Scott Cederburg is an Associate Professor of Finance and the Thomas C. Moses Endowed Chair in Finance at the Eller College of Management at the University of Arizona. He earned his PhD in Finance from the University of Iowa. His research focuses on issues related to long-horizon investment outcomes and retirement security, return predictability, and mutual fund performance.
His studies have been published in top academic journals, including the Journal of Finance, the Journal of Financial Economics, the Review of Financial Studies, the Journal of Financial and Quantitative Analysis, and the Review of Finance. He won the 2018 TIAA Paul A. Samuelson Award for Outstanding Scholarly Writing on Lifelong Financial Security for his study, "Tax Uncertainty and Retirement Savings Diversification," and his work has been covered by The Wall Street Journal, The Economist, Financial Times, and Bloomberg, among other outlets.
Our conversations with Professor Scott Cederburg from Eller College of Management have led to the most heated debates among our listeners! Today, Prof. Cederburg returns to discuss the changes he’s made to his paper that was the foundation of previous conversations - ‘Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice’. We begin with the data setup and headline findings of the paper before Prof. Cederburg defines “domestic” and “international” as they appear in his paper, why the block bootstrap approach is vital to his work, how and why the results of his paper differ from the status quo, and the evaluation metrics he uses to compare different investment strategies. Then, we explore his optimal base portfolio, the strategy he uses to derive it, how it performs in simulated worst-case scenarios, and how it changes when ditching the bootstrap approach or changing strategies from constant spending to proportional spending. To end, we learn of the importance of including the US in international stock portfolios, how it changes when the US is viewed as special above others, the correlation between labor income and domestic stock returns, and how the reviews of academics and practitioners have changed since the first iteration of the paper until this latest edition.
Key Points From This Episode:
(0:00:00) What to look forward to in today’s conversation with Prof. Scott Cederburg
(0:04:49) The data setup and headline findings from his paper, ‘Beyond the Status Quo.’
(0:07:01) Defining “domestic” and “international” as they appear in Prof. Cederburg’s paper.
(0:08:34) Why the bootstrap approach is necessary for his work.
(0:12:17) How and why the results of his paper differ from the status quo.
(0:15:11) Unpacking the evaluation metrics he uses to compare different investment strategies.
(0:16:05) Exploring his optimal base case portfolio and strategy, and how it performs in worstcase
simulations.
(0:23:05) How the optimal allocation changes when households vary their portfolio weights.
(0:27:13) What to consider when ditching the block bootstrap in time-varying optimal portfolios.
(0:29:46) Constant spending versus proportional spending: How the optimal portfolio changes.
(0:30:49) Examining the sequence of returns risk.
(0:42:14) The importance of including the US market in international stock portfolios.
(0:43:40) Why the US is treated the same as any other domestic country in the paper, and how
the data changes if it’s viewed as special.
(0:51:40) The extent of the relationship between labor income and domestic stock returns.
(0:53:01) How leverage affects optimal portfolio results.
(1:05:20) Assessing how sensitive the paper’s results are to risk aversion.
(1:06:35) How academics and practitioners have responded to this paper across all iterations.
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: Hey, great episode today, episode 350.
Ben Felix: We welcome Scott Cederburg back to the Rational Reminder Podcast for the third time. We've had two episodes, one on this same paper, and now we're having him back to discuss the updated version of this paper. They did a pretty significant overhaul of the original just based on the huge amount of feedback that they got. Scott talks about it at the end from other people in academia and from practitioners.
The way that I describe it is they added a ton of the what-if scenarios because there's so many things where people are like, "Okay. Well, your result says this, but you're not modeling this or you're not considering this and that will change your result." They modelled so many of those what-if scenarios. What if valuations are high? How does that change the result? What if you allow leverage? How do correlations over time affect things? They modelled different spending strategies and looked at how that affects asset allocation. They looked at optimizing the asset allocation in each year of the simulation instead of having an optimal fixed allocation for the full life cycle. They looked at how that changes results. If the US was special.
Mark McGrath: How important US equity returns were if you're an international. If you're an investor from another country, and then the international component of your portfolio is partially US equity, how important is that to the result that you want to hold a lot of international equity? That was really interesting for me.
Ben Felix: That's right. Does the US drive the high international stock allocation because it's had such a good outcome? And then the US special case, is the US special in a way that suggests it should have high returns in the future similar to the past? And so they did one specification where they hold the probability of US being special fixed at some amount. That percentage of their bootstrap draws come from the US sample to see how that effects optimal portfolio allocations. Other stuff too, but we talked through all of those changes that they've done to the paper and how it affected the results. I don't know. What do you think, Mark, of the overall conversation?
Mark McGrath: That was great. Surprising, I think, for me in a lot of ways. We were chatting with Scott at the end of the episode, and obviously you understand and have read the papers more frequently than I have, and I've largely just taken the synopsis of Scott's work. Some of the questions, as I was asking him, I didn't know what the answer was going to be. And you obviously did, Ben. My mind got blown a number of times throughout the conversation whereas you already knew what the answer was going to be. It was a really fun conversation for me because I thought I knew what the answer might be or at least the direction that the answer would take and I was surprised in a lot of cases. It was a really, really good conversation. I learned a ton and I think listeners are going to just love it.
Ben Felix: Oh, yeah. I mean, our last couple of episodes with Scott have been some of the most discussed episodes in the Rational Reminder community. Just by the number of comments in those threads, you're still ongoing with people discussing the implications of the research and the research itself, discussing the methodology and the data sample and all that kind of stuff. It's an important paper, at least for the amount of discussion that it's created that I think that adding all of these comments and criticisms that they have addressed with additional analysis I think really adds a lot to the overall discussion.
We asked Scott at the end if anything has surprised him going through all that additional analysis. And I loved his answer that he was mostly surprised by how resilient the results are to running all of these alternative specifications or different sets of assumptions or whatever. Things change a bit and we talk about cases where they do change. But it's a pretty stable result, which is pretty cool.
For people who don't know who Scott is, he is an Associate Professor of Finance and the Thomas C. Moses Endowed Professor in Finance at the Eller College of Management. He earned his PhD in Finance from the University of Iowa. And his research focuses on issues related to long horizon investment outcomes and retirement security, return predictability and mutual fund performance. He's been publishing lots of top journals. And as we discussed at the end of this episode, that's the next step for this paper is to submit it to top journals and hope it gets accepted somewhere.
