Comments on Ritholtz's review of William Sharpe's RISMAT

I tried the other day to read and comprehend William F.Sharpe's Retirement Income Scenario Matrices (RISMAT.  Tipped off to this by David Cantor at PwC). I tried…and failed.  It was a little heavy on things that were opaque to me.  But I also happened to read Barry Ritholtz's ThinkAdvisor piece on Sharpe's RISMAT method Tackling 'Nastiest, Hardest Problem in Finance' that gave me a fresh angle.  

Here is a digest of the Ritholtz article (in single quotes, between the dashed lines):  

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'Comprehending the range of possible future scenarios from any retirement income strategy is difficult; choosing the proper strategy seems to be an almost impossible task.'

'[retirement income planning confronts] a reality where the potential outcomes are almost infinite, or as Sharpe describes it, a “multiperiod problem with actuarial issues, in a multidimensional scenario matrix.”  To reach the optimal answer requires considering six interrelated sets of variables. None are especially complex, but combining all of them is another matter.'

1. Longevity.  'The first unknown confronting retirement planners is built out of standard actuarial tables. The multiplicity of possible mortality outcomes for any given year is simple — who survives and who doesn't. But the possible combinations during roughly 30 years for two people is surprisingly large.'

2. Market Outcomes. 'The second dimension comes from the 100,000-plus possible market outcomes for a global bond and stock portfolio each year. Apply all of those possible outcomes back to the mortality scenarios above and you begin to get a sense of the enormous range of potential outcomes.'

3. Inflation. ' Third, create a matrix for thousands of potential inflation results — this determines the purchasing power of a retiree’s income. It’s not overstating it to call this a proxy for financial flexibility, security and even quality of life for a couple living off of their investments.'

4. TIPs.  'The next matrix is tied to inflation, and it is the 100,000-plus possible market returns that Treasury Inflation Protected Securities, or Tips, will pay — a combination of the twice-annual interest payments, plus the adjusted principal at maturity.'

5. Future Income. 'A fifth matrix is all the incomes the couple will receive, including Social Security, insurance and any employment. Then take into account whatever they withdraw from their portfolio.'

6. Utility of Income. 'The final variable may be the most subjective and difficult to assess: the utility of income in each subsequent year.  Each of these six factors has an enormous range of potential outcomes; each single factor outcome must be considered in light of every other matrix outcome. The results are a vast range of choices. Selecting the proper one is as challenging '

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The epiphany I had, after failing to comprehend Sharpe's matrices and his MATLAB code, was that the large number of scenarios and joint probabilities over multiple periods is exactly why people created simulators. It's a complex problem with too many variables and too many possible outcomes.  While I can't penetrate RISMAT and it may be more efficient than simulation, I realized I already had a tool for an individual (not a couple) for my own planning and strategy analysis to do this kind of thing: the retirement simulator I built. Let's tee it up and see if there is a match between the features I threw in and Sharpe's interrelated RISMAT variables (or at least the ones in the Ritholtz article):

1. Randomized Longevity. Check. I have both the SS 2013 life table and a Gompertz equation I can fit to any other longevity distribution I wish such as the SOA Annuity Mortality life table. I also can set fixed longevities as well which is what I tend to use the most.  Age 95 seems to be a good conservative compromise.  

2. Randomized Market Outcomes.  Check.  Only four assets, though: cash, historical 10 year treasury total return, historical US Large Cap, and a custom return/vol distribution for anything else or maybe just by itself.  Not perfect but it works well enough for what I try to do.

3. Randomized Inflation. Check. I use historical data but I could create a custom distribution. I do not auto correlate the series over multiple periods but wish I could.

4. TIPS. No, but then I am not pursuing lockbox strategies.

5. Future Income. Check. I handle at least two future inflation-adjusted (or not) streams to mimic Social Security, annuities, pension, jobs, etc. 

6. Utility. Check. Except here I evaluate the utility (CRRA) of the terminal wealth (for fixed longevity runs) or the utility of present value of terminal wealth (for stochastic longevity; that was an idea from Joe Tomlinson in an email) . I am not yet comfortable or haven't figured out how to handle the utility of sim-period income because it's hard to do.  For example, in the future, 50k of income has higher utility than 40k just by the CRRA math but then: 1) what about inflation effects over time, and 2) what about assets (e.g., 50k spend on $10M is probably good but a 50K spend on 100k is probably bad).  Me? I've proposed a custom quadratic utility of a sim-period spend ratio but I doubt anyone but me would buy it.  I have some work to do here but I think I'm halfway there.

7. Other. Ok, there was no "7" above but what about stuff like: spend trends, spend "inflections," spend shocks, spend variance, dynamic allocation possibilities, return suppression regimes, age caps, and probably a few other things.  I have that too.

So did I understand Sharpe's RISMAT? Not a chance.  Do I have the capability to run large numbers of simulated, blunt-force "matricies" of the combination of a lot of variables in order to evaluate retirement strategies. While it (my tool) is not perfect and leaves some things out (e.g., spending rules for one) I think I do have what I need for now.  On the other hand I'm sure there are some good things to mine in RISMAT. I'm just not going to do it today.