Ben Mathew has a B.A. in economics from Dartmouth College, and a Ph.D. in economics from the University of Chicago, where he won the Martin and Margaret Lee Prize for the best performance on the microeconomics qualifying exam. He has taught economics at the University of Chicago and Colgate University.
What drives the best financial planning decisions? In this episode, Ben Felix and Mark McGrath sit down with Ben Mathew, a PhD in economics from the University of Chicago and author of Economics: The Remarkable Story of How the Economy Works. The discussion explores the lifecycle model of economics, a powerful yet underutilized framework for financial planning, and contrasts it with traditional approaches like safe withdrawal rates (SWR). Ben Mathew shares insights into the lifecycle model, its origins, and its practical applications in aligning financial decisions with personal goals over a lifetime. We also dig into Ben’s innovative financial planning tool, TPAW (Total Portfolio Allocation and Withdrawal) Planner, designed to bring the lifecycle model into practice. While the discussion delves into the complexities of financial planning, it’s packed with actionable insights for listeners seeking smarter, evidence-based strategies. Join us for a deep dive into the lifecycle model and discover how it compares to traditional safe withdrawal rates.
Key Points From This Episode:
(0:02:31) Identifying the main problem financial planning aims to solve and the biggest challenges in creating a plan for saving and spending across a lifetime.
(0:05:49) Exploring the effectiveness of simple rules of thumb, like the 4% rule, and the economic models available to analyze financial planning problems.
(0:09:16) Why the lifecycle model isn’t more widely adopted.
(0:12:06) The basic premise of the lifecycle model.
(0:16:45) How withdrawals in the lifecycle model relate to amortization and how risk affects amortization-based withdrawals.
(0:21:12) Examining how amortization-based variable spending aligns with consumption smoothing and responds to portfolio drops.
(0:25:25) How updating expected return assumptions mitigates behavioural worry during market drops.
(0:26:37) The variability in spending seen in historical simulations, how variable spending can be tailored to individual preferences, and the recommended frequency for updating financial calculations.
(0:38:30) What the lifecycle model advises about asset allocation.
(0:42:00) The importance of expected return assumptions in lifecycle asset allocation advice.
(0:45:28) Adjusting lifecycle advice for when you have limited information about expected returns and how retirement glide paths compare to the lifecycle model.
(0:50:03) How asset allocation in the model changes based on the time horizon of the goal.
(0:54:10) The influence of different wealth levels on asset allocation in the lifecycle model.
(0:56:43) How the safe withdrawal rate methodology works and key problems with its approach.
(01:08:11) Connecting the probability of success metric to the utility function and differentiating variable safe withdrawal rates (SWR) from amortization-based withdrawals.
(01:17:02) An overview of Ben’s exciting online tool, TPAW (Total Portfolio Allocation and Withdrawal) Planner, for bringing the lifecycle model into practice.
Read The Transcript:
Ben Felix: This is the Rational Reminder Podcast, a weekly reality check on sensible investing and financial decision-making from two Canadians. We're hosted by me, Benjamin Felix, Chief Investment Officer at PWL Capital, and Mark McGrath, Associate Portfolio Manager at PWL Capital.
Mark McGrath: Welcome. This is a really fun episode. I was looking forward to this. And I said it a couple times, I think, during the recording, I was like, "This is great." It's more my kind of wheelhouse, I think, in terms of – I mean, you're an incredible financial planner as well, but this is more stuff that I think about on a regular basis. It's a really, really great conversation with Ben Matthew.
Ben Felix: Ben Matthew, he's got a PhD in economics from the University of Chicago, as many of our guests do. He also went to Dartmouth. Clearly, a very, very smart guy. He wrote a book on economics. And as he told us at the end of the episode, he was thinking about writing a book on personal finance, and he ended up going down a different path and building this software tool, which we didn't talk about until the last couple of minutes because I asked him about it. He didn't want to come on the podcast to promote it, but it was worth talking about.
Anyway, so he built this financial planning tool that really tries to implement the lifecycle model from economics, which is the field of economics answer to financial planning. It's been around for a long time. It's been studied and built upon by many of the greatest economists that have lived, but it's underutilized in the real world. Ben's trying to change that. That's really what we discussed in this episode. We talked about the different approaches to financial planning. We talked about the lifecycle model and how it works. And we talked about, to contrast that, safe withdrawal rates. I think it's a pretty good financial planning discussion.
Mark McGrath: Yeah, lots of practical takeaways, I think, for our audience. Got a little bit geeky, but it always does. But I think for those who are devout listeners, that won't be anything new. And I think there's a lot of great insights and takeaways for them.
Ben Felix: That's good. Let's go to our episode with Ben Matthew on the lifecycle model versus safe withdrawal rates.
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Ben Felix: Ben Matthew, welcome to the Rational Reminder podcast.
Ben Mathew: Thanks for having me. I've been watching the show for many years. It's a real pleasure to be on it now.
Ben Felix: Awesome. Super excited to be talking to you. People from the Rational Reminder community or from Bogleheads will know your name at least because you write a ton on there, you put some incredible posts up. A lot of them on this topic that we're going to be talking to you about today. I'm sure many people that have read your writing are going to be excited to hear you speak about it. What is the main problem, Ben, that financial planning aims to solve?
Ben Mathew: The main problem in financial planning is retirement planning. That's usually where the biggest numbers are. And the problem there is we need to decide how much to save during our working years, how to invest those savings, and how to withdraw from that during our retirement years. There are obviously other problems like you might need to pay off a mortgage, there might be kids' college tuition payments that might be due. You might be thinking about bequest. All of those things are things that we naturally start thinking about when we think about retirement planning. If you need to send the kids to college for a few years, then those are years in which you can't save for retirement. You naturally have to think about all of these other problems when you think about retirement planning.
Retirement is this big problem around which you can hook all of these other things and come up with a plan for your life. It sounds like there are three problems. How much to save? How to invest? And how to withdraw? But the saving and the withdrawing problems are really two sides of the same coin. How much to withdraw during retirement is really a decision about how much to save for the rest of retirement. It's really fundamentally a spend now versus later decision. There are really only two core concepts involved in financial planning. The save versus spend decision, consume early versus late. And the other decision is the investment. How much do we invest in stocks versus bonds? How do we vary that across time?
Mark McGrath: Yeah, that's a great way to think about it. What are the biggest challenges in creating a plan for saving and spending throughout one's lifetime?
Ben Mathew: The two concepts that make it hard to the point that you can't just wing it or come up with a plan in your head, you have to sort of sit down and figure things out. The two things I would say, the first is pretty well known, which is the problem with compounding. We have very bad intuition when it comes to compounding. We're very good usually at adding, subtracting, multiplying, and dividing. We have good intuition about that. But when it comes to exponents, we lose all intuition. We really have no clue.
If you think about, if you take $100 and think about how it grows, if it grows at 5% per year, what would it compound out to over 50 years? We really have no idea at all what the answer to that is. If you change that from 50 years to 60 years and start saving maybe 10 years earlier or retire 10 years later, what's the impact of that? We have no idea. Do they change the interest rate from 5% to 6%? What's the impact of that? Again, no idea. To really have very poor intuition, that means that we have to sit down and do the math in order to make a financial plan.
This is fairly well known. Lots of people talk about it, gets a lot of airtime. The other issue that makes us hard that people don't talk about as much is the issue of risk. We're also pretty bad at thinking about risk. And in financial planning, risk doesn't show up in simple ways. It also compounds over time. A bad outcome is a mix of good and bad outcomes, more bad than good. How do the good and the bad average out over time? Do they cancel each other? How much do they cancel each other? How risk compounds over time becomes extra hard. You have this mix of compounding and risk sort of interacting. That really means that we have to sit down and have a formal model and do some calculations and figure out what a sensible financial plan would be.
Ben Felix: You mentioned formal models. How effective are simple rules of thumb like the 4% rule and stuff like that for long-term financial planning?
Ben Mathew: The problem with rules of thumb is that people are just too different. To come up with a rule of thumb, you sort of have to have this average person in mind and we can construct a plan for the average scenario and present that as a rule of thumb. But people are just too different. One person might be looking to retire early. Another person might be looking to work until full retirement age because their job is secure and they like it. Somebody else may have a pension on top of Social Security. Someone else may not have much of that.
And then there are preferences that are different. Some people may be more risk-averse. Some people are more risk-averse than others. Some people may be looking to consume earlier when they're healthy in early retirement. Others might be looking to leave a large bequest. People just differ in all of these ways. And if you try to create all these different rules of thumbs that get into all of these permutations and combinations, then that gets complex and hard to manage really fast. And it's just easier to go back to the original model and put in your circumstances and your preferences and come up with a custom plan.
And it's important to emphasize that financial planning is a big deal. It's going to impact to the tune of hundreds of thousands of dollars and frequently millions of dollars. A rule of thumb that may or may not be appropriate to you seems that it's not a good place for a rule of thumb. When the stakes are so high, we really should be sitting down and figuring out what's right for us and not rely on a rule of thumb that may or may not be appropriate for you.
Mark McGrath: Couldn't agree more. What economic models do we have to analyze these problems?