I think that's enough for the introduction. We're talking about the paper ‘Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice.’ And a new version of that paper by the time this episode comes out, a brand-new version. At time that we're recording this episode, which is a couple of weeks before it comes out, that version of the paper has not been published on SSRN yet. But when this is out, it will be up. If you haven't taken a look at that yet, I recommend doing so because there's lots of neat little nuggets in there.
All right. Let's go to the episode.
[INTERVIEW]
Ben Felix: Scott Cederburg, welcome back to the Rational Reminder Podcast.
Scott Cederburg: Thanks for having me back again.
Ben Felix: Excited to have you back. You've got this new draft of this paper that we've talked about before, which we're going to talk about. But as a quick refresher, since it's been a while and you've obviously made changes to the paper too, can you describe your data setup and the headline findings from the paper ‘Beyond the Status Quo.’
Scott Cederburg: We're doing a lifecycle asset allocation paper. We're really looking like you're saving throughout your working years and then going to be spending down in retirement, just the very practical question of how should you be investing during your life. There's lots and lots of papers that have been in this literature looking at this particular question. They study a wide variety of issues; labor income, how that interacts, health risk, all these sorts of things.
How we see ourselves fitting into the literature is that we're going to be very, very careful in how we're treating the data and just the investment opportunities that you have. And so that has a few different aspects. One, it's very common in this literature to just say, "Oh, you have access to stocks and bonds." It's kind of domestic stocks and bonds. We've explicitly added in international stocks. That's going to turn out to be very important for us.
We have four different asset classes with domestic stocks, international stocks, bonds, and bills. It's also true that the literature is kind of very US-centric. We think that there's relatively little evidence in the US data about the types of horizons that we're thinking about. You might have 75-year horizon or something when you start saving. We use our comprehensive dataset of developed countries. We have 39 countries, 1890 to 2023. We have over 2,650 country years’ worth of data to bring to the question.
And then, finally, a lot of the papers will either say maybe returns are normally distributed, or maybe pick a couple of state variables that might affect expected returns. We're going to apart from the literature and use a block bootstrap approach. It's going to allow us to keep a lot of the features that are in the data without having to take a strong stance on what particular aspects of returns investors might be most interested in. The headline finding is you should never own bonds, you just invest in stocks internationally diversified throughout your entire lifetime.
Mark McGrath: Can you just define what you mean by domestic and international in your data setup?
Scott Cederburg: We're taking the perspective of an investor in a developed country, and then they're going to have access to their own domestic stock market. They have international stocks, which is going to be a valuated basket of everything else in the world, and we're going to have all the currency conversions and things like that that are necessary for that. And then government bonds and government bills from your local market as well.
The broad perspective that we're taking in the paper is that developed country returns are developed country returns. And so the experiences of German investors may be informative to me as an American. That's kind of the stance that we're taking. It's also important to note that all of our returns are going to be in real terms. Everything is after inflation. And that's also, I think, very important for thinking about, for example, how risky is a bond? How risky is a nominal bond? That very much depends on whether you're in nominal or real terms.
Ben Felix: That definition of domestic international and international is something that I've found people struggle to grasp when I'm talking about your paper because people think of domestic as the US usually. You've got some misguided criticism based on that saying, "Well, they focused on US stocks." But domestic in this case is not US, it's whatever. Using your bootstrap method, kind of like a representative domestic country, which I think makes a ton of sense. Can you talk a little bit more about – you mentioned it with long horizon and the relatively limited sample of US data. But can you talk about why the bootstrap procedure is necessary for what you're doing?
Scott Cederburg: We think it's a good approach. There's very important patterns in returns, and especially what especially what we might call time series dependencies. We know, for example, that volatility clusters in time. You're in a bunch of volatile months in a row, and then you'll have a calm period. There's important properties of stocks where historically there's been mean reversion in returns across all these developed countries. We consistently see mean reversion. A large stock market crash, stocks don't always bounce back, but there's a tendency for stocks to back.
And then if we have a really hot period in stocks for an extended period of time, like the 1990s in the US, the next decade doesn't have great returns. And so there's this tendency to have mean reversion in stocks. There's all sorts of other things that are important about returns. There's skewness, there's keratosis, like fat tails, all this sort of stuff. And what the bootstrap is going to do is just sort of let the data speak and what do returns look like.
And there's a block bootstrap aspect of this where, to try to preserve these time series tendencies, we're drawing on average about 10 years’ worth of consecutive data from the same country period. We're going to try to basically – if there is a stock market crash, we're likely to also pick up the period where it may have been able to bounce back. We just use the block bootstrap to kind of just try to preserve as well as we can what are the properties of the data. And then we don't really have to take a strong stance on what are the particular aspects of the data that we're trying to capture? What's going to be important to investors? Everything like that.
A really important part of this kind of an illustration of thinking about long -term investing and the importance of maintaining these properties is if we look at bonds versus international stocks as a way to diversify away from pure domestic stock investments. You look at a monthly level, bonds have relatively low volatility and they have relatively low correlation with stocks. And so it looks like this thing that diversifies this pretty well in our classroom examples of mean variants, frontiers and everything is always kind of bonds and stocks with a lot of diversification benefits, but bonds don't really earn very high returns. In our sample, the average real return is 1% per year on bonds versus international stocks have a 7% per year average real return. And so there's this huge difference in the potential reward. You need to be getting a lot of diversification benefits out of bonds.
If you look over the longer term, going beyond monthly level and think about like a 30-year period or something, all of a sudden, the risk of bonds grows over time. There tends to be continuation in bonds. The worst thing that you have in nominal bonds is an inflationary rising interest rate environment. But if you have an inflationary rising interest rate environment, you tend to kind of stay in that environment for a while.
On a per-period basis, the risk of bonds at a 30-year horizon is 2.3 times the one-year horizon. The variance grows with horizon. Versus international stocks with the mean reversion, it actually gets down to about .75 times the one-year variance on a per-period basis. Stocks are getting safer over the long run. Bonds are getting riskier. And the other thing is that bonds actually become more correlated with domestic stocks than international stocks are if you get to a longer horizon.
You're kind of losing these diversification benefits that you initially think that you have with the bonds as your horizon grows. And there's just not really the reward there in terms of the average return to make them that attractive. But that's something that, with our approach, we can see that in the data, and we didn't have to kind of prespecify that that's what we wanted to find.
