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 the year. 
• In year 1, the stock earns a 1% return – giving you a $1 gain on $100.
• You decide to invest $100 more into the stock at the end of year 1 – so you have $201 (original $100 + $1 gain + new $100). 
• In year 2, the stock earns a 2% return – giving you a gain of $4.02 ($201 * 2%). 
What was your average annual return?  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 and a larger gain in year 2? 

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%.


So how does the TWR ignore how much money you had invested and isolate the return of the investment itself?
It focuses on the percentages only. 
In the above example, I said you gained $1 in year 1, and $4.02 in year 2.  The TWR doesn’t care about that. 
It cares that you earned 1% in year 1 and 2% in year 2.  In other words, it treats year 1 and year 2 as equals even though you had more money invested in year 2.  
How does it do that? When you calculate a TWR, it “restarts” and calculates a return each time you add or take away money.   In our example, since we contributed $100 at the beginning of year 2, we will use these two annual periods.  

We will create a similar grid for the IRR, but the key difference between the two is that the percentages above are calculated by looking at each year in isolation of one another. In the IRR calculation, the annual return is dependent on the other periods.
The steps to calculate the average annual TWR are:
1) Compute the returns for each period.  In our example, we were given the 1% for year 1 and 2% for year 2 already.
2) Compound the 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 annualize the return to get the average of 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%.



How does the IRR account for the money invested? 
It focuses on dollars and NOT the stock’s return.  It is calculating your individual return using the dollars you put in and got out.  
In our example, the IRR doesn’t use the 1% and 2% return we quoted for year 1 and year 2.  It uses dollars – the $100 you put in at the start, the $100 you put in at the end of year 1, and the $205.02 you end with. 
Here are the inputs for the formula:

Then, you use a computer (Excel has a program) to answer the question: What return would you need to tie the initial $100, the $100 contribution, and the $205.02 ending value?


Using the XIRR formula (since Excel needs dates, I used 2016 and 2017 as year 1 and 2), we find the return is 1.66%


Now, we can put this return into a similar chart as the TWR and see that if you grow the $100 by 1.66%, then contribute $100, and then grow the $201.66 by 1.66% again, you end up with $205.02.


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.
* These two will diverge when there are large flows (impacts both) or large price swings (impacts TWR only).

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