# The Sequence of Returns Matters

Written by: Corey Janoff

# The Sequence of Returns Matters

Today’s post is going to get a little technical. Some of you will find it fascinating. Others will be bored out of your minds and probably will stop reading after a few sentences. It is basically a post about math. We are going to look at how the sequence of returns affects an investment portfolio’s value, especially when making additions or withdrawals. Sequence of returns means when and how the returns occur. For example, did your portfolio experience a handful of positive years in a row, followed by a negative year? Or did you experience several negative years in a row before seeing an upswing?

For a given time period, depending on whether you were adding money to your portfolio, or withdrawing money from it, your actual realized returns could vary drastically. This is especially true when you are just getting started with investing and don’t have a large balance, or when you first retire and are beginning to withdraw money from your accounts. Thanks to additions and withdrawals, you will understand that it is very difficult to compare your portfolio's performance to that of some benchmark or index.

For the ease of all calculations, we will assume all figures presented today are net of taxes and fees. In reality, taxes and fees will impact actual results. Let’s dive into it!

**Average Return vs. Actual Realized Return**

Let’s say you are brand new to investing and you are just getting started. You begin with zero and add $5,000 per year at the start of each year to your account. In the first three years, the portfolio grows by 10% per year. In the fourth year, the portfolio declines in value by 10%. In total, you have deposited $20,000. $5k per year over four years. The average annual return over that period of time is 5%. 10 + 10 + 10 – 10 = 20. 20 divided by 4 = 5. But did the account actually realize a 5% annualized growth rate over that four-year period of time?

The negative 10% year came after the account had over $20,000 in it, whereas the positive 10% years occurred when the account values were smaller. The negative 10% year affected the account more drastically than the positive 10% years did. The portfolio value after four years in this example is $20,884.50. What was the actual annualized average return realized in this example? 1.7%. See the below table for a breakdown.

What if instead of getting the negative 10% year after the account value was built up, the negative year occurred first, followed by three straight positive 10% years? We are still starting at zero. We still add $5,000 per year to the account over four years. The average per year is still 5%. -10 + 10 + 10 + 10 = 20 / 4 = 5. However, because the negative year occurred when the account value was at its smallest, it doesn’t affect the total return as much. The final portfolio value after four years in this scenario: $24,194.50. This translates into an average annual realized return of 7.7%. Looks quite a bit better than the 1.7% figure.

By changing the sequence of returns, instead of the actual realized return falling well below the “average” return, the portfolio ends up faring better than average! See the below table.

Keep this in mind when you are early on in the savings game and still in accumulation mode. This is especially apparent when your account balance is small and your deposits are large. The timing of your contributions in relation to ebbs and flows of the market will impact your account returns. Now, there is no way to consistently predict with accuracy when the market will ebb or flow. So there is some element of luck involved in how the chips fall.

As the portfolio balance grows and the amount added each year contributes a smaller and smaller percentage of the account value, the realized returns will gravitate closer to the average returns.

Continuing with the previous examples, if we have a $20,000 balance with no annual additions to the account and let the same return sequences play out, the end result is the same, regardless of where the negative 10% year falls. See the below illustration.

Why isn’t the realized return the same as the average return? Because the balance of the account changes each year. A 10% change on a $20,000 balance is a different amount than a 10% change on a $24,000 balance.

Due to changing balances, it is inappropriate to compare a yearly average to a realized average. One is an arithmetic average, the other is a geometric average. The arithmetic average is the simple one – the 5% yearly average in these examples. It is calculated by adding up each year’s return and dividing by the number of years. The problem is, it’s not an accurate representation of the actual average return realized. In order to know the average realized annual return over a time period, we need to calculate the geometric average.

If you find yourself comparing your accounts’ realized returns to the average annual return of some sample portfolio or index, you will likely either be pleased or disappointed. You’ll be pleased if your geometric average is greater than the arithmetic average return of the sample portfolio/index over that time period (example #2). You’ll be disappointed if the opposite is true (example #1). Remind yourself that it is not an accurate comparison.

