolio itself did each month.

To get the overall return, you add one to each HPR, multiply all those together, then subtract one at the end, a process called chaining. Inside a spreadsheet, use another column for HPR + 1, and then another column of “=PRODUCT(range of locked starting row through ending row) - 1”. If you do that, you get 12.34% at the end of that year, 2017.

``````
**Date    \$\$ before CF    CF In      CF Out    \$\$ after CF    HPR    HPR + 1     TWR**
2/28/17   \$    ---      \$85,883.97 \$   ---    \$ 85,883.97    N/A      N/A       N/A
3/31/17   \$ 85,883.97   \$27,000    \$   ---    \$112,883.97   0.00%   100.00%    0.00%
4/30/17   \$112,179.88   \$   ---    \$   ---    \$112,179.88  (0.62%)   99.38%   (0.62%)
5/31/17   \$114,196.59   \$   ---    \$   ---    \$114,196.59   1.80%   101.80%    1.16%
6/30/17   \$112,749.98   \$   ---    \$   ---    \$112,749.98  (1.27%)   98.73%   (0.12%)
7/31/17   \$116,716.72   \$   ---    \$   ---    \$116,716.72   3.52%   103.52%    3.40%
8/31/17   \$121,033.60   \$   ---    \$   ---    \$121,033.60   3.70%   100.39%    7.22%
9/30/17   \$121,500.33   \$26,000    \$   ---    \$147,500.33   0.39%   100.39%    7.63%
10/31/17   \$150,798.43   \$   ---    \$   ---    \$150,798.43   2.24%   102.24%   10.04%
11/30/17   \$151,475.20   \$15,000    \$  (980)   \$165,495.20   0.45%   100.45%   10.53%
12/31/17   \$168,205.79   \$   ---    \$   ---    \$168,205.79   1.64%   101.64%   12.34%
``````

Doing the same thing for 2018 and 2019, by the end of 2018, you’re at 25.30% and by the end of last month you’re at 30.29%.

That’s total return.

This method generates a Time Weighted Return.

To annualize it, add one, raise to the power of the inverse of the number of years, then subtract one:

``````
CAGR = TWR ^ (1 / years) - 1
``````

For 30.29% over 2.25 years: CAGR = 1.3029^(1/2.25) - 1 = 12.48% on average per year.

I have a whole article laying this methodology out, as well as what you can do if you only have month-end numbers, but made deposits during the month, not just at the end (like the above assumes), here: https://www.fool.com/about/how-to-calculate-investment-retur…

Again, TWR is what mutual funds and investing shops report. You can also compare it directly to S&P 500 returns (or other index returns) to see how well you’re doing against those.

Finally, please note I have not checked the above to what Saul’s calculation would give. I suspect that they would be real close to each other (rounding, more than anything else). Just note that for both TWR and Saul’s method, you only correct for cash flows that move money into or out of the portfolio. All cash flows inside the portfolio itself are part of the overall returns.

Hope that helps.

Cheers,
Jim

46 Likes

Hi Tomas,

Here is a link to a page that Bogleheads puts out that does what Jim is referring to.

If you look at the “Download Location” section they offer a Google Docs version as well as Excel and Calc.

It takes some time to get filled out initially, but after that each month you can easily update it.

HTH,
boomer196

8 Likes

Thank you both! I’ve adjusted my spreadsheet to match what Jim suggested. I also checked bogleheads calculation to cross-reference the results. I am not able to get exact match, but close enough.

Anyone any guess as to what is the difference between these two?

I am not able to get exact match, but close enough.

Anyone any guess as to what is the difference between these two?

Hi Tomas,

Almost certainly cumulative rounding errors.

If you, in Saul’s calculation, for instance, set what is actually a 10.27938% return – to make up a number – in his new correction factor calculation step as 110.3, the correction factor will be slightly different than if you use 110.28 or 110.2794 or 110.27938. Those differences lead to slightly different results that then compound the next time you recalculate the correction factor and the next time and so on. (That is, if I recall correctly one of the steps from reading it this morning.) The two methodologies will produce different numbers that slowly drift apart over time.

