Tuesday, September 23, 2014

Asset Allocation in Smidges and Dollops

How important is it to precisely nail your asset allocation in retirement? You may be spending a lot more time than you need to fretting about investing 35% of your portfolio in equities instead of 40%.

Asset allocation affects a number of retirement plan factors including your portfolio’s exposure to a market crash, your long term expected portfolio return and volatility, and your sustainable withdrawal rate (and sequence of return risk). In this post, I'm primarily referring to your equity and bond allocations, which is the first allocation decision we make.

In his earlier books, The Intelligent Asset Allocator and The Four Pillars of Investing, William Bernstein suggested that the first step in choosing your asset allocation should be answering the question, “What is the biggest annual portfolio loss I am willing to tolerate in order to get the highest returns?"

Bernstein provided a table of asset allocations based on the answer to this question. I have included this table below alongside losses for the 2007 to 2009 market crash according to IFA.com. As you can see, Bernstein's recommendations were reasonable but were more optimistic than actual losses during that crash.

(This is a demonstration of the weakness inherent in using historical data to predict future market risk and returns. The Intelligent Asset Allocator was published in 2001 and a new low-water mark was set in 2009.)

Your individual risk tolerance – at least the risk tolerance you think you have – and your risk capacity are factors that will combine to suggest an appropriate asset allocation, according to Bernstein, and you will note that a 10% change in your portfolio’s equity exposure resulted in about a 6% change in the maximum loss you might have incurred during the 2007-09 crash.

(To clarify, a 5% increase in equity allocation here means increasing stocks from 30% of the portfolio to 35%, and not to 5% more of the original allocation, which would increase equities to 31.5%.)

How precisely you need to nail your asset allocation from the perspective of maximum loss in a market downturn depends, then, on how precisely you feel you need to limit those losses. If a 15% maximum loss versus a 20% loss feels significant to you, then a 10% change in equity exposure is important. If 20% and 30% maximum losses feel about equally acceptable, your equity allocation can vary by as much as 20%.

Asset allocation also affects the long term expected return and volatility of your portfolio. During a market crash, most asset classes tend to fall. This is referred to as “systematic risk" in modern portfolio theory (MPT) and it cannot be diversified away. Over the long term, however, asset diversification is a powerful tool.

Based on index portfolios from IFA.com, using data from 1964 to present, we can see the impact of increases in equity allocation at the conservative end (a 30% equity portfolio with the remainder in bonds and cash) and the more aggressive 70%-equity end of the spectrum.

You can see, for example, in the second row of data that increasing the equity allocation from 30% to 40% would increase the expected portfolio return from 8.01% to 8.9% and the risk from 7.13% to 9.2%.

How do you choose between a portfolio with an 11.15% expected return and a standard deviation of 15.67% and a portfolio with an 11.8% expected return and a 17.9% standard deviation? These are the parameters that would change for an investor contemplating an increase in her equity allocation from 70% to 80% (the fourth row of data in the table above). Although the expected return seems to increase significantly, so does the risk and there is actually very little difference between the two portfolios.

Using a tool provided by MD Anderson called Inequality Calculator, I compared probability density functions for the log-normal distributions of both portfolios. As the diagram below shows, even after increasing equity allocation from 70% to 80%, the probability of improving annual returns of your portfolio is only about 51%.

In other words, there isn't a lot of difference between the two portfolios. You haven't turned a low-risk portfolio into a high-risk one by increasing the equity allocation from 70% to 80%.

A small increase in returns can have a significant impact on terminal wealth after 30 years. Following is another graph from IFA.com showing the growth of $1,000 in their various index portfolios from 1984 through 2013, thirty years.

At the conservative end, an increase in equities from 30% to 35% resulted in a portfolio about 12% larger after 30 years. Increasing the asset allocation from 70% to 75%, on the other hand, increased the portfolio 9.7%. Those returns, however, are not guaranteed. The odds that your portfolio will end up larger with an 80% equity allocation than with a 70% allocation is still just a tad over 50/50.

A third factor influenced by your portfolio’s asset allocation, for those implementing a sustainable withdrawal rate (SWR) spending strategy, is the sustainable withdrawal rate itself. For a demonstration of the impact, let’s look at the original studies published in William Bengen’s Conserving Client Portfolios During Retirement

As his charts for both taxable and tax-deferred portfolios show with 30-year life expectancies, the SWR is essentially flat from about 30% to 80% equity allocations. Unless your portfolio has a very low equity allocation or a very high one, changing your equity allocation won’t have much affect on your sustainable withdrawal rate.