Mark McGrath: The paper is called ‘Beyond the Status Quo.’ Can you talk about how your results differ from the status quo?
Scott Cederburg: The status quo at this point really is target date funds. Target date fund, you might see something like a 2050 fund or something, and that 2050 is supposed to be your target retirement date. The one that we look at in our paper, it's major investment firm. It'll have you 90% in equity split across domestic and international early in your life. And then as you get towards retirement, it decreases that and it ends up parking you basically like 83% bonds and bills throughout much of your retirement.
This has become enormously popular. According to Vanguard, it's a default in 98% of employer plans. I think it's 83% of people with Vanguard plans own at least one target date fund and 58% have all their money in a single target date fund. Three out of five investors are just going to do the default TDF. And so that's really the status quo at this point. Our baseline result of be all equity throughout your entire life is going to be very different from being 83% in bonds and bills during retirement.
Ben Felix: Can you talk a little bit more about why your findings with the data set up that you just described would be different from somebody just looking at the US data as many other people have done?
Scott Cederburg: The US has had a really good run, obviously, over this time. There's always kind of this issue of what we would say is X-anti versus X-post. Before the fact, did we know that the US was going to have this run or did it end up being basically better than people may have expected? With the US, we have, I think, a relatively short sample of data. We have 130 years of data in our paper. But if you're a 25-year-old couple, there's not a great chance, but a non-trivial chance that one of you makes it to 100. And so you kind of have this 75-year horizon. We don't even have two non-overlapping 75-year period of US data. It's relatively small.
We've seen a big valuation increase in the US over this period. I guess there's some question of whether that was expected before the fact and whether it's sustainable to repeat that. And so we see around the literature, people do various kind of ad hoc adjustments sometimes. They'll use US moments, but then subtract 2% from the mean of stock returns or something to try to say like, "Hey, let's maybe have it reflect what's a forward-looking expected return."
Our strategy is not all the countries in our sample have had this kind of rosy outlook. I mean, there's been a couple of different times in our sample. For example, like the UK in 1890, in Japan in 1990, those were the two biggest markets at the beginning of those periods. And then over the next 30 years, they have pretty substantial negative real returns on stocks. That's kind of our different approach to it.
Mark McGrath: What evaluation metrics are you using to compare the different investment strategies in the paper?
Scott Cederburg: Our primary one at this point is expected utility. It's just a way of kind of measuring the overall well-being and we're getting utility over the monthly retirement consumption that you have, as well as a bequest upon the death of the last survivor of the couple. That's kind of our primary metric. And then to get intuition on what's actually driving this, we will get four other outcomes. Which strategies are generating the best retirement at wealth, like a distribution of retirement at wealth? What's providing the best retirement income? What's giving you the least chance of running out of money in retirement? How large is the bequest that you're actually able to give? We do that as kind of support of why our investors are choosing this particular portfolio.
Ben Felix: You mentioned all equities internationally diversified. Can you talk more specifically about what the optimal base case portfolio looks like?
Scott Cederburg: In our base case, we're going to be looking at fixed-weight strategies where people are going to just invest and hold those same portfolio weights through their entire life rebalancing. And the optimal is 33% domestic stocks and 67% international stocks, 0% bonds, 0% bills. We kind of do some sensitivity analysis to the exact mix of domestic versus international. The utility is relatively flat over a fairly wide range there. There's not huge differences between, if you want to be, say, 15% domestic and 85% international. Or maybe you're a US investor and you feel more comfortable at 50/50 or like 60/40 US international, something close to market weights, that's not going to be really bad deviations for you. Versus adding on bonds and bills, the investors get fairly grumpy fairly quickly when you do that.
Ben Felix: Where are the limits on that? If someone wanted to have 2% domestic, does it start to matter at some point?
Scott Cederburg: On that end of the spectrum, it doesn't matter a ton. 2% isn't going to kill you, according to the analysis anyway. 100% domestic is a bit of a problem. 80%, 90%, 100% domestic, that's when the utility losses really kick in.
Mark McGrath: How did you arrive at the optimal base case strategy?
Scott Cederburg: We're optimizing expected utility, and we just use a brute force grid search algorithm where you effectively just calculate the expected utility at every single combination of weights and then figure out which combination gives you the best, which set of weights gives you the highest utility.
Ben Felix: That's a lot of portfolios.
Scott Cederburg: Yeah, we've used some processor time on this paper.
Ben Felix: How does the optimal base case that you just described, how does that perform relative to the 60/40 benchmark and the target date fund benchmarks that you use?
Scott Cederburg: One way of summarizing this, we have in the base case, our couples are going to save 10% of their income throughout their working years. And we can calculate something that we call an equivalent savings rate, where if you had a different strategy, how much would you need to save with that strategy in order to get the same expected utility, the same overall well-being as we have with just the 10% savings rate with the optimal strategy?
The 60/40 strategy, 60% domestic stocks, 40% bonds, this is also a fixed-weight strategy. And so by definition, the optimal strategy is going to be better than this one. And we find that it's significantly better. You would actually have to save 19.1% during your working years to get the same utility as 10% with the optimal strategy. You almost have to save twice as much. Versus the TDF, there's actually a chance that the TDF can beat the optimal strategy because the optimal strategy is restricted to fixed weights. And the TDF, we're building on theory to say, "Hey, there should be this age-based approach that you're going to back off stocks as you get older." But what we find is that it's really underperforming. I think you have to save 61% more. It's like an equivalent savings rate of 16.1% in the TDF to get as much expected utility as just going 100% stocks. I mean, if you think about having to save an extra 6% to your income every year for your entire life, it's a pretty large economic magnitude, I think.
Ben Felix: I really like that metric, how much more you'd have to save, because it works with the utility, but then it's super intuitive for someone that maybe he doesn't even understand utility. Like what you just said, you have to save 6% more of your income to get the same expected outcome. I think that's such a nice way to do it.
Scott Cederburg: Thanks.
Mark McGrath: People will say it's sort of obvious that 100% equity portfolio is going to outperform a portfolio that's not 100% equity over the long run. How does the optimal strategy perform relative to the benchmarks in the worst simulated outcomes?
Scott Cederburg: If we're thinking about wealth accumulation, it's like, yeah, pick the highest expected return asset. It's really no surprise that, on average, you're going to have more money at retirement if you're 100% equity than if you're anything below 100% equity. That's pretty obvious. What's interesting, I think, again, talking about things in real terms, once you started getting into it, the all equity strategy is safer than something like a TDF. Even the distribution of wealth at retirement, all the percentiles are better. It's not only that the average is better, the median is better, or the right tail of good outcomes are better. It's the first percentile. The way left tail is better with the all-stock strategy than it is with the TDF.
