It may seem illogical, but different return types can yield vastly different percentage returns. We take a close look at the two main return types and their differences.

Jul 16, 2024

Academy

Return is not just return.

There are various ways of calculating it, each with its characteristics and benefits.

And even though it may seem illogical, the different methods can actually yield vastly different percentage returns. Therefore, it's important to be aware of how two return figures are calculated before you compare them.

There are two main types of percentage returns, namely time-weighted return and money-weighted rate of return – and they each provide different insights.

In this article, I'll go through the differences between the two return types and how they’re calculated.

Warning: This is going to be a long one, but I promise that if you make it to the finish line, you’ll become an expert in return metrics. So, load up on coffee and snacks, and enjoy the ride!

To set the stage, let’s begin by looking at what sets apart the two types of return.

The main difference between them is that the time-weighted return (TWR) *eliminates* the effect of cash flows in and out of the portfolio, whereas the money-weighted rate of return (MWRR) *includes* the effect of cash flows.

(If this doesn’t make sense now, don’t worry, I’ll give you more details and examples later in the article.)

This also means that if you calculate the return for a one-year period where no cash flows occur, the money-weighted and the time-weighted return will be the same.

When calculating TWR for a given period, you first divide the period into sub-periods, then calculate the percentage return for each sub-period, and finally link the return percentages for the sub-periods together to get a total return for the period.

The calculation behind MWRR is somewhat more complex, but the goal is to find *the average annual return on the capital invested at any given time*.

In the following sections, we delve into the two return types and the calculations behind them. Let’s begin with the time-weighted return.

The time-weighted return is the international calculation standard prescribed in the "Global Investment Performance Standards" (GIPS), which is a set of guidelines voluntarily followed by asset managers worldwide, aimed at promoting fair presentation of their performance. The time-weighted return is thus the type of return recommended for measuring asset managers.

The reason the time-weighted return is recommended for measuring asset managers is that the calculation method behind the time-weighted return ensures that cash flows in and out of the portfolio do not affect the percentage return.

The time-weighted return is calculated using the formula:

TWR = (1 + percentage return for sub-period 1) × (1 + percentage return for sub-period 2) × … × (1 + percentage return for sub-period n) – 1

The returns for each sub-period are multiplied together to account for the compound interest effect created during the period. Because the returns are multiplied together, TWR is also known as the geometric mean return.

In the following, I’ll walk you through a simple example to show you how to calculate TWR using three steps:

Identify cash flows and divide the investment period into sub-periods.

Calculate the percentage return for the sub-periods.

Calculate the time-weighted return for the period.

When calculating TWR for a period, you start by identifying the cash flows that have occurred during the period.

The period should be divided into as many sub-periods as there are cash flows, so that a sub-period ends just before each cash flow and a new sub-period starts right after each cash flow. Cash flows include capital contributions and withdrawals.

Each sub-period is weighted equally, even if more capital is invested in some sub-periods than in others.

Let's go through the calculation method for the TWR with an example:

Investor A invests 100 million on January 1st. On August 5th, the portfolio has a market value of 85 million. That day, Investor A chooses to add 25 million to the portfolio. At the end of the year, Investor A’s portfolio has a market value of 134.8 million.

As shown in the table below, we’re dealing with a total period of one year, consisting of two sub-periods: sub-period 1, which runs from January 1st until the cash flow on August 5th, and sub-period 2, which begins right after the cash flow and ends at the end of the year.

Now we need to calculate the percentage return for the two sub-periods:

Percentage return for sub-period 1: (85 million / 100 million) − 1= −15%

Percentage return for sub-period 2: (134.8 million / 110 million) − 1 = 22.5%

We’ve now calculated the percentage return for both sub-periods, which means we can now calculate the time-weighted return for the total period.

Remember, TWR is calculated using the formula:

TWR = (1 + percentage return for sub-period 1) × (1 + percentage return for sub-period 2) × … × (1 + percentage return for sub-period n) – 1

The calculation for our example looks like this:

TWR = (1 − 0.15) × (1 + 0.225) – 1 = 4.1%

Thus, Investor A achieved a time-weighted return of 4.1% for the total investment period.

As I mentioned earlier, TWR eliminates the effect of cash flows to and from the portfolio during an investment period.

Let me illustrate it by continuing the previous example:

In addition to Investor A, we now also have Investor B and Investor C, who both invested 100 million in the same investment fund as Investor A – and at the same time.

On August 5th, all three portfolios reach a market value of 85 million.

