Monday, 24 February 2014

Risk and Time

Click here for an enlarged version:

A Better Bar Chart Showing Risk Over Time

This chart shows the growth of a $1000 investment in a random walk model of the S&P 500 stock market index over time horizons ranging from 1 to 40 years. It pretty much speaks for itself, I hope - that was the intention, anyway.

The chart clearly shows the dramatic increasing uncertainty of an S&P 500 stock investment as time horizon increases. 
-  For example, at 40 years, the chart gives only a 2 in 3 chance that the ending value will be somewhere between $14,000 and $166,000.
-  This is an enormous range of possible outcomes, and there's a significant 1 in 3 chance that the actual ending value will be below or above the range! You can't get much more uncertain than this.

As long as we're talking about risk, let's consider a really bad case. If instead of investing our $1000 in the S&P 500, we put it in a bank earning 6% interest, after 40 years we'd have $10,286.
-  This is 1.26 standard deviations below the median ending value of the S&P 500 investment.
-  The probability of ending up below this point is 10%. In other words, even over a very long 40 year time horizon, we still have about a 1 in 10 chance of ending up with less money than if we had put it in the bank!

Look at the median curve - the top of the purple rectangles, and follow it with your eye as time increases. You see the typical geometric growth you get with the magic of compounding.
-  Imagine the chart if all we drew was that curve, so we were illustrating only the median growth curve without showing the other possible outcomes and their ranges.
-  It would paint quite a different picture, wouldn't it? When you're doing financial planning, it's extremely important to look at both return and risk.

There's one problem with this chart. It involves a phenomenon called "reversion to mean." Some (but not all) academics and other experts believe that over long periods of time financial markets which have done better than usual in the past tend to do worse than usual in the future, and vice-versa. The effect of this phenomenon on the pure random walk model we've used to draw the chart is to decrease somewhat the standard deviations at longer time horizons. The net result is that the dramatic widening of the spread of possible outcomes shown in the chart is not as pronounced. -  The +1 standard deviation ending values (the tops of the bars) come down quite a bit, and the -1 standard deviation ending values come up a little bit. 
-  The phenomenon is not, however, anywhere near so pronounced as to actually make the +1 and -1 standard deviation curves get closer together over time. 
-  The basic conclusion that the uncertainty of the ending values increases with time does not change.

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