Ben Mathew: Two main models that we can use to analyze the problems that come up in financial planning, one is a lifecycle model and the other is a safe withdrawal rate or SWR method. The lifecycle model is the model that comes out of economics. And I should emphasize that economics is the academic field that studies this problem. By economics, I'm including finance as a subfield.
All of the concepts involved in financial planning; consumption, smoothing, risk aversion, precautionary savings, time preferences, portfolio construction, these are all core concepts that have been developed in economics. And it's natural for people to try to put this together and try to create this model that says how we should save, invest, and spend over our lifetime.
The lifecycle model is an important part of economics. Several economists, Franco Modigliani, Milton Friedman, Paul Samuelson, Bob Merton, these are all Nobel Prize winners who have contributed to the development of the model. More recently, we have economists like John Campbell and Luis Viceira who have worked on the lifecycle model. The model without risk, the simpler version without risk, is taught in undergraduate economics. The more sophisticated version with risk is taught in graduate finance. It's an important established model in economics.
The other model is the safe withdrawal rate or SWR model. This was created by a financial planner named Bill Bengen in 1994. This ended up being widely used in industry. It's been heavily adopted. It's kind of like the standard way of doing things in industry now. But the assumptions that are made in the SWR model turn out to be very problematic. I've been arguing and others have been arguing that the lifecycle model is a much better approach to financial planning than the SWR model.
Ben Felix: We have this model that's pretty robust and pretty serious and it's been studied by literally some of the smartest people in the world that have lived over the last, whatever it is, 70 years. Why aren't more people using the lifecycle model?
Ben Mathew: That's a very good question. And for people who are aware of the lifecycle model, this kind of like, "How are people not using this?" Fundamentally, at least part of the reason I think is that the model with risk, which is really what we need to practically apply this in industry, the model with risk is more mathematically challenging. It's kind of remained, then stopped a little bit in graduate finance. But the good news is that the lifecycle model is coming out of academia and into a broader understanding and into industry.
Over the last 20 years, I'd say that the trickle has been turning into a stream. It's not a flood yet, but at least there's definitely a steady stream of talk about lifecycle model and applications of the lifecycle model. There's been a series of books that's been published over the last 20 years. Several articles have been published on it recently. The Economist had an article on it a few weeks ago. You've had several people who've been important to the development of the lifecycle model on your podcast. You've had Bob Merton, John Campbell, Francisco Gomes. These are all academics who worked on the model. You guys have contributed to it.
In terms of applications in industry, Elm Wealth, the wealth management firm has been applying the lifecycle model for financial planning for its clients. And you've had the principles, Victor Haghani and James White, who have written a very good book on the lifecycle model, called The Missing Billionaires. You've had them on your show. And even people who've not heard about the lifecycle model may be using it, because Vanguard's target date funds, for example, explicitly use the lifecycle model to construct a glide path for its target-date funds. If you're investing in a Vanguard target-date funds, you are using the lifecycle model, even though you've not heard of it.
I think the overall arc of how things are happening here, it's kind of like how index funds came. The idea first originated in academia. Some people saw it and really became convinced and excited about it, people like Jack Bogle, and then implemented it. And then it took a couple of decades to sort of get established, and then a couple more decades to become a standard way in which well-informed investors tend to invest.
I think the arc of lifecycle model is going to be the same. It's definitely been slower than index funds. Given the fact that people, as soon as they see the lifecycle model and start appreciating different aspects of it, and there are all these problems with SWR that people are aware of, and they're trying to fix it by doing all of these band-aids and saying, "Let's try this, let's try that." All of these problems are elegantly solved by the lifecycle model because it's just starting with better assumptions. Once people see that, people do get excited about it. I think that over the coming years, the lifecycle model is going to become much more widely used and the standard part of how at least some subset of well-informed investors are going to be investing.
Mark McGrath: We've talked a lot about the lifecycle model. Let's get into a little bit about how it works. How would you describe the basic premise of the lifecycle model?
Ben Mathew: To understand the lifecycle model, it's easiest to first start out with the model without risk. And a lot of the concepts can be understood easily in that context and it will apply to carry over to the model with risk. In the model without risk, we just have one riskless asset. We know what the returns are going to be. Let's say it's going to be 3%, 3%, 3% every year. There's no investing problem. You just invest in this 3% asset. The problem really is how much do you save during your working years and how do you spend out of that? How do you withdraw from that during your retirement years?
Obviously, the reason we want to save during our working years is really because we don't want to have that sudden drop in spending when we start retirement. That's obvious. But it's worth looking at this more closely so that we can make sure that this is in our model, this reason why we want to do this.
The reason we want to spread this consumption, spread spending over time and not have the sudden drop, is really because we have a diminishing marginal utility of consumption. We value the first loaf of bread more than we value the second loaf of bread, which we value more than the third loaf of bread. This means that you'd rather have one loaf of bread each period because that gives you the most value, the most bang for your buck, rather than two loaves of bread in one period and zero loaves of bread in another period. Because that second loaf of bread is not that valuable. So, your utility is declining.
That means that the utility function that's driving this, the utility increases a lot for the first loaf of bread. It goes up quite a bit on the first loaf. For the second loaf, it goes up less. The third loaf, it goes up even less. It's always positive, but it's flattening out as we get more and more. The shape is a concave utility function. And that's a really important aspect of how we behave and how we should be making decisions is respecting that diminishing marginal utility consumption, that concave utility function.
And I emphasize that because this will show up later. And the problem with SWR is it's not assuming a concave utility function effectively. It's worth thinking about the role of that utility function. This concave utility function makes us want to spread spending over time. Usually, people wonder what about lumpy expenses? My spending should not be smooth because I need to send kids to college for four years and my expenses would be high during those four years. And what about legacy and so on? We talk about smoothing consumption over and above after taking care of these lumpy expenses. Beyond these lumpy expenses, what's left over? We are going to try to smooth those general expenses, the remaining expenses effectively. Handling lumpy expenses is not a problem at all for the lifecycle model. You can easily put that into the model.
It's also important to emphasize that a smooth consumption is not necessarily a constant consumption. It's not necessarily a flat spending schedule that you're going to try to create. And there are two forces at work here and determine whether it's flat, or upward-sloping, or downward-sloping. But one is the fact that we typically get a positive rate, a real rate of interest. So after inflation, we still get more money. If you save money, you still get more later on. If you give up a loaf of bread today, you get two loaves of bread in the future. There's an incentive to try to save more and try to spend more later rather than early because you can increase your average spending if you delay spending. That's a force towards scheduling an upward-sloping spending schedule.
On the other hand, we may be impatient, we prefer consuming earlier rather than later, or we prefer consuming an early retirement when we are healthy and we can travel, we might want to spend more and value that more than spending in late retirement. Preferences like this would be called a positive time preference rate. This time preference rate is conflicting with the positive real rate of interest. And whether or not you schedule a flat, upward-sloping, or downward-sloping glide path, it will come down to which one is the net effect of these two forces. That's basically the gist of how the model works without risk. That's how we would save, invest, and withdraw if you knew what our returns were going to be every period.
Ben Felix: It makes a lot of sense. I remember before I understood what the lifecycle model meant, it always seemed like this kind of mystical, confusing thing. But when you actually hear what it means, it's relatively simple. It's smoothing consumption over life. Yeah, it's pretty simple and pretty intuitive. I would use pizza for marginal utility though, because eating one loaf of bread sounds awful. The second loaf would be worse but –
Ben Mathew: Maybe it should have been a slice of bread, huh?
Ben Felix: Yeah.
Mark McGrath: I don't know. Tell that to my kid. My kids can eat an infinite amount of bread
Ben Mathew: Yeah, slice of pizza would be the best.
Ben Felix: By the last slice of pizza, you're ready to throw up. I'd be ready to throw up after one loaf of bread though. Anyway, how do withdrawals and lifecycle model relate to amortization?
Ben Mathew: We talked about how we're going to create this either upward-sloping or downward-sloping. Some kind of spending schedule. If you try to sit down with a spreadsheet and try to figure out, "Okay, how much can we spend? How much do we need to save? How much do we need to withdraw?" We can do that with some simple math.
Mathematically, the way we try to do that is basically a two-step process. Step one would be to calculate the total value of the resource that you have available for spending. That's your total wealth. And this total value includes your savings that you have in your brokerage account and your bank account and so on, but it also includes the present value of your future income. You would calculate the value of that income, add it to your savings and say, "That's your total wealth. This is what's available to fund our spending."
Step two then is to take this total wealth and figure out what kind of spending can you schedule with this total wealth. If the interest rate is 3% and if you want spending to grow by 1%, what would you spend every year? The price of doing that, it only involves high school algebra to figure out. The price of doing that is called amortization. And it's the same technique. It's a standard tool in finance. It's the same technique that we would use to figure out what kind of monthly payments you would need to make in order to pay back a loan. That would be amortizing the loan into the series of monthly payments. In the same way, we can amortize our wealth to figure out what our spending schedule that it can fund would be.
