### 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.

*• *Y*ou invest $100 in a stock at the beginning of the year. *

*•*Y

*ou 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. *

*• 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). *

*• 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%). *

*• 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? *

*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%.*

**TWR**

##### 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%.

#### IRR

##### 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