Unless you’re managing other people’s money and need to be really precise, I wouldn’t worry too much about that. Pick a method that you understand (especially the math behind it and why it’s done that way) and stick with it. The point isn’t to get the number perfect down to the last decimal place, the point is to see how well you’re doing as a portfolio manager / investor and either method will give you that answer.

Cheers,
Jim

6 Likes

Jim, first - thank you for the very clear explanation of holding period return and deriving annual (and CAGR) from it.

Does it compare favorably (accuracy-wise) to XIRR, of course Excel’s formula for calculating time-weighted annualized return with uneven investments?

FWIW I have been using the venerable (End - additions/2) / (Start + additions/2) method for years at the whole portfolio level. But at the individual investment (or asset class) level that starts to break down, especially when the denominator is a relatively small starting number (ex - 25000 - 15000/2) / (5000 + 15000/2) indicates a 40% return, which is in reality overstated.)

1 Like

Does [TWR] compare favorably (accuracy-wise) to XIRR, of course Excel’s formula for calculating time-weighted annualized return with uneven investments?

Hi FlyingCircus,

Good question. The answer is that XIRR and TWR are two completely different things, answering different questions.

Time-weighted returns answer the question, “How good am I at investing?”

Internal rate of return (the X means uneven cash flows) answers the question, “How well am I doing at reaching my goals?” It tells you the return that the average dollar makes as long as it’s in a portfolio.

XIRR takes all the deposits and withdrawals into account and then calculates the average return that those have generated so that (the negative of*) the ending balance is what is observed. Here, unlike TWR, the timing of the cash flow is important and it changes the XIRR. For TWR, the timing of cash flows is unimportant and moving them around (or changing the amounts) has no effect upon the rate of return.
*As if the final value were withdrawn, so that the math works correctly.

Let me explain with a couple of scenarios and then give the math.

You would use XIRR if you wanted to know the answer to this: I want to have \$1 million in my account by the time I retire at age 65, 20 years from now. I have \$300,000 as of the end of last year and can deposit \$5,000 per year (on the last day of each year for 19 years), with retirement date 12/31/2038. What rate of return do I need to achieve in order to reach that? You use XIRR to answer that, 5.25%.

However, change the deposit date to 6/30 of each year (keeping 19 total \$5,000 deposits), and XIRR changes to 5.22%. That lower number is because each of those deposits had an extra 6 months to contribute to the \$1 million, so each dollar didn’t have to work quite as hard.

If you contribute the same \$95,000, but make it in 4 even deposits at the end of each of the first 4 years, with nothing further contributed, then XIRR becomes 4.89%. Again, that’s because there are more dollars present early and they work longer, so they don’t have to work as hard.

XIRR uses this:

Ending \$\$ = CF1*(1+r)^t1 + CF2*(1+r)^t2 + … + CFn*(1+r)^tn

If you know the ending value, you can solve for r via an iterative process, trying different values until both sides of the equation match. (The reason XIRR uses a negative ending value is because it subtracts ending value from both sides of the equation, leaving zero on the left. IRR is the internal rate of return if total cash flows in and out result in a zero balance.)

Note, there is a single value for return, r.

TWR, on the other hand, uses this:

TWR = (1+r1) * (1 + r2) * … * (1 + rn) - 1

That is the chaining equation I mentioned in passing in my first post on this thread yesterday. Note, that there are different values for the returns, one for each time period.

Unlike IRR/XIRR, where all you need is the beginning value (as if it were a cash flow in at the start), each cash flow in or out, and the ending value, TWR also needs to know the value of the account immediately prior to each cash flow.

Hope that explains it.

I would show the differences between the two using actual numbers and a simple example, but I’ve run out of time this morning. But I can if you or others would like to see that.

Cheers,
Jim

11 Likes

Time-weighted returns answer the question, “How good am I at investing?”

I don’t see it.

Here’s a simple example where this method seems to be telling you that you are a good investor while you’re losing money. I’m following the method as described in the Knowledgebase, Part 3 (https://discussion.fool.com/knowledgebase-newly-revised-part-3-3…).

Start with \$100, in what we like to call a starter position. Through a combination of brilliant choices and dumb luck you double your money to \$200 in a few months.

Your initial factor is 1. At this point your factor is .5.