And so you're just getting a better distribution of potential outcomes with stocks. Then this extends into retirement. The thing that people are going to be scared to death about is being 100% stocks in retirement. But if you look at the metrics, if you're actually measuring things based on retiree outcomes like the consumption that we should be caring about, then the stock strategy is still safer. The TDF, we're using the 4% rule for retirement withdrawals. 4% rule, if you have $1 million when you retire, you would initially withdraw $40,000 that year, and then inflation adjusted $40,000 each year throughout retirement.
And so just kind of as a simple rule of thumb, with the 4% rule, there's some chance that you're going to run out of money, though. You have a string of poor performance, or you live for long enough, you run out of money. And the TDF, your odds of running out of money are almost 20%. With the all-stock strategy, it's like 7%. We can delve into that a little bit more, but it's really two main things.
The couples who live a long time, if you live for another 40 years after retiring and you're 83% in fixed income, it's just going to be really tough to generate enough additional wealth to make it that far. And then the other possibility is that you hit an inflationary period in retirement. And even if we look recently, like 2021, 2022 in the US, 10-year treasuries over that two-year period in real terms lost 30%. If that's where all your wealth is and you lose 30% in a year. And then bonds don't bounce back like stocks do. If stocks go down by 30%, keep on holding, then there's at least a better than even chance that they're going to kind of bounce back over the next few years. But with bonds, that's just kind of gone.
We can even say what happens if stock returns during your retirement period are bad? And it's still better to be in the all-equity strategy with the international diversification than it is to be in the TDF. Because of stocks due poorly over a long period, bonds also tend to do poorly over those same periods. No matter how we split it, we can't find a spot where it looks like stocks are significantly riskier than bonds. What's really surprising, I think, about the results is the degree to which stocks, 100% equity portfolio, is actually better at capital preservation and not just that wealth accumulation part.
Ben Felix: The base case portfolio, as you mentioned, has this fixed allocation. One of the things you look at in the most recent draft of the paper is how the optimal allocation changes when you let the household vary their portfolio weights through time. Can you explain how you're doing that optimization and what the result looks like?
Scott Cederburg: We're letting the couple choose a different set of weights at every age. They can invest one way at age 35 and a different way at age 75. The optimization is a little bit tricky because your optimal portfolio weights at age 35 depend on what you think you're going to do at age 75 or how you're going to invest at age 75, and your weights at age 75 depend on how you invested at age 35. And so you kind of have to find the jointly optimal set of weights that maximizes the overall retirement utility, but that every decision at every age is consistent with all the other decisions that you make throughout your entire life.
And so we're doing this iterative optimization approach where we start it and say, "Oh, you're going to do this strategy," and then we just keep on in every step. We look at each particular age. But if we're looking at age 36, we're going to tell that 36-year-old, "Well, here's your optimal strategy at all the other ages. And then what do you want to do at age 36?" You just have to kind of iterate through until it converges to an optimal solution.
When we do that, it ends up being largely similar to our fixed-weight approach. You're 99% in equity on average across all the ages, and then 1% in bonds and bills. And if you look across time, basically, up to retirement, it's 100% equity. There's a little blip around retirement. At age 65, the investor puts 27% in bills and then mixes the rest of it in domestic and international stocks. But it's relatively short-lived. I think by 68, they're back over 90% in stocks. And basically by age 70, they're basically 100% stocks for the remainder of their life. It's just kind of this short -lived blip of getting some money off the table right around the retirement period is kind of the only difference between our full-life fixed-weight design and then this age-based design.
Ben Felix: That's a big deal, though, man. From a financial planner's perspective, the difference between having a client 100% in stocks forever, the difference between that and somebody who's going to be 27% in bills at retirement and then holding bills till age 70. This is no joke. If we're talking to a client, that's a very significant difference. That's a super interesting finding.
Mark McGrath: How significant were the gains or the benefits from the optimal time-varying strategy that you just described?
Scott Cederburg: If we go back to this kind of equivalent savings rate, we have a 10% savings rate with the optimal fixed-weight strategy. If you do this age-based strategy, you can reduce your savings all the way down to 9.93%. For every $1,000 you're going to save, you can buy a cup of coffee at Starbucks with the amount that you can reduce your savings by. It's a relatively low economic significance.
Ben Felix: That's interesting in two different ways. Because it's interesting that it doesn't change things much, but it's also interesting that if somebody really wanted to hold cash really in retirement because it made them feel better, it doesn't have necessarily a huge detrimental effect, it doesn't sound like.
Scott Cederburg: They are picking this as the optimum. And so it is increasing their utility by holding that cash there. But for us, it was a reassuring result where it's very difficult. In this setting, given that we have the bootstrap, we can't do some of the traditional methods of dynamic optimization. We went through and looked at different elements of, "Hey, what if we let them choose an optimal retirement age, for example, or different things like that?" just to see whether we had sensitivity, basically, to – if we have static optimization as our base case, how bad of a base case is that, effectively? Everywhere we look, it's like, "Oh, it's not that bad." The fixed-weight strategy is so close to this age-based strategy, for example. It makes that initial analysis valid in some sense.
Ben Felix: How does this time-varying optimal portfolio, how do those allocations change when you abandon the block bootstrap and just assume that returns are independent and identically distributed?
Scott Cederburg: It definitely becomes a bigger role for bonds and bills in retirement. They're still choosing all-equity up to retirement. And I believe in those specifications with the IID kind of ignoring the long-term return properties, I think they get back to all equity in late retirement, 90 years old or something like this. They're kind of back to the all equity strategy.
Ben Felix: Interesting. It's equities adding bonds at retirement and then decreasing bonds slowly back to 100% equity later on?
Scott Cederburg: Yup.
Ben Felix: Interesting.
Mark McGrath: How does that change if only domestic assets are allowed?
Scott Cederburg: Just looking at effectively excluding international stocks from the analysis, if we want to diversify away from domestic stocks, now we have to go to fixed income. That also increases the role for bonds and bills. In those analyses, you have some fixed income allocation throughout your entire retirement. The working years, we're still seeing 100% equity even with just access to domestic stocks. But once retirement hits, you're always going to have some portion in fixed income.
