In part one, we examined some the basic charactistics of historical S&P 500 data.  Most importantly, we noticed that month to month, S&P 500 returns are terribly unpredictable.  However, in this part, we will exam how time will be our great risk reducer!  We will model our historical S&P 500 data to answer one very important question: long do I need to leave my money invested in the market to reasonably ensure I will have solid returns?  I’ll conclude that from historical data, planning on 10 years seems to do the trick. 

(I’ll remind everyone that the data has had inflation removed (by the CPI), so all returns are real returns.)

Modeling the Time Averaging Factor:

Now that I bored you to death with some analysis in part one, let’s get to the big question.  As we noticed, any given month’s return is completely unpredictable.  But you probably also noticed that except for the big dot-com bust, the overall trend is positive.  Therefore, the question is how long do I need to leave my money invested in the market to reasonably ensure I will have solid returns?  This is ultimately what I hope to answer.

Using various lengths of investment times (holding times), I calculated the annualized return for each occurrence of that investment time throughout this data.  For example, there were 1270 different times in which you could invest for 1 year during this ~106 year time period.  There were 82 occurrences of 100 year investment periods.  Remember the data is monthly.  I used a sliding window (sliding 1 month at a time).

We can now answer this question: how often do I get at least a certain return if I put my money in for a given length of time? More specifically, I determined the lowest return you could expect to get for 1%, 10%, 33%, 50%, 66%, 90% and 99% of the time for different investment time lengths (varying from 1 year to 100 years).  Confused?  Let’s look at the plot.

First, looking at the curves at different points on the horizontal axis corresponds to different investment length periods.  The vertical axis shows the annualized return.  Now, to the curves themselves.  Each curve represents the probably (percent of time) of getting at least the corresponding annualized return.  For example…

Looking at the bright green curve (on top), you will only do this well 1% of the time if you invest your money for the time specified by the horizontal axis.  This is the best you should expect to do.  The dark brown is the opposite.  You should get this return or better 99% of the time.  Hence, this is almost the worst you can do (you will do better than this 98% of the time!).  The colors in between show the other percentages.  The 50% curve means your return would be that good or better 50% of the time.  Your return will be worse 50% of the time too!  So this is the “average” return for a given investment length.  We can use this plot to see what chance we’d have at a given annualized return as a function of how many years we have the investment invested.

Analyzing the Time Averaging Factor:

Let’s look at the plot.

First most, notice how the envelope gets tighter as the investment period increases in length.  We expect this because longer periods have more up’s and down’s which tend to balance each other out (akin to the chances of flipping 2 tails in a row versus the chances of flipping 20 tails in a row).  Time is averaging out the odds!

Second, we notice that all the curves converge to about 8.5% annualized return for the longest investment periods.  This is also expected for the same reason as above.  As the investment period lengthens, the best and worst probabilties become the same since both have enough up’s and down’s to be statistically identical!

Now for the good stuff.  Let’s look at the 90% curve (close to the bottom of the statistical barrel!).  This plot shows that historically, if you invested for at least 7 years, you’d have a real (remember inflation!) positive return (given, the gain may be insignificant for some time).  Looking at the 66% curve, even if you only held your investment for 1 year, you’d have had a 2.2% positive return 2/3 of the time!  Here’s a zoom-in of the plot.

So the question is how long do we need to plan to leave our investment invested to assume a good return.  Our plot shows a few knees in the curve.  Most of these knees occur within 10 years.  The 66% and 33% curves’ knees occur even sooner — maybe 5 years.  The worst return has another knee ending around the 18 year period.  What this means to us is that much of the risk is reduced within 10 years — depending on how safe (i.e., which curve) you look at.  Being able to wait another 10 additional years will significantly increase the returns of even those worst odds.

Concluding Part Two:

My last comment… You’ll notice how the best returns are lessened as the investment period increased just like the worst returns improved.  This truly shows the gambling nature of short term investing.  The highs are high and the lows are low.  And unless you can find a pattern to the 3rd plot above, you truly are rolling the dice.  In the end, the average person will pick as many winners as losers, and he’ll end up getting the same total return as if he had simply invested for the long term, except one thing… transaction costs.  Each time he buys or sells, returns are eaten up by fees.  Sure, plenty of people will beat the long term return.  But they are lucky and even more are unlucky (due to transaction fees).

My advice?  Don’t gamble with your investment money.  It’s worth too much.  Invest long term, and invest with index funds (their low turnover makes them long term investments by definition).  You’ll minimize your expenses and minimize your risk.  It might not be glorious or exciting, but it gives us all the best shot.