You decide you like this result so you go bigger by adding \$1000 to the account. You now have \$1200 and as you must continue to show a 100% gain, your factor becomes 200 / 1200 = 1/6 = .16666…

But over the next few days your luck runs out and you lose 1/4 of your money, leaving you \$900. But you aren’t discouraged because you can see that 900 * 1/6 = 150, so you still have a 50% return on your money. And the index was up only 5%! Brilliant you!

So why do you have only \$800 left when you put in \$1100? The answer is that the method doesn’t take into account capital. You were a successful investor with a little money and a failure with a lot of money. So long as the amount of money you have invested doesn’t change all that much, then this method yield something reasonable. Otherwise not so much.

Note that it also ignores time (which seems odd for a method called “time-weighted”). The fact that in the example above you were successful for months and then failed for a few days does not affect the result in any way.

So maybe this method answers some question for people who use it, but I don’t think it necessarily tells you how good you are at investing.

-IGU-
(who believes that if you make lots of money then it doesn’t matter much how you measure)

1 Like

Sorry, that should be “So why do you have only \$900 left…”

-IGU-

I built a time weighted rate of return spreadsheet that’s set up to record one’s progress monthly. It’s what I use to track my own investing returns. It factors out new money added in and/or existing money taken out so you get just the investing return.

Mike

2 Likes

I don’t see it.

Here’s a simple example where this method seems to be telling you that you are a good investor while you’re losing money. I’m following the method as described in the Knowledgebase, Part 3 (https://boards.fool.com/knowledgebase-newly-revised-part-3-3…).

Hi IGU,

OK, I just worked through Saul’s calculation method and can say that the return number it kicks out is identical to 1 + TWR, but without the % symbol. Let me work this through, demonstrating this, and then I’ll turn to your question.

Quoting from that page: Here’s how to calculate your overall returns ignoring cash flow in or out. Say you start the year with \$14,000. You want to equate that with 100% and calculate gains and losses from there. So you ask yourself “What number (factor) would I multiply \$14,000 by to get 100?”

By simple arithmetic we have 14000 x F = 100

And thus F = 100/14000 = .0071428

Sure enough 14,000 x .0071428 = 100

What this is doing is converting the \$14,000 into 100 (which is equivalent to setting it to 100% but without the % symbol) and finding the multiplier (what Saul labels the “factor”). If you start with \$14,000 and equate that to 100, then what must you multiply \$14,000 by to get 100? F = 0.0071428571 (it goes on, but he rounded it to 0.0071428).

Now say three weeks later you have \$14,740 and you want to see how you are doing, you multiply that number by .0071428 and you get 105.3 (so you are up 5.3%).

This is fine. 105.3 / 100 - 1 = 5.3% growth. Same as \$14,740 / \$14,000 - 1 = 5.3% growth.

So, without adding cash, you just take your ending balance, divide by your beginning balance and subtract one to get the return. Or you multiply your ending balance by F and then divide by the beginning 100 and subtract one to get the return, which is the same number. Two ways to do the same thing.

Now here’s the cash flow correction part: Now say you add \$2300 of fresh money, but you don’t want that to screw up your estimate of how well you are doing.

You add the \$2300 to the \$14,740 and get \$17,040 which is your new balance that you are investing with. That’s your new starting point. It doesn’t affect how you’ve done up to here. You haven’t suddenly done better because you added money. You can’t still multiply by .0071428 because you’d get 121.7 and it would look as if you were up 21.7%, when you are really only up 5.3%.

So you need to change your factor to make it smaller so it will still reflect just the 5.3% gain you’ve made so far.

F x 17,040 = 105.3

F = 105.3/17,040 = .0061795

And that’s your new factor. If you multiply it by 17,040, sure enough you get 105.3. Now you continue to see how you will do for the rest of the year.

After adding the cash – because you can’t count it as investment return – the balance is bigger, so the factor has to be smaller in order to remain at 105.3. This method corrects for the cash addition here.

That making F smaller so that you still have 5.3% return at this point is exactly what the TWR calculation is doing. Except TWR corrects for it by adding the cash to the balance – after calculating the return – and creates “\$\$ After CF” to use as the starting point for the next holding period return.

Finally, here’s the proof that both methods give the same answer:

If a little later you are at \$18,000, you multiply 18,000 by .0061795 and you get 111.2, so you know that your investing is now up 11.2% for the year.