And if you combine these two things and imagine that you're looking domestic stocks, bonds and bills, and then you're also going to say IID, and this is a little bit similar to the setup of a lot of academic papers anyway, you have pretty sizable fixed income exposure throughout retirement at that point. So at age 65, for example, you go from your working years, you're 100% equity, and then at age 65, you switch to 60% in bonds and bills and just 40% in equity. That really swings the analysis quite a bit.
Ben Felix: It takes you back to the status quo, I guess?
Scott Cederburg: In some sense, it's like, yes, our results are sensitive to this block bootstrap assumption and the assumption of putting international stocks in, but I have access to international stocks. And we know that returns aren't IID. I feel like those are pretty easy assumptions to get behind.
Ben Felix: Yeah, it's sensitive to the assumptions. But if they're the right assumptions, then people should be sensitive to them. We had the time-bearing optimal portfolio that loads up on bills for 27% at retirement. And that was with the 4% constant spending. If they're spending $40,000 in the first year, if they have $1,000 ,000 and then adjusting that for inflation every year, how does the optimal portfolio change when you switch from the constant spending to a proportional spending strategy?
Scott Cederburg: We're using 4% of wealth. But if you just spend 4% of your current wealth at all times, it's going to fluctuate your consumption around a lot. But your optimal strategy at that point is 100% equity for your entire life and it's almost completely flat in terms of the domestic international allocation. It's nearly identical to our fixed-weight optimal strategy. The blip is gone.
Mark McGrath: What is the interaction between that, the spending strategy and the optimal portfolio? What does that say about sequence of returns risk?
Scott Cederburg: 4% rule is kind of as exposed to sequence of return risk as you can potentially be. I think the entirety of that blip where you're getting money into bills for the beginning of your retirement is just to reduce your exposure to that sequence of returns risk. You're trying to make a sudden drop in stocks less damaging to your full retirement. I think that's driving the entire allocation to fixed income in the base case.
Mark McGrath: Michael Kitces had an article out a number of years ago, about a bond tent, and it sounds like that's kind of it, which just basically play defence for a couple of years in case you get really, really unlucky. But then the kind of glide path resumes back to 100% equity. Sequence of returns risk, if I've understood you correctly, it's largely solvable by variable withdrawals.
Scott Cederburg: There's a range of hybrid things that people have done where you try not to have the extraordinary volatility if your portfolio goes up 30%, you withdraw 30% more. But you also don't have such a rigid rule as is implied by the 4% rule. Presumably, there's a degree to which sequence of returns risk exists in things that are closer to the 4% rule, and it's probably going to be very muted in the things that are closest to the totally variable rule.
Ben Felix: How do the optimal portfolio allocations change when you allow the couple to condition their investment strategy on the domestic stock valuations on the price-to-dividend ratio?
Scott Cederburg: It's pretty common in this literature to think about time-varying expected returns and how would market conditions affect things. Our approach to it in the simulations is to basically give the couple information every month about, is the valuation higher or low currently in the market that they're investing in. And we break it up into quintiles of the price dividend ratio, like the domestic price dividend ratio. The lowest quintile with the low prices is roughly less than 20 for a price dividend ratio and then the highest is roughly greater than 50 for a price dividend ratio. The US right now is in the highest valuation bucket. I think a lot of the rest of the world is not right now.
In the middle three buckets, like the middle three quintiles, we get all equity strategy that's pretty close to the unconditional base case, 33%, 67%. It's really on these two ends. If we look at the lowest valuation bucket, domestic stock prices are low. The couple chooses to do 65%, domestic, 35% international. Basically, buy the cheap stuff locally and just reduce international allocation.
In the highest bucket, I believe the number is it's 75% international. You're really upping your investment internationally. And then it's 16% domestic stocks and 9% bonds. That's where the bonds finally sneak in. We see a little bit of bonds. If your domestic stocks are very highly valued, you get this modest allocation to bonds.
Ben Felix: That kind of speaks to some of the criticism from the first draft of writing this paper, when US stock valuations are as high as they are, it doesn't make any sense. But you kind of addressed that now. Do you think that this analysis also addresses the idea that expected stock returns are just generally a bit lower now than they may have been in the distant past because markets have gotten safer or whatever?
Scott Cederburg: To the extent that the price dividend ratios now are directly comparable to what they have been. I mean, obviously we've had some shifts away from dividends, tortury purchases and things like that. If we had all the data, we could probably turn it into like a payout ratio sort of thing. But I think it's probably the case that we're going to hang out a little bit more in the top three quintiles than in the bottom three quintiles or at least hopefully to some extent. Getting to that lowest quintile is not good times. Post-financial crisis type of stuff was probably getting towards that lowest quintile in some of the countries.
Mark McGrath: When you offer this conditioning based on valuations, how significant were the gains for the optimal portfolio?
Scott Cederburg: If we go back to the optimal savings rate, if we have 10% saved in the fixed weight strategy, we've now given the couple more latitude to optimize. It's going to be better. And so they can get down to about 9.7% savings. They get a decent gain, I think, out of that. We do some additional analysis just on, is it the bonds that are coming in and saving it? Or is it that domestic versus international allocation? And about 80% of the gain comes from switching across domestic and international? Basically, in those two extreme states, betting a lot on domestic when prices are low, getting the heck out of domestic when prices are high, that's where about 80% of that economic gain is from.
Ben Felix: What's the advice here, I guess? Should people actually be conditioning their domestic allocations on domestic valuations?
Scott Cederburg: I'm right now about 50/50 US international. I guess I just haven't really changed since our first draft that had a 50/50 rule of thumb. That means I'm underweight the US relative to market weights. I think I'm perfectly comfortable being underweight in the US given US prices versus European prices right now. On the other hand, you look at all the academic evidence and institutional performance management around trying to time the market. It's not easy to do.
Ben Felix: You've sorted valuations into quintiles based on the full set of available information?
Scott Cederburg: Yeah.
Mark McGrath: But any investor today does not have the full set of available information. They have past valuations. They don't have future valuations. Your investors have past and future valuations. Is that right?
Scott Cederburg: At any given time, we're just telling the investor, "This is your price dividend ratio right now." It will end up kind of mattering how you're investing at age 75. And the utility that you're getting does depend on the wealth that you built up over time. It depends on your strategy performance and such up to that point. But I don't think we have a pure look ahead bias necessarily in terms of we don't tell the investors that prices are going to get higher than they currently are.
