Average, Compound, and Sequence of Returns: Why They Matter

Disclosure: This article is written for entertainment purposes only and should not be construed as financial or any other type of professional advice.

When making financial plans, average investment returns can be useful in calculating the future value of my investments. But the results can also be misleading, potentially leaving me with a shortfall during my retirement or spending years.

The benefits of using average returns

For general planning purposes, using an annual return based on historical averages can help me determine how much money I should set aside and invest periodically to reach my goals.

For example, let’s say I’m 25, plan to retire in 40 years with $1 million, and hope to earn 11.23% annual investment returns (based on the arithmetic average of S&P 500 returns from 1965 to 2014). I’ll need to set aside and invest $1,613.23 each year. Alternatively, if I planned on investing in short-term treasury bills and earning an average of 5.04% annually, then I’d set aside $8,197.70 every year to reach my million-dollar target. (See my article on formulas for financial goals to calculate savings and investing rates.)

Using average returns, I would realize that I need to set aside at least $1,600 each year from now until retirement.

Further, if I considered the difference between the long-term returns of the S&P 500 and treasury bills, and the amount I’d need to save to reach financial goals (approximately $1600 in the S&P 500 vs. $8200 in treasury bills), then I may decide to accept the risks associated with stock-market investing.

So, the use of average returns can give me a starting point for determining my annual savings rate AND give me insight into how more risk and higher returns over long periods of time are beneficial to attaining my financial goals.

Why compound return is better for planning purposes

Average (arithmetic) returns can be misleading, though, because investment balances don’t grow on a linear basis as the math and concept suggest.

For starters, an average arithmetic-based return doesn’t account accurately for actual growth or decline in investment balances on a yearly basis. Such a return is simply the total of all returns divided by the number of years.

For long-term planning purposes, a more meaningful number is the geometric average (or compound) return, which represents the actual rate of return. This approach accounts for the impact of positive and negative years.

Notice that the compound return of the S&P 500 from 1965-2014 is 9.84% whereas the arithmetic average is 11.23%. (Similarly, the compound return for three-month treasury bills is 4.99%, compared to an arithmetic return of 5.04%; the less dramatic difference here can be attributed to less dramatic swings in annual returns compared to stock-market activity.)

In his book, How Much Money Do I Need to Retire?, former hedge fund manager and financial mentor Todd Tresidder gives some simple examples of these calculations to illustrate this concept.

Let’s say I experience investment returns of -20% one year and 20% the following year. If I started with $100, I would have $80 at the end of the first year [100 + (100 x -.20)], and $96 at the end of the second year [80 + (80 x .20)]. Alternatively, if my first year return was 20% and my balance grew to $120 [100 + (100 x .20)], but was followed by -20% returns [120 + (120 x -.20)], I’d also have just $96.

The arithmetic average annual return is 0% (-20% + 20% = 0%). Following this formula would mean that I have $100 at the end of two years. But because of the impact of negative returns, my actual balance is $96. The compound (aka geometric average) return is about -2%.

During the years I’m saving toward a goal, using average arithmetic returns for planning purposes may cause me not to set aside enough money for investing each year. So, I should consider using a rate that is closer to the compound return for planning purposes. (I’ll also mention that historical returns, even over 30-50 years, may not accurately predict future returns; but for now, I’ll consider the past as a relevant indicator of the future over the long haul).

How and why the sequence of returns matters

Calculations (and investment-return projections) become more complex when I’m actually ready to spend money to realize my goals. At this point, when I’ve stopped adding to my investment balances and am starting to take distributions, I need to be concerned about the sequence of returns.

Let’s say I’ve amassed $1 million and am now planning on withdrawing 5% each year, which seems reasonable considering average investment returns from the past. Initially, I envision the next five years looking like this:

But I’ll experience returns as they happen, not as a steady average. Instead of the originally-envisioned scenario, this realistic scenario could happen:

In the second scenario, my average (arithmetic) return over 5 years is 8%; however, the sequence of returns results in a spend down of my principal, even though I adjusted my withdrawal rate based on the declining investment balance. So, the sequence of returns matters.

This set-up above is a fictional illustration. But if I had retired in 1999 and held investments in the S&P 500, then I would have experienced these returns:

Year | S&P 500
2000 | -9.03%
2001 | -11.85%
2002 | -21.97%
2003 | 28.36%
2004 | 10.74%

And my million-dollar portfolio would have shrunk to $681,000 even if I adjusted my spending. So, a few bad years can derail my retirement plans, particularly if I had been counting on average returns.

How to plan for uneven investment returns

In Todd Tresidder’s books on retirement, he offers deeper insights in regard to anticipating and dealing with these periods of decline. Right now, though, I’ll focus on the main idea that investors experience returns as they occur, not as averages.

There are at least a handful of ways I can deal with uneven investment returns, particularly stock-market returns. These include:

• build and manage a diversified portfolio, increasing the weight of bonds and fixed-income components as I get closer to needing money for expenses
• save and invest much more each year than plans created with average returns suggest
• hold a certain number of months’ worth of expenses in cash so that I can avoid cashing in investments during years with negative or low returns
• accumulate enough wealth and structure investments so that I can live off of interest and dividends (and avoid spending down balances altogether)
• reduce or eliminate withdrawals during periods of sluggish or negative returns through temporary adjustments in my lifestyle

When young and starting to accumulate wealth, I considered compound returns (or geometric average returns) to calculate how much to save for future goals. However, as I approach spending my investment balances, I’ve learned how the sequence of returns can impact my wealth over the long term and have started to plan accordingly.

How have you managed the sequence of returns risk when planning and living your retirement?