## 2013-04-18

### Simulating Historical Investment Returns

All investors must keep in mind that historical returns do not guarantee future returns.  However, the past is often a useful place to look to get some sense of what to expect in the future.  This article shows quantitatively that long-term, annualized, inflation-adjusted returns on the US stock market during periods from 1950 to the present have been approximately as follows:

40 years - - - - - - - (5.0 to 7.5%)
35 years - - - - - - - (5.0 to 7.0%)
30 years - - - - - - - (4.0 to 8.5%)
25 years - - - - - - - (3.0 to 11.5%)
20 years - - - - - - - (1.5 to 13.0%)
15 years - - - - - - - (-1.0 to 14.5%)
10 years - - - - - - - (-3.5 to 16.0%)

And here's the graphical representation of the data, where each color is a different starting year, the x-axis is the number of years invested, and the y-axis is the annualized, inflation-adjusted rate of return:

 Play with the original graph here

For short investment horizons (<10 years), the annualized rate of return is highly dependent on the exact date you started investing.  Over longer periods of time, the short-term variability fades out and the range of performance for different start dates starts to narrow off.

I've received several requests to talk about historical stock market returns.  Most discussion of the matter online is extremely imprecise, alluding to yearly gains anywhere between 3 and 12%.  It's difficult to find analyses that take into account inflation and clearly state whether or not they assume that all dividends paid are reinvested.  When I couldn't find a decent tool online, I built my own.

I created this graph using my SimVestment spreadsheet - you can make a copy and play with it yourself.  It's made possible by high-quality, no-cost data on the historical prices and dividends of the Standard & Poor 500, a stock market index commonly used to represent the overall performance of US companies (1).  From this, I constructed my own historical investment model that takes into account inflation and assumes reinvestment of all dividends, a typical investment practice.  This simulation does not take into account any transaction costs, taxes, or fees.

This model can simulate the historical outcomes of a highly-realistic investment strategy:  investing the same amount of money, adjusted for inflation, each month.  This feature makes this model more useful than the typical S&P500 return calculator, which only considers how much a certain amount of money, invested at some previous time, would have grown in value to the present day (2).

It's important to keep in mind the power of compound interest: even at fairly low average annual rates of return, compounding growth can really work for you.  The net real returns - the percentage increase in the inflation-adjusted value of the money you've invested, a certain number of years after you began investing - looks like this:

 As the Rolling Stones said: Time Is on My Side (3).  Original graph here.

Each color represents, as in the previous graphs, an investor starting in a different year.

Perhaps the volatility in the graph above makes you a little sick, and you'd like to put that money under your mattress instead?  Long-term inflation rates have averaged 3-5%, and that's how fast your money, when held in cash, is losing value.  Investing in cash is still investing: very low volatility, but an absolutely terrible return!

### A Side-Note About Annualized Return

There are several different ways to calculate investment return (4).  Many discussions of market return make statements about 'average annualized return'.  They are often referring to the arithmetic average return.  This value is calculated as you might expect, by summing the returns over several years and dividing by the number of years:

Arithmetic Average Return = (Year #1 Return + Year #2 Return + ... + Year #N Return) / (N # of years)

This value is not only completely useless, it's highly deceptive.  Consider the following scenario: you invest $100. The first year, the value of your investment drops 50% and is worth$50; the second year, the value increases 50% and is worth \$75. Your arithmetic average return over these two years is 0%, but you've lost 25% of the value of your original investment. Beware this misleading metric.

In the previous example, the value you care about - what your investment is worth now versus what it was worth when you bought it - is the net return.  What you'd really like to know is, on average, how much the value of your investment has changed per year (or month, or day) since you bought it; this is the compound, or geometric, average annualized return.  But be careful!  You can't simply divide net return by the number of years to get the compound average return:

Compound Average Return = (Year #1 Return) x (Year #2 Return) x ... x (Year #N Return) ^ (1 / N # of years)

The situation gets more complicated if you want to analyze a strategy that invests money regularly, all the while dealing with inflation and the reinvestment of dividends.  Problems like these are best handled by a computer program or a spreadsheet like the SimVestment simulation I used above.

### The Moral of the Story

Historical returns are quite variable over the short term, but the long-term growth trends are clear.  This means you should invest as much, as early, and as regularly as possible!  If you don't have an IRA, open one immediately; if you're not contributing to your workplace retirement plan, especially if there's a company match, fix that!  If your expenses are equal to or exceed your current income, you may want to check out some of the articles on saving money.

Investments in a Vanguard 500 index mutual fund (VFINXVFIAX) or ETF (VOO) will track the S&P500.

(originally published on 2013.04.18, this article was reposted with clarifications on 2013.05.28)

(1) Robert Shiller, Online Data - http://www.econ.yale.edu/~shiller/data.htm
(2) S&P500 Return Calculator - http://dqydj.net/sp-500-return-calculator/
(3) The Stones were covering Jerry Ragovoy's original work - http://en.wikipedia.org/wiki/Time_Is_on_My_Side
(4) Investopedia: Calculating Investment Return - http://www.investopedia.com/articles/08/annualized-returns.asp