Sunday, July 17, 2011

"Dynamic Allocation Strategies for Distribution Portfolios: Determining the Optimal Distribution Glide Path"

Today's classic withdrawal rate study is David Blanchett's "Dynamic Allocation Strategies for Distribution Portfolios: Determining the Optimal Distribution Glide Path" from the December 2007 Journal of Financial Planning.  This article deservedly won the 2007 Financial Frontiers Awards Competition.

Most retirement withdrawal rate literature assumes that retirees maintain a fixed asset allocation over their retirements. This article investigates a variety of asset allocation glide paths in retirement in order to capture the idea of lifecycle asset allocation or target date funds.  The general idea is that as people get older, they tend to shift to more conservative asset allocations. I think the fundamental point coming out of the article is that there is that assuming a fixed and balanced (between stocks and bonds) asset allocation strategy works quite well, and so we do not need to worry much about this simplying assumption used in most withdrawal rate studies. There is a lot of material in this article, so let me touch upon some of the highlights.

Life Expectancy

Though its not directly connected to the later results, the article includes a nice discussion about longevity and life expectancy as a way to justify the choice of a 30 or however many year retirement duration. The article shows the probability of still being alive between different start and end ages for males, females, both members of an opposite-sex couple, and at least one member of such a couple. Some withdrawal rate studies like to incorporate survival probabilities directly (not this one though), so that instead of planning for a 30-year horizon, other studies like to more formally plan for a retirement horizon for which you only have a 5% (or 1% or whatever) chance of still being alive.  The standard default assumption is a retirement which lasts for 30 years. If this is thought of as someone retiring at 65 and living to 95, the paper shows that for a male, there is a 4% chance of living this long from age 65. Females live longer, and they have a 10% chance of achieving this milestone. For a couple (whose lifespans are assumed to be independent of one another) the chance of both being alive rounds down to 0%, and the chance of one member being alive is 14%.  I myself tend to prefer just using a fixed planning horizon such as 30 or 40 years and not worrying about the associated probabilities for surviving this long, but the study provides a nice introduction to the issue. At some point with this classic withdrawal rate literature series, I would like to further consider some articles that incorporate mortality directly.  Moshe Milevsky is the name which is probably most associated with such an approach.

Withdrawal Rates, Asset Allocation, and Failure Probabilities

This article actually also analyzes the results in a similar way as the “Guidelines for Withdrawal Rates and Portfolio Safety During Retirement” article I discussed at my blog on July 16. Mr. Blanchett's paper also shows how for low failure probabilities there is a hump shaped pattern in which asset allocations mixing stocks and bonds support higher withdrawal rates than either all stocks or all bonds. However, when the acceptable failure rate increases enough, an all-stocks portfolio eventually supports the highest withdrawal rates. Actually, this article takes the earlier article a step further by showing the withdrawal rate pattern for retirement durations lasting between 20 and 40 years, not just for 30 years.

Asset Allocation Glide Paths During Retirement

Now we are ready for the highlight of the paper, which is to investigate the performance of different age-based asset allocation strategies in retirement. A caveat of much withdrawal rate research is that while the research assumes a fixed asset allocation strategy, real-world retirees will probably reduce their stock allocations as they get older and older. The pattern used to do this is called the "glide path", and different target date funds and lifecycle asset allocation funds use different glide paths.  The important result that Mr. Blanchett finds is that the standard fixed asset allocation strategies perform remarkably well, and that there is little need to worry about other glide paths. In other words, the standard simplying assumptions of most existing research are actually getting things right. Mr. Blanchett draws three lessons from this analysis:

1. For short retirement horizons (20 years), a 100% bonds strategy tends to provide the lowest failure probability.  However, for longer horizons (40 years), a 100% bonds strategy tends to provide the highest failure probability.  Retirement duration does indeed matter quite a bit for choosing a withdrawal rate and asset allocation strategy.

2. For short retirement horizons, though, the differences in failure rates between different strategies are very small.  The asset allocation strategy hardly matters.  The big differences come with longer retirement durations.

3. Assuming fixed asset allocations is fine.  They usually provide the lowest failure probabilities when compared to other various lifecycle-style strategies that reduce stock allocations over time.

I will also add that this section of the paper is confounded by the fact that 100% stocks provides the lowest failure probabilities when withdrawal rates and retirement durations are sufficiently high.  It is hard to beat 100% stocks in this regard.  Even when Mr. Blanchett removes the fixed asset allocation strategies in order to just compare the lifecycle strategies, the majority winner becomes the "concave" strategy that starts with 100% stocks, because this will be the strategy with the highest average stock allocation.