Note, that’s the total return over the entire period, what TWR itself produces. Does TWR give the same result? Yes.

``````
Period  \$\$ Before CF  CF In/Out  \$\$ After CF  HPR     TWR
0       \$     0      \$14,000     \$14,000    N/A     0.0%
1       \$14,740      \$ 2,300     \$17,040    5.3%    5.3%
2       \$18,000      \$     0     \$18,000    5.6%   **11.2%**
``````

Remember, HPR = (Previous \$\$ After CF) / (Current \$\$ Before CF) - 1 and TWR is the chaining of the individual (1 + HPRs) and minus 1 at the end. (1.053)*(1.056)-1 = 11.2%

Now, let’s look at your example.

Start with \$100, in what we like to call a starter position. Through a combination of brilliant choices and dumb luck you double your money to \$200 in a few months.

Your initial factor is 1. At this point your factor is .5.

I’m sorry to say that you’ve made a mistake, here. Your factor at this point is still 1. You only change the factor at points where you have a cash flow event and, at this point, you don’t have that. Therefore, F is 1 and what I’ll call the F-return number is 200, not 100. Remember, you just doubled your money.

You decide you like this result so you go bigger by adding \$1000 to the account. You now have \$1200 and as you must continue to show a 100% gain, your factor becomes 200 / 1200 = 1/6 = .16666…

Here, you’re right. The previous F-return number, 200, is divided by the after-cash-flow balance of \$1,200 to give a new F = 0.1666667.

Now, to the crux of your question. But over the next few days your luck runs out and you lose 1/4 of your money, leaving you \$900. But you aren’t discouraged because you can see that 900 * 1/6 = 150, so you still have a 50% return on your money. And the index was up only 5%! Brilliant you!

So why do you have only [\$900] left when you put in \$1100?

The weird thing is that you can end up with less money, but have a positive TWR (or F-return, if we can use that phrase for the 200 or the 150, subtracting 100%). Why?

Well look at it. TWR = (1 + 100% gain) * (1 - 25% loss) - 1 = 2 * 0.75 - 1 = 0.5 or 50% return.

You were brilliant during the first period and earned 100%. You had bad luck and lost 25% the second period – both of these results of your investment decisions, not the cash deposited – and you ended up with a TWR of 50%. The reason you ended up with less money at the end is because your decisions had bad results after adding a big chunk of money to the account. That’s all.

You didn’t have a “50% return on your money” (the part I bolded), you had 50% time-weighted returns on your investments. You got a 100% return on your investments in the first period and a (25%) return on your investments in the second period. They’re not returns on your money, they’re returns on your investments.

It’s just your misfortune to have gotten bad results in the second period when you had more money to invest.

Suppose you added only \$200 instead \$1,000. With nothing else changed, you would have begun the second investment period with \$400 and lost 25% of that, ending with \$300.

The after-cash-flow F would be 200 / 400 = 0.5 (instead of 0.1666667). And the F-return would be \$300 * 0.5 = 150, or 50% gain overall.

Here, you’ve put in a total of \$300 (the original \$100 and the \$200 addition) and ended up with that same amount at the end, yet you still have an overall TWR or F-return of 50% on your investments to date.

Work it through with adding only \$50 cash instead of \$1,000 or \$200. F = 200 / 250 = 0.8. You lose 25% and end with \$187.50. \$187.50 * 0.8 = 150 or 50%. It’s always the same total TWR or F-return of 50% on your investments to date, no matter how much cash you add. But here, you’ve put in \$150 and end with a cash gain of \$37.50.

It’s a subtle distinction, but one with very big consequences. TWR and the F-return are returns on investments, not returns on money.

What you’re calling “return on money” could be called a cash-on-cash return, comparing the end result to the total amount deposited. This type of return depends on both the amounts deposited and the performance the investments. In your example, you have a \$900 / \$1100 - 1 = (18.1%) return; in my first example we have a \$300 / \$300 - 1 = 0% return; and in my second example we have a \$187.50 / \$150 - 1 = 25% return. TWR and F-return are independent of the cash flows.