Even below 30% equities, the impact on SWR is on the order of a quarter- to a half-percent and it becomes less as retirement progresses. Of the three impacts we are considering, SWR is the least sensitive to asset allocation.

To summarize, you won't change your portfolio's volatility much by changing your equity allocation a 5% or 10% step up or down. You will improve the expected portfolio return, but the probability of improving your actual return or terminal wealth is roughly a coin toss. It won't have an impact on your sustainable withdrawal rate unless you move below about 30% equity or above about 80%.

The factor most sensitive to asset allocation seems to be maximum loss in a bear market. I personally pay the most attention to this dimension of risk because I am just finishing the first decade of retirement and sequence of return risk is front and center of my attention. Bernstein refers to this as "deep risk", a risk from which one might not recover, as opposed to long-term portfolio volatility risk. Antti Ilmanen refers to it as "bad returns in bad times".

Of course, the "best" equity allocation depends on what future market returns turn out to be, which is, of course, unpredictable. If 2007 found you woefully below the equity allocation most experts would recommend, you would've enjoyed the next three years much more than they did. We're trying to find a bet that will work more often than others, not the "best" bet.

Bernstein recommends portfolio allocations in "smidges of natural resources" and "dollops of Treasuries", which tells you what he thinks about our ability to make precise bets. In his words, "Once you’ve arrived at a prudent asset allocation, tweaking it in one direction or the other makes relatively little difference to your long-term results."


  1. Excellent Dirk. You've summarized in one article the most important variables (portfolio loss potential, return and volatility and sustainable withdrawal rate) to consider when deciding upon one's appropriate asset allocation. I have seen most of them (but not the Inequality Calculator) in one form or another before, but having these, but having them in this single article makes it easier to see how they interact (the tradeoffs between them -there is no free lunch). This along with your commentary also makes it easier to come to a decision about one's appropriate asset allocation. I can't wait to share this article with my wife to make sure we are on the same page. I agree starting with maximum acceptable loss one is willing to accept is a good idea. I like another comment by William Bernstein I believe in this regard - Don't take more risk than you have the ability, willingness or NEED to take (and that you don't receive a premium for taking). For me another concept I value in determining appropriate asset allocation is to take the minimum risk one needs to in order to reach one's goal. As I believe you may have mentioned by Bernstein as well - once you've won the game why keep playing. Adopting this attitude affects one's asset allocation decision as well. Thanks, Brad.

  2. Dirk, I do have one other comment/question. In addition to knowing the maximum expected loss with various asset allocations (say about 15% with 30/70 stock/bond allocation) it would seem to me to be valuable also to know the expected and maximum time (based on historical stock and bond returns) to recoup (get back to one's pre-crash asset levels) that loss. It seems to me that while the initial loss is important (15%) it would also make a difference to me in deciding which asset allocation level to select how long I had to endure that loss as I would assume it is not permanent (at least not over some length of time). I understand that one could mitigate the initial loss by having a reduced stock/allocation prior to the loss (sequence of returns aversion), and by subsequent to the loss reducing withdrawals and re-balancing. It just seems to me that if someone told me with a 30/70 stock bond allocation you run the risk of losing 15% of your assets, but with a certain level of confidence based on historical subsequent stock/bond market returns you might be back to even in 2 yrs say then I might feel better about taking more risk vs thinking the 15% loss was permanent. I know there are not guarantees that the loss would be recouped especially the shorter the time period, but I would guess based on historical returns all, but the most recent stock market maximum losses have been recouped. I would be interested in your thoughts please. Thanks, Brad.

    1. Have the 2007-2009 stock losses been recouped? By whom?

      People still working and contributing savings from their earnings have no doubt recovered, even faster than the market as a result of those new contributions.

      But how about retired people who had to sell stock to pay the bills since 2007 and didn't have job earnings to contribute new savings? Also, once you lose money in a crash, you have less money to invest in lower priced stocks to recover faster.

      I wrote about this in Even Your Portfolio Heals More Slowly After You Get Older at http://theretirementcafe.blogspot.com/2013/07/even-your-portfolio-heals-more-slowly.html.

      I've been paying three tuitions during that period and my portfolio hasn't fully recovered. Working people who contributed new savings recovered sooner than the overall market. Retirees who are spending from their portfolio will recover more slowly than the market.