You can do it with the high school algebra with formulas and so on. But in a spreadsheet, you can use a convenient function called the PMT function. A lot of people who are amortizing their portfolio using this technique are typically using that PMT function in Excel or Google Sheets.
Mark McGrath: And how do amortization-based withdrawals change when you add risk?
Ben Mathew: When we add risk, we don't know that the returns will come in at 3%, 3%, 3%. We might expect that the returns come in at 3% per year, but returns are going to come in either higher than expected or lower than expected and rarely sometimes even as expected.
What do you do when returns come in higher than expected or lower than expected? It's simple and straightforward, you just recalculate. You just amortize your wealth again. If returns came in higher than expected, then your wealth is – let's say it's 10 % higher than you thought it would be, if you try to amortize that, you would get a spending schedule that's 10% higher than it was before.
The important thing is you're rescheduling all of your spending, it's not just the current year. You're rescheduling all of your spending and lifting all of it up by 10%. And then the next year, if your wealth is 5% lower, your spending goes down by 5%. You keep jumping on to these new schedules. You jump up to a higher schedule when the returns come in better than expected and down to a lower schedule. The spending sequence that it traces out is basically variable spending. It's not fixed spending because you're constantly recalculating.
That's the process of how you would do this. Because we're doing this, because there's uncertainty about future returns, a new force comes into play, and that's precautionary savings. That's a very natural instinct that we have. Because we don't know what the future is going to be like, it makes sense to be cautious and spend a little bit less now, just in case the future turns out to be lower than expected.
Now we have a third force to add to our real rate of interest and the time preference rate. Now you have this precautionary savings motive that will say that you should try to create an upward slope other way or you should increase the slope of your spending more than you would based on just these other two factors.
Ben Felix: Just to make sure I understand, precautionary savings suggests that you should increase the slope of your spending so that you're starting out with more and increasing your spending later?
Ben Mathew: No, starting out with less. You spend less early on so that you'd spend more later on. So, the slope goes up.
Ben Felix: You have more capital early on. You're spending a lower amount of your capital. And then as you're expected remaining lifespan gets shorter, you're able to spend at a higher rate.
Ben Mathew: Yes. The lifespan thing is already included in that original amortization. We've already scheduled that out. If returns go as expected, you'll stay on that original schedule and you'll keep shortening your lifespan and you've already accounted for that in that original schedule. The lifespan itself would not drive increased spending in later years. What's driving it would be the fact that you have chosen to schedule less early and more later.
Ben Felix: It's just a preference, really?
Ben Mathew: Yes.
Mark McGrath: Yeah, just precautionary buffer, essentially, against the uncertainty of future returns or the downside of that.
Ben Mathew: Exactly.
Ben Felix: So, we're talking about variable spending now, amortization-based variable spending. How does that fit with the consumption smoothing that we talked about earlier?
Ben Mathew: This is an area where there's a lot of confusion or a lot of misconceptions. Usually, people think that fixed withdrawals would be most consistent with consumption smoothing, because what could be more smooth than just keeping your spending the same as it was before?
And the problem is that when you have a portfolio with risk, you don't really have the option of truly fixed spending. Fixed spending is just spending that's fixed for a while, and then you run the risk of a big drop in spending if you run out of money. That's a really bad thing because that first loaf of bread is very valuable to you, or the first slice of pizza is really valuable to you. You don't want to put that at risk.
The most smooth you can make spending when you're spending out of a risky portfolio is to make adjustments as quickly as possible, so those adjustments will be small. Quick also means small adjustments. If you wait, you will have to make big adjustments. You'd want to make frequent small adjustments so that you don't face this risk of potential big drops later. This is a variable spending that keeps updating to the new realities is the most smooth that we can make consumption be when your portfolio is risky.
Mark McGrath: With amortization-based variable withdrawals, you talked about how spending needs to change. How would it change if the portfolio dropped, say, 10%?
Ben Mathew: This is something that people are concerned about a lot. Whenever they start thinking about variable withdrawals, the first thing they worry about, and it makes sense to worry about, how variable is that? And how low can it go. That's exactly the right thing to think about.
Usually, when people think of a crash, the most dramatic crashes are the stock market crashes which can drop by a lot in a year. It's important to remember that your stock portfolio is only a portion of your savings portfolio and that's only a portion of your total wealth. There are some layers between the stock crash and the total wealth.
A 15% drop in the stock market might only be a 10% drop in the savings portfolio, and that might only be a 7% drop in your total wealth when you factor in your future income. Even beyond that, only part of your total wealth is allocated towards retirement spending. A lot of people have legacy goals. Your wealth is funding both retirement spending and legacy. It's appropriate to take more risk on legacy than on your retirement spending.
That 7% drop in total wealth might be only a 5% drop in the wealth that funds your retirement spending. So that's an extra layer of separation from the portfolio down to your spending. But let's say we have a 5% drop in the wealth that's allocated that's funding our retirement spending. Then do we need to reduce our spending by spending by 5%, less than 5%, or more than 5%? That depends on what you believe about expected returns.
If you think that expected returns after the crash is the same as it was before. Let's say you thought it was 5% real returns for stocks and 2% real return for bonds. After the crash, you still think it's 5% stocks and 2% real for bonds, then your wealth has declined by 5% and it's not growing any faster because your expected returns is staying the same. When you amortize your spending, that would drop by the full 5%. Then you would try to reduce your spending by 5%.
But, usually, after a crash, you can reasonably expect that the expected returns has gone up. Because if you base your expected returns on valuations, which fundamentally makes sense, part of the drop of stocks and all of the decline in the price of bonds can be attributed to changes in the discount rate, which is the expected return. It's not necessarily because your future payouts are reduced, it's because you're valuing it less. Expected returns goes up. If you adopt that model, then even though your wealth went down by 5%, it's going to grow faster now when you amortize your spending, you need to drop that down only by 3%, for example.
This actually brings up the fact – and I think John Campbell and John Cochrane have emphasized this, is that it's important to focus on spending. What did the crash do to your spending? And that may look quite different. Usually, it's better news after a crash than if you just focus on what's your asset's worth. If you move from that assets that you have, what the brokerage statement says, factoring your future income and then factoring the increased expected returns, that's what tells you your spending. That usually is not as bad as the market crash.
Ben Felix: When COVID happened and asset prices fell a whole bunch, we tried to really quickly update our expected return assumptions because clients' financial plans looked a whole lot worse with lower asset prices and no change in expected returns. But they actually didn't look that bad once you accounted for the increase in expected returns based on lower valuations. That definitely makes a lot of sense.
Ben Mathew: It's a very important safeguard against behavioural worry, trying to sell during the stock market crisis and stuff. If you make that adjustment, it's just a lot smoother and just feel a lot more calm.
Mark McGrath: And Ben, to that point, that doesn't even include the present value of future earnings as well. That's just looking at the portfolio itself. And so I think it's obvious, but it follows from that that younger people who have a longer runway, I guess, for earnings are even less affected than somebody approaching retirement with the lifecycle model.
Ben Mathew: And usually, young people would be benefited. They'd actually welcome a crash. Factoring in the future income, now it's going to grow faster. They might have only a few thousand dollars in their portfolio and that crash by half, that's not a big deal compared to the fact that all of their future savings is going to grow faster now.
Ben Felix: You've done a ton of modeling on this, Ben. We can talk about your tool maybe later. When you run simulations in historical data, how much variability and spending do you see when you're using this approach?
Ben Mathew: I looked at US data from 1871 onwards to try to simulate what would happen if you followed the lifecycle model. And this is definitely not an exhaustive study by any means. I didn't look at all possible cohorts. I lumped things up into years rather than months and things like that. It's sufficient to give a flavour of how the lifecycle model would work.
I assumed a 35/65 fixed asset allocation on total wealth, which because of the presence of sources security was on average about a 50/50 allocation on on the savings portfolio during retirement. And think of that as the normal thing that people would have done historically in terms of asset allocation.
I assume that the investors would update their expected returns based on valuations. CAPE or the price earnings ratio for stocks and the estimated real yield for bonds. These are nominal bonds, so they can't see the real yield. But I assume they were estimating it based on the nominal yield and past inflation.
In that setup, with those assumptions, the year-to-year variability in retirement spending that I saw for the cohorts that I looked at, and I look at cohorts every 10 years, not every year, but for the cohorts that I looked at, the standard deviation of the year-to-year spending variability was 6%. That means roughly two-thirds of the time, the change in spending would be 6% or less. About 95% of the times, almost all of the time, the change in spending would be twice the standard deviation or 12% or less. The biggest decline that I saw in one year for one of these cohorts was 16%. That gives a flavour of the year-to-year variability.
But if you look at the big events that people are most worried about, the Great Depression and things like that, there would have been seven events over the last 150 years during this time period. There's World War I, Great Depression, the 1937 Recession shortly after World War II, then the 1970s where there was the bond crisis and then the subsequent bond crash, and then the tech crash of 2000 and the subprime crisis of 2007-2008.
If you look at all of these seven events and see how did spending respond cumulatively over the course of these events, the worst events were not the Great Depression. Because even though stocks are really badly during the Great Depression, bonds would have helped a lot. What matters is how the combination of both stocks and bonds do. For that, the worst declines in spending was actually World War I, where spending would have declined 26% over five years from 1916 to 1920. The 1970s spending would have declined by a cumulative 37% over nine years, from 1973 to 1981. These were the two worst periods.
