Does time diversification work in the real world? Do portfolios get less risky – i.e., converge to a more reliable expected return – the longer we wait?

Or do we believe in time diversification because we are not very good at mathematics?

To get into a fierce dispute where the person on the other side of the argument will not hear any contrary evidence, try talking to a mathematically oriented advisor about time diversification.

In the heated discussions that I’ve been involved in, the person on the other end of the argument is a proponent of dynamic or tactical asset allocation, meaning that they shift allocations according to investment regimes, economic scenarios, or various stages of the economic cycle. They tell me that this is necessary because without their intervention, the actual client investment experience would become increasingly volatile over time.

The simple version of their argument is that it’s just mathematics; time diversification is an illusion. The spectrum of expected outcomes in a diversified portfolio doesn’t narrow over time; it actually expands dramatically.

The mathematics of this argument are similar to what you see in Monte Carlo analyses. You start with a certain expected return and standard deviation of returns around it. The Monte Carlo engine then pulls random returns out of a hat, year after year, for, say, 10,000 30-year sequences. Some of those sequences are going to be catastrophic: the engine will, somewhere in those 10,000 iterations, pull out a sequence that starts with a return like we experienced in 1931 (-43.34%), and 1974 (-26.47%), followed by 2002 (-22.10%), 2008 (-37.00%), 1930 (-24.90%), 1937 (-35.03%), 1930 (-24.90%) –you get the picture. Two or more of those 10,000 random selections might just be combinations of all those disagreeable possibilities.