The Lifecycle Model Vs SWR

A few weeks ago The Rational Reminder podcast did an episode on the Lifecycle Model.

The episode features Ben Matthew, an economist with a PhD from the University of Chicago, who has developed a financial planning tool based on the lifecycle model from economics. This model aims to optimize financial planning by spreading consumption and risk over time, contrasting with the widely used safe withdrawal rate (SWR) model. The conversation delves into the lifecycle model’s approach to saving, investing, and withdrawing funds, emphasizing the importance of variable spending and risk management. They also critique the SWR model for its oversimplifications and discuss the practical implementation of the lifecycle model in financial planning. Ben Matthew’s online tool, tpawplaner.com, aims to make the lifecycle model accessible for comprehensive financial planning, including considerations for taxes and duration matching.

Here is the link to the transcript (and the audio, duh :)).

I found the conversation interesting, so much so that I wanted to write down all my comments. TDLR: I realised that the SWR model is not that bad, provided we approach it with the necessary (mental) flexibility.

I found myself in a similar situation when discussing the concept of the efficient frontier or Risk Parity. Not sure why many want to read in those model outputs “the truth”, the perfect mix of stocks and bonds is 63.47% and 36.53%, which will produce a Sharpe ratio of exactly 0.6745, while both ‘models’ simply give you useful INDICATIONS.

Same with the SWR: it provides a fixed annual budget because we work enjoy our life better (and spend carefree!) when it is presented as something that should be fine under most of the possible scenarios. We hate volatility! Once we understand how the model is built, its assumptions and limitations, we can re-adjust as the times passes. We are not lemmings (ok boomer)

Anyway, here are the salient parts of the conversation with my comments.

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. … That 7% drop in total wealth might be only a 5% drop in the wealth that funds your retirement spending. … When you amortize your spending, that would drop by the full 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.

The main drawback of the Lifecycle model is that it allows for variable spending. Which is its main advantage too, when compared to the SWR. Here Ben tries to hide downside volatility under the mental rug.

It is true that after a crash I should not worry “too much” about the value of my assets because there should be a regression to the mean. But if I am forced to sell because…I have to eat, the expected returns are less relevant, I am still bound by the price I get today to fund my expenses. The expected return model might still work and I can still end up broke because of the sequence of returns.

What Ben describes works during the accumulation phase, to prevent you from panicking because you want to sell thinking your financial plan is ruined. In the decumulation phase, all the above is irrelevant because all your wealth is targeted for retirement.

[Assuming a 50/50 allocation in retirement] 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%.

This looks fine. Adjusting your budget by 12% is not a big deal, especially considering that the Lifecycle model is designed to allow for a bigger spending budget compared to the SWR. Now the bad news:

There would have been seven [crisis] events over the last 150 years: World War I, the Great Depression, the 1937 Recession shortly after World War II (sic), the 1970s with the bond crisis and the subsequent bond crash, the tech crash of 2000 and the subprime crisis of 2007-2008.

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%.

I do not know how many would survive a 37% cut in budget. That’s the main issue with the Lifecycle model: in this instance, it doesn’t formally FAIL but in reality, it does. It might not be the end of the world spending some years just eating and sleeping (i.e. paying for food and shelter and that’s it…I mean, 80% of the lads that are “FIRE” in the UK live just like that ALL THEIR retirement LIFE) but the model has its own way of failing, let’s be honest about it.

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.

Maybe Ben. I am not sure.

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.

But this is the same as doing the SWR and then re-calculating it every 5 years. Your budget will go up if a catastrophe didn’t happen in the previous 5 years.

The only solution the Lifecycle model has to reduce this spending volatility is to…reduce spending and use massive doses of inflation-linked bonds, duration matching [This is explained in the episode, I did not invent it ;)]. Not a great solution, uh? First, you depend on the institution issuing those bonds; if they stop issuing them, as is the trend around the World right now, your plan is screwed. Second, your spending is bonded to whatever real rate the market is offering: we might look at decades with real rates close to zero. Third, you can only lock rates for max 30 years, after that it is just fingers crossed.

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%.

These are real numbers, psychologically the recovery is faster because we tend to look at nominal figures. Still, being down after 10 years sucks. If you consider you started cutting your spending at least 5 years prior, that’s 15 years out of…40? of retirement spending less than you thought. Good times :S

On the asset allocation side, my understanding is that the Lifecycle model works exactly like the SWR: fixed asset allocation throughout. No glidepath.

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.

Trying to forecast future expected returns is a useless exercise and I do not understand why (well, I know, it is sales material) investment houses still do it. I do not even have to mention GMO, no one gets the right number so…why do it? Why pretend it is useful?

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. 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. 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. 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.

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. 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.