Mr. Blanchett also makes an important point in this section about the sensitivity of the results.  He finds in one case that when the withdrawal rate increases by 0.2 percentage points or the retirement duration increases by 2 years, the strategy providing the lowest failure rate changes from fixed 30% stocks to fixed 80% stocks.  Because he doesn't trust that retirees will successfully use 100% stocks, and because of concerns about the sensitivity of the results to small changes, he concludes that a balanced 60/40 fixed asset allocation strategy will best serve the needs of retirees.  This is more or less in line with what most retirement withdrawal rate studies use.

Adjusting the Results for Risk

Mr. Blanchett rightly notices that minimizing the probability of failure is not the only criteria that may matter to people.  100% stocks does so well, but he is concerned that with such volatile portfolios retirees may be tempting to make grave mistakes such as departing from the strategy and selling stocks at their lowest points.

He provides an alternative measure which he calls the "Success to Variability ratio".  It is the failure rate for a withdrawal rate and asset allocation strategy divided by the standard deviation of the underlying portfolio of assets.  In maximizing this ratio, he finds that the strategy which works most frequently changes from 100% stocks to 100% bonds.  An exact reversal. He concludes that both strategies are still too extreme, and again supposes that a more balanced 60/40 portfolio will provide the best path forward for retirees.

While his points are quite valid, there is a lot more to this risk story to consider as well. Even if retirees don't suffer the sleepless night worrying about a 100% stock allocation, the probability of failure is not the only important criterion for them to consider.  Retirees may also wish to know how spectacularly they might fail as well, such as how many years pass before the portfolio hits zero.  While 100% stocks might provide the lowest probability of failure in some circumstances, it may nonetheless still provide some of the very worst outcomes of any strategy.  This is something that risk averse retirees may wish to protect against.

More generally, economists have used the concept of "utility" since the 19th century. The basic idea is diminishing marginal utility.  As one's wealth or income increases, the additional enjoyment experiences by the wealth increases but at a decreasing rate.  Just think of visiting a buffet restaurant when you are very hungry. Those first bites are so satisfying, but as you eat more and more, your marginal gains to your utility decrease. A $5,000 difference in income means a lot more for someone with a $10,000 income than for someone with a $100,000 income.

Before learning about this article, I had written a similar kind of article about saving for retirement, while Mr. Blanchett focuses on spending during retirement.  I was specifically responding to research such as this article by Harold Schleef and Robert Eisinger, which argues that lifecycle asset allocation strategies (which reduce the stock allocation as retirement approaches) are bad because keeping a higher stock allocation increases the probability of reaching a high wealth target. While that is true, my point is that high stock allocations also increase the chances of having a final wealth accumulation that is strikingly low as well.  I used Monte Carlo simulations to calculate the entire distribution of possible wealth accumulations for a wide variety of asset allocation glide paths over 40 year long careers (some glide paths keep the same stock allocation, some reduce the stock allocation over time, and some even increase the stock allocation over time).  Then I calculate the "expected utility" provided by each asset allocation glide path strategy and I find that lifecycle asset allocation strategies are indeed justified for risk averse investors in spite of the findings from Prof. Schleef and Prof. Eisinger.  For instance, out of 2,211 different glide path strategies I test over a 40-year working period, I find that the strategy which maximizes the expected utility of a relatively risk averse investor (risk aversion=5) is one that uses 100% stocks for the first 10 years, gradually shifts down to 50% stocks until there are 15 years left before retirement, and then keeps 50% stocks for the rest of the time.  This paper is published as "An Optimizing Framework for the Glide Paths of Lifecyle Asset Allocation Funds," in the first 2011 issue of Applied Economics Letters.

My point of going on this tangent is that I do very much agree with Mr. Blanchett that considering risk is also very important.  I'm not necessarily sure that his Success to Variability ratio is the best way of tackling the problem though.  Mr. Blanchett lists three limitations of his ratio, namely that it can only be used with fixed allocation strategies, that people may worry more about losses than just the standard deviation of their returns, and that different people will respond differently about what they feel are acceptable failure rates or standard deviations.  An expected utility framework can correct for all three of these issues. I think there are still very fertile grounds for making another study which combines aspects of this study with aspects of my Applied Economics Letters study.

More generally, it does kind of make sense to me that fixed allocation strategies work best for retirees.  During retirement what matters most is what happens in the first years after you retire, so that your asset allocation in later years becomes less of an issue.  As well, as we learn in this study, higher stock allocations actually reduce the chance for failure when withdrawal rates are high.  Well, in the bad luck cases that are heading toward failure, the current withdrawal rates will be pushed up, and a lifecycle asset allocation strategy will be reducing stocks at the time retirees are already heading toward ruin.  In this regard, in updating this study as a suggest above, it would also be worthwhile to also consider the reverse glide paths as well that increase stock allocations over time.  Then I think he we can have a better study about the appropriate glide paths for asset allocations in retirement.

All in all, I think this is a very good study, but I would still like to see another study which pushes these ideas further.

Update: I made a "Part II" for this topic in my July 21st blog post.