# How We Calculate Returns

**By the Editorial Staff **

Betterment Resource Center |
Published: September 1, 2018

#### TABLE OF CONTENTS

- How does Betterment calculate the earnings percentage?
- What is a time-weighted return?
- Why does Betterment use time-weighted returns?
- Why do I have a negative % time-weighted return, but positive earnings?
- Why do I have a positive % time-weighted return, but negative earnings?

## How does Betterment calculate the earnings percentage?

Betterment reports two main types of returns calculations:

**Earnings performance**is found under the “$ VALUES PERFORMANCE” sub-tab, and takes into account the timing and size of cashflows into and out of the account.**Time-weighted return**is found under the “% RETURN PERFORMANCE” sub-tab, and reflects the returns of your portfolio ignoring size and timing of cash flows.

This answer will focus on Simple Earnings performance.

**Simple Earnings Percentage**

The Simple Earnings Percentage is a simple measure of how much your portfolio has grown, as a percentage of how much you invested. It should not be used to compare to other accounts, unless those accounts had the same exact cash flows (which isn’t a likely situation).

The earnings percentage is generally calculated as:

- The amount your account has earned
- Divided by the amount you have invested (there are exceptions to the rule—read on to learn more.).

Your earnings percentage is a very simple and intuitive way to represent how much you have earned by investing. It does have some drawbacks.

**Adjusting the Simple Earnings Percentage**

The simple earnings percentage has drawbacks that can lead to very unintuitive results. Whenever the current net amount invested is very different than the amount that was invested for the majority of the period, then the simple earnings percentage communicates very little about the success of the account.

In these cases, Betterment adjusts the simple earnings percentage so that the calculation provides a useful picture of the account. Our adjustment consists of dividing the investment earnings by the average amount invested over the period—rather than the current net amount invested. This alternative calculation is invoked whenever the value of the current net invested amount is less than 80% of the average daily invested amount. We’ll explain this logic with some examples.

Imagine that you invest $100,000 with Betterment and earn $1,000 in the first 30 days. Your account is now worth $101,000. Your earnings percentage is equal to 1%, which is calculated by dividing the earnings, $1,000, by the net amount invested, $100,000.

Now, imagine that on the last day of the month you withdraw $90,000 to put a downpayment on a house. Your net total investment is now $10,000 (100,000 – 90,000), but your balance is $11,000. By the simple earnings percentage calculation, your return is now $1,000 divided by $10,000, or 10%. This number does not accurately reflect your actual returns.

In these cases, your actual earnings percentage is better represented by dividing the amount earned by your average invested amount over the time period. Because you had about $100,000 for most of that month, except the last day when it was $10,000, your average invested is $97,000. So your earnings percentage in this case is $1,000 / 97,000 = 1.03%. While this adjusted percentage isn’t a perfect reflection of reality either, it does tend to be much more representative of your actual return than the distorted 10% number.

In order to decide when to use this alternative earnings percentage logic, we check if your average daily invested amount is substantially different than your current invested amount.

**Annualized Simple Earnings**

If you hover on the “Total Simple Earnings” card, you may also see your annualized simple earnings. This value will only show if that goal has been invested for more than one year.

The annualized simple earnings adjusts your simple earnings percentage for how long you’ve been invested. For example, suppose you’ve been invested for 4.12 years (just over 4 years and 1 month), and you have an Simple Earnings Percentage of 20.9%. You might ask “How much is that, on average, for each year?”

To calculate the Annualized Simple Earnings Percentage, we adjust simple earnings using the formula below:

Annualized Earnings = [(1 + Earnings Percentage) ^ (1 / years invested)] – 1

In the example above, we’d have:

4.7% = [(1 + 0.209) ^ (1/4.12)] – 1

## What is a time weighted return?

We use a standard time-weighted return to calculate percentage returns for each goal on the Summary page, and to display returns over time on the Performance page. This return can be thought of as the amount one dollar would have changed if it was invested at the same time as your first deposit.

The time-weighted return is unaffected by deposits to and withdrawals from your account, and allows for easy assessment of your investment, and a fair comparison with other investments. In the investment industry, “a time-weighted rate of return best reflects the firm’s ability to manage [their] portfolios according to a specified mandate, objective, or strategy”. You can read the full explanation of time-weighted returns here.

As an example, because this return calculation removes the effect of specific deposit patterns, two investors that start investing at the same time in a 80/20 Betterment portfolio will always have the same time-weighted return, regardless of their deposit or withdrawal pattern.

This is true if we assume perfect rebalancing. In practice, different deposit patterns will produce slightly different rebalancing patterns (at Betterment, more frequent deposits mean more frequent rebalancing), and so slightly different returns will arise.

If one investor consistently experienced very good luck, always depositing when the portfolio had decreased in value and withdrawing when the portfolio had increased in value, they could well end up in the short term having made money, even during a time when the assets in the portfolio had gone down in value overall. However, they would still have a negative time-weighted return, reflecting how their portfolio had actually performed independently of their timing.