The other five periods range from 11% to 20%. And interestingly, the Great Depression was on the lower end of that, in the 11 to 15% range. And the two recent crises, the tech crash and the subprime crisis would also be on the lower end of that, between 11 and 15% decline in spending. Also, keep in mind, this simulation is assuming nominal bonds with no duration matching. If you use inflation-adjusted bonds and duration match that, you could potentially reduce the variability beyond this.
Ben Felix: That sucks that your spending declined. As I'm thinking through it, doing it this way sucks less than just spending less over your whole life like you would be with a safe withrawal rate.
Ben Mathew: If you want to just be cautious and spend less so that these kinds of crashes don't affect us too much, we can just reduce spending early. You can create a spending schedule that starts out slow and is expected to go up a lot. So that if a crash happens, it doesn't go that low. We can tune that and that can be our preference.
Look, I'm worried about the Great Depression, or the World War 1, or the 1970s. I want to be very cautious. And you can amortize with that in mind. Here I assumed a zero-spending build. They were not doing that. You can definitely tune that, so that when you compare what the outcome of a crash like this would be compared to your starting spending, you don't want it to drop too low. So you start out low and then slowly climb up if the market does well.
Mark McGrath: This all sounds great from a spreadsheet perspective. But I think Ben would agree with me here that, in practice, people or at least the clients that I've worked with don't like variable spending or at least not large swings in variable spending. How can this be tailored to individual preferences?
Ben Mathew: One of the big variables about how much variability we want to inflict on the plan would be one's risk aversion. We'd have to try to figure out how risk averse they are. The more risk averse they are, the more they're willing to have a lower expected spending, but with less variability around that. You'd have to put them more in bonds and try to duration match inflation adjusted bonds and so on, and try to reduce the risk on the portfolio side to produce less variability in the model itself.
And then there's this thing that we can do, which it sounds like you guys are doing, which is to update your expected returns. So that even though the market crashes, the spending doesn't decline by as much. That's a sensible thing to do. I think it's okay to delay our adjustments. I think it should be explicitly okay to delay our adjustments because we can't change all of our spending at the drop of a hat. There are consumption commitments. We can't move into a smaller house at the drop of a hat.
Even if the model says you're consuming $50,000 before, but because the markets did badly, you need to drop to $40,000. I think it's important to see that new $40,000. Be clear that, "Okay, we have to head towards this new reality of $40,000." But you can take your time doing that. The sooner you do, the less it's going to drop below $40,000. But it's reasonable to take our time to do that.
And I think the more dangerous thing is to not know that. To not know that the new reality is $40,000 and hide that and keep going at $50,000. And then you may be in for a root shock later on. I think it's better to see that and then be slow to adjust than to not realize that in the first place.
And then there's also this other thing that we talked about before, which is sometimes when people talk about year-to-year variability and expressing concern about year-to-year variability, they may not care that much about year-to-year variability. They may be worried more about absolute drop in their spending. That the spending doesn't decline as much as down to like really low levels.
If that's what they're concerned about, then we can control that with that spending tone. Use precautionary savings, spend less now, schedule more later so that things don't drop as low. That doesn't help with year-to-year variability, but it's the separate thing. I think it's useful to try to separate out what is it that you're worried about? Is it the year-to-year variability or is it the absolute decline in absolute spending that you're worried about? It's different tools to address the two different things.
Mark McGrath: We haven't really explicitly called it out, but you've been talking about real returns. These are all inflation-adjusted numbers. And so when you mentioned your spending might have to go from 50,000 to 40 ,000, maybe it makes sense to delay that adjustment. Would another way to do that be to just keep the withdrawals perhaps fixed if the model allowed for it and not make those inflation adjustments? That might be easier to stomach perhaps for some investors.
Ben Mathew: That would be a behaviour filter on this. And people definitely care about nominal numbers. And if people are comfortable taking a real cut, but much more uncomfortable to take the nominal cut, then I think it makes perfect sense to be a little bit generous on the nominal side and say, "Okay, let's not try to cut below that nominal amount, but let's give up the inflation adjustments." Given the fact that people do care about nominal numbers, I think that does make sense, absolutely.
Ben Felix: One thing I was thinking about as you were talking about different ways to limit the variability in spending is the episode we recently did with Peter Mladina about immunizing a portion of your spending. We don't have the best tools to do that in Canada because the real return bond program that we have is being wound down by the government. But in the US, for example, you could use tips to make it so that that portion of your expenses could be totally fixed and you wouldn't have to make adjustments. And then it's just down to the mix of how much risk you want to take with your spending variability.
Ben Mathew: Yeah. I heard that news recently that Canada is winding down the real bonds. And it's a shame because it just makes so much sense to have inflation-adjusted bonds. Nominal bonds don't make any sense. Why would you want a hundred dollars 30 years from now? I want to know how many loaves of bread or slices of pizza I can get 30 years from now. Real bonds make a lot of sense and duration matching that to your liabilities makes a lot of sense.
I think starting with your liabilities, things that you're not very flexible on, like maybe your mortgage payments and maybe some part of your kids' college tuition and things like that, and creating a liability match portfolio that takes care of that and either nominal if the liability is nominal, like mortgage liabilities would be nominal, but real liabilities matching that with real bonds and duration matching it so that you're immune to interest rate risk. I think that makes a lot of sense. That's a good starting point. And then take risk. Hold both bonds as well as stocks above that.
Ben Felix: We talked about some of the instances where spending has declined when you model this out in historical data and the magnitude of changes in spending. But if we think about a spending drop, how quickly does it tend to recover back to the previous real spending amount?
Ben Mathew: Because during a crash, we reduced our spending in line with the crash. We kept re-amortizing, recreating the schedule, just updated our spending. As the crash happened, we went down with the crash. If the markets recover, we get to recover with the market. It would be immediate. Or as soon as the market recovers, the spending would recover. But it's important to emphasize what market recovery and portfolio recovery means in this context.
Market crash was lower than expected returns year after year after year. Let's say three years of lower than expected returns brought you to the bottom of the crash. And to get back to the top to where you were before, we need higher than expected returns. The expected returns won't take us back to the original schedule. We need higher than expected returns to bring us back.
The investor at the bottom of the crash is not expecting to come out of the crash because they don't know that returns are going to be higher than expected. But we as researchers, we can look at the end of the crash, we can say, "Well, this was the bottom of the crash." And we can see that the market will recover from this point on. And we can ask how quickly did their spending recover with the market.
With that benefit of hindsight, the seven crashes that I mentioned earlier, the average drop in spending was 21% at the bottom. If you look at what spending would have been like three years after the bottom, the drop had reduced to a 15% drop. And then if you look 10 years after the crash, the drop would have reduced to 6%. 21% drop would have reduced to 6% 10 years after the crash. The investor would not have known that at the bottom of the crash. But we can look back and see that it did recover. And the main point here is that if the market recovers, the spending would also recover with it.
Mark McGrath: Is this a continuous calculation? How frequently are you updating or reamortizing these calculations?
Ben Mathew: For the historical analysis that I did?
Mark McGrath: Yeah.
Ben Mathew: I did it at a yearly basis. All the returns, I made it annual returns and then assumed they're recalculating every year. I may not have gotten the absolute bottom of the crash and so on because the monthly would have been much better.
Mark McGrath: I'm just thinking in practice how often somebody should consider updating their own model of this. Making sure I understand that what you're talking about is an annual update. But it depends, I guess. It depends on the severity, the speed, the depth of the crash. Something might happen externally that would trigger you to update this more frequently than once a year, right?
Ben Mathew: If the markets go down a lot and you hear about it in the papers and stuff, I think you'd want to update with some big movements. But with the regular market, maybe once a year is enough. Some people may want to do it once a month. That separation between seeing what the target is and actually making changes in our lives, I think it's good to have that separation. Seeing it frequently is okay as long as people don't feel anxious and feel that they have to change right away.
Mark McGrath: Switching gears a little bit, what does the lifecycle model say about asset allocation?
Ben Mathew: When it comes to spending, the lifecycle model was telling us to spread spending over time. And when it comes to asset allocation, to investing, it's telling us a similar thing. It's telling us to spread risk across time. What do we mean by that? Let's think of a case where we have some resources now, $10,000, say, we are going to use that to fund spending 30 years from now. This is the only goal. Let's remove all of the other years to keep the model simple. We have this money, and we have this goal, and how do we allocate those funds?
The big driver there is going to be our risk aversion. The more risk aversion we are, the more we want to invest in bonds and have less variability around that outcome. Let's say we have the sort of person that should have 50% stocks and 50% bonds. Now the question is, what is the glide path that you should have? Should you maintain a fixed 50/50 for all 30 years? Should you start lower than that, 40%, and then increase to above 50%? Go up to 60%? Or should we start at 60%, come down to 40%? What should be the glide path that averages out to 50%?