If the same investment choices were made and the same investment results obtained, then you will always end with the same 50% overall total TWR or F-return, no matter what amounts were deposited or withdrawn. That’s why these numbers answer the question, “How good am I at investing?”

I hope that clears it up.

Cheers,
Jim

6 Likes

At this point your factor is .5.

I’m sorry to say that you’ve made a mistake, here. Your factor at this point is still 1.

Well, since I didn’t use that .5 for anything it was an irrelevant mistake. What I was planning to point out was that if you decide at that point to do something like add \$1 to your account you would recalculate your factor and it would be .5. I decided that was unnecessary for the illustration but failed to remove that observation.

That’s why these numbers answer the question, “How good am I at investing?”

Except they still don’t. They mix together various time periods and capital allocations and treat them all the same.

And if you look at the Knowledgebase, it says: “Here’s how to calculate your overall returns ignoring cash flow in or out.” That’s rather misleading, don’t you think? My example shows “overall returns” of 50% while turning \$1100 into \$900. I would call that not intuitively obvious, wouldn’t you?

I wonder how many people are using this method and because they have big variations in the amount of money invested at various times they are getting totally bogus results. Or at least results that are easy to misinterpret. I would guess it’s pretty typical for newcomers here – they play with the approach with a small amount of money, then get serious when they get good results. In such circumstances one might see “overall returns” computed by this method that are grotesquely wrong.

-IGU-

2 Likes

They mix together various time periods and capital allocations and treat them all the same.

Hi IGU,

Except, the time periods do not matter. One period could be +150% and the next period could be -50%. The return over the total time period will always be +25%. The periods could 2 years and 6 months, respectively, they could be 8 weeks and 12 weeks, respectively. It doesn’t matter. If you’re calculating total return over the total time period, you will have it over 2.5 years in the first case and 20 weeks in the second case.

My example shows “overall returns” of 50% while turning \$1100 into \$900. I would call that not intuitively obvious, wouldn’t you?

You’re example shows a loss in the total value of the portfolio relative to what was put in, yes. And, it still shows a +50% return on a TWR basis. And I agree, those two seem to contradict each other. These two facts are not intuitively obvious, one from the other. Yes, it seems obvious that if you have a 50% return over some time period, you should have more money than you started with.

But, as I tried to make clear in my previous answer, those two things are not talking about the same type of return calculation. The 50% is how the investments themselves performed over that time. As I tried to show, it doesn’t matter if you put in a bunch of cash at the start of the second time period, or just a little, the investment returns remained the same. Because the investments themselves behaved as stated – +100% for the first period, -25% for the second.

And I also tried to show that if you’re looking at the ending value vs. the amount deposited, you are not looking at TWR or how the investments, themselves, performed. It’s a completely different return calculation and should not be compared to TWR or what I called the F-return.

Suppose the investor had reversed the cash flows? \$1000 at the start, \$100 later – same \$1,100 invested and same returns for the two periods? \$1,000 goes to \$2,000 (+100%), and \$2,100 goes to \$1,575 (-25%). That person still got the same 50% TWR / F-return.

Let me try to illustrate with stocks. John and Jenny each invest in Netflix. John puts \$100 in, Jenny puts \$1,000 in. Netflix doubles and they both sell. John loves it, adds a whole bunch of money (\$1,000) and invests in Nvidia. Jenny is happy, too, but cautious, and adds \$100 to the account before investing all in Nvidia. Both experience a 25% loss before selling.

John ends up with \$900 and had a 50% TWR / F-return. Jenny ends with \$1,575 and also had a 50% TWR / F-return. The fact that John invested more later while Jenny invested more earlier has nothing to do with what TWR / F-return is showing. But it does have everything to do with how much money they end up with.

Which brings in this: They mix together various time periods and capital allocations and treat them all the same.

If you say that capital allocation matters, which it does, then you have to include all the capital available to be invested before doing the calculations. One of the assumptions behind TWR / F-return is that there is no other capital to be invested. That is, we are looking at a stand-alone portfolio. If there is other capital available, however, it has to be included because not investing other capital is itself an investment decision. A capital allocation decision.

Using my example, if John has \$1,000 sitting on the sidelines in cash before putting it to work (and Jenny has \$100), you must include those amounts as part of the total portfolios. You can’t hive off that cash and pretend it’s not part of the overall portfolio, because it’s also invested, but in cash. That changes the whole thing.

