Saturday, May 26, 2012

Reality Check on Retirement Planning Assumptions


Before reading the May 12th issue of the Economist, I was flipping through the pages of the May 19th issue and saw that Peter David, the Lexington columnist and Washington bureau chief, had died in a car accident the previous week in Virginia after having given a talk at the Charlottesville Committee on Foreign Relations. It’s a real reminder about the frailty of life and how we should cherish every day.

And this meant that the May 12th Lexington column would be his last. I think with his final paragraph, he left the stage on a fine note:

Charles Dickens said of the United States that if its citizens were to be believed America ‘always is depressed, and always is stagnated, and always is at an alarming crisis, and never was otherwise.’ On a variety of objective measures, it is in an awful mess right now. And yet America of all countries still has plenty of grounds to hope for a better future, despite its underperforming politics, and no matter who triumphs in November.

I do believe this is true. 

But nonetheless, when it comes to retirement planning, we need to keep in mind two very important facts: (1) bond yields are currently at extremely low levels, and (2) the equity premium earned by stocks in U.S. history was abnormally high and we should plan for a more reasonable premium in the future. 

We have got to use capital market expectations that are linked to reality. That means we can’t use historical averages to guide simulations, and it means that the Trinity study and its brethren are of no particular use.

The historical data averages used to guide most withdrawal rate studies are shown in Table 1:

Table 1
Summary Statistics for U.S. Real Returns Data, 1926 – 2010




Correlation Coefficients

Arithmetic
Means
Geometric Means
Standard Deviations
Stocks
Bonds
Inflation
Stocks
8.70%
6.62%
20.39%
1
0.1
-0.2
Bonds
2.52%
2.28%
6.84%
0.1
1
-0.6
Inflation
3.07%
2.99%
4.18%
-0.2
-0.6
1
Equity Premium
6.18%





Source: Own calculations from Stocks, Bonds, Bills, and Inflation data provided by Morningstar and Ibbotson Associates. The U.S. S&P 500 index represents the stock market, intermediate-term U.S. government bonds represent the bond market, and bills are U.S. 30-day Treasury bills.

I’m now trying to finalize a set of assumptions to use in my new research. Table 3 shows my current planned assumptions, though I do encourage and request any feedback you may have about these as I don’t fancy myself to be much of a market forecaster:

Table 3
Assumptions for Real Asset Returns




Correlation Coefficients

Arithmetic
Mean
Geometric Mean
Standard Deviation
Stocks
Bonds
Inflation
Stocks
5.1%
3.1%
20.0%
1
0.1
-0.2
Bonds
0.3%
0.1%
7.0%
0.1
1
-0.6
Inflation
2.1%
2.0%
4.2%
-0.2
-0.6
1
Equity Premium
4.8%





Note: Standard deviations and correlation coefficients are based on Stocks, Bonds, Bills, and Inflation data provided by Morningstar and Ibbotson Associates, in which the U.S. S&P 500 index represents the stock market and intermediate-term U.S. government bonds represent the bond market. The arithmetic mean for bond returns is calibrated to recent TIPS yields. The arithmetic mean for inflation is based on the breakeven inflation rate implied by TIPS and Treasury yields. The arithmetic mean for stock returns is calibrated to allow an equity premium of 4.8% above the bond return, which is the equity premium for a GDP-weighted portfolio of 19 developed market countries between 1900 and 2010 from the Dimson, Marsh, and Staunton Global Returns Dataset provided by Morningstar and Ibbotson Associates.

With these assumptions, failure rates for the 4% rule are quite shocking. With 50% stocks, the 4% rule can be expected to fail 47% of the time. Retirees are pushed toward 100% stocks to minimize failure, and even that failure rate is 39%. Is this too pessimistic?

23 comments:

  1. I am retired at 50 yo. My withdrawal rate is about 1% of investable assets which represents about 70% of my net worth. My investment portfolio is about 50/50, passively invested with the bond portion being 100% munis. 100% taxable account. I have no debt. One line of reasoning that I keep returning to is that if I can't make it on 1%, what's going to happen to everyone else? pension funds? 401k's? I think we would be looking at a breakdown of society at that point.