The answer that the lifecycle model tells us, what it's saying is hold it steady at 50/50. Keep it flat. Give it a fixed asset allocation at 50%. And it's important to note right away that this is on all of your resources. This would be the recommendation on total wealth, not on the savings portfolio, where people are more used to that downward-sloping glide path. It turns out that this fixed asset allocation on total wealth will imply a downward-sloping glide path on your savings portfolio.
Look at this case where you actually had the $10,000 in your hands. This year, total wealth. And there's no more income coming in to fund that goal. The asset allocation on this should be that fixed 50% the whole time. And the intuition for that is time diversification. This result is referred to as time diversification. Basically, what you're doing is taking an equal bet every year, every period. So keeping risk the same.
Rather than take on a lot of risk in one year and less risk in some other year, you're taking on the same risk every year. That's what maximizes this risk sort of averaging out. Risk doesn't completely average out, it doesn't go away, but you're trying to get it to average as much as possible by taking a series of small bets rather than a big bet followed by a small bet.
And it turns out that if you keep a fixed asset allocation, because of this time diversification, there will be no sequence of return risk on how much balance you're going to have at the end of your 30 years is going to be independent of the order of returns that it came in. If you look at the math of the compounding, you can see that it's all multiplicative. You can put it in any order. So this $10,000, it doesn't matter if you've got 10% followed by 5% or 5% followed by 10%, all of that will compound out to the same amount. You eliminated sequence of return risk in this problem.
Now there's a limited problem. We want to think about the whole many different years, and many different goals, and future income, and things like that. But this is the basic principle around which that's built. So when you have multiple goals all with the same asset allocation, your glide path will still be flat because all of the individual goals are being allocated at 50%. That fixed asset will carry through to multiple years, even though here we just looked at one specific year.
Of course, if we have multiple goals, and usually people have legacy which will be allocated more riskily, then you would have that coming in and it won't be flat. But if you just talk about all retirement years all funded with 50%, the fixed asset allocation would apply to total wealth, not to the savings portfolio.
Ben Felix: We've alluded to expected returns a few times. How important are expected return assumptions to lifecycle asset allocation advice?
Ben Mathew: The expected return assumptions will matter a lot. The small changes in the expected return will imply large changes in the asset allocation. But I think of that as the nature of reality. Expected returns do have a big impact on the financial plan. Any reasonable model will have to assume an expected return and it's going to have a big impact if it's a sensible plan that's looking at how things compound over time.
And usually, when people think that they're not making an expected return assumption, it's because they're doing it implicitly, usually by doing a historical simulation. And if they're doing that, then basically the expected return assumption is the historical average, which is quite high. Given current valuations, that would be a very optimistic expected return assumption to use.
I think that's why it's important for people to not hide the expected return assumption like this and to pull that out and stare at it and see if it makes sense. People like to hide it because it's hard to think about and it's hard to face the fact that expected returns do matter. When it comes to stocks, we don't know. We kind of have to guess a little bit and try to make our best guess and it's not very obvious what that number should be. Bonds is easier because we can see real returns of bonds, the inflation-adjusted bonds. But stocks is harder. We really have no other option and it's good to face that fact.
To put some numbers on how much it matters. If you assume an expected a return of 5%, real return of 5% for stocks and 2% for bonds, so that's an equity premium of 5 minus 2 equals 3%. For investor with a relative risk aversion of around 3, Mertn's formula would imply a stock allocation of around 30%. And if you increase the equity premium by 1%, from 5% to 6%, then that would increase the stock allocation recommendation to around 40%. Again, these are asset allocation on total wealth, not on the savings portfolio, which is different.
The 1% increase in the equity premium caused an increase in the stock allocation from 30% to 40%. And that seems pretty significant to people. And that is significant. And people are uncomfortable with this. Because if you're basing expected returns on valuations, that's going to change from week to week and month to month, and they'll see large changes in what the model is saying the asset allocation needs to be. If you look at what happened with the equity premium, it increased from 3% to 4%. That's a 33% increase in the rewards offered by stocks over bonds. That is a big deal. In a sensible model, that would have a large impact on how much stocks versus bonds you hold.
We can create a model that doesn't have that impact. You can take the lifecycle model and then dampen the change in expected returns before we feed it in. When you see a 1% equity premium change, you'd say it's only a half percent or a quarter percent before you throw it in there. And we'll get a model that's not very sensitive to the expected return, but that would be the wrong model. It's not telling you the information that you need to know. And the information is that your belief is that stocks are going to be returning a lot more over bonds than you thought before. So you should increase your asset allocation by quite a bit. It doesn't mean you have to adjust right away, but it's good to have that clarity and, "Okay, this is the new recommendation. Let's work towards that. Let's apply new contributions towards that. We don't have to go out and sell a lot of stock in a taxable account and things like that." But it's good to have clarity on what the goal is and what we need to be working towards.
Mark McGrath: So how does the advice change if we assume that we have limited information about how expected returns vary through time?
Ben Mathew: The best guess about future expected returns is the current expected return. There's a very simple reason for that. And that is if you can predict the direction of the change in expected returns, you should be able to make a lot of money. There's huge arbitrage opportunities available. Because even if you can predict it just a little bit, you can predict that it's going to go down by a quarter percent or a half percent, that will imply a large change in the price of the asset. And so you should be able to do short-term trading to profit off of that.
Given the fact that well-functioning financial markets cannot leave such opportunities on the table, our best guess is that future expected returns, we're expecting that it'll be the same as the current expected return. But we know that these things do vary over time. We just don't know in which direction they're going to vary. Assuming that expected returns are constant is not exactly right, but it's not too bad because you're at least in the middle of the set of possibilities. You're kind of in the average. You'd be right on average.
Full financial planning, I think it's not too bad to assume constant expected returns. But that said, we recognize the fact that interest rates do change over time. On the bond side, we can use duration matching to limit the impact of that. So that would be a sensible thing to do in light of the fact that we don't know how it's going to change. And we want to minimize the impact of changing expected returns.
Ben Felix: How does the typical retirement asset allocation glide path that we see in, like you mentioned, Vanguard's target date funds, how does that compare to advice from the lifecycle model?
Ben Mathew: This comes back to that fixed asset allocation result on the total portfolio. And what would that imply on the savings portfolio? The savings portfolio, we are basically going to try to create an asset allocation on the savings portfolio in order to get that fixed asset allocation on the total portfolio. You look at a person at the start of their career, they might have only $1,000 of savings, let's say. And almost all of their wealth is in the form of future income that they're going to receive over their career.
Let's say the value of that is $2 million. Their wealth is $2 million and $1,000. Most of it in the form of this human capital, this present value of your income. The question is, how should they think about that human capital? Is it more stock-like or bond-like? Our incomes tend to be relatively safe. It's not perfectly safe. Of course, we don't know exactly what our income will be, but it's a lot safer than stocks. And it's closer to bonds than it is to stocks.
An assumption that economists have suggested is to assume that this human capital is bond-like, that this $2 million is bond-like. Then that tells you what you need to do in your savings portfolio. The savings portfolio is only $1,000. Even if you invest all $1,000 into stocks, when you look at your total wealth, that's still too little stocks. You want to put all $1,000 into stocks.
And then over time, the human capital part reduces because you have less and less years remaining to collect your future income. The financial capital, your savings portfolio increases because you have more and more savings that's grown. At some point, the savings portfolio is gonna be large enough that you shouldn't be 100% stocks on that. You'll need to hold some bonds in order to get to that 50/50 target on your total wealth.
And then as you keep moving forward, that allocation will keep reducing until when you reach retirement. If you don't have any further pensions or social security coming in, then all of your total wealth is in that savings portfolio. So you should apply a 50/50 allocation on the savings portfolio and then hold that constant at 50/50 through the rest of retirement because you don't have any more income coming in. That's your full wealth.
The glide path would be 100% stocks in early career and then dropping down below 100% in the second half of your career. And then becoming flat at your target allocation in this example of 50/50 in retirement. If you have some pensions and social security, then instead of 50/50, it might raise to reflect that. It might be 60/40 in retirement. But it would basically be roughly flat in retirement if you have pensions running all the way through retirement.
The basic shape is flat, downward-sloping, and then flat again. And this is quite different from a straight line going down. A linear rule like agent bonds and so on, that would have a linear constant slope. This is very distinctive. It's flat, and then downward-sloping, and then flat again. If you look at Vanguard's target date funds and actually other target date funds as well, if you look at the slope of those glide paths, it does follow their slope. It's flat, and then downward sloping, and then flat. And that's because it's coming from this lifecycle model that's telling us to try to maintain that 50/50 allocation or some fixed asset allocation on the total portfolio.
Mark McGrath: I think you've already answered this next question. How does asset allocation in the model change based on the time horizon of the goal, the specific goal being funded?
Ben Mathew: This is an area where there's a lot of confusion. Generally, people think that stock risk goes away over time because of the law of large numbers, because of averaging out. If you look at longer horizons, if you look at the average stock return over long periods, you're averaging over more returns, and you should expect a tightly distributed return. You do get that. The returns of longer and longer horizons get more and more tightly distributed. There are very dramatic graphs that show this. That's not wrong. Even if returns are independent, the return distribution will become more and more tight.
