Tuesday, July 1, 2014

New Research on How to Choose Portfolio Return Assumptions

Monte Carlo simulation is a popular tool for projecting a lifetime financial plan. When using Monte Carlo with a low failure rate, an underlying implication is that one is implicitly using a lower portfolio return assumption in order to have a plan that works in most any market environment. The plan has to work in poor market environments as well to get a high success rate. It must work even when the underlying compounded portfolio returns are low. But the portfolio return sequences are not usually seen as part of the output from Monte Carlo, and so this point may be missed.

An alternative to Monte Carlo analysis is to develop a spreadsheet with a single number for the portfolio return in order to create projections for a lifetime financial plan. In many cases, the default way to approach this is to plug in what one things to be the average or expected rate of return over the long-term horizon. The problem is that using the "expected" return is the equivalent of accepting a 50% failure rate with Monte Carlo analysis. A conservative projection will require a lower rate of return assumption.

This is one of the themes of my July column at Advisor Perspectives, "New Research on How to Choose Portfolio Return Assumptions."

The other related theme is that when developing portfolio return assumptions for a spreadsheet about a retirement plan, it is important to make further reductions to the rate of return in order to maintain the same overall probability of success. This is because of sequence of returns risk. The increased vulnerability to the returns experienced in the early part of retirement will create greater variation for the internal rates of return over a 30 year period than one would get from just investing a lump-sum amount for 30 years. These differences are further compounded if one considers that risk capacity will be less after retiring, leaving one feeling compelled to use a safer percentile from the distribution of outcomes (i.e. one might feel comfortable using the 25th percentile during accululation, but only the 5th or 10th percentile in retirement).

For the example I give in the article, if one believes that the expected arithmetic real portfolio return is 5.6% with a volatility of 11%, the implied compounded portfolio return with a 90% chance for success for someone retired and sustaining withdrawals from their portfolio is only 1.9%. If investing a lump-sum, the assumed return could have been 2.5%.  For high confidence about retirement success, the financial plan would need to work even if their wealth only grew at this rather low rate of return. Plugging in an "expected" return would expose someone to a coin flip about their retirement success.

21 comments:

  1. This and the prior blog of the Guyton and Kitces videos base their underlying research on history. History admittedly adds precision to the "science", but the question remains as to what extent history is valid or even helpful in this context.

    Many scholars, including Jack Bogle and Bill Bernstein, believe that historical returns are unrealistic, and instead compute fundamental expected equity returns, such as those derived by the Gordon equation. The general consensus among these scholars is that the 7% real equity returns of the past will not be repeated and a more realistic expected real return is about 5%.

    Likewise, Monte Carlo Simulations often use historical data inputs. The 100,000 iterations are based upon historical data inputs, but the historical data need not foretell the future. Wade's schedule of "The Greatest Hits" illustrates that the US history alone need not reflect what possible declines should be considered. Japan is still waiting for the market to return to pre1990 levels.

    Bottom line is that reliance on history seems to add precision to the science, but if the premise is suspect, the results are unreliable.

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    1. John,

      I'm with you on this point. I've written a lot about not using historical numbers, especially when bond yields are low. But as this column went in a different direction, I decided not to further confound the issue by adding in this matter as well. One issue at a time.

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    2. Wade

      If history is unreliable, and if the claim that "history is the best evidence of future market performance" is false, then alternative approaches to SWR and MCS sequence of returns analyses are necessary.

      An excellent case can be made that fundamental returns are more realistic than average historical returns. Your "Greatest Hits" demonstrates that basing a worst case on US historical sequencing of returns may come up short. So why not focus retirement planning on the more realistic (and conservative) fundamental returns median base case and use reasonable worst case scenarios?