This is an interesting point worth mentioning. Even if the range of average returns shrinks the longer the horizon, the effect of compounding makes those smaller differences still relevant from a terminal value point of view. A person saving for 35 years might start retirement with their portfolio averaging close to what they had in mind in terms of returns and still be a couple of hundred thousand back in terms of wealth.

Lowering that sequence of returns matters in the accumulation phase too.

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.

Fixed withdrawals are a feature or a bug? There is a lower bound we do not want to breach, the basic expenses we plan to have. In this regard, the SWR method works well: by starting at a conservative level by model design and using a 95% success rate, we would only have to trim the budget if the markets go nuts, doing something that has never happened before. And it has to do it in the first years of our retirement. I see it as a great starting point and something anyone would want to know even if they decide to use another model.

If we dodge that scenario, the only issue we would have is to be the richest person in the cemetery.

This risk is largely unavoidable for two reasons:

• longevity risk: we do not know how long we will live. We need to hold a ‘high buffer’ because of this reason, knowing that the worst scenario then is…to pass the wealth down to heirs.
• health risk: there are scenarios when we stop being independent and our fixed expenses explode. Again, a high buffer is needed. (There is an interesting inter-generational pact at play here: tell my sons I’ll buy you that house today provided you keep a room for me if I’d need it when I’m 80 ;))

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.

This is true in Excel but not in real life. Since we do not know when we are going to die and how much money we will need during retirement, a failure IS a failure. There’s no model that can solve for these unknowns. You do not know if you failed by one dollar because you do not know if you are going to die tomorrow.

By design, the only solution that prevents failure is the one that goes parabolic in the majority of scenarios.

That’s why we look at the worst-case scenarios. Ben Mathew sort of admits this here and there. Even with the Lifecycle model, people do not start at full budget but keep a safety amount…which leads us back to the SWR. After the initial years, no one prevents our retiree to re-run their model and obtain a higher SWR going forward (assuming the first years were fine).

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.

The only way the SWR fails is if the future behaves very differently from the past. But in that scenario also the Lifecycle would not fare better, because it is largely built on the same economic and financial assumptions (expected returns, innit?). Sure, instead of a catastrophic moment, the year you run out of money with the SWR, you would spread the outcome over some years in the Lifecycle. I am not sure how happier you would be living 3 years with a budget that is half your fixed expenses: there is a moment where you would say “fuck it, I rather eat today than in 3 years”.

I understand that the SWR model is simply a subset of the Lifecycle model. On the fixed vs variable budget, it is clear that no one sees the SWR as fixed-fixed. No one is going to walk to the edge of the cliff pretending they do not see it and, if things turn well, we would increase spending. It gives you peace of mind knowing you can very reasonably spend X every year and be fine.

What I really hate is the concept of the utility function: no one knows what their utility function looks like. Really, there is no way of knowing it. There are plenty of studies on this. Thinking you can solve the pass-fail grading scheme of the SWR with the utility function is embracing the illusion of certainty so dear to Gigerenzer. When you stare into that left tail, you are at the mercy of uncertainty. That’s it.

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.

We cannot do these calculations in our head, sure. Like we do not try to solve the SWR on the back of an envelope. A calculator would go a long way in helping people: we all love PortfolioCharts for this reason. In its absence, I do not agree we would resort to the zero-one utility function…provided that in some situations, the zero-one utility function depicts reality well: if you need to eat and cannot work anymore, it is a devil bargain or nothing.

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.

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.

Instead of looking at the median budget, the SWR looks at…the safe one. As long as it is clear to everyone what we are talking about, I do not see that many differences. It makes sense for this exercise to look at the bottom of the distribution instead of the mean: you want to be cautious!

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.

Ben has an issue with this but it is simply a consequence of how cautious we want to be. That’s it. I think people would rather decrease the probability of success (use the SWR with a probability of success of 90% instead of 95%), knowing they can lower spending if things are not going as expected (again, it is just about the first years) than increase the slope by employing the Lifecycle model…which means a MORE volatile budget. If we can agree on something, is that very few are willing to see their budget move a lot just because the market is moving a lot. The slow growth is a feature, not a bug.

there’s no point doing it like this because the amortization does this very easily. In the amortization [the Lifecycle model], 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.

Again, the illusion of certainty. No one knows if 1.5% is the right number because no one cares about it: we care about the budget volatility. And the solution is, guess what, moving towards a solution like the SWR.

On a spectrum where we have the SWR on one extremity and the Lifecyle on the other, I think we would land closer to the SWR than not. Because we despise budget volatility. But we are all grown-ups enough to understand that ZERO volatility is not desirable either, considering the issues it comes with.

The SWR model has its shortcomings and the more we talk about them, the better. It was a great podcast episode and I wish more to come in the future. Unfortunately, I did not have the time to check the online tool, maybe it will be the topic of another post.

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