### Key Points

- Since 1973 the S&P 500
^{® }Index has posted considerable gains—over this period the index has averaged over 10% per year in gains after reinvesting**dividends**, before**taxes**and**fees**. - However, investigating other 45-year periods (going as far back as 1871) leads to a more useful picture of the index’s performance across differing economic environments.
- According to history, it’s better to invest in the index over longer periods in order to increase the likelihood of providing favorable returns and decrease the likelihood of losing money.

### Recap

In what seems like a lifetime ago, in Part 2 of this series we looked at the potential benefit that an individual might experience by investing in the S&P 500^{® }Index over an entire lifetime (95 years). In that post, we showed that had a hypothetical $100 investment in the index in 1923 (which is worth about $1,500 in today’s dollars) would have grown to over a million dollars by the end of 2017, before fees and taxes.

In a later post, we looked at the potential benefit of investing in a **passively invested** index fund, with low fees whose benchmark was the S&P 500^{® }Index, but this time over 45 years, which might be considered the *investment lifetime* of an individual. This time we showed that an investment of $1,728.03 in 1973 (which is worth about $10,000 in today’s dollars) would be worth around $144k today (see **Figure 1** below).

In this post, we’ll provide a more realistic analysis of just how much the S&P 500^{® }Index can return over an individual’s *investment lifetime* by studying the index’s returns over a multitude of 45-year periods. We’ll still be using history as our guide in this analysis, but our goal is to include additional data in order to generate more robust insights. So let’s see where this analysis takes us.

### A Little Goes a Long Way

Over the last 45 years (January 1, 1973 through December 31, 2017) the S&P 500^{® }Index (with dividends reinvested) has returned about 10.3% annually (before taxes and fees). In the past we simulated the performance of this index with a modest fee of 0.08% per year to provide some insight into the performance of a simple passive strategy. According to the hypothetical simulation in **Figure 1** below, the performance of this simple strategy can be quite compelling to someone saving for **retirement**.

But this simulation was performed using just a single 45-year period—the 45-year period ending in 2017. If we are to gain some confidence in this type of passive strategy it behooves us to explore other 45-year periods to see if this additional data might impact our potential investment decisions.

### Keep On Rolling

Given this, let’s consider rolling 45-year periods. This means that not only will we look at January 1, 1973 through December 31, 2017, but also we’ll consider December 1, 1972 through November 30, 2017, and so on. Thus, we can step back our 45-year investment horizon one month at a time and analyze the performance of the S&P 500^{® }Index across all of these periods to obtain a more meaningful insight into how the index behaves over many different environments. Similarly, it may be helpful to explore other investment horizons beyond just 45 years. As such, we’ll also look at 5-year, 15-year, 25-year, 35-year, and 45-year rolling periods as well. The results of this analysis are presented in **Table 1** below.

This table was created from an online calculator provided by DQYDJ, so feel free to play around with my assumptions in order to explore on your own. The data for this analysis goes back to 1871, well before the S&P 500^{® }Index was created so there has been some extrapolation and interpretation done on the part of DQYDJ in order to assemble this particular dataset.

As is often the case with financial analysis, it’s great to have more data, but this can come at the price of having to rely on imperfect information. Accordingly, we must do the best with what we have at our disposal, while still maintaining an understanding of the relative concerns and drawbacks that we must face using imperfect information. Given all this, it makes some sense to leverage this longer history in our analysis even though the older data is not perfect; but nevertheless, we’ll dig into some of these data concerns later on in this series. But for now, let’s dig deeper into the details of this analysis.

The data used to create the results presented in **Table 1** runs through December of 2018, and the returns have been adjusted for **inflation**. Adjusting for inflation is important whenever we compare returns across multiple time periods because a 10% return in the S&P 500^{® }Index when inflation is 10% has a different significance from a 10% return in the index when inflation is 0%. In the former case, the real (inflation adjusted) return is zero, while in the later case, the real return is still 10%. In addition, it’s important to note that the hypothetical results in **Table 1** do not account for fees or taxes.