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  2. Given the 1.9-2.5% real projected returns at the 10th percentile that you use for the example, by the time you subtract any management fees, transaction costs, and/or fund expenses, the real returns would be in the range that's quite attainable with a carefully laddered long bond-only income portfolio where the bonds are held to maturity. Even if the 50/50 portfolio at the 10th percentile might do slightly better than the bond ladder, the difference in real return might not be worth the risk (financially and in terms of peace of mind) to many retired folks. So just where does this leave the plethora of investment advice that one *must* own equities in their retirement portfolio?

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    1. Right, this is an important point about how a conservative rate of return assumption starts getting close to the internal rate of return from a bond ladder.

      There is one important difference, however: the bond ladder will not have upside potential, while the diversified portfolio could perform better. Remember, this is a conservative return assumption.

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  3. A very interesting article and blog discussion Wade. A couple of thoughts about Monte Carlo simulations versus expected returns.

    - Oftentimes expectations turn out to be the opposite of what actually does happen (classic example is people continuing to buy expecting prices to continue to go up – or vice versa). Thus, whose expected return data would one use? And wouldn’t a collection of all those expectations be closer to eventual outcome (wisdom of the crowd)?

    - The use of Monte Carlo tends to focus on the 50th percentile results which, as you point out in the article, tend to cluster near the average rate inputted. However, one could still use historical data as the input and then evaluate the other percentile simulation results to adjust expectations. In other words, if the expectations sense are lower returns, then look at the simulation percentile results that are from lower market return sequences; and vice versa for higher than historic market return expectations.

    - The longer the simulation period, the more likely outcome will be different than expectation. Thus, Dynamic Updating and revisiting each retiree each year helps stay on top of future uncertainty (which is always there regardless of age). Each year, updated data (returns and period life tables) incorporate what was once uncertain in last year’s simulation.

    Moral of the story, facts need to be used somewhere and historical data is more factual than any one person’s expectations. If one starts with facts, and more importantly Dynamically Updating (discussed in a blog post which Kitces tweeted-click on name for link to it) how the facts have changed during each annual review, one can look deeper at the other simulation result percentiles to get some sense of what may be prudent and feasible in possible alternate unknown futures. This, in effect, is no different than making a data adjustment for expectations, which in themselves, are unknown in outcome – however, in my humble opinion, provides more insight through percentile evaluation since one can see how much of a deviation may be needed from historical data.

    The future is always uncertain no matter which method is used. The question is to be sure one understands how a deviation also affects the outcomes. Rather than focus on the single answer simulations provide, one should also look at the other percentiles to evaluate the range of possible outcomes - the power here is that one would need to input multiple expected returns to get a range of similar evaluation possibilities.

    Stepping back to see the forest for the trees oftentimes is helpful. Excellent food for thought in all your posts Wade - to simulate conversation and further insight.

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    1. Apology for typo missing t in last sentence ... should say stimulate.

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    2. Thanks Larry. I don't think I said anything that is inconsistent with what you are writing. Especially with this article, these simulations are based on historical averages. I didn't make my customary reductions for current bond yields.

      But perhaps someone wishing to do the dynamic updating might wish to assume a percentile from the return distribution that is different from the average return. This article could then be used to help fill in that hole about what return assumption to use, based on percentiles of what could happen as they are linked to historical averages.

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  4. IMHO, this brief and unexpected discussion spawned by Wade's column (we did hijack his column) goes directly to the heart of the retirement planning challenge. We are trying to predict this future.

    Apparently, none of our methods of predicting the future work even fairly well. Humans are quite bad at it, as research shows. Monte Carlo simulations and historical data provide a possible future scenario, as does analyzing the fundamentals. At present, they're pretty different.

    The fact is, some retirement strategy will prove to have been the best 30 years from now, and none of us knows which that will be. It might even be a bad one. A friend split a pair of 5's in a hand of blackjack once, not realizing how "dumb" that was, and won both hands.

