Episode 57: Sequencing Risk: Why The Expected Value Is Not What You Should Expect | Cockroach Strategy (Part 2)

In this second episode of the Cockroach Series, Jason Buck (Mutiny CIO) and Taylor Pearson (Mutiny CEO) delve into the intricacies of sequencing risk and its profound impact on portfolio construction.

They explore concepts like expected value, ergodicity, and the importance of return order on investment outcomes. Whether you’re planning for retirement or just starting your investment journey, this discussion offers valuable insights on how to navigate and mitigate the unpredictability of financial markets.

Please see our Insights Page for blog posts featuring notes from the Cockroach Approach whitepaper. Additionally, you can access the Cockroach Approach summary and download your own copy of the whitepaper!

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Have comments about the show, or ideas for things you’d like Taylor and Jason to discuss in future episodes? We’d love to hear from you at info@mutinyfund.com.

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Transcript Episode 57:

Taylor Pearson:

Hello and welcome. This is the Mutiny Investing Podcast. This podcast features long form conversations on topics relating to investing, markets, risk, volatility, and complex systems.


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Taylor Pearson:

Welcome back to part two of the Cockroach series. I’m here with my partner, Jason Buck. I’m Taylor Pearson. We’re going to be talking about a lot of fun topics today, get excited. We got sequencing risk, ergodicity, retirement planning, all the hot topics of our day. But as we’ve said before, this series is us talking through some of the research we’ve done and our thinking about portfolio construction over the last 5 or 10 years, as we’ve thought more and more about it.

And today, we want to talk about some of those sorts of things and I think want to start with expected value. I think probably most people listening are familiar with this topic, but the rough idea here, is that expected value is multiplying the probability of some outcome times the payoff of some outcome. Right? So if you were rolling a dice and let’s say, if you roll a six, you win $10, you bet $1 to win $10 if you roll a six. So your expected value is your probability of winning, so in this case, one-sixth times the payout, which is $1.66. So you bet $1 your expected value is $1.66. This is great, a lot of people would like to make this bet.

And I want to talk about this because I think, implicitly and to a large extent, explicitly, expected value is how most investors think about portfolio construction and picking assets. They’re looking at it, they’re like, “This stock and that stock, do I like this fund or that fund?” Yeah, “Do I like this asset class or that asset class at any given point in time.” And they’re doing sometimes explicitly, I think a lot of time implicitly, some sort of expected value calculation that, “I think this is going to do well or I think this is going to do poorly over the long run.” And I think there’s a few, as we talk about some nuances around how people think about stock market investing, I think some nuances around how people think of expected value, that we want to talk about here.

Jason Buck:

Yeah. Like you just said, this is our sweet spot, so you’re joking about it, but this is what we talk about all day, every day and why we build portfolios around ergodicity problems. And I think like you said, people understand EV because it’s like more of a betting scenario for discrete events, so it does make a lot of sense. But, speaking of betting, I think it seemed to popularize the idea of a casino. If you had everybody going into a casino, and this is the way to talk about ergodicity in a more simplified version, is the ensemble versus the path or time or singular approach.

If you have 50 people going in to play a casino game and they have a positive expectancy or a positive EV on those bets, but you have a chance of risk of ruin, 50 people play at the same time, the one person risking ruin doesn’t hurt you. But if you went into the same casino and played 50 times in a row and you’re compounding your winnings every time, well as soon as you hit that absorbing barrier, you’re going to lose everything. You brought it up last time, but I think the much more, we don’t like to be macabre, but I think the best example is the Russian roulette. So I’ll let you hit the Russian roulette again because that’s much more visceral then thinking about 50 of your friends going into a casino.

Taylor Pearson:

Yeah, so we mentioned this last time, but just to briefly recap. So I will create some terms here. So let’s call one sort of an ensemble scenario. So you have an ensemble of individuals that are taking some action, making some bet in this case and a path scenario, which is you have one individual that’s doing something over the course of time. And so yes, the fun example is certainly Russian roulette. Six people play Russian roulette, it’s fun, post-purchase survey for six people playing Russian roulette, five out of six think it’s a terrific game, where you win lots of money and is very enjoyable and they would recommend it to anyone and one out of six people does not respond to the post-purchase survey.

