Monte Carlo simulations: Monte Carlo is a form of stochastic model that produces results based on repeated random sampling. The idea is to simulate thousands of possible market scenarios and identify a plan’s probability of success or failure.
Monte Carlo modelling is a significant improvement on deterministic models. They take into account the unpredictability of returns, inflation and longevity. They’re based on an assumed mean, standard deviation and correlation. They express potential outcomes in terms of the probability of successfully meeting clients’ objectives.
This is a valuable aid to client communication. It gets clients and their advisers talking about financial planning and retirement outcomes in terms of probability rather than certainty. And this goes right to the heart of communicating and demonstrating clients’ capacity for loss.
By its very nature, the future is unknown and unknowable. Monte Carlo simulations don’t try to predict the future. In fact, it’s the contrary. They generate thousands of possible future scenarios and identify what type of market conditions could ruin the client’s plan. More importantly, this helps advisers and clients identify and agree what action they’d take if any of those nasty market scenarios happen. This to my mind is real financial planning.
One common criticism of a Monte Carlo model is that, given the low level of numeracy in the country, it might be hard to explain the results to clients. The joke is that 50% of the population don’t understand probability and the other 50% have no idea what you’re talking about.
Seriously, though, Monte Carlo is really easy to explain. I suggest that people think of the simulations as simply giving the client 10,000 lives (or 20,000 or whatever number of simulations you run). Each of those lives represents what your retirement could look like. We just don’t know which one. We worry about the scenarios that result in the client running out of money and figure out what to do in advance.
You could use a simple, visual traffic light system to explain the success rate of a plan. Success rate of less than 60% could be red, between 61% and 80% is amber and between 80% and 99% is green.
Monte Carlo simulations have their own weaknesses. The chief one is that returns in any one year are entirely independent of previous years. The implication is that Monte Carlo analysis tends to overstate tail risk, compared to the actual historical worst case. This is because Monte Carlo simulations don’t account for mean reversion, which is a key characteristic of most asset classes.
As financial adviser and researcher Derek Tharp PhD notes: ‘Whether the prior year was flat, saw a slight increase, or a raging bull market, Monte Carlo analysis assumes that the odds of a bear market decline the following year are exactly the same. And the odds of a subsequent decline in the following years also remains exactly the same, regardless of whether it would be the first or eighth consecutive year of a decline!
Yet, a look at real-world market data reveals that this isn’t really the case. Instead, market returns seem to exhibit at least two different trends. In the short-run, returns seem to exhibit “positive serial correlation” (ie, momentum – whereby short-term positive returns are more likely to be followed by positive returns, and vice-versa), and, in the long-run, returns seem to exhibit “negative serial correlation” (ie, mean reversion – whereby longer-term periods of low performance are followed by periods of higher performance, and vice-versa).’
So what?
My view is that both historical and Monte Carlo simulations are useful and certainly more robust than straight-line projections. Given that history represents past reality, many people, including me, give it more credence than most Monte Carlo simulations. Of course, it’s possible that the worst years the stock market will ever see are in front of us.
If an adviser uses extensive historical data, they don’t have to make assumptions about the behaviour of underlying asset classes. Historical data may only provide a limited sample of what’s possible in the future, but the range of outcomes is wide enough to help us make informed decisions.
As Bernstein again noted, ‘We all have to make decisions on the basis of limited data. One sip, even a sniff, of wine determines whether the whole bottle is drinkable. Courtship with a future spouse is shorter than the lifetime that lies ahead. A few drops of blood may evidence patterns of DNA that will either convict or acquit an accused murderer. Public-opinion pollsters interview 2,000 people to ascertain the entire nation’s state of mind. The Dow Jones Industrial Average consists of just thirty stocks, but we use it to measure changes in trillions of dollars of wealth owned by millions of families and thousands of major financial institutions. George Bush needed just a few bites of broccoli to decide that that stuff was not for him. Most critical decisions would be impossible without sampling. By the time you have drunk a whole bottle of wine, it is a little late to announce that it is or is not drinkable. The doctor cannot draw all your blood before deciding what medicine to prescribe or before checking out your DNA.’
Bernstein concludes that38:
‘We cannot enter data about the future into the computer because such data are inaccessible to us. So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician’s trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. History provides us with only one sample of the economy and the capital markets, not with thousands of separate and randomly distributed numbers. Even though many economic and financial variables fall into distributions that approximate a bell curve, the picture is never perfect. Once again, resemblance to truth is not the same as truth. It is in those outliers and imperfections that the wildness lurks.’
Bernstein, Peter L.. Against the Gods: The Remarkable Story of Risk (Kindle Locations 172-174). Wiley. Kindle Edition.
Bernstein, Peter L. Against the Gods: The Remarkable Story of Risk (Kindle Locations 537-539). Wiley. Kindle Edition.