    Just eyeballing where 1% and 2% withdrawal rates would fall on your graph would seem to indicate the probability of failure is pretty close to zero no matter what the stock allocation.

    I have arrived at similar real returns going forward as you going forward using the Gordon equation. Warren Buffett's observations along these lines are similar. I am having difficulty justifying such a large fixed income position.

    I believe people like me may be facing a one in a generation opportunity to shift fixed income investments into equity investments. I can stomach portfolio fluctuations due to my low witdrawal rate. My overriding goal is to leave a large estate. Therefore, I am considering increasing the equity allocation to 75%, heeding Benjamin Graham's advice not to exceed that level. Doing so may create a taxable event since the fixed income position will be subject to capital gains. If there were ever a year to know definitely know the tax consequences of such a move, this is it. Nonetheless, a small tax bite now may compound to a large legacy later.

    So, to address your question; too pessimistic? Not at all. I think the Oracle of Omaha has pretty much said the same thing.

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  2. Well, the future is of course unknowable. But I do think an estimated real arithmetic return of 0.3% on bonds is really pessimistic. It calibrates returns to the current environment of very low interest rates, the lowest in a generation. It is true that current rates are the best predictors for the future of money invested in bonds now; but your assumption implies that future investments, including reinvestments of interest, will also be at a historically low rate. If I had to guess, I'd put the arithmetic real return somewhere around 1% plus or minus, still quite pessimistic by historical standards. Because this feeds through to equities via the risk premium, I would expect this relatively small change to have major implications for failure rates. Stated differently, using this approach, projected failure rates are likely highly sensitive to the assumed real interest rate on bonds.

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  3. Wade –

    Maybe part of the adjustment of assumptions should be to increase the SDs??

    Your post makes me think of that wise mathematician active at Bogleheads, Rodc. He frequently points out that –- even if we assume the stocks return-rate probability distribution has been an unchanging normal distribution through the past hundred years -- with 20% stocks return-rate SD, our 100-year sample of potential past means has an SD of 2%. So just considering history, the “true” past mean could be 2% or 3% lower than shown by calculatiing our historical sample’s mean. That’s before considering that the future “true mean” may be lower than that of the past century.

    So just considering inadequacies of our sample of history, Rodc advises test our plan with stocks mean down 2 or more from the mean we calculate from history.

    On the other hand, maybe the future mean will be the 8.7 you calculated from history??

    And for SDs too, our historical sample is not big enough. You could say there is uncertainty about our calculated uncertainty, which means the uncertainty is more than we calculated from the inadequate history.

    I like some lowering of the stocks mean, for your reasons and for Rodc’s. But clearly, what the future holds is considerably more uncertain than suggested from the SD we calculate from history. How about increasing SDs??

    Dick Purcell

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  4. Is this too pessimistic? Simmple answer - yes and no. My own spreadsheet model using your data arrives at an even more pessimistic result. However, if luck is with us, the real-life outcome may be much better than we think. Predicting the future is not (yet) an exact science, at best it may be one of many outcomes. "With four parameters I can fit an elephant, with five I can make him wiggle his trunk." -- John von Neumann, Hungarian mathematician

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  5. Hi all,

    Thank you for the comments! Also, thank you Early Retirement Forum for more comments.

    For a quick starter, do note that the assumptions here don't necessarily have to define the entire 30 year retirement period. With sequence of returns risk what happens in the early part of retirement matters a great deal more than what happens later on. Even if conditions "normalize" to the historical averages in 15 or 20 years, that will provide only a quite small amount of help to those retiring today. Wealth depletion in the mean time will be hard to overcome. It is like the worst-case scenario retiree from history: the 1966 retiree. The last half of this 30-year retirement was the 1980s and 1990s bull market, but by then it was too late, too much wealth was depleted to enjoy the recovery.

    Comment #1: You are certainly right... if 1% does not survive then it will imply a massive society breakdown with any well conceived plans thrown out the window. About using this to increase stock allocations, do also keep in mind that a limitation of using failure rates is that it ignores the magnitude of failures. In this case, wealth will tend to be depleted more quickly with higher stock allocations when the worst-case scenarios arrive.