By contrast, in the path scenario, one person plays six times, there are no responses to the survey, the person does not come out the other end. And as Jason said, there’s a number of others for examples to talk about this, right? If you have someone with edge in a gambling game, some counting cards in blackjack or whatever, and you have 10 of those people going to a casino versus 1 person go in 10 times and those are going to receive different outcomes, 1 person playing over time, as opposed to 10 people playing once. Because as Jason was saying, if you have 10 people and 1 person goes broke, that can be okay, the other 9 might do very well and so your average could still be good. If you have 1 person playing 10 times and they go broke on day seven, they’re broke, it drops off as absorbing barrier, I think is the fun term, but going broke is maybe the more descriptive term.

Jason Buck:

Yeah. And we have to get better at that. Right? And I’m usually the biggest party fellow on this. I love learning new vocabulary words, so obviously I love ergodicity and non-egodict systems, but we always are trying to get better on using different examples and different words. Like you’re saying, the ensemble approach versus the individual path or time approach, but we can get better, going broke versus absorbing barrier. So yeah, we can always get better about these ideas and we constantly strive to and try to come up with different ways of saying it.

But I think historically, like we said in this essay too, it’s like sequencing risk, that’s the way people talk about your time horizons of when you’re making money in your younger years, but then your primary years in your ’40s and ’50s and then your retirement years, is like that sequencing of events affects what your total outcome’s going to be and what your income’s going to be in retirement and especially when you have those mandatory withdrawals. But I think one of the best ways, examples is, shout out to Resolve Asset Management, is the idea of Nick and Nancy going into retirement and maybe you can simplify it versus, whether your returns come early or late in your own life cycle of going into retirement over a 30, 40 year time horizon.

Taylor Pearson:

Yeah, I think a descriptive example here is, if you look at the Dow Jones Industrial Average, the returns from the period of 1966, 1997, so roughly a 30 year period, 31 year period, the average return was 8% over that period. And so if you were to draw sort of a naive extrapolation of, “I have $1 million today and it compounds at 8% per year, how many dollars do I have in the future?” This is an interesting example because from 1966 through 1982, roughly the first half of that period, the returns were close to zero. It basically ended roughly around where it went. And then from 1982 through 1997, the returns were about 15% per year. So you had an 8% average over this whole time period, but if you sort of spliced that time period in half, you had two very different outcomes. And so yeah, we originally got this example from, as you mentioned, Resolve Asset Management, they have a great blog post on this.

But you take a couple, Nick and Nancy. Nick and Nancy are 63 years old. They’ve accumulated $3 million in savings, which is great for them and they’re ready to retire and they’re expecting that their lifestyle costs are $180,000 per year. They’re going to factor in a 3% increase per year for inflation. And if you just sort of draw the averages out from there, let’s say, they’re retiring in 1965 in this example, and you just take that average 8%, their assets last them until 1997, so they’re going to be 95 years old, seems like a reasonable sort of period. But the order in which those returns come, matters quite a lot. So if they get the actual returns over that period, starting in 1966, where you’re basically flat for the first half of that period, they go broke in 1977, basically 12 years. Because what happens, they’re drawing down, drawing down every year as they pull out their retirement savings. It’s not growing, they’re taking their $180,000 plus 3% out and it’s depleted after about 12 years.

Take the opposite scenario, let’s say, they retire and they get the best period of returns first. They get really strong returns, what’s starting in that 1982 period. Well now, even as they’re drawing down, their wealth is growing, so they’re withdrawing less and it’s compounding. They reach over $12 million in assets after they’ve been retired for about 15 years and then they slowly draw down on that. So let’s say, they die at 95, they have over $6 million in assets. So more than what they started with and whatever, great outcome. This is the same return, I just delivered in different orders-

Jason Buck:

Different sequences.

