Time-Weighted Return (TWR) vs. Internal Rate of Return (IRR)

When looking at your investment statement, you could see two types of returns reported:
* Time Weighted Return: attempts to show you what the return was regardless of how much money was invested.  In other words, if you invested $1 at the beginning, and didn’t add or take out any money since then, how much would that be worth now?
* Internal Rate of Return (also called Money Weighted Return, or MWR): shows you what the return was based on the growth of your investments as well as the timing and amount of money invested throughout the period.  If you invested $1 now and then another $1 a year from now, and the return was higher when more money (the $2) was invested, the overall IRR will be closer to the higher return since you had more money invested then.
But let’s simplify this with an example.
You invest $100 in a stock at the beginning of 2016. 
• In 2016, the stock earns a 1% return.
• You decide to invest $100 more into the stock at the end of 2016. 
• In 2017, the stock earns a 2% return. 
How much did you make per year on average?  Was it 1.5% (which is in the middle of 1% and 2%) or was it closer to 2% since you had more money invested then? Please note, we are referring to how much you made on year per average, because people compare the TWR and IRR, they are comparing average returns.  

Spoiler: TWR has an average of approx 1.5% (in the middle of the 1% and 2%) since it does not look at how much you had invested, while IRR is higher since you had more money invested when the return was 2%.

TWR

1) In order to calculate a return, you need to be clear on the data inputs.  When you calculate a TWR, the inputs will segregate the values, money in and out, and gains and losses by period:

You invested $100 in the stock at the beginning of 2016 so it earned $1 (1% x $100). At the beginning of 2017, you invested another $100 for a starting balance of $201 (the $101 you ended with from 2016 and the $100 you added). The 2% return on $201 is $4.02. 

2) Based on #1, we have the returns for each period – 1% for 2016 and 2% for 2017.  To figure out what the average annual return is (remember, we can only compare average annual returns to the IRR, I will show you why later), we need to first see what the time-weighted return is over the full two year period.
To figure out how much you made over the 2 year period, we need to compound the return the two returns together to get what is called a cumulative return (how much you accumulated over the full period).  The cumulative return is 3.02%.
3) Then we need to divide it by 2 to get the average of approximately 1.5%.  
However, we can’t just simply divide by 2, we need to geometrically divide by 2.  Huh?  Basically, we need to see what 2 returns when compounded together would give us the 3.02% return.   To do this, we raise the 3.02% to the power of 1/2.  the formula would be:
[(1+ 3.02%) ^ (1/2)] -1
This gives us approximately 1.5%.
Conclusion: The time-weighted return ignores the fact that you had more money invested in the second period.  It treats the 1% and 2% equally, which is why you get a return in the middle of 1% and 2%.

 

IRR

1) First let’s get the inputs.  The IRR doesn’t use the 1% and 2% return we quoted for 2016 and 2017.  It uses dollars – the $100 you put in at the start, the $100 you put in at the end of 2016, and the $205.02 you end with.
So here are the dollars we put in:

2) You actually have to use a program (or Excel formula XIRR) to figure out what return you would need to fill this chart:

 

Using the XIRR formula, we find the return is 1.66%

 

And we can put the 1.66% in the chart, and see that we end at $205.02.  Amazing! 

 

Side by Side Comparison

 

Wrapping It Up: Which One Should I Use, the IRR or TWR?

Well, it depends on what question you are trying to answer.
If you want to know what your actual average return was, incorporating the fact that you had more or less dollars in when the market was up or down, then you should use IRR.  This is how much you actually made accounting for how much money you had invested.
If you want to know how the investments themselves did, without regard to how much you chose to invest, then you should use the TWR.  The TWR is a good measure for many investment managers, since most times they can’t control the amount of money a client invests.
For more details on each of these calculations, please visit their dedicated pages:
Time-Weighted Returns
Internal Rate of Return
Here are a few points to take note of:
* When there are no flows, the IRR and TWR are the same.
* Since TWR uses the portfolio value in the middle (e.g., $201), prices fluctuating will impact TWR. IRR doesn’t look at prices until the end.
* These two will diverge when there are large flows (impacts both) or large price swings (impacts TWR only).
 
Posted by / February 3, 2019
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