### The Results

The first row represents the average annualized real return over a given investment horizon. For example, the average return for all the 45-year rolling investment periods is 6.434%, while the average return for all of the 5-year rolling periods is 7.081%. The average return seems to go up slightly as the holding period goes down, but this is just happenstance based upon the specific time periods used in the analysis.

The second row represents the median annualized real return over these five holding periods. The median return signifies that for a given holding period, half of the annualized real returns are above this return, and half are below. For the most part, the average return seems to be similar to the median for a given investment period.

The third and fourth rows represent the maximum and minimum annualized real returns, respectively for a given holding period. For the 45-year holding period the range from minimum to maximum is from 3.539% to 10.209%, while for the 5-year holding period the range is from -13.323% to 33.346%.

The fifth and final row represents the **standard deviation** of the average return. For a more formal understanding of standard deviation, I suggest you check out Part 2 of my series on **Risk Management**, where I provide an introduction on this concept. Essentially, this fifth row tells us by how much from the average annualized real return would we expect a given holding period’s return to deviate. For example, we would expect 68% of the 45-year investment horizon annualized real returns to fall within one standard deviation of the average annualized real return, which is 6.434% plus/minus 1.270%, or a range of 5.164% to 7.704%. At the same time, we would expect 68% of the 5-year investment horizon returns to fall between a range of -0.848% to 15.010%.

### Insight Time

So here are some basic insights that we can draw from the rolling period analysis presented in **Table 1**:

- As the investment horizon increases, the minimum observed return improves; essentially, time is your friend. The longer one invests, the lower the chances of losing money. This notion once again highlights the power of
**Investing Forever**. Essentially, every 25-year period within this dataset produced a positive return, even after adjusting for inflation. So if you’re worried about preserving the purchasing power of your wealth, an easy solution is to simply wait it out—if you happen to have a few decades of time at your disposal. - However, just as the worst-case, minimum return softens as the holding period increases, so does the the best-case, maximum return. As noted, the best 5-year annualized real return is 33.346%, while the best 45-year annualized real return is only 10.209%. This should make sense, as it’s much more difficult to average a +33% return over 45 years, but quite possible for the market to pull this off for just one 5-year period. No surprise here, I hope.
- The average return is fairly stable across holding periods. This is helpful to understand, and essentially tells us that we can expect about 6-7% in return on average (after adjusting for inflation) when investing in the S&P 500
^{® }Index. Further an interesting shortcut to remember is that a 7% annualized real return means your money will double (even after adjusting for inflation) every 10 years. Not a bad return, right? - Further, the standard deviation of returns tends to decrease as holding period increases. This is another benefit of Investing Forever—meaning the deviation from this 6-7% annualized return with a 45-year holding period is much smaller than compared to a 5-year holding period. This means that you’re more likely to come close to this 6-7% annualized real return the longer you keep your money invested in this index, so if you’re Investing Forever, then more power to you.
- The worst 5-year annualized real return for the index was -13.233%. This worst-case observed outcome would result in a loss of about 50% of your capital’s purchasing power over five years, which can be concerning for even the boldest investors.
- However, if you can hang on for longer, the worst-case 15-year annualized real return ends up being -2.133%, which would result in a loss of about 30% of your capital’s purchasing power over fifteen years. One interesting point to consider is that if you had left your capital under your mattress for 15 years, it’s likely that you would have also experienced this loss of purchasing power as well, given that inflation averages 2-3% a year on average.
- But if you can hang on for even longer, the worst-case 25-year annualized real return ends up being 2.074%. Over this period, your purchasing power would have grown by about 67%. So according to history, if you can hang on for twenty five years it’s quite likely that you would have a profit, even after adjusting for inflation.

Putting this all together, one comes to understand that the average real return for the S&P 500^{® }Index is stable across holding periods, but to reduce **risk** of under performing this average return or even losing money in general, it behooves investors to invest into this type of strategy for as long as possible. But just how good is a 6-7% real return? Is the risk of losing money really worth the benefit? And just how useful is that data from the late 1900s in our analysis. Let’s continue this inquiry in Part 4 of this series for more color on all this.