Now, let’s take a look at how the sequence of returns affects things if we are withdrawing money from the account.

**Sequence of Returns and Retirement Spending**

Young investors typically aren’t overly concerned with portfolio returns early on in their careers. This is a good thing. Whether it is apathy or an innate understanding that they can’t control returns is debatable. Portfolio returns and the sequence of returns are out of your control. Early on, your main focus should be on saving enough to reach your long-term goals and periodically reviewing and revising your strategy to stay on track.

On the other hand, most people approaching retirement or in retirement *are* concerned with portfolio returns. Once in retirement, people don’t have the ability to save more. They have to trust that what they did over their career will be enough. For those who planned and saved diligently, keeping the faith should be easier than it is for those who procrastinated and didn’t take saving as seriously. Also, when a 10% change in value is a six-figure sum, it can be a little gut-wrenching. In retirement years, the reviewing and revising part of financial planning can be crucial.

Let’s take a look at some examples of how the sequence of returns while making withdrawals can impact the value of a portfolio. We’ll start with the ugly one and then move onto the pretty one.

It is not uncommon for the market to deliver two to three negative years in a row. 1929-1932. 1946-1949. 1968-1970. 1973-1974. 1980-1982. 2000-2002. 2007-2009. Buckle your seatbelt. It will likely happen multiple times during your life.

For a retiree, the portfolio returns during the first handful of years of withdrawals can have a major impact on the potential longevity of the portfolio. If you retire at the top of a bull market and then you see a few negative years at the beginning of retirement, it could make you question your decision to retire.

If we use the same 10% numbers as before for the annual returns, what happens if negative years occur at the beginning of retirement? We’ll assume a person retires with $2,500,000 and withdraws $100,000 per year from their account at the beginning of the year to cover spending for the year. Take a look at what happens if we get three negative years, followed by three positive years.

If we suffer three straight negative 10% years, by the end of year three this person might be shaking a little bit. Three years ago, they had $2.5M. Now they are down to under $1.5M after they take out $100k for annual spending in the beginning of year four! Originally this looked to be a safe withdrawal rate (4% of the original balance). Now, this person may need to revise their strategy a bit and reign in spending. The new safe withdrawal rate after year three might appear to be between $65-80k.

If the three negative years are followed by three positive 10% growth years, the portfolio balance grows, even with the $100k annual withdrawals. Things are looking a little better after year six.

Now let’s look at a happier example where the retiree experiences three years of positive 10% growth at the beginning of retirement.

In this example, after year three of retirement, this person is pretty happy! Spending $100k per year and still seeing the initial portfolio balance increase by $500k! They might decide to fly first class on the next trip to Hawaii! They’re off to a very comfortable start to retirement.

Now, if three positive years are followed by three negative years, they might come back down to earth from Cloud 9. Similar to the first three years for person number 1, their portfolio value changes by $1M in three years. Still, sitting at $1.9M after six years in retirement feels a bit better than the person who is sitting at $1.7M.

Don’t discount the impact of luck in our lives. This is just an example and odds are the actual results for everyone will be different, but the element of luck will still be there. Some of us will be a little luckier than others in how the sequence of returns plays out in relation to our additions and withdrawals.

**Reviewing and Revising the Strategy**

This is why financial planning is crucial. Reviewing and revising the strategy over time can help you to remain on track to achieving your goals. Some years may have to be leaner than others. Other years may allow us to afford more luxuries. Goals may need to be revised a bit as time goes on. We can’t control what the sequence of returns will be, but they do matter. We can control how much we save, where we invest, and how much we spend. Focus on those three things and try to spend less time worrying about the rest.

*Disclosures:*

*All examples are hypothetical and for illustrative purposes only. All investments have the risk of loss, including total loss of principal. Saving more or spending less does not eliminate investment risk. Investments involve fees and expenses, which will impact the net results. Taxes can further impact net portfolio results. Consult with a tax advisor for your specific tax implications. Consult with a financial advisor before implementing or changing your investment strategy. *