But that still does not mean that stocks are becoming less risky over time because what you care about is not the average return over the full period. You care about the final balance because that's what you're going to spend. You're going to be spending dollars, so we should be looking at how many dollars you have at the end. Small changes in the realized average return over long periods compound out to large in the portfolio balance. If you look at the portfolio balance, that is becoming more and more widely distributed when you look at longer and longer horizons if returns are independent.
This was the fallacy of time diversification. I mentioned there was the correct version of time diversification. There's the fallacious version of time diversification that says that for longer and longer goals, you should hold more stocks because if returns are independent, then they average out, and you can appeal to the law of large numbers. But let's look at the wrong thing. Let's look at stock returns instead of look at the balance. It turns out that even though risk is increasing over time, the reward is also increasing over time. Longer periods also have a high reward because that equity premium compounds out to a very massive difference over long horizons. Both risk and reward are increasing over long horizons. If returns are independent, they're increasing at the same rate, and so the asset allocation becomes independent of the time horizon. You call the same asset allocation over long horizons as you do over short horizons.
If you don't assume independent returns, if you have mean reversion in returns, good returns are more likely to be followed by bad returns. Bad returns are more likely to be followed by good returns. Then you get this extra cancelling out happening beyond the independent return assumption. Then the risk would decline. Even now, risk is increasing over time. Over long horizons, risk is still more than over short horizons. But it's increasing at a slower rate than the reward is increasing. The reward to risk ratio improves over long horizons. Based on that, you can say that you can hold more stocks for long-term goals and more bonds for short-term goals. But it's important to recognize that it requires mean reversion and not independent returns.
Ben Felix: That part's super interesting because it depends how you look at it, I guess, and how much statistical reliability you want to say that it's there. But there's probably some mean reversion in stocks and probably some mean aversion in bonds, which makes that whole time horizon versus asset allocation thing extra interesting.
Ben Mathew: We should generally expect that there would be mean reversion because of that expected return. When things go down, the expected return goes up, so you can expect something going on. If you're considering duration-matched bonds, then there would be mean reversion because mathematically it came down, so it's going to go up faster. But, yes, it's when we look at interest rates are moving all over the place. It's not duration match.
But even with mean reversion, things depend on the horizon. You could have that thing slowly go down and then over the long run go up. You may have momentum over short horizons and then reversion over long horizons. But if the bonds are duration-matched, then we can say at least over the long horizon, there would be.
Ben Felix: I was thinking nominal bonds for real liabilities. That's where some of the empirical research that I've seen in a couple of different papers recently using two different data sets come to a similar conclusion that bad nominal bond returns in real terms tend to be followed by more bad real returns.
Ben Mathew: I think there’s just a lot of things we can do on the bond side to improve things. It seems like there's some things we can do mathematically that would improve on outcomes compared to holding nominal bonds without considering duration.
Ben Felix: Definitely. What about wealth? Time horizon is one thing. How does asset allocation in the model change with different levels of wealth?
Ben Mathew: We can ask a question. If our wealth doubled, it's total wealth. Our savings portfolio doubled because, let's say, returns came in higher than expected, and value of income doubled because we got a proportion, and salaries doubled. Everything doubled. Wealth is twice as much as it was before, and so spending is twice as much as it was before. So then the question is let's say we were holding a 50% stock allocation, 50/50 stock bonds. Now, should you increase beyond 50/50? Should you make it 60%? Or should you decrease your risk and make it 40%? Or should you keep it the same at 50%?
The answer is that all three are reasonable. You could reasonably have preferences that need you to do any of these things. You could be the sort of person who says after the wealth and spending has doubled, they say, “Well, now the downside is not scary anymore from taking risk. I have so much wealth. I'm still not going to lose my house and car, so I'm going to take more risk and increase my stock allocation.” On the flip side, you can say I have everything that I need. What can I do, even if markets do well? There's nothing more that I value.
There's a person whose utility curve is really flattened out. It may still be upward sloping, but it's flattened out, and they're just very satisfied with where they are. That's a person who would want to cut their risk. From 50%, they'd bring it down to 40%. This would be called increasing relative risk aversion because their risk aversion has increased when their wealth increased. The other one would be decreasing relative risk aversion. In between these two, we have constant relative risk aversion, a person who would maintain the same allocation as they did before.
I think it's important to recognize that all of these are reasonable utility functions. They can all be expressed by a nice concave utility function. There's nothing illogical about any of these things. I think it's important to say that because sometimes people argue about this. They're like, “Oh, it should go down.” That's usually because they're looking at only one side of it. They are focusing on the fact that they can't afford to take more risk, while they're focusing on the fact that they don't need to take any more risk. They're really arguing for their own preferences that everybody should think like this, but it's really a matter of preference, and all of these are reasonably related functions.
Mark McGrath: We've talked a lot about the lifecycle model. In the beginning, we said there's basically two models. There's the lifecycle model and the safe withdrawal rate model. I think most people are more familiar with the safe withdrawal rate model. I think it's just intuitively a lot easier to understand as well. Let's talk about that for a little bit. Can you tell us how the safe withdrawal rate methodology works?
Ben Mathew: The safe withdrawal rate method, so let's say you have a 65-year-old retiree, they're just starting retirement, and let's say they have a million dollars in their savings, and they need to know how much they can withdraw from this portfolio. You're going to assume that they're going to take a fixed amount with inflation adjustment, so fixed in real dollars. They can ask themselves, "Should I take $50,000 from my portfolio, five percent of my portfolio, $50 ,000?” Let's say they're planning for 30 years from 65 to age 95. At 30-year horizon, if I take out $50,000, will I run out of money or won't I run out of money? If I don't run out of money, I'm going to call that a success. If I do run out of money, I'm going to call that a failure.
Then we look at a bunch of different scenarios, different sequences. It could be based on historical sequences. It could be Monte Carlo simulations. But you look at what fraction of the time would this retiree have succeeded or not run out of money? What fraction of time would they have failed or run out of money? The fraction of time that they have succeeded would be the probability of success. That's going to be the key metric that we would focus on.
Let's say if they take out 5% of $50,000 per year, their probability of success was 80%. They would have run out of money 20% of the time. The retiree thinks about that. Is that okay? They decide that's not okay. I don't want to run out of money 20% of the time. I want to make sure I'm safe in large and fractional scenarios. They would have to cut their spending. They might try four percent of $40,000 and see what are the odds now. What is the probability of success now? They see that they're running out of money only 5% of the time or 95% probability of success.
They may say, “Well, that's tolerable. That's acceptable. This is going to be my strategy. I'm going to take out $40,000, four percent of my starting portfolio or $40,000 constant fixed throughout retirement.” They're not going to make any adjustments for if the portfolio does better or worse than they expect. They're going to keep their fingers crossed and hope that they are in that 95% chance of not running out of money and not in that 5% bad outcomes.
That's how withdrawal would work. You can connect that back to savings. If this person says, “Well, $40,000 is not enough for my retirement. I want to spend $50,000, but I don't want my probability of success to go down,” they would have to save more so that they have a larger portfolio. The four percent of that portfolio would be $50,000. They'll save more or retire later. They'd have to adjust on the savings front.
When it comes to investment, the third problem, how do you invest, how do you choose between stocks versus bonds, you could look at different glide paths, look at different fixed asset allocations or upward sloping or downward sloping glide paths, and see what is the glide path. What is the asset allocation glide path that will maximize the probability of success? This is something that people do frequently. People say, “Well, the one that maximizes the 60/40 or the 40/60.” Or you increase it over retirement and so on. These are all based on this probability of success metric that comes out of a safe withdrawal rate model.
Ben Felix: We talked a lot about the benefits and the logic of the lifecycle model to contrast with that. What are the problems that you see with the safe withdrawal rate approach?
Ben Mathew: There are two problems with the safe withdrawal rate methodology. One is that fixed withdrawal assumption. We're not changing depending on how the portfolio does. We know instinctively that if the portfolio does well, we can take out more than what we originally thought. If the portfolio does worse than expected, then we should cut back and try to conserve our portfolio. That's something that we naturally understand, and the lifecycle model will tell us to do that through that variable withdrawals.
But here we are assuming that away. We're basically tying our hands behind our backs and saying that even if bad things happen, we're not allowed to. That's a problematic assumption because it's not matching what we're going to be doing in retirement. It's assuming something different, and that's going to have some implications.
The second issue is the grading scheme. We're grading outcomes as just success versus failure. The magnitudes don't matter. Failure is a failure is a failure. Even if you fail by one dollar in the last year of retirement, you run out of money in the last day of retirement versus you run out of money right in the middle of retirement. Both of these count as failure, even though to the retiree these are vastly different outcomes. One is kind of okay, and the other is a fiasco. Our grading scheme is not reflecting what the retiree cares about.
On the flip side, success, if you just squeak through with one penny left versus if you leave millions of dollars behind, all of that is just lumped together as just success. Maybe people may care about leaving money to their heirs, and the million dollars left to their kids and charity is preferable to squeaking by with a penny. It’s this pass-fail grading that doesn't capture how the retirees actually feel. There's that mismatch in the grading scheme.
