Historical vs Monte Carlo
@wallace471 Robert, thanks for the two references. I struggled with what capital market assumptions to use, so I have stress tested my plan in the past using very conservative assumptions, however, using these same stress test assumptions to make other decisions (e.g. Roth Conversions, Social Security etc.) can have unintended consequences. I now use a more "consensus" view based on sources that are also included in the Horizon study.
Since I do not want to rely on returns from my portfolio to fund my spending, I have decided to annuitize my pensions rather than taking lump sums. This income combined with social security covers all my essential expenses plus some reasonable amount of discretionary expenses. This "safety First" strategy works for me, however, I recognize we all have different preferences.
Here is a paper by Pfau and Marguia that outlines their research on retirement income styles. I have taken the RISA survey and it confirmed that the "Safety First" approach is my preference. This is a useful tool for individuals and especially for advisors to better understand their style. I think advisors who have a strong opinion about what strategy to use would better serve their clients if they had them take the survey and then provide a strategy that matches the "clients" preferences, not the "advisors".
The paper by Young and Pfau points out what I think most of us already know but it sheds additional light on what the ramifications of either using optimistic or pessimistic ROR assumptions based on the example case that they presented. Below are some quotes from the paper that I think are very insightful.
"While there is no clear answer for how to choose an appropriate level of stress (or, more generally, which CMAs to use), showing more dire assumptions may prevent bad outcomes for clients and give them more comfort that their plan will not turn out disastrously. On the other hand, using more dire CMAs may exacerbate the problem of underspending – if the prediction turns out to be too extremely pessimistic, clients will live well below their means and leave behind more than they might have intended."
"As an alternative to this approach, advisors could consider other ways to generate retirement income that do not rely so heavily on forecasts of returns, volatilities, and correlations."
@golich428 Understood. I've said many times that Pfau works for the insurance industry, indirectly (why hide it?). Just please, please read the annuity contract very carefully. It's designed to make you give up, but read through every line. Immediate is better than deferred, and of course the pensions you're annuitizing are annuities anyway, and carry their own level of risk and fees, so it's not like you're handing over your nest egg. But make sure you understand every line in the contract - the one they actually give you to sign at game time, not any 'preview' or 'preliminary' one.
PRC’s Monte Carlo (MC) analysis generates 500 projections using an average inflation rate (that you input) and randomly varying ROR to simulate market volatility. It uses the following for its analyses:
1. The long-term average ROR for S&P stocks is 11% and its SD is 19%; our algorithm would yield an SD of 16.5%.
2. The long-term average ROR for T-Bonds is 4.8% and its SD is 7.5%; our algorithm would yield an SD of 7.2%
So, if I understand correctly, if you have significant allocations in equities other than the S&P 500, such as foreign market funds, and bonds other than US T-bonds, such as foreign bond funds, or in commodities, REITs, or whatever, your MC results may not be representative of you asset allocation. Using a fixed inflation rate would be another source of non-representation. Thoughts??
@hines202 I want to clarify that I am not purchasing an annuity from an insurance company. The payments come from a trust that has been set up by the employer and yes there is still some risk. Do you ever recommend to your clients to take a pension as an annuity or is your preference to take the lump sum? I see pros and cons of each.
FYI, the rules (e.g. interest rates and mortality tables) for annuitizing the lump sum are set by the IRS with some flexibility for the employer to make slight modifications. The monthly benefits are calculated using three interest rates based on high quality bond yield curves every month and the IRS mortality tables.
@golich428 I always take a close look at the pension details/options with clients. For example, if a pension annuity has a COLA adjustment, it becomes more tempting to take that option, although I rarely see that these days. After so many decades of pensions failing, struggling, mismanagement, grift, fraud, etc I'm very hesitant to risk someone's retirement on them. Some don't give you a choice, like TIAA (an experience with a recently retired professor client I have) don't even allow lump sums now! Boy, was he mad. Me too.
I'm a fan of first and foremost, the fewer people between you and your money the better. Getting the lump sum, setting it up so it's invested properly, inexpensively, simply is going to be by far a bigger win for you than some rando out there somewhere playing fast and loose with their "investing theories" on your retirement money. That's how it all goes bad. It's not that complicated to get this set up and on autopilot through a retirement, with that annual check and rebalance exercise. That's what I teach my clients, and I'm always there for help if they want a second pair of eyes or run a decision by a neutral party (part-time marriage counselor 🙂
Good article by Forbes that talks about the things mentioned by @golich428 in his Jan 21st post: https://www.forbes.com/sites/ebauer/2019/04/04/what-you-need-to-know-about-pension-lump-sums/?sh=4cf15a7b29fd
In addition, in some cases, retirees accepted lump sums only to turn around and buy individual annuities, and found that they got much less value for their money than the original pension benefit, which is inevitable not just because of the expenses and commissions of individual annuities but because of the different risk pools -- that is, pension plan participants include the sick and the healthy but only those who are in good enough health to fear outliving their assets will seek out individual annuities, unavoidably driving up their cost.