That day, Investor A, as we already know, chooses to add 25 million to the portfolio. Investor B, on the other hand, chooses to withdraw 25 million from the portfolio, while Investor C does nothing.

At the end of the year, Investor A’s portfolio has a market value of 134.8 million, Investor B’s portfolio has a market value of 73.5 million, while Investor C’s portfolio is worth 104.1 million.

As you can see, we’re still dealing with the same investment period and the same sub-periods.

We already know the percentage return for sub-period 1 and Investor A’s percentage return for sub-period 2. Now we need to calculate the percentage return for sub-period 2 for the other two investors:

Investor B’s percentage return in sub-period 2: (73.5 million / 60 million) − 1 = 22.5%

Investor C’s percentage return in sub-period 2: (104.1 million / 85 million) − 1 = 22.5%

As you can see, the three investors achieved the same percentage return for sub-period 2, despite achieving different absolute returns for the period. The different absolute returns are due to the investors’ different decisions between sub-periods 1 and 2, which resulted in them starting with different market values in sub-period 2.

We’ve now calculated the percentage return for both sub-periods for all three investors, which means we can calculate the time-weighted return for the total period for each investor.

Since the percentage returns for sub-periods 1 and 2 were the same for all three investors, and the calculation for time-weighted return is based on percentage returns and not absolute returns, the calculation of the time-weighted return for the period looks the same for all three investors:

TWR = (1 − 0.15) × (1 + 0.225) − 1 = 4.1%

Thus, Investor A, B, and C all achieved a time-weighted return of 4.1% for the period, despite achieving different absolute returns after the investment period ended. And the result would’ve been the same if the cash flow movements had occurred at different times of the year.

This makes sense when you consider that they all invested in the same investment fund, and we’ve eliminated the effect of their cash flows.

The example thus illustrates that cash flows have no impact on TWR, and that the portfolio's performance is measured independently of whether you withdraw money from or add money to the portfolio.

As such, this return type gives you insight into the performance of the investment fund and not the investor’s ability to time cash flows.

TWR gives you insight into the performance of the investment fund and not the investor’s ability to time cash flows.

This is why it can be argued that TWR is the return type that most accurately reflects a portfolio's performance.

When calculating performance with TWR, you may sometimes encounter percentages that contradict intuition. This is often because capital has been withdrawn from or added to the portfolio.

For example, for a given period, you can have a positive absolute return but a negative percentage return. In our example, this applies to Investor B, who achieved a negative absolute return of -1.5 million for the total period but a positive TWR of 4.1%.

This is because the calculation of the time-weighted return multiplies the percentage returns, not the absolute returns. The calculation is thus independent of the actual amounts behind the percentages.

This is precisely why this type of return is suitable for comparing your managers' performance, despite them investing different amounts of capital and you possibly adding or withdrawing capital from the portfolios at different times.

At the same time, this means that TWR does not necessarily tell you how much you actually earned in dollars and cents on the invested capital. For that, you need to look at the money-weighted rate of return.

(This might be a good time to get a coffee refill while you download our eBook (further up) about private equity – a definitive guide to the popular alternative asset class – if you still haven't grabbed your copy.)

Moving on to the money-weighted rate of return!

Unlike TWR, MWRR *includes* the effect of cash flows and thus illustrates the advantages and disadvantages of an investor's decisions to add capital to or withdraw capital from their portfolio at a given time.

The money-weighted rate of return is the average annual return on the capital invested at any given time.

The money-weighted rate of return is the average annual return on the capital invested at any given time.

As mentioned, the calculation behind the money-weighted rate of return is somewhat more complex than the calculation behind the time-weighted return.

**Note:** If you want a detailed walkthrough of how to manually calculate the money-weighted return and thus gain an in-depth understanding of the metric (nerd alert!), I recommend reading our article "Money-Weighted Rate of Return (MWRR): Explaining the metric and how to calculate it" before reading on here.

Fortunately, there’s an Excel function that can help us easily calculate MWRR, namely XIRR, and in the following, I’ll show you how to do it in just two steps.

To calculate the money-weighted rate of return, we need to know the timing of all cash flows during the investment period and their nominal value – that is, how much was added or withdrawn in dollars and cents.

Both the original investment and the final market value of the portfolio are also considered cash flows.

To calculate the MWRR of an investment for a given period, you need the following information:

The value of and the timing of the original investment.

The value of and the timing of all cash flows to and from the portfolio during the period.

The market value of the portfolio at the end of the period.

Let's again take Investor A as an example:

Investor A invests 100 million on January 1st – this is the original investment. On August 5th, Investor A chooses to add 25 million to the portfolio, which means a cash flow occurs. At the end of the year, Investor A’s portfolio has a market value of 134.8 million, which is the final market value.

