By Rick Ashburn
While I do not believe that wise investing involves any sort of gambling, the mathematics of randomness can teach us a thing or two about making plans for the future.
The basic process of financial planning involves adding up what we have now and projecting how much we are going to save and spend over our lifetime, while also considering inflation. We then apply an assumption for our investment rate of return.
We need to know whether these numbers add up. Spend too much or save too little, and our financial model runs out of money while we are still around to need it.
A key input to any financial plan is the investment rate of return. The fact of the matter is this: Future investment returns are wildly uncertain. Next year’s stock market return is unrelated to what happened this year.
A pair of dice behaves the same way. When forming a plan for our future financial security, we are best served to embrace this uncertainty.
We are delusional if we simply assume some fixed average rate of return. After all, the average number on the face of a die is 3.5. Do you ever actually roll a 3.5, let alone 20 in a row?
It makes more sense to view our financial futures in terms of ranges of possible outcomes. If I save X and spend Y for 20 years, and invest in strategy Z, then I can expect a certain range of outcomes at the end.
I don’t know which result will actually come true, but I can have good confidence that I will be somewhere in that range.
Monte Carlo is a term used to describe a process in which randomly generated annual return figures are applied to your personal financial model. Rather than assume a single number, say 8 percent, and apply it to every year of the plan, we allow a computer to randomly select each year’s return for every year in our plan.
When the computer is finished with the first set of 20 years of calculations, we ask the question: Did the plan work? We make note of the result, and we have the computer run another 20 years of random annual returns. Again, we take note of the result.
Each of these runs is called a trial. We might run 1,000 trials, 1,000 random simulated passages through our future. Naturally, the computer does this in seconds.
After our 1,000 simulated passages through our retirement years, we tally up the results. Let’s say we were using a 100-percent stock portfolio in our analysis, and 650 out of the 1,000 trials produced success. We can say, “If I were to invest in stocks, I have a 65 percent chance that I won’t run out of money.”
I would consider a 65 percent chance of success to be far too low. So, we run another 1,000 trials, but this time we test a mix of 50 percent stocks and 50 percent bonds. This batch of trials produces a 90 percent success rate. I call this 90 percent number the Portfolio Confidence Number.
As you might already be thinking, a critical part of this process is the assumed future ranges of returns of various investment types. I have written on that topic a few times this year and won’t revisit it here. Write or e-mail me, and I’ll get you a copy of the earlier columns.
Suffice it to say that you should not merely recycle the return figures from recent years.
I am not a gambler, but I readily embrace the inherent uncertainty and randomness of the financial markets. The challenge is not to simply tolerate that uncertainty, but to harness it and gain confidence in it.