Rolling Returns for the S&P 500: Understanding the Concept and Calculation

Rolling returns for the S&P 500 are important to understand. Not only for S&P 500 but rolling returns are essential for any investment you make. What are rolling returns and how do you calculate them? What have been the rolling returns for S&P 500?

Rolling returns are returns annualized (or any time frame you prefer) from one period to another. It shows how an asset or stock has performed in the past and gives you an indication of how the annual returns vary. Rolling returns are based on CAGR and the principle of moving averages.

We start by explaining what rolling returns are:

Table of contents:

What are rolling returns?

Rolling Returns - Understanding S&P 500 Performance

Rolling returns are the current returns of a time series annualized for a certain period of N years (or bars), ending with the latest year. Rolling years are useful when investigating how previous periods have fared, and evaluating what is the most likely best and worst scenario of an investment based on historical numbers over that particular time span.

We use CAGR (Compound Annual Growth Rate) to measure annual returns. A rolling return might be, for example, when you look at the CAGR from 2000 to 2003, 2001 to 2004, 2002 to 2005, and so on.

Rolling returns are useful when you are looking at long-term time series:

Why use rolling returns?

The main advantage of rolling returns is that it makes it possible to average out the returns from a stock, index, or for example a mutual fund or ETF. Because rolling returns measure the CAGR/annual returns over many periods, it can be very helpful for gauging an investment’s historical performance and how likely you are to face losses over that period (see examples further down in the article).

For example, if you are looking to invest in stocks, you should have at least a 5-year investment horizon, but preferably ten years in our opinion. By looking at the rolling 5-year returns throughout history, you get a good sense of what kind of returns you can get over such a time span, even though history never repeats itself.

Why are rolling returns important?

It’s important because we know that retail investors are terrible investors, according to research. Retail investors are bad investors because they make behavioral mistakes. All investors and traders are prone to behavioral biases and these influence our thinking and behavior in the markets in a bad way, unfortunately. And the reason why we make poor decisions is due to drawdowns.

When you are in the middle of a recession and the stock market has gone down 25% or more, many investors are prone to sell and give up. They simply can’t take the pain of seeing losses – often at the exact wrong timing.

Below is a quote we have used several times on this blog (found in Quantitative Value by Wesley Gray and Tobias Carlisle). In the decade ending in 2010, the majority of the investors in the best-performing fund managed to lose money!

In the decade to December 31, 2009, the Wall Street Journal reported that the best-performed U.S. diversified stock mutual fund according to fund-tracker Morningstar was Ken Heebner’s CGM Focus Fund. Over the decade, the fund had gained 18.2 percent annually, beating its closest rival by 3.4 percent per year, which is exceptional. The typical investor in Heebner’s fund, however, lost 11 percent annually. Investor returns, also known as “dollar-weighted returns,” take into account the capital flowing into and out of the fund as investors buy and sell. The investor returns were lower than the fund’s total returns because investors bought into the fund after it had a strong run and then sold as it hit bottom. Heebner’s fund surged 80 percent in 2007, and then investors poured in $2.6 billion. The following year, the fund sunk 48 percent, and investors yanked out more than $750 million. Said Heebner: “A huge amount of money came in right when the performance of the fund was at a peak. I don’t know what to say about that. We don’t have any control over what investors do.” This behavior caused the investor returns in Heebner’s fund to be among the worst of any fund tracked by Morningstar. Amazingly, this means that the worst investor returns were found in the decade’s best-performed fund. We are each our own worst enemy.”

This is why you must look at long-term rolling annual returns when you are investing and trading. You need to avoid knee-jerk decisions in the midst of a crisis and be prepared for drawdowns and temporary inevitable losses and setbacks. Even though a market returns 9% annually, it doesn’t grow in a straight line, unfortunately. The ride is very erratic and the media is filled catastrophic headlines all the time. As you will see in our graph below, the S&P 500’s return always ebbs and flows.

How are rolling returns calculated?

We prefer to use monthly data when we are looking at rolling returns. That doesn’t include all the drawdowns between the months as you’ll have on daily bars, but we believe it’s a good approximation.

Let’s show a practical example of how to calculate rolling returns:

How to calculate rolling returns

Let’s assume you want to look at 5-year annual returns of the S&P 500 (SPY) from 1993 until today.

First, you need to decide how long lookback period you’ll use. If you use 5 years you can start in February 1993 and end in February 1998 (SPY started trading in February 1993). Then you go forward and the next observation is from March 1993 until March 1998. You go on like this on each monthly bar all the way until you have the current and latest data.

This is all there is to it. Pretty simple!

Or is it?

It’s slightly more complicated because you want to look at geometric returns and not arithmetic moving averages:

The correct measure is to use the compounded annual growth rate (CAGR) and not the arithmetic measure. These two are very different! We have explained why arithmetic and geometric averages differ.

Below is a screenshot of how we did the calculations in OpenOffice:

The calculations for CAGR are in the circle. You can, of course, calculate the CAGR in Amibroker or any other trading software, but we found it to be much easier and faster in a classic spreadsheet.

What are the annualized rolling returns for the S&P 500?

Let’s end this article by showing the rolling returns of the S&P 500. We use the SPY (the ETF):

The S&P 500’s annual rolling returns fluctuate wildly depending on how long (or short) lookback period we use: the shorter the lookback period, the more swings up and down.

The chart below shows the annual rolling returns for S&P 500 for 3 (blue line), 5 (red line), and 10 years (yellow line):

The 3-year rolling returns are frequently showing negative returns over a 3-year period, while the yellow line shows that the ten-year annual rolling returns only once were negative – in the middle of the financial crisis in 2008/09.

This is as expected: the longer the time span you use on the rolling returns, the less likely you are to have negative returns. This is because of the long-term upward bias in stocks due to monetary inflation and productivity gains. We have covered this bias in our night strategies trading article.

Hopefully, after reading this article, you can compute the rolling returns of the S&P 500 yourself. It’s not difficult and you can use a template and just copy and paste your own numbers into it.

FAQ:

What are rolling returns, and why are they important for investment analysis?

Rolling returns represent annualized returns over specific time frames, providing insights into historical performance. They are crucial for assessing an investment’s likelihood of success and potential losses. Rolling returns are calculated using the Compound Annual Growth Rate (CAGR) and moving averages. The process involves selecting a time frame, such as 5 years, and updating the data on a rolling basis to observe trends.

Why use rolling returns for long-term time series analysis?

Rolling returns help average out the performance of stocks, indices, or funds, providing a comprehensive view of historical performance. This is especially valuable for investors with long-term horizons, allowing them to anticipate potential returns and losses. Rolling returns are essential for mitigating behavioral biases in investing, such as the tendency to make impulsive decisions during market downturns.

What is the role of rolling returns in dealing with market volatility?

Rolling returns offer a way to navigate market volatility by smoothing out short-term fluctuations. This long-term perspective helps investors stay focused on overall performance and avoid reacting impulsively to temporary market downturns. Investors should consider 5-year or 10-year rolling returns to gain insights into long-term performance trends.