*one*of the possible outcomes -- many of which are significantly

*worse*than average. Unless you have an understanding of the

*variability*of stock market returns, you will likely overestimate the likelihood that your retirement plan will work.

In this post, I am again taking the viewpoint of an investor planning for retirement. We'll assume the same situation we assumed in Don't Plan Retirement Assuming Average Stock Market Returns. That is, we have a 45 year old who wants to retire at age 65. He has received a $100,000 inheritance, and wants to accumulate $670,000 in the 20 years remaining before he retires. It turns out if he receives the average 20-year percentage return in my Dow history database, his ending portfolio will be about $670,000. Do you think if he invests the $100,000 in the stock market at age 45 then all of his retirement planning problems are solved? Think again.

### How Much Will Your Stock Investment Grow? What Will $100,000 be Worth Invested in the Stock Market for 20 Years?

*(Note: if you want to know what $100,000 will be worth invested at a*

**fixed**rate of return (e.g., in Treasury Notes/Bonds or a CD), or NOT invested, see footnote.)### The Variability & Distribution of 20-Year Stock Market Results

In Range of Stock Market Returns in Dollars, we looked at the increasing gap between the best and worst outcomes as the holding period went from 10 to 100 years. From the high-low bars in that chart, we saw that in 20 years $100,000 could grow to as little as ca. $150,000, or as much as ca. $2,750,000. Think about the implications that gap has on your retirement planning! The above chart*(click on image to enlarge it)*fills in some of the detail; it gives us an idea of the probabilities in between the two extremes.

**This is critical information for retirement planning purposes.**

The graph shows the historical results of investing $100,000 in the stock market for 20 years. The horizontal axis shows values of the portfolio at the end of the 20 years assuming dividends have been reinvested. The lines and bars reflect the frequency of various outcomes for 92 20-year periods beginning year-end 1899. (Note: to calculate ending portfolio values for an initial investment of $1,000, divide by 100. To calculate the results for n thousand dollars, multiply the results for $1,000 by n. For example, for a $25,000 investment, multiply the results for $1,000 by 25.) Following are some questions this chart can help you answer.

### How Often Will My Ending Portfolio Be, For Example, Between $200,000 & $300,000?

The blue vertical bars show the number of years with ending portfolios in a given range. The scale for the bars is the vertical axis on the left labeled "frequency." For example, the second blue bar on the left shows that there have been seven times when the ending portfolio was between $200,000 and $300,000. (The labels show the upper boundary for each bar.) So, results have been in this range about (7/92=) 8% of the time.It's worth mentioning that over 20-year periods, unlike for 10-year periods, there have been no cases where the ending portfolio was less than the original investment. The worst performance was again turned in by 1928 -- i.e., the last year before the 1929 crash. Investors putting $100,000 into the market at that point would have had about $160,000 20 years later. While $160,000 is greater than the initial investment, performance like this would wreak havoc on most retirement plans.

What Are The Chances I Will Retire With $1,000,000?

The green line shows the percentage of years with ending portfolios

*above*a given level; the percentage is read on the right vertical axis. Remember, we're assuming that future results will be similar to results of the past century -- a reasonable assumption, I think, but certainly not a guarantee. Reading the green line above the $1,000,000 bar, we see that on the right scale the probability of an ending portfolio of more than $1,000,000 is between 30% and 40% (by my calculation, it's 33%).What Level Can I Be 80% Sure of Achieving?

To make this estimate, start at 80% on the right vertical axis and see where the 80% grid line intersects the green line. As you can see, it is somewhere between $300,000 and $400,000.

### What Are The Chances Our Investor Will Reach His Retirement Savings Goals?

Okay, back to our original investor. In this specific case, we want to know the likelihood that our 45 year-old investor's $100,000 investment will grow to $670,000 by the time he is 65. The probability of an ending portfolio of more than $600,000 appears to be a little over 50% (read on the right vertical axis); the probability of more than $700,000 appears to be a little less than 50%. Therefore, the probability of more than $670,000 is about 50%. (Or, more precisely, that has been the experience in the past.)If our investor plans based on the average percentage return of 10%, because of the variability, he may have only about a 50-50 chance of reaching his retirement goals. This variability in results is a concern for investors in the "accumulation phase" of their retirement plan. However, when things don't go as planned, they have options (because they're still working and saving). For example, they might decide to delay their retirement a few years. Unfortunately, those in the "distribution phase" (already retired) have many fewer options. As a result, it is critical that they be conservative in their estimates. In those cases, I think relying on a plan with only a 50-50 chance of success is playing retirement roulette; I try to assure an 80-90% success rate.

### Footnote: What Will $100,000 be Worth in 20 Years? (*Not* in the stock market)

What will $100,000 be worth in 20 years if it is *not*invested in the stock market is a somewhat easier question to answer. Whether the money is "put under a mattress" or invested in fixed income investments such as bonds and CDs, the value at the end of 20 years is more predictable -- at least in dollars. Predicting what those dollars in some future year will be worth compared to current dollars is a different issue. The compound growth/inflation calculator addresses both of those issues (for any amount, and for any timespan).

Notes: The above chart is based on DJIA (Dow Jones Industrial Average) data from my Stock Market Analysis Model/Spreadsheet. Results would be essentially the same if we used S&P 500 data. For this theoretical analysis we're ignoring the impact of taxes, commissions, management fees, etc. Years covered include year-end 1899 through 2010. Earnings & dividends prior to 1929 have been estimated based upon another market index. If you have trouble downloading the Excel spreadsheet, see this post.

### Related Posts

What Would $1 Invested in 19xx be Worth Now? Calculate the results for a*specific*20-year period (or between any other 2 years).

**Other looks at variability of returns/results**

Stock Market 20-Year Rolling Returns Graph of all 20-year (percentage) returns since 1900.

Don't Plan Retirement Assuming Average Returns: A slightly different and more complete presentation, including a table of 20-year probabilities. Best read in conjunction with this one.

The Variability of 10-Year Stock Market Returns: Similar to this post, but for 10 years.

Why Investing in the Stock Market for Less Than 5 Years is Risky: Similar to this post, but for 1 and 5 years.

Range of Stock Market Returns in Dollars for 10-100 Years Best & worst returns for each time period, in dollars. The current post is the detail of the 20-year bar in this post.

**Potential causes of the variability**

Dow P/E Ratio Impact on Future Returns: A factor influencing whether your results will be on the high end or low end.

The Impact of Initial P/E Ratio on 20-Year Stock Market Returns: another look at a factor impacting the variability in the size of the ending portfolios in this post.

The Stock Market Analysis Spreadsheet introduced in this post can be used to do additional analysis.

**For lists of other popular posts and an index of stock market posts, by subject area, see the sidebar to the left.**

Copyright © 2010. Last modified: 2/12/2012

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