1/ Great example of ergodicity and why it matters from @InvestReSolve - investresolve.com/blog/path-depe…
I'll summarize the key takeaways: Consider the example of a retiring couple, Nick and Nancy, both 63 years old.
I'll summarize the key takeaways: Consider the example of a retiring couple, Nick and Nancy, both 63 years old.
2/ Through sacrifice, wisdom, perseverance – and some luck – the couple has accumulated $3,000,000 in savings.
Nancy has put together a plan for how much money they can take out of their savings each year and make the money last until they are both 95.
Nancy has put together a plan for how much money they can take out of their savings each year and make the money last until they are both 95.
4/ She expects to draw $180,000 per year with that amount increasing 3% each year to account for inflation.
The blue line describes the evolution of Nick and Nancy’s wealth after accounting for investment growth at 8% and their annual withdrawals
The blue line describes the evolution of Nick and Nancy’s wealth after accounting for investment growth at 8% and their annual withdrawals
5/ For the sake of this example, let’s assume that Nick and Nancy know for sure that their average annual return will be 8% over this 32 year period. That’s great, they’re guaranteed to have enough money then, right?
6/Turns out, no. It is non-ergodic and so it depends on the sequence of those returns. From 1966 to 1997, the average return of the Dow index was 8%. However those returns varied greatly.
7/ From 1966 through 1982 there are essentially no returns, as the index began the period at 1000 and ended the period at the same level.
Then, from 1982 through 1997 the Dow grew at over 15% per year taking the index from 1000 to about 8000.
Then, from 1982 through 1997 the Dow grew at over 15% per year taking the index from 1000 to about 8000.
8/ Even though the return average out at 8%, the implications for Nick and Nancy vary dramatically based on what order they come in.
If the big positive returns happen early in their retirement (blue line), they will do much better than Nancy’s projections.
If the big positive returns happen early in their retirement (blue line), they will do much better than Nancy’s projections.
9/ However, if they get the returns in the order they actually happened, with a long flat period for the first 15 years, they go broke at age 79 (green line).
10/ The model is assuming ergodicity, but the situation for Nick and Nancy is non-ergodic. They cannot get the returns of the market because they do not have infinite pockets. In non-ergodic contexts the concept of "expected returns" is effectively meaningless.
