“Optimal Asset Allocation in Retirement: A Downside Risk Perspective”

Today’s classic withdrawal rate study is only one month old.  Perhaps it is too new to already be considered a classic.  But it is interesting for me, because it ties in well with my last few blog posts about asset allocation during retirement.  It is W. Van Harlow’s paper, “Optimal Asset Allocation in Retirement: A Downside Risk Perspective”, released by the Putnam Institute.

This study is getting press coverage as it recommends that the optimal stock allocations for retirees are actually quite low, at perhaps 5-25%.  Not only that, but the paper talks about doing this with rather high withdrawal rates.  He looks at 6, 7, or 8% for males, and 5, 6, or 7% for females.  Such combinations of withdrawal rates and asset allocations are rather out of line with results I have been discussing here.  I’d like to figure out why.

The answer is not just because of the downside risk framework used in the paper.  Though I’m not patient enough right now to replicate the whole thing, I have also been looking at results which allow for a rather conservative investor to make their decisions.  Looking at the 0.1% or 1% failure rate situations will mean that there is not much downside risk left over and I think the results should be somewhat similar in that regard.

So, in looking at the situation, I think there are basically two reasons for the differences:

1. The paper incorporates mortality rates and survival probabilities into the calculations

2. The paper assumes a real stock return of 6% (I suppose this is an arithmetic return, but the paper is not clear on this point).

Survival Probabilities

At first, I thought the whole difference could be explained by #1.  As I was saying when discussing David Blanchett’s December 2007 paper about optimal glidepaths in retirement, I prefer just assuming a fixed retirement duration that is long enough to make it rather unlikely that someone will live longer.  This is a common assumption, and 30 years is the usual baseline.  Mr. Blanchett’s paper shows the Social Security mortality tables, which indicate that a male aged 65 only have a 4% chance to survive for 30 years to age 95.

However, there is an alternative way to conduct these studies.  W. Van Harlow assumes people might live to 110, but for each age he weights the outcome by the probability of surviving to that age.  It effectively makes the time span much shorter.  As just mentioned, if we assume a 65 year old retiree, there is only a 4% chance he will make it for another 30 years.  So the optimal asset allocation for a 30-year retirement effectively gets very little weight.  People are unlikely to live that long, and this shows up in the results.  In fact, there is only a 35% chance that a 65-year old male will last another 20 years.  So, with these mortality-based calculations, a lot more weight is placed on what works best over short time horizons.

This is important, because David Blanchett already gave us two results about short time horizons: a 0% stock allocation provides the lowest probability of failure for 20 year horizons, and anyway for these short horizons the differences in failure probabilities between low and high stock allocations are quite small anyway.

So which assumption is better: assuming a long retirement horizon, or applying survival probabilities to each age?  I think there is no correct answer.  I personally feel it is more conservative to assume a long-fixed time horizon.  Sure, maybe someone only has a 4% chance to live another 30 years, but a conservative retiree might like to plan with the possibility in mind to be part of that 4%.  Using survival probabilities really discounts the chances for this outcome.  But I understand why people think it makes more sense to use the survival probabilities.

And Lower Stock Returns

At any rate, I thought these shorter time horizons caused by using survival probabilties could pretty much explain W. Van Harlow’s results for low stock allocations.  Then I saw his footnote 4, which indicates that when he tried a fixed 30-year retirement period, he found that the optimal asset allocation is 12% stocks, 31% bonds, and 57% cash.

I think the rest of the story can be explained by the assumptions used for the Monte Carlo simulations.  For someone working with the SBBI data since 1926 (such as the Trinity study or William Bengen’s research), real stock returns averaged 8.7% between 1926 and 2010.  W. Van Harlot assumes a real return of 6%.  Actually, it makes sense to do this, as I have argued a lot that U.S. returns in 1926-2010 are rather high by international standards and we shouldn’t assume such high returns in the future.

So I ran some simulations with these assumptions, and I’m getting somewhat similar results as this paper about what minimizes the failure probabilities, at least for a 15-year time horizon.  For a 30-year time horizon, more stocks are called for.

To wrap things up, I still have some trouble accepting the low stock allocations from this paper.  Perhaps because I am already anchored to higher allocations.  I’ve been thinking mostly about 30 or 40 year retirement periods as well, not the effectively shorter 15-20 year type periods coming from the use of survival probabilities. I did not replicate the paper’s downside deviation measures, but anyway I think expected utility provides just as good of a way to deal with that problem.

On the issue of asset allocation for retirees, I do still think the framework from Spitzer, Strieter, and Singh explained here provides the best way to think about asset allocation in retirement.  You have to consider asset allocation together with failure probabilities, withdrawal rates, and bequest motives.  They can’t be separated. Also, in this post I consider the possibility that conservative retirees might actually be better off by starting with a balanced asset allocation in retirement but actually increasing their stock allocation as time passes.


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