Ben Felix: We're just trying to think through that. If the valuations are organized into quintiles, they don't know which quintile they're in?
Scott Cederburg: They know which quintile they're in. We're letting them optimize their asset allocation within that quintile. If they're in that bucket, this is what they're choosing. They also know if in other years they fall in one of the other quintiles, they know what their strategy would be if they move from quintile 3 to quintile 5 and get into high price territory. They know that they're going to back away the domestic stocks a little bit. We do the joint optimization across the five strategies. They know how they will dynamically react, but they don't know what the future is going to look like.
Ben Felix: That's a cool piece of analysis. One of the other things that I've gotten kind of pushback on when I say that your methodology with the bootstrap makes a lot of sense is that some random small country that gets pulled into the bootstrap to represent a domestic country like Canada or the US, that it just doesn't make sense. How important is the inclusion of small countries or countries with small stock markets to the main results in the paper?
Scott Cederburg: I guess we've heard this before, too. We had a reader pretty recently that seemed pretty offended about Iceland being in the sample. One of the things that we've done, we've looked at, say, just include large population countries as one way of splitting on this. And we've looked at .2% of the world and .5% of the world. And so for context, Canada is exactly .5% of the world. It's basically Canada and bigger countries.
And if we just throw out all the smaller countries than that and redo the analysis, we'd get 27% domestic, 73% international, 0% bonds, 0% bills. And some of the narrative around this too is, well, of course, somebody from a small country is going to want to get most of their money in international. The numbers, if we just look at the analysis, it actually is going the opposite direction where it's like the larger the countries, they're actually trying to do more international. That sort of narrative doesn't really hold up in the data.
The other thing that we've done, there are differences across countries and how important the stock market is or the breadth of industries in the stock market. We can condition on the stock market capitalization being at least half of GDP in a country. The US actually doesn't hit that until the 1990s. It's a fairly stringent thing. And I think these screens do the things that we're trying to do if we look at which countries are in the sample for which times. And that's also 27% domestic, 73% international, 0% bonds, 0% bills. We've tried a lot of stuff and people seem to think just this little tweak of the data and everything's going to fall apart, but it just doesn't seem to fall apart.
Mark McGrath: What happens if you take out Germany?
Scott Cederburg: Germany is another one of these little stories. Germany has hyperinflation following World War I. 1920 to 1923. 1923 in particular, bond returns look weird. There was, whatever it was, trillion percent inflation or something like this. Summary stats on Germany look weird. And it makes our overall sample summary stats. If you did a standard deviation, it makes bonds look risky because we had really extreme returns in a couple of months in Germany.
I kind of had the stance, it's obviously not one out of the 2,650 years’ worth of data driving our thing. And Ben was like, "Well, I've heard it said by a lot of people. So you might as well just run it." Went ahead and ran it, and it's 34% domestic, 66% international, 0% bond, 0% bills. If we just throw out all the data from Germany through the entire sample, just urge it from the sample.
Mark McGrath: Virtually no change.
Scott Cederburg: Yeah.
Ben Felix: Yeah, that's crazy. If you just change this one thing, I bet you the results will change. Pretty funny that it doesn't. Not funny. It's like fascinating. Also, funny though, because people are so sure this is going to change the result. What about all pre-World War II data?
Scott Cederburg: The pre-World War II, there's two concerns. One, we have some data from 1890, and is that comparable to today? And then the second, people seem to have think that war risk has gone away. Apparently, they're a little more optimistic than I am. But we can just drop everything World War II and before. I think it's 31% domestic, 69% international, 0% bonds, 0% bills. It's just the same thing.
Ben Felix: Crazy.
Mark McGrath: Nothing changes virtually.
Scott Cederburg: Yeah. The big thing in terms of sample period is you need to have a long enough sample period where you're including bond market cycles. Interest rates go up, interest rates go down. Interest rates after World War II are roughly what interest rates are now. And we've had a couple of different interest rate cycles where interest rates go up, interest rates go down. If you were to say start the sample in 1980 when all the bond yields are at, whatever, 15% to 20%, bonds had good returns in the 40 years following 1980 because you get this enormous capital gain from yields falling from 15% to 5%. And so that's the data that a lot of people are used to looking at on bonds. Well, the '80s was a good decade. The '90s was a good decade. The 2000s was a good decade. The 2010s was a good decade. Well, the 1970s were terrible, and the 2020s have been terrible. If you're including a full bond market cycle, you have enough of the terrible bond stuff going on. We just can't get the same bond performance as we had since 1980. If we're starting at 4% now, we have to go to negative 11% or something to get that same set of capital gains.
Mark McGrath: For international stock portfolios, how important is the inclusion of the US market? If my domestic market is not the US and I'm outside the US, how important is the US inclusion in the international component for those investors?
Scott Cederburg: This might be about the biggest change that we saw on any of them. Obviously, the US has been a big part of the international portfolio for quite a while and has had that good performance. If you completely exclude the US from the entire analysis, you get 45% domestic, 55% international, 0% bonds, 0% bills. International stocks don't become so bad that you're going to go to bonds. You still want to diversify with international stocks, but instead of the base being like 33% domestic, it's like 45% domestic. If you just take out the exposed winner of stocks over our sample, if you take that out, then the international stocks don't look quite as rosy, but they're still preferred bonds.
Ben Felix: It's still crazy though, because that's another one where people are like, "Well, of course, international stocks look good when you're including US and international." That's true to an extent, but it's not that sensitive to that.
Scott Cederburg: Yeah, it's kind of eye of the beholder, whether the 45, 55 result is very different from our base case or whether it's the same thing. Because in some sense, it's kind of the same thing. It's a different allocation, but it's 100% equity with a lean towards international.
Ben Felix: You talked earlier about how the utility is fairly flat within a pretty big range. It doesn't sound like this is a huge deviation from that. Another one that comes up a lot when I've talked about any of your research, when I make a video about it, there's certain parts of the internet that get extremely upset with me because they think that the US is special. I hear that all the time. And therefore, treating it like every other domestic country, the way that you do in your sample, is a mistake. How do your data change if the US is in fact special?
Scott Cederburg: There's certainly a view that the US is special and that the US being special is going to manifest in the US continuing to have high returns. The way that we can try to model this is we have – on the one end of the spectrum, we're not treating the US any differently, and that's our base case where we just rode in there with all the other developed countries. We're going to view this as a 0% view on the US being special in this particular way. And so that's our base case analysis, 33% domestic, 67% international.