## Why does Betterment use time-weighted returns?

Betterment calculates the time-weighted return for you in the Summary and Performance pages of your account. Because our customers are buy-and-hold investors making multiple deposits into their accounts over time—or retirees making multiple withdrawals—this is by far the most intuitive way to measure, compare, and judge the performance of a Betterment account.

A time-weighted return can be thought of as the simple return of the first deposit into an investment account because it compounds the simple returns between deposits and withdrawals so that their timing or size do not distort the percentage return. Common indices, such as the S&P 500, are reported in time-weighted returns.

If you have an investment account for which you, the investor, control the cash flows into and out of the portfolio, and you want to judge the performance of the portfolio without your cash flow timing, you would use a time-weighted return. For that reason, it is the only method you should use to compare the performance of different investments or of a single investment against a benchmark, making it the industry standard return methodology for financial advisors.

Below, we provide a description of the other common return metrics and why we believe they are less suitable than a time-weighted return.

**Money-Weighted Return**

If you have an investment account where the investment manager controls the cash flows into and out of the portfolio and you want to judge their overall performance, including their timing of the market, then you would use a money-weighted return. You would do the same if you were attempting to time the market yourself and wanted to check your performance.

The math gets more complicated here, but the concept is simple: When there is more money in the account, its performance is given more weight than when there is less money in the account. That way, a manager who has a lot of your money invested when your portfolio is increasing, and then only a little when it is decreasing, will have that good timing (or good luck!) reflected in a money-weighted return.

If you or your investment manager don’t engage in market timing, then this is not a useful judge of performance because it will overweight or underweight different periods of returns for reasons that are unrelated to the execution of the strategy.

### Simple Return

The return on an investment is most simply defined as the amount you gained as a percentage of the amount you invested. The simple return can be a good back-of-the-envelope calculation that works perfectly when you’ve only made a single investment, but in most common circumstances it will not be a good judge of the growth of your portfolio.

If you invested $100,000 in a Betterment account today, and after a year you have $110,000, you can safely describe your return as 10%.

But, consider what happens if you were to invest an additional $400,000 at the end of that year. Using the same calculation, you’d now find your simple return to be 2%. Did your investment performance suddenly drop by 8%? Thankfully, no. That is the limitation of a simple return—it treats all of the deposits into an investment account as having happened at the same time as the first deposit.

## Why do I have a negative % time-weighted return, but positive earnings?

With a time-weighted return, which is the industry standard return calculation used by Betterment, it is entirely possible to have a negative % return, despite having a net gain on your investments (or conversely, a positive % return with a net loss on your investments).

A time-weighted return assesses the performance of the underlying investments without being distorted by the timing or size of cash flows in and out of the portfolio (i.e. deposits and withdrawals).

Your time-weighted return is negative because the underlying portfolio that you are invested in has decreased in value since you began investing. You can see that graphically by looking at the % Returns graph from “Performance”.

However, your dollar earnings are positive because you deposited the majority of your current investment when the value of your underlying portfolio was lower than it is now. You can see that by comparing the % Returns graph to the $ Values graph on your “Holdings” page.

**Here’s an extreme example to illustrate this:**

Suppose, I invested $10 to start, and the market loses 50%. Now I have $5 in the account! Let’s say I then make a $100,000 deposit and the market goes up 10% immediately after that. In this case, I would have positive dollar gains, since I just gained about $10k (much more than my initial $5 loss). It was not because the portfolio has performed well thus far – in fact, it’s been negative overall since I started (it went down 50% and then up 10%). However, most of my money was invested when I was at the bottom.

In short, my time-weighted return is negative because my portfolio performed badly. My simple dollar return is still positive, because of the timing of my cash flows.

## Why do I have a positive % time-weighted return, but negative earnings?

With a time-weighted return, which is the industry standard return calculation used by Betterment, it is entirely possible to have a positive % return, despite having a net loss on your investments (or conversely, a negative % return with a net gain on your investments).

A time-weighted return assesses the performance of the underlying investments without being distorted by the timing or size of cash flows in and out of the account (i.e. deposits and withdrawals.)

Your time-weighted return is positive, because the underlying portfolio that you are invested in has increased in value since you began investing. You can see that graphically by looking at the % Returns graph on your Performance tab in your account.

However, your dollar earnings are negative because you deposited the majority of your current investment when the value of your underlying portfolio was higher than it is now. You can see that by comparing the % Returns graph to the $ Values graph on your portfolio page.

**Here’s an extreme example to illustrate this:**

Suppose, I invested $10 to start, and the market gains 50%. Now I have $15 in the account! Let’s say then I make a $100,000 deposit and the market goes down 10% immediately after that, In this case, I would have negative dollar gains, since I just lost about $10k (much more than my initial $5 gain). It was not because the portfolio has performed poorly thus far – in fact, it’s been positive overall since I started (it went up 50% and then down 10%). However, most of my money was invested when I was at the top.

In short, my time-weighted return is positive because my portfolio performed well. My simple dollar return is still negative, because of the timing of my cash flows. You can see both of these numbers in your own situation in the Summary tab of your Betterment account, by simply expanding each goal.

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