Monday, September 24, 2012

Efficient Frontiers with Stocks and Something Else

Yesterday, I posted about my new research article, "An Efficient Frontier for Retirement Income."

In the comments, Aaron wrote:

Great article and I love your paper.
Getting the right splits in the product allocation is something we are spending some time considering here.
The dominance of the partial annuity strategies in your chart is consistent with out work here, but I suspect many will find the level of dominance a little surprising.
One question I have is in regard to the nominal/ indexed annuity differences. I understand why the nominal is on the frontier, given pricing and the effective discount rates. However, how far away is the indexed frontier in your model, and indeed the VA frontier. I would be very interested to see your figure with the 4 frontiers of stocks with bonds/ fixed SPIA/ nominal SPIA/ VA as a comparison.

Aaron, thanks, and here's the answer. This figure shows all of the combinations between stocks and one other asset (bonds, VA/GLWBs, inflation-adjusted SPIAs, and fixed SPIAs):

To just provide more intuition about what I'm doing, I will explain why the allocation to 100% Real SPIAs is where it is.  The lifestyle goal and minimum needs are a real 6% of assets. 2% comes from Social Security. The real SPIA payout is 3.88%.  Thus, every year of retirement, the real SPIA supports  (2 + 3.88) / 6 = 98% of retirement spending needs. That is constant every year in every simulation. It is the only point that won't have any variability in the outcome. Since lifestyle goals are not met with this allocation, nothing is ever returned to the investment portfolio, and the remaining financial assets are always 0. Thus, the point is at x=98, y=0.

P.S. I'd like to thank Taylor Larimore for starting a thread about the article at the Bogleheads Forum. More discussions can be found there.

An Efficient Frontier for Retirement Income

I’ve finished a new research paper called, “An Efficient Frontier for Retirement Income.” 

First, the punchline: with a 4% withdrawal rate to meet lifestyle spending goals, a 65-year old heterosexual couple is best served by combinations of stocks and fixed single-premium immediate annuities (SPIAs). At current product pricing levels, there is little need for bonds, inflation-adjusted SPIAs, or immediate variable annuities with guaranteed living benefit riders (VA/GLWBs).

This paper provides a framework for retirees to choose how to allocate their retirement assets between stocks, bonds, inflation-adjusted SPIAs, fixed SPIAs, and VA/GLWBs.

The basic idea is not original to me. As I often say: Moshe Milevsky already did it. In this case, he developed the ideas of product allocation and the efficient frontier for retirement income. But I think I’ve made some useful enhancements and improvements to his underlying framework.

As I’ve been thinking about financial goals for retirement, I think they can be boiled down to two objectives. It’s not just a matter of avoiding financial wealth depletion as is assumed in safe withdrawal rate studies. Rather, the two competing objectives are (1) to support minimum spending needs and lifestyle spending goals as best as possible, and (2) to maintain a buffer of financial assets either for a legacy or to use as a reserve for managing risks, such as expensive health shocks, divorce, unexpected needs of other family members, severe economic downturns, or other types of emergency needs. Generally, there is a tradeoff between these objectives, and retirees need to determine how much they value each objective and where they find the appropriate balance between them.

This research will help with the decision by plotting how 1,001 different product allocations perform with respect to meeting the two objectives, and then identifying the efficient frontier of product allocations. This efficient frontier tells you the allocations which support the highest reserves of financial assets for a given percentage of spending needs which can be satisfied, or, alternatively, the highest percentage of spending needs which can be satisfied for a given reserve of remaining financial assets. Any of the product allocations on the efficient frontier represent a potentially optimal point, and retirees can then choose which one they think best balances their own objectives.

The basic case study I use is a 65-year old couple who has an inflation-adjusted lifestyle spending goal of 6% of retirement date assets. Following the arguments made by noted financial planners such as Michael Kitces, Jonathan Guyton, and Harold Evensky, I also assume that this couple will be quite sad if they can’t meet their lifestyle goal, and so I assume their minimum spending needs are also 6%. They have a Social Security benefit equal to 2% of their retirement date assets, and so to meet their lifestyle goal, they need to generate additional income equal to 4% of their retirement date assets.

The following figure shows how their 1,001 product allocation possibilities perform. I’ve highlighted in blue all of the allocations which only consist of stocks and bonds without any annuitization. These outcomes reflect some of the worst possible results for meeting spending needs. Also, I’ve highlighted most of the efficient frontier with a red curve. These are the allocations between only stocks and fixed SPIAs.  

With the characteristics of this case study, what I find supports my earlier intuition that optimal retirement income strategies consist of partial annuitization with SPIAs. More strongly, it consists of mixing stocks with fixed SPIAs. I was surprised that fixed SPIAs perform better than inflation-adjusted SPIAs, but Joseph Tomlinson explains that this is because inflation-adjusted SPIAs are relatively overpriced. Also, interestingly, there is no need for retirees to hold bonds. SPIAs are like super bonds with no maturity dates and which boost retiree returns with mortality credits. Also, confirming my earlier intuition, GLWBs don’t really help and retirees can find some combination of stocks and fixed SPIAs which will better support both financial objectives than any allocation that includes a portion devoted to GLWBs. Again, these results are specific to the case study in question. Changing lifestyle goals, minimum spending needs, age and marital status of the retirees could all change which product allocations are on the efficient frontier.

Improvements I’ve tried to make to existing studies include basing both the annuity prices and the market return assumptions on current market conditions so as to avoid biasing the results against annuities, using low cost versions of each strategy as are available from companies like Vanguard, and discussing results in terms of different percentiles from the distribution of outcomes, rather than just the mean or median. Also, I think the way I’ve defined the percentage of lifetime spending needs which are satisfied is a step forward to more properly define the magnitude of success and failure. It is broader, as it can deal with both inflation-adjusted and fixed guaranteed income sources, and also it can better account for what happens with strategies using variable spending patterns.

If you are interesting in the process of building retirement income strategies, please have a look at this new article.