We now have all the information we need to calculate MWRR for the period, and we enter it in Excel. (Be aware that some date formats can cause the Excel function not to work.)

When calculating MWRR using the Excel function, the values that are outflows from the portfolio must have a negative sign. The final market value of 134.8 million is considered an outflow, as it is viewed in the calculation context as the amount received from selling the investments and subsequently withdrawn from the portfolio. Therefore, it must have a negative sign.

We’re now ready to calculate MWRR.

Click on the MWRR field, type "=", and search for the XIRR function.

Once you’ve selected the function, first highlight the column with your cash flows, insert a semicolon, and then highlight your dates.

Finish with a parenthesis, press "enter," and now you have your MWRR:

Investor A thus achieved a money-weighted return of 8.9% for the period.

As I’ve mentioned, MWRR includes the effect of cash flows to and from the portfolio during an investment period.

Let's illustrate this using the example of Investor A, B, and C.

By following the two steps we just went through, we also calculate MWRR for Investor B and C:

As you can see, the three investors achieve vastly different MWRRs, even though they invested in the same investment fund. This is because MWRR reflects the actual return on investment and thus the different market values the investors achieved. This is why it’s called the money-weighted rate of return.

Investor A's decision to add 25 million to his portfolio at that specific time proved to be a good decision, and this is reflected in their MWRR.

Investor B, on the other hand, withdrew 25 million from their portfolio at the same time, resulting in a negative return.

Investor C did nothing during the period and thus achieved a return of 4.1%. Investor C's MWRR is thus the same as their TWR since no cash flows occurred to or from this investor's portfolio during the investment period, and the investment period lasted exactly one year.

MWRR is ideal when you need to know the actual return on the invested capital.

The money-weighted rate of return thus tells a completely different story than the time-weighted return and is ideal when you need to know the actual return on the invested capital. However, it’s certainly not preferable for comparing the performance of different asset managers.

If a significant capital addition is made to a portfolio just before a period of:

High performance: MWRR will be higher than TWR.

Low performance: MWRR will be lower than TWR.

Conversely, if capital is withdrawn from a portfolio just before a period of:

High performance: MWRR will be lower than TWR.

Low performance: MWRR will be higher than TWR.

*drum rolllllll*

Okay, sorry to disappoint you, but the boring answer is that it depends on the situation and what insight you want to gain.

**The time-weighted return is best if:**

You want to evaluate your manager's performance, as the calculation ensures that your decisions to add capital to or withdraw capital from the portfolio are not reflected in the return.

**The money-weighted rate of return is best if:**

You want to know the actual return on your investments.

You want to see the effect of your decisions to add capital to or withdraw capital from the portfolio during the investment period.

That said, it’s not a question of choosing between the two return types, but of understanding them and knowing what insight each one provides.

First and foremost, you should never compare the TWR of one portfolio with the MWRR of another portfolio. When comparing across portfolios, this should always be done based on the same metrics calculated based on the same principles.

However, you can compare a portfolio's TWR with its MWRR if you want to see the difference between whether the effect of cash flows is included or not.

In this context, it’s important to note that TWR always reflects the return for precisely the investment period it was calculated for, whereas the MWRR by definition is the average *annual* return (on the capital invested at any given time).

If you want to compare TWR and MWRR, you need to adjust the MWRR so that it reflects the same period as TWR.

If you want to learn how to do this, check out our article "Money-Weighted Rate of Return (MWRR): Explaining the metric and how to calculate it" where I go into more detail with the metric and the calculations behind it (and yes, that is possible).

If you have any questions about this article or want to know more about how we work with return reporting at Aleta, you’re more than welcome to reach out!

In the meantime, here are the key takeaways from the article.

TWR does not reflect cash flows in and out of a portfolio, ensuring that a portfolio's performance is measured independently of the investor's decisions to add or withdraw capital from the portfolio.

Therefore, TWR is preferable when comparing and benchmarking asset managers.

MWRR is the average annual return on the capital invested at any given time and corresponds to the internal rate of return (IRR) of your investment.

MWRR includes the effect of cash flows, illustrating the advantages and disadvantages of an investor's decisions to add or withdraw capital from their portfolio at a given time, as both the size and timing of cash flows to and from the portfolio influence the metric.

MWRR is preferable when you want to know the actual return on the invested capital.

One of the most commonly used forms of return is the money-weighted rate of return (MWRR). This article will give you a deeper understanding of the metric and teach you how to calculate it.

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