People recognize this. I mean, this is obvious to people that these are simplifications, and people usually say, "Yes, of course, I'm not going to adhere to a fixed withdrawal during retirement. That would be crazy. I'm just making this assumption for the calculation to get a rough idea how much I can spend during retirement.” All models do have to be simplifications. Otherwise, they're not useful.
It's important when we're looking at these models to make the right kind of simplifications. We should retain the important parts of the reality and then simplify away the less important. The safe withdrawal rate method is not being the right choices. It's simplifying away these important parts of how we behave and what we care about. It's not a good model in order to get that rough approximation. You don't get a good rough approximation by using a model that has simplified away the important parts of the problem.
For example, these fixed withdrawal assumption will tell you to have an overly conservative starting withdrawal, given reasonable assumptions. That's because we're tying our hands behind our backs. We're saying that we are not allowed to adjust if bad things happen. You had to preemptively adjust and start out with a low amount, just because we are preventing ourselves from adjusting. In reality, we would adjust, but the model doesn't know that. The model is saying, “You're telling me you're not going to adjust. Well, then you really need to start out with a very low withdrawal to prevent running out of money.” This actually plays out a lot in practice because sometimes people do take reasonable return assumptions, and they come up with very low withdrawal recommendations using SWR. They might say, “You should only take out two percent of your portfolio, three percent of your portfolio.”
People hear that and they're like that strikes them as wrong, so they're making bad expected return assumptions. They blame the expected return assumptions, and they usually prefer to use historical because those are very high expected return assumptions in order to get a normal reasonable withdrawal rate. The problem is really the strategy, the model that you're using to come up with the withdrawal. People are angry with the wrong thing very often I find. This is actually pretty obvious in some ways that it will do this.
But there's another one that's actually much more insidious and not obvious at all, the impact of this fixed withdrawals. When you assume fixed withdrawals, the nature of risk changes dramatically. When you assume variable withdrawals, if the portfolio does better than expected, all of spending increases. Then bad news comes in. All of spending goes down. Risk looks like this. It's evenly distributed across all of spending. But if you assume fixed withdrawals, you're fixing that initial withdrawals. Then if the portfolio comes in lower than expected, all of that impact of that is being applied to the final year. Risk looks like this. The final year has become funded or not funded. The initial years don't bear any risk.
Once you fix this, all of the portfolio gets concentrated here. This looks very different from this, and the math of that will work differently. One of the things that this will lead to is a recommendation of an upward sloping glide path. When risk looks like this, in the fixed withdrawal model, you're concentrating it all on the last year. That can imply that upward sloping glide path would reduce risk. If you're actually using a variable strategy, then a fixed asset allocation from the lifecycle model tells us it makes sense. It would be the right approach in retirement. Vastly different recommendations. It's quite hard to see, I would say, that the fixed withdrawal assumption is actually impacting the asset allocation coming back an upward-slipping glide path.
Then when it comes to pass-fail grading, the other bad assumption, you can get, for example, that stocks look less risky over long horizons so that the old fallacious version of time diversification would be supported by the safe withdrawal rate analysis because you're not looking at the severity. You don't look at magnitudes. You're doing just pass-fail. Over longer horizon, stocks become less likely to underperform bonds. But when they underperform bonds, they underperform by more. It's more severe underperformance.
We know that intuitively when we look at one day versus one year horizons. Over the course of a day, stocks are very likely to underperform bonds roughly 50/50, but they'll just underperform by 100%. But over the course of a year, they're less likely to underperform bonds, but more likely to underperform by more than 20%. The same thing holds. If you assume independent returns, the same things hold between the 1-year and the 30-year horizons. Stocks become less likely to underperform bonds. But when it underperforms, it will be severe.
If you're looking at the probability of success, you don't look at the severity of the failure. You're just focused on counting the times that you were successful. You draw this false conclusion that stocks are safer over long horizons because the probability of success increases. If you try to fix all these problems, if you fix these fixed withdrawals and the pass-fail grading scheme, you get the lifecycle model. That's the only difference between the safe withdrawal rate methodology and the lifecycle model. In the lifecycle model, you insert fixed withdrawals. We allow it to be variable. We don't insist that it be variable. We say you can be variable if you want it to be.
Then the grading scheme, the evaluating outcomes, we replace the pass-fail grading with the utility function. There's decrease in marginal utility of consumption. If you replace this grading scheme and the fixed withdrawal assumption, you just get back to lifecycle model. Really, when you think, “Should I use SWR,” you should be thinking, “Should I use these two assumptions?”
Ben Felix: I was laughing earlier because I did a video on safe withdrawal rates using what I would say is better data than what it was developed on. It comes out to like – I think I said 2.7%. It's probably closer to three percent. People get so mad at me for daring to say that they can't spend four percent or five percent of their portfolio. But I said at the end of the video exactly what you said. This is more of a commentary on why safe withdrawal rates and fixed real spending for retirement don't make any sense. Not so much a comment that you should be spending 2.7 % of your portfolio, but people either didn't watch to the end or were too triggered by the first part to actually hear what I had to say.
Ben Mathew: It's a very common pattern for people to be really mad when they see a low withdrawal rate coming out of SWR and saying, "This data doesn't make any sense," instead of seeing SWR doesn't make any sense.
Ben Felix: I still want to do a video on the title being Safe Withdrawal Rates, Answer the Wrong Question and basically summarize some of the stuff that you just said, I think.
Ben Mathew: Absolutely.
Ben Felix: I think a lot of people need to hear that.
Ben Mathew: That'll be fun. It's a very important message to get out. The problem is that SWR is so widely used in industries. People just think that this is a standard, and there's no other options. It’s understandable for people who are not digging into it that much to sort of feel that SWR is the way to do things because that's what they see out there, so they don't question that.
Mark McGrath: I think you've largely answered this. But maybe just really quickly, how does the probability of success metric that drives the safe withdrawal rate, how does that relate to the utility function that we've been talking about in economics?
Ben Mathew: That's actually interesting to look at because even though you can't perfectly match the SWR model to the utility function, this past-fail aspect of how you're grading things can be thought of as a binary utility function. It’s a zero-one utility function. You have some sort of threshold. Let's say it's like $50,000 of consumption. If you're below that threshold, you failed, so it's zero. If you're above that threshold, it's, one, you've succeeded and you can assign that a utility of one.
Then calculating the probability of success would be equivalent to taking the expected utility of this binary utility function. Once you think about it like that, you see immediately the problem with this binary utility function. There is this flat, and then step up, and then flat again. Compare that to the utility function used in economics, which is this concave upward sloping but flattening out utility function. With this binary utility function, you get very weird risk aversion, depending on where you are on the curve.
If you're above the threshold, so you've already succeeded, you become infinitely risk-averse because there is no benefit to the positive side of risk, and there's only that cost to dropping below the threshold. Even if you're offered a very attractive bet, a million percent expected return, you say no because I don't care about the plus side of things. I only worry about dropping below the threshold, so you become infinitely risk-averse.
Then on the other side, on the failure side of the threshold, you can become risk-loving because you've already failed. You're just trying desperately to jump over into success. Even if you're offered a very unattractive bet with a very low expected, negative expected return, you will take it because you don't care about how bad things get on the downside. You only care about having that small probability of jumping above the threshold and attain success. This is risk-loving behavior. It's not just not risk-averse or risk-neutral. It's crossing over into risk-loving territory.
This is a very bad utility function. This doesn't capture how we should behave or how we care about things. But this is what's effectively being used in the safe withdrawal rate methodology that's widely used in industry. People then complain when economists whip out the utility function and start talking about decreasing marginative consumption. Usually, people would say that, “Oh, you know, that's too geeky, and that's geeks-bearing mathematics, and investing is more of the heart.”
The problem is that people do have to do calculations because you can't do it all in your head, and we don't have enough intuition to just be able to do it all in our head. We have to sit down and do some calculations. Then we have to try to evaluate the outcomes. In the absence of a sensible utility function, people, it's not that they become wiser and use more nuance and so on in their evaluation. They resort to the zero-one utilities function that produces very bad recommendations and inappropriate results.
Using the toolkit of economics, the economists have thought hard about this and try to understand how we think about risk versus return. The toolkit that economics provides is, I think, the right tools to use. When you try to do things without those assumptions, without that toolkit, I think people run into trouble without knowing it, usually.
Ben Felix: It sounds like the people who are investing in Fartcoin, hoping to do really, really well, but probably going to lose, should be using the safe withdrawal rate methodology.
Ben Mathew: They're on the zero side, and they're trying to get to the one.
Ben Felix: One of the things that's happened with the safe withdrawal rate literature is the idea of variable safe withdrawal rates. Instead of having a real inflation-adjusted amount that you're spending, there's various ways of approaching rules that change over time. How is a variable safe withdrawal rate different from an amortization-based variable withdrawal?