    Comment #2: My starting comment applies here. I think the current bond yield is more relevant than a more normalized bond yield. As well, you must think about for retirees with long-dated bond funds, interest rate increases will result in capital losses that may offset any benefit coming from reinvesting coupons at higher rates. On the other hand, having only shorter-term bonds currently means getting real yields even lower than 0.3%.

    Dick: Yes, I could make this even more pessimistic by increasing the standard deviations to better account for our uncertainty. That is important for sensitivity analysis. But I do have to draw the line somewhere, and what I've got already is pretty darn pessimistic. Actually, I just show the failure rate for 4% here because it is a convenient metric that people are already familiar with, but it does not really play any role in the article I am writing now and hope to get finished by the end of the week. (By the way, this will provide my first attempt to look at floor/upside strategies as well as variable withdrawal rate strategies)

    Comment 4: Thank you, and good to see a John von Neumann quote. Indeed, predicting the future is not a science at all and I prefer avoiding it as much as possible, since our predictions tend to be SO CRAP (a convenient memorization tool for the CFA exam). But I think something better is needed than just throwing in the historical averages.

    Psychological Traps for Forecasting: SO CRAP

    Status Quo
    Overconfidence
    Confirming Evidence
    Recallability
    Anchoring
    Prudence

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    Replies
    1. Wade --

      I don't wanna upset what you're probably almost finished writing, but for after that I think we could consider this thinking:

      Stocks down 3.6 from history is pretty stark departure from the stocks "facts" we have, namely stocks history . . maybe we should think "not sure" the future will depart from history that starkly, and instead drop from history only half that much -- and to put in the "not sure," increase the SD. In "conservativeness," the result could be close to what you now have but with more of it expressed as uncertainty about what's in the fog ahead.

      Dick Purcell

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  6. SO CRAP...that's a good one!

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  7. Please, please, when you next run simulations, look at glidepath allocation strategies, such as "age in bonds". In Figure 4, high bond allocations show disproptionately larger failure rates. By age 80, someone following "age in bonds" will be at 80% bonds. True, half of the 30 year period is over by then, so that the high bond allocation may not matter much in terms of portfolio survival, but what if it does? All of those people trying to reduce risk by moving into bonds will be moving in the wrong direction.

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  8. I just wrote a program to perform the analysis using your numbers, and I get somewhat (not very) different results. Four questions: (1) I believe from your previous posts that you make the distribution at the beginning of the year, not at the end. Is that correct? (2) I also believe that you rebalance at the end of each year. Is that correct? (3) Do you use the same set of random returns, perhaps by using the same original seed to generate the random numbers, for all the withdrawal percentages and stock allocations, or is each estimation independent? (4) How many replications do you do for each combination of withdrawal percentage and stock allocation (so I can estimate standard errors)?
    Thanks.

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  9. Thank you for the continued comments, both here and at Early Retirement Forum. I should get signed up there one of these days.

    At some point it is worth discussing further, as I think a lot of confusion arises since it is not always clear when someone is talking about real or nominal returns, and when someone is talking about arithmetic or geometric/compounded returns.

    Here I am showing only real returns, but you could see the nominal returns by adding the inflation numbers to the real returns.

    I didn't double count inflation, the stock return falls so much in Table 3 because it is tied to the bond return through the equity premium, and I lowered the bond return to reflect current conditions and lowered the equity premium to reflect the international average.

    Dick: you make an interesting point, but I do want to have some justification for what I am doing. I'm not sure I should just start moving the numbers around without a clear basis. I do agree with you about the parameter uncertainty. U.S. had both high arithmetic returns and low standard deviations, and therefore also high geometric returns.

    ourbrooks: I will write up something about this in the next couple of weeks. I've already run the simulations, I just need to write it up.

    Anonymous: about your replication exercise:
    (1) yes, beginning of year
    (2) rebalance at end of year
    (3) Though I should do it, I don't bother to set a seed to use the same random numbers. Things are slightly different each time I run it.
    (4) For final versions to be published somewhere, I like to use 10,000 simulations. But to save time for blog figures, I like to use less. The particular figure here has 1,000 simulations.