      Maybe they're earning 7% a year on their portfolio plus returns on new investments. If you're earning 7% and spending 4% with no new savings to add, you're netting 3%.

      You could look at average times for the market to recover from a crash, but that would only be an average. Then you would also need to know how much stock you personally might need to sell during the recovery. I wouldn't hazard a guess.

      It took about 15 years for the market to recover after 1929. The crash was great for young people just beginning to save. They bought stocks cheap. It was deadly for retirees.

      Of course, if you have a floor, it doesn't matter as much.

  3. Yikes!! I re-read the 'even your retirement portfolio heals more slowly' article. Scary. I've got to paste this to on my fridge. Choosing an asset allocation is hard work. One part of me says be more aggressive than 20% (say 30%) which I chose based on Wade Pfau article (sequence of returns article), and then I read the article referenced above, and think no way 20% sounds good. Bottom line I guess at this point (a couple years before we are both retired) I'll stick at 25% rather than go to 30% for now. I've got a floor in bonds and cash, but its still hard to see your balance go down when you are not working. Thanks for the feedback Dirk.

    1. Don't lose sleep over a 5% difference.

      You might also want to read Bernstein's Rational Expectations. He has an interesting lesson about who won and lost after 1929. (Hint: retirees weren't the winners.)

    2. With a 30% stock allocation the 1929 crash would not have been so bad. You would have suffered a 21% loss but there was an accompanying deflationary episode so prices dropped around 20% so basically you were even. If you had the nerve to increase your stock allocation to 40% near the bottom you would have made out okay.

    3. Wesley, there are lots of things people MIGHT have done during the 1929 crash so that things MIGHT not have been so bad. As you know, hardly anyone did any of them. Hindsight is 20/20. I don't recall ever hearing someone who lived through the crash say or write that "it wasn't that bad."

      IF you still had stock at the bottom of the crash AND you somehow knew you were at the bottom, life would be grand. But like my grandfather always said, "If a frog had wings. . ."

  4. Thanks Dirk. Completely different mindset between retired and working. I will look at Rational Expectations again. I quickly scanned, and pages 127-8 seem relevant to your comment above, but it might not be what you had in mind. Regardless, thanks as always. Brad

    1. It's a completely different game once you retire, and you become a very different player.

      That's probably the right page. He tells the story of "Ted Twenty-Five".

  5. When discussing asset allocation I would add this basic but often ignored first issue: how to compute total assets. For many it may be clear cut - their investable assets are their total assets. But for others there may be assets that are not clearly included or excluded. Examples would be fixed income annuities or rental property. How to treat such assets (that is, to include their present value in the total asset calculation, or not) is not clear nor consistently applied. Another complexity: How to think of the equity/mortgage in one's residence. For example, take two similarly situated retirees. Each has $500,000 in investable assets and each has a home mortgage of $200,000. They have both decided to allocate their portfolios 50/50, thinking this reflects the highest level of risk with which they are comfortable. However, Investor A decides to pay off his mortgage. As a result he now has only $300,000 in his investment portfolio, while Investor B still has $500,000. Their total net worths remain the same, but how would we now describe the "total assets" each has to allocate, and what would it mean if they both stuck to their 50/50 allocation? If total assets is defined as equal to investible assets, then Investor A would have only $150,000 invested in stocks (50% of $300,000) while Investor B would have $250,000 (50% of $500,000). Clearly Investor B would be subject to more risk and more potential gain. For Investor A to retain a similar level of risk and potential gain (that is, with $250,000 at risk in stocks), he would need an allocation closer to 83/17.

    My calculations here are inexact and overly simplified, but the point remains: Discussion of differing asset allocations is meaningless unless there is clear agreement as to what constitutes the total assets to be allocated. Put another way. one man's 50/50 can be very similar to another man's 83/17.

    1. Barry, your 50/50 scenario is actually quite different than your 83/17 scenario. Your Investor A, who has no mortgage, cannot match Investor B’s risk by increasing his retirement portfolio equity allocation. In addition to market risk, which they will both have, Investor B now also has margin risk (he is investing borrowed money), margin cost, and foreclosure risk.

      I agree that there is more to consider overall in retirement portfolio asset allocations. In particular, the greater your ratio of wealth to annual spending, the less important asset allocation becomes (really wealthy people have greater risk capacity). Also, the more of your spending needs that are covered by non-asset income like pensions and Social Security benefits (a “floor”), the less you need to worry about your asset allocation.