On the other extreme, the US is special. 100% guaranteed. And future returns in the US are going to look like past returns in the US. Then we just use 100% the US sample to do the analysis. If you run that through, you get 100% domestic, 0% international, 0% bonds, 0% bills. You just throw it all in US stocks and you're good to go. Then what we can do in the middle of these two is basically mix the two. If you think about running a million simulations, you can run it where 90% of the simulations come from the US and 10% come from our full developed sample. We're giving you a 90% belief at that point that the US is just going to be special and earn higher returns than the rest of the world. If you do that, you're already backing off just a little bit on the 100%. You're at like 96% domestic, 4% international.
Then as you go, if it's 50/50 on whether the US is special or not, then it's 60% US and 40% international. That's about the market weights right now, the world market weights. In order to have like a home bias, as a US investor to have a home bias, you have to have more than a 50% belief that the US is going to continue to earn higher returns than the rest of the world effectively, which there are certainly people who have more than a 50% belief that this is true just from casual observation of things on the Internet and conversations with various people.
Ben Felix: I know you didn't run it, but could you do the same thing for like Canada? Up until 2009, Canada and the US were pretty close. If we made a Canada special case, would it have a similar effect do you think or Australia?
Scott Cederburg: I would guess so. We haven't run it country by country. It's potentially something to do to just see how much variation there is across those things. I think to say that that means more to countries or to investors in that particular type of country, I think we would tend to argue against getting too granular in that. Yes, this country got unlucky, but is it a country that just gets unlucky, or did it just get unlucky?
Ben Felix: You said earlier that people have to believe that the US is special, and that's going to manifest as higher future returns. How else could that manifest?
Scott Cederburg: If the US has structural advantages, and people will talk about innovation and different institutions and all this stuff, an alternative is that we just have higher prices and, if anything, lower risk premiums, so lower future expected returns. That would be consistent with – there's evidence by Fama and French and Avdis and Wachter that a lot of the couple percent of the historical US average return was just the increase in valuations that we had. It’s possible there's a paper that's now forthcoming at the Journal of Finance by Binsbergen, Hua, Peeters, and Wachter in their model. We have a theoretical model. Their investors are learning about the probability of crashes, essentially, like disasters in each country. Over the sample, they become convinced that the US is different from many of the other countries.
But now, those investors would just price the US higher and have a lower risk premium because it's not as risky. The investors in their model would believe that the US is special, but they believe that that warrants a higher price and lower returns because of the higher price. That seems like an easier equilibrium argument to make to say that all the institutional investors in the US think that the US is special, and they're all overweighting the US. Then that doesn't have an impact on the valuations that's going to hurt future performance. I think the rationale for the US is always going to earn higher returns is just pretty tough to figure out how that's going to work.
Ben Felix: It's like the opposite of what people think. People think that it's special. Therefore, it'll have high returns. But in reality, it may be special and therefore have lower returns because it's a safer, higher quality market, which is true. But that doesn't mean it's going to have higher future returns.
Mark McGrath: I got it from you, Ben, I think a while back or from maybe one of your guests. But, yes, if it's the biggest safest market in the world, why would you expect higher returns from that? How important are the relatively low historical correlations between domestic and international stocks? How important is that to the performance of the optimal portfolio?
Scott Cederburg: We've seen the domestic international stock correlation vary across time. It's gone up. It's gone down. It's gone back up. It's relatively high right now. If you look over shorter periods, and I haven't done this super formally, but it tends to be the case. If you're looking at the US correlation with international stuff, it tends to be pretty high most of the time, and then there are just these little periods where it's zero percent correlation or negative correlation for just a short period of time. Then it kind of goes back up to very high correlations. It'll be interesting to see whether we're just in a high-correlation regime now, and it's less likely that we do that kind of switch. Or it's just one of those that hadn't happened in a little while.
But one of the things that we can do, we do this split where you take your retirement periods. I think we focused on retirement periods. But you take the retirement periods, and you can split that into quintiles based on the realization throughout your retirement of how high is that correlation between domestic and international. Then you can look at the low-correlation regime versus the high-correlation regime. The stock strategy of the strategies that we consider, it's still the best strategy across all five buckets. One of the things that we see is that we're looking specifically at the probability that you run out of money in retirement. In that high correlation bucket, so this is very high correlation across all world markets, all of the strategies have very low ruin probabilities.
In the low correlation, we see much more spread. Ours is the least sensitive to the correlation, but some of the other strategies get really bad when the correlations are low. My guess is that the correlation across markets is some sort of proxy for whether it's worldwide macro stuff or whether it's war stuff or whether it's trade stuff. There's all kinds of things that could be going on to kind of drive wedges between different markets in the world. But I think most of those wedges are probably bad wedges. There may be a degree to which high correlation is going to hurt the diversification benefit of domestic stocks versus international stocks, but that may be the state of the world where there's not as bad of a set of risks.
Then in the times when the world is a little more risk laden, there's going to tend to be lower correlation, and you get more of the diversification across international markets. It's a little tough to exactly tease that out on what's driving that result, but that's kind of my sense.
Ben Felix: Those are the two probably most intelligent pushbacks that I've seen against your paper. Current valuations are higher than a lot of the sample. Therefore, it's not valid or correlations. Valuations, correlations, you've addressed both of them, I think, pretty well in this version. What about labor income? How does an increase in correlation between labor income and domestic stock returns affect the optimal portfolio?
Scott Cederburg: There's a lot of disagreement in the literature on exactly the extent of this correlation. We've had everything from – some of the older literature was basically saying that there would be effectively zero correlation between labor income and stock returns. There's others that depending on how you're splitting workers on education levels, income levels, things like this, there's a set of workers. Probably realistically the most likely retirement savers are probably on the higher end, 0.3 correlation or something like this between the labor and the stock market.
We look at a range of everything zero percent in the base case but everything up to 0.5 percent. Basically, you do that. The investors are going to get away from domestic stocks a little bit because they're already exposed to that correlated risk with their labor income. They never run to bonds. They just put more internationally and diversify a little bit more that way. Effectively, their labor income becomes a little bit domestic stock-like. They already have a bit of that exposure, and so then they just go more towards international stocks. But the pattern turns out to be reduce the weight in domestic stocks by three percent for every 0.1 of correlation.