Kitces., M (2015) Is Financial Planning Software Incapable Of Formulating An Actual Financial Plan? Nerd’s Eye View. https://www.kitces.com/blog/is-financial-planning-software-incapable-of-formulating-an-actual-financial-plan/
Blake, David P., Independent Review of Retirement Income: Consultation (March 1, 2016). Independent Review of Retirement Income, 2016. Available at SSRN: https://ssrn.com/abstract=2753689
Bierwith, Larry (1994). “Investing for Retirement: Using the Past to Model The Future.” Journal of Financial Planning; Jan1994, Vol. 7 Issue 1, p14 https://www.onefpa.org/myFPA/journal/Documents/FPA%20Journal%20January%201994%20-%20INVESTING%20FOR%20RETIREMENT%20USING%20THE%20PAST%20TO%20MODEL%20THE%20FUTURE.pdf
Bengen, William P. (October 1994). “Determining Withdrawal Rates Using Historical Data”. Journal of Financial Planning: 14–24.
Hopewell, Lynn (1997). “Decision Making Under Conditions of Uncertainty: A Wakeup Call for the Financial Planning Profession.” Journal of Financial Planning; Oct97, Vol. 10 Issue 5, p84 https://www.onefpa.org/myFPA/journal/Documents/Best%20of%2025%20Years%20Decision%20Making%20Under%20Conditions%20of%20Uncertainty%20A%20Wakeup%20Call%20for%20the%20Financial%20Planning%20Profession.pdf#search=Lynn%20Hopewell
Bernstein, Peter L.. Against the Gods: The Remarkable Story of Risk (Kindle Locations 241-248). Wiley. Kindle Edition.
Does the past predict the future? https://www.economist.com/blogs/freeexchange/2009/09/does_the_past_predict_the_futu
Bernstein, Peter L. Against the Gods: The Remarkable Story of Risk (Kindle Locations 6827-6833). Wiley. Kindle Edition.
CHAPTER 8
Adapting sustainable withdrawal strategies to longevity
It takes two to tango but who’s going to last longer, you or your portfolio?
So far, we’ve considered withdrawal strategies based on a fixed planning horizon. For consistency, we’ve used the 30-year retirement period but you can adapt all the approaches for any planning period.
The natur
al next step is to apply life expectancy, or more precisely longevity, into the sustainable withdrawal rate calculations. You can use mortality data available at the Office of National Statistics. Sustainable withdrawal rates should be based on survival probability, rather than a fixed (often longer) planning horizon.
Life expectancy: flawed measure for retirement income planning
Looking at life expectancy tables, based on the client’s age and sex, is a common but flawed approach to estimating how long someone is likely to live. For instance, a 65-year-old man in the UK has a remaining life expectancy of 19 years, while it’s 21 years for a woman of the same age.
This approach is flawed for several reasons. One, life expectancy is the mean number of remaining years. There’s at least a 50% chance that someone in that age group will outlive their life expectancy! But more crucially, it fails to account for improvements in mortality as people get older.
The ONS has two types of life expectancy measure:
the period life expectancy which shows life expectancy at a given period eg for a 65-year-old in 2015
the cohort life expectancy which tracks a given cohort who share the same year of birth and takes account of improvements in mortality
The table below shows that mortality improvements add about three years to life expectancy for a 65-year-old male and female, depending on when they reach that age.
Cohort data is more appropriate for retirement planning purposes, because it takes into account likely future mortality improvement.
Fig. 53: Cohort and period life expectancy for 65-year-old male and female. Source ONS, Dr Paul Cox39
Using survival probability
An obvious way to manage longevity is to use an annuity to ensure against the risk of living too long. Short of that, longevity in the context of retirement planning is best approached in terms of survival probability. This gives us a clearer idea of the chances that someone will live to a certain age.
The ONS cohort data in the chart below shows the survival probability for a 65-year-old male and female.
There’s an 11% chance a 65-year-old male will celebrate his 100th birthday, and that rises to 15% for a female of the same age. For a couple of the same age, the probability that at least one of them will live to age 100 is a whopping 24%!
We need to bring the survival probability context into retirement income planning. This is one reason I believe that straight-line cash flow projections are inadequate. The challenge we’re dealing with is – by its very nature – uncertain and so probabilistic.
This data is based on the general population in the UK so it’s broadly accurate. But we can improve accuracy by using ONS cohort data for each part of the country.
Advisers can adjust survival probability even further to take account of a client’s lifestyle. It’s unrealistic to assume that a 65-year-old who smokes 10 packs of cigarettes a week, with mild health conditions, has the same survival probability as a health fanatic who goes to the gym three times a week and hasn’t touched a cigarette in their life! Engaging in non-judgmental, grown-up discussions with clients is vital.
