The shackle of time 2

In the last post, we removed the time dimension in order to clarify certain aspects of the S&P 500 returns.  We found that with an investment horizon of five years, there was historically about a 25% chance of losing money and a 25% chance of more than doubling.

Even though we looked at cumulative returns, it was still the case that the data was serially correlated; in other words, it could be that the eventual return was not independent of the starting year of the five-year period.  To gauge this, we must return to the time dimension that was previously removed.

The chart on the right plots the five-year returns for all five-year periods starting from 1910.  What it shows is that even with longer time frames, timing or luck still plays a key role. 

For example, any such investment in the S&P 500 between late 1950s and 1980 did not double in five years no matter which year the investment was made.  Then again, if the investment was made in the 40s and 50s, no one lost money in a five-year period, similarly in the 1980s.

So the fact that we saw a 25% chance of doubling (or losing money) over history says much less about what might happen in the next 5 years than the simple number suggests.

In response to a reader's comment - the data series was described as "real total return" so these are inflation-adjusted.

Comments

[Ken]

I always find these graphs a bit misleading because a 100% increase balances with a 50% decrease. It would be nice to have a graph that was symmetrical about 0 in the case of zero return over time but it probably isn't possible.

[Tom]

A logarithmic scale on the vertical axis would do what you want. I think you can make a case for both ways of presenting the data though.

[Isaac]

I thought you might find this graphic interesting: http://www.theatlantic.com/images/issues/200901/bush-map.gif