    I think trying to predict the future, with whatever method, is a losing hand. I have come to the conclusion that a better approach is to generate multiple scenarios of the future using multiple techniques, consider the probabilities and outcomes of each, plan to take the worst scenarios off the table, and keep options open whenever possible so we can alter course after time passes and we have new data.

    Why argue over which method best predicts the future when we know neither does it well enough?

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    1. Well said Dirk! A rational assessment of possibility and probability is not the same thing as predicting the future. Prediction is not possible especially over longer periods of time. I think the paradigm should shift from interpreting results as being predictive to the perspective of what is prudent given the facts at that particular moment.

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    2. Dirk

      You said: " I have come to the conclusion that a better approach is to generate multiple scenarios of the future using multiple techniques, consider the probabilities and outcomes of each, plan to take the worst scenarios off the table, and keep options open whenever possible so we can alter course after time passes and we have new data."

      I agree with all of that except your suggestion to use "multiple techniques". I agree that these techniques can't predict to future, so why use any such techniques? Instead start with fundamental returns, which is NOT a technique that is used to predict the future; then consider reasonable worst case scenarios, etc. proceeding as you suggest.

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    3. Dirk, I agree that this is a good assessment about how to proceed. I'm never really trying to predict the future, but just trying to come out with what I think are reasonable market forecasts to guide the analysis.

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    4. I would like to add an important point to the overall discussion that can be easily missed along the way ... the data used in analysis should match the practitioner's overall portfolio application to the retiree!

      Otherwise what the retiree actually gets going forward has little resemblance to calculated outcomes. Basically apples (analysis) and oranges (application) should not be mixed and oftentimes I see just this happens.

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  5. So, Wade, creating "a reasonable market forecast" isn't trying to predict the future?

    I think we're all trying to predict the future. I think our clients expect us to predict the future. I have a hell of a time explaining that we can't.

    When we use SW, we're trying to predict safe withdrawal rates based on what worked in the past. When we pick a portfolio allocation, we're guessing what might work best in the future, again based on past data. When we buy an annuity, we're predicting that the future might hold a long life for us or that future market returns might be so-so.

    Fundamental returns are absolutely a way to predict the future. Why else would we use them? (BTW, I think that's a fine way to generate one future scenario.)

    I believe this sub-thread began on the merits of monte carlo based on historical returns versus fundamental analysis. To my knowledge, no one is consistently outperforming the market with either. Why argue which is better? Use them both. Neither will ultimately be right. Hopefully, they'll both be in the ballpark.

    I think that as retirement planners, we are in the business of predicting the future, or more specifically trying to narrow down the future, which is, when you think about it, pretty much the same thing.

    My point in all this is that, while our job is to predict the future, all empirical evidence indicates that human beings suck at predicting the future, even -- and perhaps especially -- "experts". It would probably serve us well to recognize our weakness.

    Take your best shot at a range of future outcomes using any reasonable tools available, recognize their uncertainty, and adjust next year when retirement is a year shorter and you have new information about your wealth. Repeat as needed.

    Bayesian, I know.

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    1. Dirk,

      I mostly agree with you, but just a couple comments.

      >>When we buy an annuity, we're predicting that the future might hold a long life for us or that future market returns might be so-so.

      It's not so much that you are predicting a long life or so-so returns, but that you are building insurance to protect against these possibilities

      The reason fundamental analysis makes more sense to me than historical averages when talking about retirement is the sequence of returns risk. When bond yields are low, forget about getting historical average bond returns. This matters, because your portfolio will be drained much more in early retirement than implied by historical averages.

      About your suggestion for dynamic updating. This is certainly the more academic approach. But it is much more difficult to do without the help of an "expert". Nonetheless, this is Michael Zwecher's description of the basic solution from the academic research: build a floor to cover basic lifestyle and then spend x% of the remaining discretionary wealth, where x is a function of many parameters and assumptions used in the utility model.

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    2. I suspect we agree more than you realize, Wade.

