Magnitude/Likelihood Matrix of Real Returns

May 11’s post and May 12’s post described extreme results—the worst and the best—for stocks and bonds over three different time frames. But hidden within the charts in May 11’s post is a third facet of risk and uncertainty: It’s an entire matrix of possible outcomes ranked by magnitude and likelihood.

You can—and should—use bad extremes to eliminate investment and spending plans with outcomes you just couldn’t stand. (Or should I say “investment-spending plans,” the way physicists say “space-time,” since the two are so intimately linked.) But then you’re (hopefully) left with a range of remaining choices. It helps to have a sense of (a) just how good (or bad) an outcome might be, and (b) the likelihood of that size outcome.

One way to get a sense of life’s magnitude/likelihood matrix is to look at historical percentiles. You surely remember percentiles from when you took the SATs. For example, in the numbers below, the 30th percentile real return is 8.6%. That means 8.6% is the aggregate real return that is better than 30% of all the outcomes studied. Looked at another way, you stand a kinda’ sorta’ 70% likelihood of realizing an 8.6% or greater real return; and a 30% kinda’ sorta’ likelihood of realizing less than 8.6% aggregate real return. You gotta’ be real lucky to experience a 90th percentile future; and real unlucky to experience a 10th percentile future.

With that as background, and by way of example, here’s the magnitude/likelihood matrix for aggregate real returns on a portfolio with a 50%-50% mixture of stocks and bonds over 60-month periods between 1926 and 2008.

90th percentile: 67.8%
80th percentile: 55.5%
70th percentile: 44.2%
60th percentile: 36.1%
50th percentile: 27.7%
40th percentile: 19.0%
30th percentile: 8.6%
20th percentile: 1.4%
10th percentile: -5.1%

Two caveats:
1. Don’t get fooled into thinking these percentiles tell you the probability of future outcomes. They’re only "kinda’ sorta’" probabilities. You can’t use the past to predict the future; but you can use it as a tool to help you plan in the face of uncertainty.
2. The foregoing figures represent the aggregate five-year growth (or shrinkage) in the real (inflation-adjusted) size of a pot of assets. As pointed out in yesterday’s post, that’s not really the right yardstick. Ultimately, your allowance is the right yardstick when planning your retirement. I chose this particular measurement because it’s an easy one to measure, and it’s useful in illustrating the concept of a magnitude/likelihood matrix.