# What is the time-weighted rate of return (TWRR)?

A time-weighted rate of return is a great metric for comparing the performance of different fund managers and investment portfolios, but it does have some limitations.

## What does TWRR measure?

The time-weighted rate of return, or TWRR, is a way to measure the investment performance of a managed fund or portfolio. It is unique because it attempts to remove the distortive impacts that large deposits or withdrawals can have on a fund's returns.

For example, a fund may have outperformed its peers all year, but then a significant investor suddenly decides to cash out their holdings. If you were to calculate the fund's annual return by comparing its value after the withdrawal with its value from 12 months ago, you would be doing the fund manager a disservice.

That major withdrawal would reduce the fund's overall ending balance, making the return you calculate appear lower than it actually was.

Similarly, if you did the same with a fund that had underperformed all year but suddenly had a large new deposit, its returns would seem higher than they were in reality.

This distortion caused by cash inflows and outflows can make comparing the relative performance of different funds difficult. As an investor, knowing where to put your money is more challenging. You might be drawn to one fund manager, but high cash inflows might artificially have inflated their returns.

But that's where TWRR can help.

TWRR breaks a fund's return down into smaller subperiods, with a new period beginning every time money is added to or withdrawn from the fund. We compute returns for these subperiods by comparing the fund's value at the end of each subperiod with its value at the beginning (after whatever cash flow has occurred).

Finally, we can calculate a time-weighted rate of return by multiplying each subperiod's returns by one another.

## How to calculate TWRR

Although my explanation might sound like a word salad, calculating TWRR is surprisingly simple. But it's probably best illustrated with an example.

Let's say you want to calculate the TWRR for Fund A over the past year.

Fund A started the year with an investment portfolio valued at \$1,000,000. By 1 April, the fund's value had increased to \$1,100,000, at which point a new investor contributed an additional \$200,000 to the fund's coffers.

By 15 September, the fund's value had increased to \$1,450,000. At this point, a different investor decided to take some profit, withdrawing \$100,000. The fund then had a rocky end to the year, and by 31 December, its value had fallen back to \$1,150,000.

You could calculate a simple return using the following formula:

Return = (Ending value – Beginning value)/(Beginning value)

In this case:

15% = (\$1,150,000 – \$1,000,000)/\$1,000,000

But does this number capture the actual performance of the fund manager? Much of the fund's performance was driven by investors depositing and withdrawing money from the fund. To get around this – and calculate a more accurate rate of return – we can use TWRR.

### Calculating the holding periods

First, we break up our overall return into three subperiods: the first from 1 January to 1 April, the second from 1 April to 15 September, and the third from 15 September to 31 December.

We then calculate a return for each of these subperiods (often called 'holding periods') using the below formula:

Holding period return = (Ending value – (Beginning value + cash flow))/(Beginning value + cash flow)

For our first holding period, from 1 January to 1 April, there is no cash flow, so our return is:

10% = (\$1,100,000 – (\$1,000,000 + \$0))/(\$1,000,000 + \$0)

For our second holding period, from 1 April to 15 September, there is a cash flow of \$200,000 (the deposit from the new customer) to account for. This is an adjustment to our beginning value, with our ending value being the fund's balance on 15 September. This means our second holding period return is:

11.5% = (\$1,450,000 – (\$1,100,000 + \$200,000))/(\$1,100,000 + \$200,000)

We do the same for our third and final holding period, from 15 September to 31 December. The beginning value is adjusted for the customer withdrawal, and the ending value is the fund's balance on 31 December. Remember that, from the fund's perspective, a withdrawal is a cash outflow that we must subtract from the opening balance.

-14.8% = (\$1,150,000 – (\$1,450,000 – \$100,000))/(\$1,450,000 – \$100,000)

Now we have our returns for our three holding periods. Holding period one's return is 10%, holding period two's return is 11.5%, and holding period three's return is -14.8%. Now we have to link them together by multiplying the returns by each other like so:

TWRR = (1+ HPR1) × (1 + HPR2) × (1+ HPR3) – 1

Where HPRN represents the holding period return for each sub-period. If you want to sound clever in front of your friends, you can sagely tell them that the TWRR is a type of 'geometric mean' rather than an 'arithmetic mean' because it calculates the average of a set of products rather than of values.

Anyway, here is the TWRR for Fund A:

4.5% = (1 + 0.10) × (1 + 0.115) × (1-0.148) – 1

This return of just 4.5% is significantly different from the simple return of 15% we calculated earlier – but is a more accurate representation of the fund manager's actual performance.

## Should I use TWRR or IRR?

TWRR is just one way to measure a fund's return. Another standard measure is the internal rate of return or IRR. Analysts define IRR as the discount rate that would make a series of cashflows' net present value (NPV) equal to 0.

This definition might sound technical, but it tries to answer the question: "If the fund was a term deposit account at a bank, what hypothetical interest rate has it earned, taking into account all its cash flows?"

Whether TWRR or IRR is the best return metric often depends on the type of fund being analysed. Because TWRR deliberately removes the impact of cash flows in and out of the fund, it is generally the best return metric to assess retail funds. This is because it more accurately reflects the performance of fund managers with little control over when investors enter or exit the fund.

However, IRR is a better return measure for private equity funds. Managers of these types of funds exercise greater control over when (and how much) cash enters and exits their funds. In fact, managing these cash flows is a central part of their role.

## How do money-weighted and time-weighted rates of return differ?

As we've just discussed, IRR is the more suitable performance metric for fund managers with greater control over their cash flows. This is because IRR includes the impacts of any cash flows, while TWRR calculation deliberately excludes them.

This makes IRR a money-weighted rate of return rather than a time-weighted one. Or, to put it another way, TWRR puts more value on subperiods with higher returns, while IRR puts more value on the size of the cash flows.

## How does the IRR calculation differ from TWRR?

Calculating IRR can be a complicated iterative process requiring a financial calculator or special software. Luckily, Microsoft Excel has an IRR function that allows you to calculate the IRR for a series of cash flows relatively easily.

Using our example from before, our cash flows would be:

IRR assumes the beginning value is the initial investment in the fund, and the ending value is returned to investors. This is why, from an investor's perspective – and that's your perspective if you're assessing which fund to invest in – Cash flow 1 is negative, and Cash flow 4 is positive.

Other inflows to the fund are also negative from your perspective (like Cash flow 2) because these represent additional investments. And outflows are positive (like Cash flow 3) because these represent distributions.

If we plug these numbers into Excel's IRR function gives a return of just 1.5%. This is significantly lower than the TWRR.

### Comparing IRR and TWRR

So why is the IRR so much lower than the TWRR?

In the TWRR calculation, the returns in two of the three holding periods were positive, which outweighed the one negative return in the third period. However, when calculating the IRR, the \$200,000 negative cash flow outweighs the \$100,000 positive cash flow, resulting in a much slimmer positive return overall.

In other words, one is time-weighted, and one is money-weighted!

## Limitations of TWRR

While calculating the TWRR seems relatively simple in theory, applying it to real retail funds can be incredibly complicated and time-consuming. This is because large funds can process many investments and redemptions daily, and a new holding period begins every time there is a new cash flow.

So – unfortunately – although the TWRR might be the best measure of a retail fund manager's true performance, it often requires sophisticated software to perform the return calculation.

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