    I'm running this a few more times now and I do see that the failure rates are still bouncing around a bit from simulation to simulation. The minimum failure rate for 3% is coming out in the range 12-16%, and 4% has failures in the neighborhood of 35-39%. It was merely a coincidence, but the version of the figure I posted does seem to be leaning toward the high failure rate side. Is that what you are finding? It is always good to have replications.

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  10. Clearly a 4% withdrawal can easily fail. For anything approaching certainty, you have to drive that % down, probably below 3%. But why not simply buy an inflation adjusted annuity? Recent quotes for a 65 year old show payouts of 4 -5%. If you want to leave a legacy - set that aside and invest it as you see fit. If you want assured retirement income, why not do the obvious and annuitize?

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    Replies
    1. Thank you for the comment. Yes, that is the annuity puzzle in a nutshell.

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  11. What about the folks whose entire retirement portfolio consists of one or more non-ROTH IRAs? For them, RMDs apply and they don't have the option of withdrawing only 1 or 2 or 3%. By age 70, they are required to withdraw more than 3.5% and by age 73 it's more than 4% and keeps increasing.

    I suppose one answer would be to advise pre-retirees to have significant retirement savings outside the IRA (and an annuity could be a part of that strategy). I hope when you complete your analysis on safe withdrawal strategies, you include some discussion on the affect of RMDs on your proposal.

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    Replies
    1. Maybe you are required to withdraw that amount, but you don't have to spend it all - you could reinvest it in a taxable account.

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    2. Thanks Fat Bob, that is what I would have said.

      Also, the 4% rule is based around a 30-year retirement. As one gets older, at some point it is no longer necessary to plan for 30 years.

      The traditional 4% rule is that you withdraw an amount that is 4% of retirement date assets, and then adjust this amount for inflation in later years. So in the later years, the percent of your remaining assets that you withdraw will not be 4% any more. It could be more or less, depending on how markets perform.

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  12. If you are putting stock returns around 5.1% and I see a vanguard fund of high yield corporate bonds with a yield of 5.73% (VWEHX, 6/1/2012), then does it make more sense for me to put money in stocks or the high yield corporates?

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    Replies
    1. I don't think there is any obvious answer. One could argue either way. I don't really have a strong opinion about this.

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  13. Wade, you write: "Retirees are pushed toward 100% stocks to minimize failure, and even that failure rate is 39%."

    But is that first clause true? In my experience, retirees and immediate pre-retirees are pushed to reduce their stock exposure. Bogle's rule was "age in bonds," which would give the usual retiree a 35% exposure to stocks. How does that affect your failure rate?

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    Replies
    1. Larry, I just meant "pushed" in the sense that higher stock allocations suggest lower failure rates. No one is actually doing any pushing.

      Here I am looking at fixed asset allocations. I've also run the numbers for age in bonds and other types of changing asset allocations, as has William Bengen, and usually plans which continue to lower stock allocations over time cause lower sustainable withdrawal rates. I will write more about this one of these days.

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  14. Thanks, Wade. I'm particularly interested in this comment — "usually plans which continue to lower stock allocations over time cause lower sustainable withdrawal rates" — because it appears to directly contradict the usual wisdom that one's allocation should become more conservative over time. And in fact your chart indicates that a 40% stock allocation @3% withdrawal rate has a higher chance of success than a 0% allocation at the same rate. Vanguard's Target Retirement Fund (VTINX), for example, allocates 30% to stocks, 65% to bonds, and 5% to cash, which from the sound of your comment suggests that a more aggressive approach would be more successful.

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    Replies
    1. Larry,

      Bill Bengen and the Trinity study suggestion stock allocations for retirees in the neighborhood of 50-75%.

      With Monte Carlo, something a bit lower like 40% can do just as well.

      But this is only about the failure rate measure. It doesn't capture the magnitude of failures. I've got bits and pieces about this spread around my blog, and I will try to synthesize it all some time soon.

      Best wishes, Wade

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    ReplyDelete
  16. Hi, Great Post about retirement
    My retirement advice is "As much as you can".The best way to determine your savings target is to use an online calculator like this one. Thanks

    ReplyDelete