      I think of the asset definition this way. We have assets that will not generate retirement income and those that will. A retirement income portfolio contains only the latter and this is a discussion of how to allocate assets in a retirement income portfolio to make sure you can pay your bills for the rest of your life.

      Assets that will not generate retirement income might include a home that a retiree never plans to sell or a piece of art one purchases but that will be donated to charity through a will, or stock we buy and put into a trust for our children.

      For short, let’s call those retirement assets and non-retirement assets, though both are clearly part of our total assets. Non-retirement assets may be important to us when we consider our net worth or a bequeath, but they won’t affect the retirement income we need to pay the bills and that is what this post addresses.

      We can further divide "retirement assets” into a volatile portfolio of stocks and bonds, and a portfolio of non-volatile assets like a TIPS bond ladder, a pension, Social Security benefits or fixed income annuities. The latter is sometimes referred to as a “floor” that generates safe income no matter what the market does. The former is sometimes referred to as an “upside portfolio.” This post discusses the allocation of the assets in the upside portfolio.

      Could we consider this one giant portfolio and just add the floor assets to the fixed asset portion of the portfolio allocation and increase the spending level? We could, but since the floor income is “safe”, many planners simplify the problem by using it to offset spending needs and then address only the “shortfall”, or the spending need net of Social Security benefits and pensions. Then we know what spending is safe and how much is at risk.

      If you break the problem into its key components, the issues are not as unclear as you suggest.

      Thanks for writing!

  6. Thanks, Larry!

    I have always been amazed by the lack of attention paid to the "expected time remaining in retirement" factor. Even the earliest SWR studies, Trinity and Bengen, note that SWR's are higher for expected retirements of 10, 20 or 30 years. And Mileksky's "sustainable spending rate without simulation" equation clearly shows the role of this variable (lambda).

    Yet, many interpreted SWR as being "locked in" for the duration of retirement. It isn't. Portfolio survival probability is a function of spending amount, portfolio balance and time remaining in retirement and those change constantly. The "locked in" notion is one that badly needs forgotten.

    Thanks, again, for your comments, Larry.

  7. Dirk I am coming up to retirement. What SWR can be considered "bombproof", i.e. likely to survive any likely bad outcome for a 40 yr retirement. Is a 2% SWR bombproof? Thanks

    1. Wesley, I wouldn't characterize any SWR as "bomb-proof". If you invest in stocks and then spend from that portfolio, there is always a chance that you will run out of money if you live a long time. 40 years is a long planning horizon, making the odds even greater that you can deplete your portfolio.

      2% or less, however, seems pretty safe. It isn't as safe as a fixed income annuity or a 40-year TIPs bond ladder, but it may be safe enough that we are now quibbling.

    2. Bernstein wrote this in a classic series of blog posts called "The Retirement Calculator from Hell". This is an observation I believe every retiree should keep at the center of their plans. I highly recommend both authors.

      The important point is that there are many risks to a successful retirement. Some we can manage, like portfolio volatility with asset allocation, and some we cannot, like societal upheaval.

      Great comment. Thanks for writing!

    3. I just recalled this post from Wade Pfau a few years ago where he did a quantitative assessment of what Bill Bernstein approached qualitatively. The 4% rule is based on US stock and bond returns in the "American Century". My conclusion based on his analysis is that in order to have a 4% SWR rates, you have to avoid the following: civil war; coup; lose a big war; be invaded even if you win in the end; or bankrupt yourself winning a war. Any of these puts you at SWR levels of 0,5% to 3%. The only exception to these rules was Denmark that was invaded so fast in WW II that there wasn't any damage; they were not occupied too badly in WW II; and weren't on the aerial bombing and war-fighting route of the Allies at the end of WW II.

      So the big question for the 4% SWR is whether or not the charmed life of the US and Canada in the 20th century will persist in the 21st century. It is nice having a big moat around North America without a lot of separate governments fighting within the boundaries of North America. But that was not the case in the 19th century with the War of 1812, the US Civil War, various US wars with Mexico and Spain, and the Metis Rebellion in Canada.


    4. A valid argument for any retiree to ponder. There are far greater risks than market volatility and little or nothing you can do to mitigate them.