The TWR / F-return calculations are completely independent of only the cash flows coming in or going out. But, if there’s cash that could be invested and isn’t, then that has to be included from the beginning, which means John and Jenny will have completely different results and return calculations. In fact, if they both had \$1,100 to start with and allocated it differently (as described above, but with no deposit part way through, just allocation of the remainder of the cash), then John ends up with (18.2%) TWR / F-return and Jenny ends up with 43.18% TWR / F-return.

The cash flows and the timing of them are completely irrelevant. But cash balances, as part of an overall portfolio, are very relevant and change everything.

I wonder how many people are using this method and because they have big variations in the amount of money invested at various times they are getting totally bogus results. Or at least results that are easy to misinterpret. I would guess it’s pretty typical for newcomers here – they play with the approach with a small amount of money, then get serious when they get good results. In such circumstances one might see “overall returns” computed by this method that are grotesquely wrong.

Yes, they can be easy to misinterpret. But that comes from not understanding what the return calculation is actually doing, as I think I just illustrated. Further, it comes from not understanding which return calculation to use:

1. If you want cash-on-cash performance results, look at the ending balance vs. the amount invested over time.

2. If you want to know how good a stock picker you are, use TWR / F-return.

3. If you want to know if your current starting point, your planned deposits, and an assumed return on average cash balance will get you to your goals, use XIRR.

Each of these is a different return calculation addressing a different topic. Of course it will be misleading or grotesquely wrong if one is used where it shouldn’t be.

Finally, make sure that the portfolio is properly defined. If it’s defined as a sub-portfolio with no cash balance and looking at only the results within that with cash transfers in (as I first assumed), then you can get wonky, non-intuitive results (like ending up with less money but a 50% TWR / F-return). But, if you include cash that could be invested, but isn’t, as part of that sub-portfolio, then you end up with much more sensible-looking results.

Hope that clarifies it.

Cheers,
Jim

9 Likes

I think it is fair to say that for a fund manager who cannot control the amount or timing of inflows and outflows from his fund, TWR gives the best measure of his performance (and I’ve seen Jim write that before).

For an investor who does manage how much gets invested over time, controlling the inflows and outflows for maximum return, then XIRR gives the best measure of his performance.

Thanks, Jim, for the detailed explanations and examples.

Enjoy,
Brian

1 Like

Thank you, Jim!

I know this has probably gotten somewhat off topic for this board, or at the least is boring for folks that already understand all this, but with that last post of yours, I finally got it, understand the difference, and realize why it’s coming out the way it is!

Thanks for all the examples and detail!

1 Like

I know this has probably gotten somewhat off topic for this board… but with that last post of yours, I finally got it,

Great, Please take any more exchanges on this off-board. Thanks,

Saul

Thanks TMFT, great information. It seems that TWR is a better method for me to use. Your opinion welcome on the below.

Briefly,

• I follow Meb Faber’s global tactical asset allocation (GTAA) “aggressive” 6 approach. (Generally, not “perfectly”). This is across a few investment accounts.
• that means monthly re-evaluations of momentum ranks and allocations to up to 6 specific assets, and frequent increases and decreases in those allocations at (generally) monthly boundaries as their rankings change.
• those classes that have weaker relative and absolute momentum may be zero for months at a time (“out”), followed by a number of months of being “in”.

As that seems more aligned with how “ETFs” and mutual funds operate, if they use TWR then this case is probably appropriate for TWR too.

I’ve used both the (EV - CF/2) / (SV + CF/2) -1 classic method, XIRR as well as trying (EV+ABS(Total withdrawals)) / (Total investments). That last one definitely understates annual or period returns.

Great, Please take any more exchanges on this off-board. Thanks,

Hi Saul,

While I believe that accurate measurements should be used to inform future decisions, and thus am somewhat passionate about accurate return calculations (perhaps you noticed), I appreciate that this board is mostly about finding strong growth companies.

Thanks for your and the board’s indulgence in letting me write a lot on this topic. I’ll stop now and let you guys get back to the serious business of finding great companies to invest in.

Cheers,
Jim

6 Likes