I'm a Non-Practicing Compound Growther

Quick question:

You have $1000 in a brokerage account. You will have a fixed rate of growth for ten years, except for one year where you’ll lose 20%. What timing will have the least impact on the plan?

I was building a client plan with an advisor and we were stress testing the plan under a fixed rate of return. When we modeled a down year moving earlier and earlier in the plan, nothing happened to the overall income plan. Obviously, the earlier the down year occurred the greater the impact should be on the plan.  I immediately thought we had a software bug. So did the advisor. It was embarrassing, frankly.

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After sitting down with it, I was embarrassed for a different reason. Both I and the advisor had years of financial experience but our “common sense” overpowered our knowledge of the basic math on compound interest. compound

(A is future value, P is current principle, r is rate of return, n is number of years of growth.)

Written another way:

compund expanded

If you have one single year with a different rate of return, the commutative property of multiplication gives us the same future value regardless of what year it occurs. (Dipped into my fourth grade math skills on that one.)

In this basic model, it doesn't matter at all when the down year occurs. Completely counterintuitive yet absolutely right.*

We all have areas where we’ve learned something and filed it away under the “No Need to Analyze Further” label. I never would have challenged what I “knew” if I hadn’t looked at it in a different way.

For those of you have been in the advisory business for a long time, I encourage you to take a fresh look at what you’re recommending to your clients. RetireUp is shamelessly good at educating clients, advisors (and me) on financial concepts from the seemingly simple to the incredibly complex.

*Of course, it does matter in a variable returns model and after asset drawdowns begin.