      I agree that buying an annuity is buying insurance. But when you do you are predicting that you might NEED that insurance. If your prediction were that the market would return 18% a year for the next 50 years, you wouldn't buy an annuity. My point, which I seem to have made poorly, is that no one builds a retirement plan beginning with "I have no idea what the future will bring", yet our beliefs about what will happen in the future haven't served us well since we began walking upright.

      We buy TIPs, annuities, stocks or all of the above based on what we believe is most likely to happen in the future. A big reason people won't buy annuities is that they predict they won't live a long time despite a total lack of evidence on which to base that prediction.

      I totally agree that fundamental analysis makes more sense than historical averages. (I think the entire SW model is flawed.) But being better doesn't make it good.

      And I don't believe we should throw away fundamental analysis because it isn't very predictive. It's one of the best approaches (of a poor lot) that we have.

      I believe we should use them both because, ultimately, they're both guesses. Weigh them as you see fit. "Well, history says 4%, but my fundamental analysis says its closer to 3%. . ."

      I'd go with something closer to 3% because I believe (as did Bayes) that you need to modify your view of the world when you get new information, like low bond yields. People who sell stocks like 4% better.

      PE10 looks good in a long-term, ballpark sort of way, but even Shiller says he's not sure how long it will work.

      I suspect that all of us (except maybe for Shiller) are way too overconfident in our abilities to assign probabilities to future events. And that's really the point I'm trying to get across.

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  6. Dirk

    I know no one who believes that fundamental returns predict the future. Many agree what fundamental returns are (at least within a narrow range), but none believe fundamental returns are expected returns -- sequence of returns, shallow risk, deep risk, etc. will determine actual future returns. SWR and MCS (using either historical returns or fundamental returns as inputs) are techniques used to predict expected returns.

    In contrast, fundamental returns are one important piece of information that, when combined with all other relevant and material information, can be used to establish a workable retirement plan. So, IMO, it is not about taking all techniques, most of which we agree are unreliable, and hope we can guess right after considering each.

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  7. John, I agree but I'm using it in a broader sense than "prediction technique." I believe you are still using fundamental returns to guide your opinions about the future. If you are not using them for that purpose, why are you using them?

    You say "establish a workable retirement plan", Wade says "provide reasonable forecasts". Those sound a lot like "predictions" to most people. Whatever you call it, you're trying to predict the future, if perhaps only in a limited way.

    And my point is that human beings don't predict the future well at all and that it's really important to keep that in mind.

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    1. Dirk

      The approach that I use is very much like that which you suggest: "Take your best shot at a range of future outcomes using any reasonable tools available, recognize their uncertainty, and adjust next year when retirement is a year shorter and you have new information about your wealth. Repeat as needed."

      I use a range that is between a fundamental return base case and a reasonable worst case. The reasonable worst case selected is tailored to the specific individual situation. The model I use is continually updated; investments and spending are continually reevaluated. I think that we agree that there are no reliable formulas, and I use none. I have an article in the most recent Advisor Perspectives that discusses my methodology.

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    2. We are in complete agreement. I think you should consider the most likely outcomes but always be prepared to survive the worst case, no matter what.

      I believe the divergence of opinion came from whether one should use current fundamental data or historical returns to base one's opinions on the future. Personally, I would consider both and weigh the former more heavily. But I'd be extremely skeptical of both. There is no evidence that I'm aware of that shows either is a good predictor. MCS is in the same boat, since you have to base simulations on one or the other.

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    3. Dirk

      The issue is not whether fundamental returns are a good predictor, because they are not used to predict expected returns. Instead the issue is whether fundamental returns can be reasonably estimated within a narrow broadly-agreed range. There seems to be widespread agreement that they can, and that they are appropriate to use as a base case.

      In contrast, there is 100% agreement on what historical returns are, but many or most do not believe that the historical (10% nominal) returns make a good base case.

      Better to think of fundamental returns as high probability facts that are useful in the planning process, IMO.

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