Taylor Pearson:

… and in both of these cases, they were investing something that had an 8% average return. So I think it’s an interesting thing. I think it’s something, people close to retirement, it’s particularly relevant because you can be in the Nick and Nancy situation, you need to think about, what is the sequence and we’ll get into that more. So I think, start thinking about diversification, how do we reduce that sequencing risk? That we don’t necessarily need to have as high returns, if we want to reduce our sequencing risk. I think the other thing, the sort of simulation we ran here that I think is maybe more interesting, more interesting to me, is what if you’re a relatively young person? Let’s say, you’re 34, 35 years old, you have $100,000 in savings, you’re working a job, maybe you’re adding $1,000 month to savings. How does the sequence of return risk affect you then, to be a fun thing to again, poll. But I guessed what the answer is, but I wasn’t particularly confident actually. I was curious to see what happened when it came out.

What it comes out to is, it’s the opposite of the retired person. So if you get the returns late, that’s to your advantage. So you have this flat period early on, but you’re working that whole period. You’re not drawing down from the portfolio, you’re contributing to the portfolio and even though it’s not really growing, you’re building up and you’re building up a capital base. And then once you’ve accumulated a significant amount of savings, you get to this period, where the returns start to get very good. It grows very quickly and in this scenario I gave starting with $100,000, adding $1,000 a month, you end up with a little over $3 million, like $3.2 million. I’m eyeballing the graph here, which is pretty close to the average portfolio. The average works out to something like $2.9 million.

Now if we flip the sequence, you have very strong returns early on in your career or relatively early on in your life, let’s say, in your ’30s and ’40s, and then you get flat returns later, you get a very different outcome. So again, run this same sequence. You take the 1982, 1997 strong period of returns first and then the flat period after that, your wealth peaks at around $1 million and then it’s basically flat at $1 million for the last 15 years of that period. It’s growing a little bit as you’re increasing it, but you’re not getting any of the returns. Right? You were compounding off a relatively small capital base. Right? You read relatively little savings, you’re relatively early in your career and then you hit this flat period, where all of a sudden, you’re looking at retirement or whatever your savings are at that point, and your average prediction, you’d have $2.9 million and the actual number is going to be less than $1 million.

Jason Buck:

For those of you who plan at home. I think it’s fascinating to think about, we don’t want to get into these okay boomer scenarios, but if you think about the baby boom generation, the last 40 years, they’ve had pretty solid steady returns. And do we know then, are they going to go through a flat period for a decade or two now that they’re in retirement and have those mandatory withdrawals? It’s hard to know, right? [inaudible 00:13:42]. And then the flip side of that, if you’re 30 years old now, what’s your expectation moving forward? Do you think you’re going to have as good 40 year run and is it a 60-40 portfolio that the boomers had just went through as they were building up their savings in their prime earning years, contributing more and more? Meanwhile, they’re clipping along at great returns.

This is the sequencing risk that really matters to us, about how we are going to live a certain type of lifestyle in retirement. And I think that’s great about the essay too. You’re showing what the actual income difference is. I think if I recall correctly, it can be anywhere from like 30,000 to 150,000, depending on the sequencing of those returns, on what are your lifestyle costs in retirement, that you can safely withdraw at that alleged 4% rate? I mean that’s a vastly different lifestyle between 30,000 and 120,000, these days.

Taylor Pearson:

Yeah, I think what’s interesting here is, people make moral judgments. This is the same person-

Jason Buck:

Right. Right.

Taylor Pearson:

… with the same intelligence level, making the same reasonable decision of, “I’m saving this much money.” And I think that I did that, if you take the 34-year-old scenario I gave and the good scenario where they get the returns late, so they’re able to build up a capital base. If you want to calculate their safe withdrawal rate, it’s $134,000 a year approximately, which you can live a pretty nice life on $134,000 a year. And the alternate scenario, same person, works just as hard, saves just as diligently, the outcome is $36,500 a year, is their safe withdrawal rate. So a very different outcome than this $134,000 scenario. And I think as we talked about earlier in the previous podcast, you do not get the average returns of the market. We don’t know what the future average returns are, but let’s just say we do. If you don’t know the sequence of those returns, you can have very different outcomes unless you’re doing something around how the portfolio is constructed, to try and reduce that sequencing risk, to try to make the returns more consistent over time.