Ben Mathew: People have recognized that fixed spending doesn't make any sense. You can't just do a calculation at the start of retirement and stick with that the whole way through. People are doing the next reasonable thing that they can think of, which is redo the calculation and update this number. You can create a variable strategy using SWR by just recalculating the safe withdrawal rate every period, once a year or something like that. Some people call this re-retiring. That's much better than using a fixed withdrawal scheme. Now, the portfolio does well. You’ll adjust to that. The portfolio does badly. You don’t adjust to that. It’s definitely better than using fixed.
The problem is that it really comes down to clarity and communication about what's happening with the variable withdrawal strategy that the safe withdrawal rate creates, that re-retiring creates. For one, the success rate has lost its meaning. It doesn't mean anything anymore because you are not going to stick to a fixed withdrawal, you are going to adjust. You're not going to succeed or fail. You're either going to spend more than you thought or less than you thought. It's some sort of variable scheme saying that you have a 95% probability of success or a 60% probability of success. It doesn't translate to anything meaningful here. It did mean something in the fixed withdrawal scheme, but it doesn't mean anything in the variable withdrawal scheme.
What you really want to know is that trajectory of what your spending is going to look like in the future with the variability of the spending. You can first think about what would spending look like if returns came in as expected. That would be the expected trajectory. If returns came in like clockwork, like expected, what would your spending be? That's step one that you would want to think of. Trace that line out. Trace that trajectory and see, look at whether that makes sense. Then if returns come in better than expected, you'd end up higher than this line. If returns come in lower than expected, you would end up below this line. That creates some variability, a cloud of possibilities around that line.
This is really what you want to see. But just hearing that 95% or 80% probability of success doesn't create this picture, doesn't tell you this trajectory and the cloud around it. Supposedly, you are targeting an 80% probability of success. Usually, with variable withdrawals, you can target a lower probability of success. You don't have to be 95%. You could knock that down to 80% or 50% or something else that might be appropriate. But let's say you've decided to target 80% probability of success. Let’s say that gives you $50,000 per year this year.
Now, next year, even if returns come in as expected and you do the calculation again with the same 80% probability of success to target that same 80% probability of success, the spending that you're going to calculate now is not going to be $50,000 again. It's going to be higher. It's going to be lower. It's likely different. But the problem is we don't know. It's not obvious whether your trajectory is going up, whether it's sloping down, or whether it's constant. That's what we would really like to know now. It is variable, and we want to know whether it's going up or down.
Not only do you not know that. It turns out that if you use a constant probability of success, like 80%, 80%, you keep doing that, the trajectory that it's going to trace out, even if returns come in as expected, let's say it's upward sloping. Let's do a simulation. Let's try to figure out that it's upward sloping. It turns out that the rate of growth changes over time. Initially, it tends to be slow. It's upward sloping. It’s growing slowly over time. But later, it speeds up. It might be one percent early on, but later it goes up by three, four percent per year.
That's not something that we asked for. We didn't say, “Let's try to create a trajectory like that.” It's just a side effect of using the safe withdrawal rate process. That probability of success, broadly speaking, it controls that slope. The higher the probability of success, the less you spend now, and the more you spend later. But you don't have a lot of information about what that slope is. You're not able to control like whether it's going fast or it's producing this inconsistent growth rate. If you want it to be consistent, you have to keep dialing that probability of success. Early on, you have to pick lower probability of success to increase the speed. Then later, you have to reduce the probability of success to decrease the speed. All of this in order to get a consistent, let's say, one percent growth or two percent growth per year.
All of this is completely unnecessary. It can be done, but there's no point doing it like this because the amortization does this very easily. In the amortization, you would create this schedule that you want. Let's say you wanted to go up by 1.5 % per year. You'd put that in the amortization. It's an input into the amortization. You amortize with the 1.5 % spending growth, and you will get an expected spending trajectory of 1.5 % with spending coming in above that or below that, depending on how the market does. You can replicate that with the safe withdrawal rate method, but there's no benefit to doing that. It's just a complicated way of achieving this.
Ben Felix: They're really interesting. Our final question that we always ask guests – but before we go there, I do want to ask if you want to talk at all about your online tool. You didn't come on here to plug it because you helped me write the questions and didn't have anything in here about it. But since you're here, I may as well ask you to talk about it.
Ben Mathew: I'm creating a website called tpawplaner.com, which implements the lifecycle model. It kind of started because I was going to write a book on personal finance. I wrote a book on economics, and my second book was going to be on personal finance because I taught economics and finance when I was a professor at Colgate. I figured I'd cover my areas of knowledge. I did the economics. Economics was easy, but personal finance was hard. I started learning more and more about it. I got into the lifecycle model and looking at safe withdrawal rates and how they're different and what's happening in academia and what's happening in industry and looking at that gap.
Then interestingly noticing that some people are already doing amortization, already adopting tools not because they heard that Merton is doing it, and that's what's from academia. But they naturally started doing it because it's so natural to amortize your portfolio to calculate withdrawal. So then it seemed like academia and at least what some people are doing are so close that the gap seemed bridgeable. If I just write a book about it, people read it and say that's interesting, but you really need tools to implement it. I started out by creating some spreadsheets to do these calculations. Spreadsheets are always cumbersome to customize, change the number of rows and so on.
My brother is a software engineer, so I recruited him. I asked him if he can help turn the spreadsheet into software. He started doing that, and he got really into it after a while. It was supposed to be like for a few weeks, he's going to turn that spreadsheet into software, and then he got really into it. He was like, “Oh, wow.” This thing where people hear about the lifecycle model, and they get excited. First, he thought it was just retirement planning, but then he saw how other things would fit in. It's like, “Whoa, this is all a financial planning. Wow, this is so interesting.” He’s been very excited about it, and he continues to build, so it's getting more and more features. Hopefully, soon we'll add duration matching and taxes. Then I think it'll be kind of like a full-blown planner at that point.
Ben Felix: We use financial planning software in Canada that has all of the Canadian tax rates and government benefits and all that. It's incredible software, but it doesn't have this in it. I'd love to find a way to get the lifecycle model into more traditional financial planning softwares.
Ben Mathew: Our goal is to do it the other way, to put all of those taxes into the lifecycle model. Some of the people who are using the planner are from other countries. It's people from Canada and people from the Netherlands and so on who are using it. Right now, it's just general because there's no taxes. When taxes come, I'm sure I'll hear complaints about, “Hey, these are US taxes. What about Canadian taxes or Netherlands taxes?”
I think there are financial software are able to cater to more than one country. I think there may be some toolkits and stuff. Somebody mentioned there were wealth tax in their country. I think if you have a bunch of toolkits to sort of incorporate various things, fundamentally taxes work the same. But people can customize the tax rates and so on. We're hoping to make it available to a wider audience than just the US.
Ben Felix: We'll be keeping an eye on it for sure.
Mark McGrath: Listen, Ben. This has been an incredible and very insightful conversation. As I said, I think before we started recording, I was very excited for this because I know financial planning is more my realm than portfolio management. A lot of the guests we have on are a little bit more maybe market and portfolio-centered, so this was a really, really great conversation. I learned a ton. We've got one more question for you, and that is how do you define success in your life?
Ben Mathew: It's definitely multidimensional. The top few would be that I've invested enough in relationships with the people around me, that there are people who care about me and who I care about a lot, and that I've cared more broadly about the wider world of people that I don't know and try to have a positive impact on that broader world. Then that I've always kept learning new things. Importantly, that I've tried to be correct and try to figure things out and not just pick a side and wave a flag. I think the Internet makes it easy to do both. There's a lot of information, but there's also a lot of following aside and following a crowd.
For me, it's far more fun to try to use all of these tools that we have at our disposal now with the things that people are discovering and things that people are putting online, all the books and stuff that are being written about things that you can easily find now and order on Amazon and have it delivered. We're living in a wonderful, amazing time to be able to do that. I hope that I keep learning and actually try to figure things out for what it's like and not for what I want it to be.
For all of these things, I would also emphasize that it's important for me that I focus on the input and not on the output. If I've been making the right decisions and made the good faith effort and tried my best, then I try not to be too hard on myself if the impact is not as big as I expected because there's a lot of luck involved in the impact in the output side. Conversely, if I made bad decisions, if I go out and buy a lottery and it happened to win, I would not be happy with myself if my whole life was like that.
Focusing on the input is important. That’s something that I emphasize a lot with my kids. Tell them frequently that what they need to do is just try their best. It doesn't matter if it doesn't turn out as great as they expected or hoped. What we owe society, what we owe other people, and what we owe ourselves is really to try our best and then try to maintain some sort of equanimity when it comes to the output of that.
Ben Felix: Great answer, Ben. All right, this has been great. We really appreciate you coming on the podcast. If people want to follow up with questions, they can find you on Bogleheads or in the Rational reminder community. Great conversation, really useful, practical information.
Ben Mathew: Wonderful. Thanks for having me. I've been watching the show for so long being here. It was very strange, but I love it.
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Books From Today’s Episode:
Economics: The Remarkable Story of How the Economy Works — https://www.amazon.com/Economics-Remarkable-Story-Economy-Works/dp/0988669102
The Missing Billionaires: A Guide to Better Financial Decisions — https://www.amazon.com/Missing-Billionaires-Better-Financial-Decisions/dp/1119747910
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