Does all of this mean that individual retirees who may be offered a lump sum option in the future should accept it?
By no means! Individuals should consult a reputable financial advisor (one who's not trying to sell them money-management services), to be sure, but lifetime benefits provide a security that is incredibly valuable to their recipients in a manner that exceeds the present value an actuary would calculate.
@wallace471 The two articles you referenced in your Jan 17th post are excellent! Question, in the Horizon report it states - The expected returns shown below are annualized (geometric) over the indicated time horizons. How does this correspond to real rate of return (ROR) and nominal rate of return?
@pizzaman: As far as I understand it, the geometric return is "preferred" by investment gurus over arithmetic returns for investment portfolios as they better reflect longer time horizons associated with the correlated values found in the portfolio components (bond yields, stock returns, etc.) which are impacted by compounding.
Investopedia provides a comparison here: https://www.investopedia.com/ask/answers/06/geometricmean.asp
Note that geometric returns are generally less than the arithmetic returns from a given set of data. Most firms post geometric nominal returns in their forecasts (I think), but it is not always explicitly stated in their reports, unfortunately.
In contrast, the "real" vs. "nominal" return refers to the impact of inflation on the given return, where the [real ROR] = "inflation adjusted return". This is described here: https://www.investopedia.com/terms/r/realrateofreturn.asp
According to the Pralana Gold 2023 manual (p.113), the [real ROR] is to be entered for each asset in the Financial Assets/Asset Class page. Pralana Gold then converts to a [nominal RoR] for the assorted calculations. The formula relating these returns is provided in the manual as follows:
[nominal RoR] = [real RoR]x(1+[inflation])+[inflation]
with a little algebra, we then have:
([nominal RoR]-[inflation])/(1+[inflation])=[real RoR]
So if the [nominal ROR] and [inflation] are positive numbers, the [real ROR] is likely less than the [nominal ROR]. From Investopedia:
"nominal rates are almost always higher, except during those rare periods when deflation, or negative inflation, takes hold."
It would seem that the resulting [real ROR] would therefore provide a somewhat more conservative assumption for long term asset returns; that is, inflation decreases the nominal ROR value as the inflation rate is typically positive.
So, for example, if inflation is forecast to be say 2.5%, and a (geometric) nominal RoR of 6% is forecast for US stocks, the resultant forecast for the real RoR is:
real RoR = (0.06-0.025)/(1+0.025)= 0.034 = 3.4%, which is MUCH less than the 6% nominal return. (Sobering given a 20y time horizon!)
Therefore, when taking return values from the various firm forecasts for inputs to Pralana Gold, it is important to identify if the returns provided are "nominal" or "real" in their tables, if possible.
Presumably, one would use the inflation rate associated with a given firm's capital market assumptions, and adjust the returns they quote (if they are not already inflation adjusted...that is, if they offer only nominal returns in their forecast). So, one would presumably just use the firm's forecast inflation rate associated with the firm's asset forecast returns provided by that firm to be consistent when determining a [real RoR] from [nominal RoR] values in their tables.
I posted links to a Morningstar article summarizing various firm longer term predictions in another post recently (Jan 26) under the "Asset Allocation" topic. It also includes the links to various original firm return forecast reports. The differences in the reported forecast returns (nominal vs. real) are mentioned, and a summary figure for 10 year forecasts for some asset classes is provided in the Morningstar article. It seems that an inflation rate around 2.5% is typical among the firms. I assume 3% in my Pralana Gold modeling...
Of course, these are all just long term models of asset returns, but they are produced by very capable experts at these firms...and they provide a starting point basis for our individual Pralana Gold modeling that has some reasoning behind it.
@wallace471 Given that these investment firms limit their projections to 10 years, I'm wondering how this would translate to setting up the Asset Classes and Allocations page. Designate just one 10 year period which you update every year based on these reports, or go with more periods to accommodate asset mix shift and use the same ROR for all periods?
Morningstar summarizes just the 10 year forecasts, although several firms offer additional time frames. See the links that are in the post for the firm report website. More generally, I wonder if forecasting returns beyond a decade is feasible with accuracy. I suppose that one could just update their 10 year numbers each year as a reflection of the economy, market, etc.?
@wallace471 You may have something there. It may be more precise to go with the expert consensus for the ten year period, and set that up as a timeframe in Pralana, and just put the long-term averages for anything beyond that. And then update each year when those updated analyses come out. Could be overkill, I suppose, but for folks that are into this and want to do the work, it doesn't sound like a bad approach. Also factor in how much you trust each source though, and the always-present threat of another black swan event.
Going back to the original question, to me bootstrapping has the best of both worlds. 1) It preserves actual historical relationships year-by-year between stocks and bonds, and the overall non-normal curve, especially if you use "chunks" of 3-10 years, 2) it has the random ordering of Monte Carlo that allows many alternative realities.