Fig. 54: Survival probability for a 65-year-old male, female or couple
Longevity: human vs. portfolio
Once you’ve established the survival probability for an individual or a couple, you can estimate their probability of running out of money during their lifetime. The probability of success or failure should be based on how long the individual is likely to live, not a fixed period.40
To do this, there are two important factors at play:
the probability of failure of a withdrawal rate over any given fixed retirement period (eg 30 years)
the probability that at least one member of a couple will survive that period, given their current ages
These two factors are distinct and independent of each other – ie the chance of one happening doesn’t depend on the other. (Although running out of money could well lead to an early grave.)
As these factors are completely independent, the probability of both happening is less than the probability of either of them happening. This is what maths nerds refer to as conditional probability!
Earlier we said that a 3% inflation-adjusted withdrawal rate (net of 1%pa charges) from a 50/50 UK-centric portfolio has a 82.6% probability of success over a 30-year horizon. This means a 17.4% probability of failure. Or more precisely, a 17.4% chance that they’ll need to make some adjustment to their withdrawal in the event of poor sequence of return.
But, for a 65-year-old couple, there’s only a 48% chance that at least one of them will live to age 95.
The overall probability of running out of money during their lifetime is actually 8.4% (17.4% × 48%). So, the overall longevity-adjusted probability of success for a 3% inflation-adjusted withdrawal rate is a whopping 91.6%!
There are two unrelated probabilities here. So, for a client to run out of money, they need to experience both events at the same time – ie poor sequence of return that ruins a 3% withdrawal rate over a 30-year period AND at least one member of the couple surviving 30 years41.
Dealing with declining financial capacity in retirement
One final issue worth thinking about is that as people get older, their ability to make financial decisions is impaired. As discussed earlier, it’s estimated that financial capability declines at a rate of 1% to 2% each year from age 60. So, expecting clients to understand the vagaries of managing a drawdown portfolio (or even to provide their adviser with informed consent to do so) is unrealistic.
One way to address this is to have a withdrawal policy statement42 signed and pre-agreed by clients while they’re still financially capable. Of course, clients over 65 should use Power of Attorney, particularly clients in drawdown. The attorney should be involved in the planning process as early as possible.
Longevity is a huge consideration in retirement, and it’s an area where financial planning can add real value. The best approach to managing it is to use survival probability rather than putting a randomly selected age into the cash flow tool.
See Paul Cox (2015): Helping consumers and providers manage defined contribution wealth in retirement. https://www.sanlam.co.uk/Sanlam/media/Retirement-Income-Service/Paul_Cox_Report.pdf This is an excellent discussion and essential reading on longevity assumptions in retirement planning.
See Stout, R. Gene and John B. Mitchell. 2006. “Dynamic Retirement Withdrawal Planning.” Financial Services Review 15, 2 (Summer): 117–131
As you can see, the calculations are getting a bit more complicated. That’s why a software tool is recommended for this – see www.timelineapp.co
See 10.1 on the power of withdrawal policy statement
CHAPTER 9
Asset allocation and sustainable withdrawal rate
Asset allocation is a key factor when deciding the sustainable withdrawal rate from a retirement portfolio. Earlier versions of SWR research have been based primarily on domestic large-cap equity and bond portfolios. But an increasing body of study points to the vital role that broader diversification can play to improve retirement income sustainability.
Are you a stock or a bond?
One of the most important decisions a retiree must make is what proportion of their portfolio should be allocated to equities.
The received wisdom is that allocation to equities should be lower during the retirement income stage. Reasons include the fact that retirees tend to have lower risk appetites and reduced risk capacity.
Yet, this common industry practice isn’t supported by cold, hard, empirical evidence. Indeed, in his seminal 1994 article, Bill Bengen recommended, ‘a stock allocation as close to 75 percent as possible, and in no cases less than 50 percent. Stock allocations lower than 50 percent are counterproductive, in that they lower the amount of accumulated wealth as well as lowering the minimum portfolio longevity. Somewhere between 50-percent and 75-percent stocks will be a client’s “comfort zone.” ’
Other research, inclu
ding mine, corroborates this view. Higher equity allocation tends to support higher sustainable withdrawal rates.
Fig. 55 overleaf shows the historical withdrawal rates for a 30-year retirement starting after 1900, using various asset allocations.
Fig. 55: Sustainable withdrawal rates for various asset allocation
Fig. 55 shows higher equity allocation tends to support higher withdrawal rates. This is consistent through most historical periods.
Fig. 56 shows a summary of the historical worst case, 10th, 50th and 90th percentile net withdrawal rate (net of 1%pa fee) for varying degrees of allocation to equities, based on a 30-year horizon.
Fig. 56: Gross withdrawal rates for various equity/bond allocations
Another way to view this is to look at the success rate of various asset allocations for a given withdrawal rate over multiple time periods. The chart below shows that higher equity allocations are consistently associated with a higher success rate over all time periods between one to 40 years.
Fig. 57: Success rate for £3,000pa real income withdrawal from £100,000 portfolio
This raises an important question about how we assess risk in the context of meeting a retirement income goal. Why is higher equity allocation deemed to be higher risk, when it actually has a higher success rate?
Beyond The 4% Rule Page 9