Jason Buck:

Right. We’re also not trying to create a generational argument and we can just use ourselves as proxies to put a finer point on it. But I remember a conversation you and I had years ago, you’re like, “That was me when I graduated college into 2008, 2009? There’s no jobs available.” And I’m like, “Yeah, that part sucks but as soon as you get a job and start investing in assets, you’re investing at the nadir and you likely have a run ahead of you even though we don’t know the future.” Then I think about, I was born in ’78, so people in mine are getting out of college, 2000, 2001 going through the .com bust, into 9-11, and then for me, commercial real estate.

Let’s say I start buying my first properties in ’01, ’02, you get a five, six year run of building up assets and then all of a sudden, real estate completely collapses. We go into the biggest recession or depression in 100 years and it really matters how lucky you get on that sequencing risk. And I was even talking to a mutual friend of ours the other day, and he was talking about, he was in not high frequency trading, but similar, a lot of really technologically advanced options trading, and he was talking about kids now, that they’re asking him for advice. And they’re probably going to lose their jobs to AI and to all these other things and he had a great 20 year kind of bull run, he just hit that sweet spot. That’s what we’re trying to say, is you can get lucky or unlucky and we always think about portfolio construction via ergodicity because we’re just trying to reduce the luck. We’re trying to reduce-

Taylor Pearson:

Reduce the impact of luck.

Jason Buck:

… right. Yeah, exactly. Reduce the impact of luck. Where I feel like a lot of people’s portfolios, it’s a lot of luck involved and they’re hoping for good luck. Maybe we’re just not that optimistic or hopeful, I don’t know. We’re just trying to reduce the bans or the opportunities, where bad luck can hurt us, I guess is a good way of saying it.

Taylor Pearson:

Yeah, and I think there’s something that’s not entirely intuitive. I had a phone call with someone earlier this week and they showed me some pie chart of how wealthy people are invested or whatever, and they’re like, “Oh look, this is how you should be invested because this is how wealthy people are invested.” I was like, “Well, maybe, but by definition, whatever did the best over the last 10 or 20 year period, is what all the wealthy people will have, and does that indicate it’s good to invest over the next 10 or 20 year period?” No, at any given point in time, if you just take a snapshot, arbitrary or whatever, the wealthiest people are, it’s going to be whatever went up the most in the previous time period, over the last 10 or 20 years.

So I think last time we talked about longer run return stuff, and we do try to take that historical view and I think that’s important, but as you say, we don’t know the future. We don’t know the sequence. We don’t believe we can predict that, with that, what is the best way to think about portfolio construction? So we’ll talk more about that. We’ve got some fun topics coming up, volatility drag, a riff on Herschel Walker and more, so stick around, we’ll be back.

Jason Buck:

That was great to learn about the Great Train Robbery, so we’ll leave that out there. That was a great one to learn about. So dangle that carrot.

Taylor Pearson:

Thanks for listening. If you enjoyed today’s show, we’d appreciate if you would share this show with friends and leave us a review on iTunes, as it helps more listeners find the show and join our amazing community. To those of you who already shared or left a review, thank you very sincerely, it does mean a lot to us. If you’d like more information about Mutiny Fund, you can go to mutinyfund.com. For any thoughts on how we can improve the show or questions about anything we’ve talked about here on the podcast today, drop us a message via email, I’m taylor@mutinyfund.com and Jason is jason@mutinyfund.com, or you can reach us on Twitter, I’m @TaylorPearsonmutiny and Jason is @JasonMutiny. To hear about new episodes or get our monthly newsletter with reading recommendations, sign up at mutinyfund.com/newsletter.

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