Lately, as we've had returns outside of the historical range (viz the worst inflation-adjusted intermediate bond results since 1871), I've started coming back to Monte Carlo, a bit. The mean and deviation for Monte Carlo come from historical data; all the monte carlo does is assume it's a normal curve. This is more pessimistic than boostrapping/historical. I'm starting to be more sympathetic that the way to "get around" the accidental history of bootstrap and historical is by assuming a normal curve but using historical data. To state the obvious, you have a spectrum here because the smaller your Bootstrapping chunks (e.g. 1 year chunks) the closer bootstrappnig is to monte carlo. And vice versa (e.g. 12 year chunks) will more closely fit historical patterns.
As others have noted in this thread, all these analyses have to be interpreted in context. I don't like phrases like "fail safe", because even 100% probability is based on historical. 100% failsafe just means 100% of the cases as drawn by what we've seen so far in history. To me all of these are still valuable data points in making a decision: Assuming history is roughly how these assets will behave in the future,
1) What would the results had been if I had started in years x, y and z in American history? (historical analysis).
2) What does bootstrapping say is the generalized success if history had repeated in random order 1000 times?
3) If my assets were not correlated and completely random, how does it hold up?
I'm a visual person, so when I plot monte carlo probability lines I like to also run a few speicific one year lines over top so I can see just how much any one "reality" can vary. The lines give the illusion of smoothness when the one-particular-reality-you-live goes all over in between.
A nice article by Massimo Young and Wade Pfau states that "The results from Monte Carlo are entirely determined by the capital market assumptions (CMAs) used." Meaning the rate of return (ROR) of stock and bonds. They talk about the Horizon Actuarial Services published in August 2022, which is also talked about in PRCs forum thread Asset Allocation. From the Young/Pfau article: "Our results suggest that probabilities of success, and more generally “safe” withdrawal rates based on Monte Carlo analysis, depend heavily on the accuracy of CMAs. Even relatively small errors in the inputs – 1 or 2 percentage points – will generate meaningful differences in what advisors might consider a “safe” withdrawal strategy." "It’s possible that using the average or median of different investment firms’ CMAs may lead to more accurate forecasts. The “wisdom of the crowd” has proven true in other cases. However, our results still imply that if the average CMA is off, even by relatively small amounts, it will significantly impact recommendations given to retirees."
This ties together the PRC forum threads Historical vs Monte Carlo and Asset Allocation nicely!
They then talk about modifying the Monte Carlo analysis "For advisors who can modify the CMAs within their Monte Carlo tool, one remedy could be to stress-test the portfolio by changing the CMAs." Not sure Stuart wants to go down that path 😮 .
Many of the CMA forecasts use a building block approach. For example, Research Affilities calculates 10year real expected returns for US Large Cap by using the Dividend Yield + Real Earnings Growth Plus Valuation Change (based on CAPE10). Their current estimate is 1.8+2.5-1.9 = 2.4%. As you can see starting conditions matter. For example, using historical data would assume a much higher Dividend Yield than what we see today. Many historical return series will not match the starting conditions we are seeing today so they may not be very valid. The first 10 years of market returns will have a sizeable impact on the success of your plan.
Below is a link to an article by Larry Swedroe about forecasting. Here is one paragraph if you don't want to read the entire article.
What can we learn from the preceding data? First, starting valuations clearly matter, and they matter a lot. Higher starting values mean that not only are future expected returns lower, but the best outcomes are lower and the worst outcomes are worse. The reverse is true as well—lower starting values mean that not only are future expected returns higher, but the best outcomes are higher and the worst outcomes are less poor. However, it’s also extremely important to understand that a wide dispersion of potential outcomes, for which we must prepare when developing an investment plan, still exists — high (low) starting valuations don’t necessarily result in poor (good) outcomes. In other words, investors should not think of a forecast as a single point estimate, but only as the mean of a wide potential dispersion of returns. The main reason for the wide dispersion, as Damodaran noted, is that risk premiums are time varying (if they were not, there would be no risk in investing!). It is the time-varying risk premium, what John Bogle called the “speculative return,” that leads to the wide dispersion in outcomes.
The fact that a wide dispersion of returns occurs around the mean forecast is why a Monte Carlo simulation is a valuable planning tool. While the input includes an estimated return, it also recognises the risks of that mean forecast not being achieved — which is why volatility is another input. Because most simulators allow you to examine thousands of alternative universes, they enable you to test the durability of your plan — you can see the odds of success (such as not running out of money or leaving an estate of a certain size) across various asset allocations and spending rates.
Monte Carlo analysis gives you the probability of success based on what you've told it for your goals, inputs, and assumptions. No more, no less.
Michael Kitces tweeted this a few days ago:
Why I advocate the use of Monte Carlo analysis. "I'd rather be vaguely right than precisely wrong." - Keynes