      The first sentence of your second paragraph also deserves a great deal of thought. SWR's are based on the assumption that the American financial future will look a lot like the last hundred years or so. There isn't a strong argument that will be the case, though there are many strong arguments that it won't. It seems like a poor assumption to me.

      Thanks for writing.

  8. Dirk
    First I have to compliment you on what a great job you have done with this blog. I will be retiring in the next year or two and have found it a great resource. I am a little confused as to why the following is not a floor and upside strategy
    #1 9 yrs of income in short term treasury bond fund
    #2 25 yrs income in an intermediate bond fund
    #3 13 yrs income in stocks
    #4 5 yrs income in "safety" investments: gold coins, rental real estate,etc
    I realize that it is essentially a liability matching portfolio. Why does the floor and upside strategy have to consist of just TIPS and annuities. Won't bond instruments serve as well. Again many thanks for the blog

    1. Wesley, let me add something to my comments below. You seem to have a well-diversified and adequate retirement savings portfolio with a low spending rate (2%?). While your portfolio doesn't include a floor at present, you probably have a floor of Social Security benefits. It is very unlikely, under these conditions, that you will need more floor. The only question is whether you want more.

      If you feel that even in the very unlikely event that you run out of money (it is possible, just not likely) you would want more guaranteed income than SS benefits provide, then you can buy more floor. Otherwise, your current portfolio seems perfectly reasonable.

  9. Thanks. And good question.

    Floor portfolios are not subject to market risk or interest rate risk. You mention TIPS and annuities. TIPS would only be included in the floor if they constituted a bond ladder, which would make them somewhat impervious to interest rate risk. So, it isn't TIPS that go into floor portfolios, but TIPS ladders. Any other type of bond could go into the floor portfolio if they were laddered, but TIPS work best because they are risk-free.

    The portfolio you propose here is subject to both market risk and interest rate risk. That's why it isn't a floor.

    A floor would typically include Social Security benefits, pensions, fixed income annuities and bond ladders. All of these provide the same amount of income every year no matter what the stock market and interest rates do in the future.

    Your portfolio looks more like a time-segmentation strategy, which is perfectly reasonable. But if interest rates shoot up your bond values will fall. If stock prices crash, your portfolio will also fall. In either of those cases, you would be better off with some guaranteed income in a floor portfolio that is independent of stock and bond prices. If neither of those things happen, you'll be better off with this portfolio.

    I'm going to be posting more on this topic over the next two weeks, so check back.

    And thanks for writing.

  10. Really excellent article.

    I did not understand the section starting with ...."How do you choose?" and I think it must be an important distinction between a) the expected return difference, and b) the probability of out-performance. I understand (a) but I don't understand (b).

    1. I was only trying to illustrate that the difference between those two allocations is not dramatic and that most investors would have trouble choosing between the prospects of a 70% and 80% stock allocation.

      Thanks for writing!

  11. Further to your reply above...
    You are using the math equation to justify 'little difference'. But what does the math really measure? I looked up the equation (sum of multiples of prob-distributionX multiplied by cum-prob-distributionY) and the paper that gave rise to it.
    But that does not 'inform' me. Why should I think it measures 'little difference'? Why should I interpret it to be a decision metric?

    1. The easy way to see that there is a very small difference between these two portfolios -- and therefore to have little reason for preference for one over the other -- is to note that the red and blue curves almost totally overlap.

      The second way to be informed that there is little difference is to note the numbers at the very top of the graph. They show that the probability that the 70% portfolio will outperform is 0.4891 and the probability that the 80% portfolio will outperform is 0.5109. That's basically a coin-toss.

  12. Continue.....
    For example I used the software to compare
    (A) before-tax equity returns (10% return, 20% sd), with
    (B) after-tax (at 20%) returns (8% returns, 16% sd).
    The probability of A outperforming was only 53%. So should we conclude that saving 20% taxes in an IRA 'is not worth it"?

  13. Of course, not.

    Paying lower taxes is always good, all other factors being constant. Your comparison assumes that your after-tax return is independent of your before-tax return.

    Your model incorrectly assumes that you randomly pick a before-tax return from one sample and then randomly pick an after-tax return from another. The model should assume that you randomly pick a before-tax return from one sample and then subtract taxes based on that return.

    The probability that a specific before-tax return will be greater than or equal to to its after-tax return is 100%. In your terms, the probability of A outperforming B is 100%, not 53%.

  14. I totally agree with the author that a person should start focusing towards the total loss, which can be tolerated rather than the profit they will make.