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Thursday, March 3, 2016

Is Monte Carlo Analysis For Retirement A Winner?

In my last post, I despaired over the latest Monte Carlo analysis of my retirement plan done by Vanguard.  They advised reducing expenses because their new Monte Carlo analysis uses 100 for the life expectancy of me and my spouse, and they made a few other adjustments.

But is Monte Carlo analysis really the best way to predict whether a retirement plan works?  I did some digging and found out that Monte Carlo analysis as performed by Vanguard may have a weakness.

The Vanguard model effectively assumes the probability of you and your spouse living to 100 is 100%, i.e. you will live to 100 and need a retirement plan that provides you with income until then.  This seems unrealistic to me.  My probability of living to 100 is about 11% according to some online mortality calculators.  In Vanguard's defense, they do not target 100% success for your retirement plan, (target is 80-85%) so they do take mortality into account in some fashion.

So to explore this further, let's consider a hypothetical Monte Carlo Analysis of my situation where we have retirement assets and small social security pensions:
  • The Monte Carlo model does 5000 scenarios and in 80% of the cases, there is enough money to for our retirement, meaning 1000 scenarios failed and 4000 succeeded.  I have an 80% chance of my plan succeeding.
  • In each of these 1000 failed scenarios, the money runs out in a particular year meaning a particular age for me and my spouse.
  • However, the probability that we are alive diminishes over time. If 100 scenarios fail in 2057 when I am 99 and my spouse is already deceased, that is much less "important" or "probable" than 100 scenarios failing in 2037 when I am 79 and my spouse is 89.
  • The figure below depicts the probability of running out of money (the Monte Carlo analysis) and the probability of not being alive as time progresses.  It is just a representation but it shows that your probability of being alive goes down over time, and your probability of running out of money goes up.  Makes sense, right?
  • So the question is: should a good financial planning model take into account that the probability of us being alive in a particular year decreases? 

Probabilities of Being Alive and Running Out of Money in Retirement (Representative Data, not based on actual results)

Unfortunately, I don't have the knowledge of probability and statistics to create a new modified Monte Carlo model, and besides that, I am a lazy SOB.  I described my idea to Vanguard, perhaps they will research it and see if it makes sense, and if yes, modify their model.

What do you think, does my idea make sense?

3 comments:

  1. If you take into account the likelihood of living to each birthday, you could create a plan that has an 85% chance of success but has only a 20% chance of providing income until you're 95. The problem with longevity risk is that we must follow a plan that is likely to leave money unspent just to take care of the case where you happen to live a long life.

    One alternative is to use some of your assets to buy an annuity to lay off some of the longevity risk, but today's low interest rates make this unattractive. A better alternative is to devise a plan where you adapt your spending if markets don't give the returns you expect. With such a plan, success or failure is defined by whether you're ever forced to reduce spending below say 80% of your starting spending level (adjusted for inflation).

    Unfortunately, most people who tinker with different types of plans tend to just pick the one that has them spending the most today. This is why even those who make a plan often end up running short of money.

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    1. Thanks for the well thought out comment. Vanguard ran a scenario where I added a "longevity insurance" annuity. For about $50K, it increased my probability of success by about 1%. Hard to know if it is worth it.

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  2. So few folks take the time to actually think through what is under the hood of retirement planning. Well done. Like you, I've used Vanguard's planner, plus Principal's, Personal Capital, Fidelity's, and Morgan Stanley's. All this after an old school hard drive crash tanking my large DIY spreadsheet model of lifetime networth forecasts. This class of models share a common flaw: they start with "how much do you need to spend in retirement?" Then move on to their simulations and forecasts. The right start question is: "given what I have saved plus SS, what is the maximum I can spend and not spend out before death?" That second question, not the first, is the right point of departure for all this type of thinking for folks who are at retirement age. Cheers.

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