Mark McGrath: Your paper talks a lot about leverage as well, so I'm going to switch gears a little bit and talk about leverage. The base case has a no-leverage constraint. How do the optimal portfolio results change when you allow for leverage?
Scott Cederburg: We've kept no leverage as a base case because outside of some of your listeners, I don't know a lot of people who are levering up their retirement savings within the actual retirement accounts. You're typically restricted from doing a lot of this stuff, so we're kind of trying to write to just the average person who's picking a default fund in their retirement account and probably isn't trading futures or anything.
But if we do introduce leverage, it tends to be the case. Depending on risk aversion and depending on how expensive the leverage is, we do see our investors wanting to take on some leverage. One of the issues around leverage is figuring out what's the cost of leverage. We do three different approaches. One's like very high cost of leverage. But I have an E-Trade account after about 15 different mergers or something like that. I looked it up yesterday, and they would charge me, I think, 12% for margin. There’s that on the one extreme. We have a middle ground of 1.4%. That's the lowest margin rates that we could see.
Then if you go into derivatives markets, there's a paper by Binsbergen, Diamond, and Grotteria. They estimate the risk-free rates that are implicit in futures contracts. What's your implicit borrowing cost if you're trading in futures? That's about 0.37 percent above treasury bills. That's the lowest spread that we consider. We talked to another large asset manager in Europe about this, and we're asking them what their clients do. They're talking about like the Lombard loan market. Then we asked the question, what happens around financial crisis or something? They're like, “Yes, that market dries up, and you can't borrow.” We're kind of assuming that away and just saying, “Hey, regardless of the market, you're not going to have to reverse out of your leverage at the worst possible time.” I think we're given pretty favorable conditions, at least at the lowest leverage cost level. I think it's pretty favorable conditions, giving leverage the benefit of the doubt.
Ben Felix: How important is the cost of leverage to the optimal use of leverage and the optimal levered portfolio when you model it out?
Scott Cederburg: It's very sensitive. Nobody wants to pay 12% margin rates. That couple is zero percent leverage, and the no leverage constraint is not binding, so they pick the same optimal portfolio as in the base case. At the medium 1.4% spread above treasuries, that's again the lowest margin rate that you're going to be able to get on your own. They choose 55% leverage, and they invest 34% domestic, 66% international, 0% bonds, 0% bills. It's effectively the exact same portfolio just leveraged up. At the very low cost of leverage, like the 37 basis points, they do 100% leverage. We do cap them out at 100% leverage. They do 100% leverage. I think that one is 15% in bonds at that point. The rest is split across domestic and international stocks in about the proportion that you would assume. But at 100% leverage, they are finally going to start getting some bonds in there.
Mark McGrath: With some of these products that are available out there, there's leverage inside the product itself. You're going to have to pay a fee on top of the borrowing costs for that. How do you think the product fee for a fund using leverage should be accounted for in the total cost of leverage?
Scott Cederburg: One of these funds, they're actually going to be able to access something like this 37 basis point spread. If they're using futures or other ways of borrowing, they're probably within the fund being able to do that. So then there becomes this issue of management fee, plus borrowing cost. I think a good comparison is I can be unlevered in a passive fund for two basis points. So then what's it cost me to lever?
As soon as you're doing leverage, now you have to have active management. The leveraged ETFs do daily rebalancing. If you're going to maintain a specific leverage level, you have to trade every day. You're going to have to pay somebody to do this. I don't think anybody's doing this on their own. If it costs me one percent to invest in that and then 37 basis points within the fund for leverage, that's 1.37%. Our middle case is 1.4%. I think it's effectively getting us to about the same place.
Ben Felix: In that middle case, it was 55% leverage or 155% exposure to the same optimal portfolio as the base case. Does that suggest that, at least based on that analysis, people should be optimally using some leverage in their portfolios?
Scott Cederburg: I mean, if they have access to borrowing cost, then I think this is going to depend on risk aversion to the medium borrowing cost. If you have low risk aversion, you're still 100% equity in there. It just depends. I don't think I am personally going to go out and start levering up. But if somebody has the risk tolerance for it, then I suppose our data are suggesting that there is a strong enough return reward for taking on the risk that you're not crazy for doing it.
Ben Felix: It's a dangerous thing to say. We once did an episode years ago on leverage and talking about how a lot of models suggest that it is optimal, particularly for younger investors. Man, people went pretty crazy over it, for lack of a better word. All of a sudden, everybody that listened to our stuff wanted to use leverage, and we're like, "Whoa, we weren't necessarily saying that you should do that."
Scott Cederburg: I think this is one of those things. We all have some prior beliefs on things. I guess I have a pretty strong prior that I should not be levering up my retirement savings, and that's going to be strong enough to outweigh any of this other evidence. Then I do think, coming back to this unmodelled aspect of it where what happens if your leverage channel dries up in the financial crisis, I mean, that's what happened in the financial crisis to everybody running these leverage strategies on mortgage-backed stuff. This is when credit disappears.
If you have to unwind your two times levered equity position in whatever, late 2008 or early 2009, then you miss out on the bounce back, perhaps as another argument for maybe don't take that part quite so literally. I think that is a risk, and that seems to be a risk that large institutions are internalizing that risk when they're doing arbitrage strategies and things like that, that their liquidity dries up, and they have to get out at the wrong time. I think levered investors are going to face that same potential issue.
Ben Felix: We had talked years ago to an asset manager who was building concentrated portfolios to try and get access to higher expected returns. Their reasoning was that leverage in bad times really, really sucks. If you have to choose how to get higher expected returns, you're better off concentrating in higher expected return assets than you are levering up lower expected return assets for the exact reason that you just said. Knowing that that is an unmodelled risk to get to that result is a pretty important piece of information for people listening.
Mark McGrath: Good point. Okay, so we're talking about this optimal levered strategy, the middle case. I think you said the spread was 1.4% above treasuries. In that scenario, how significant were the gains of that optimal levered portfolio versus the optimal unlevered portfolio?
Scott Cederburg: I don't think we've run that number specifically. I was kind of eyeballing the expected utility, and I've got a pretty good sense for these things. I think it would turn out to be around 8.8% or so for an equivalent savings rate. I think they're perceiving an economically significant gain from this, but subject to the caveats that we just went through.
Ben Felix: What about levering up a 60/40 portfolio? How would that compare to levering up the optimal levered portfolio?
Scott Cederburg: A common argument is that you shouldn't be 100% equity. You should do the 60/40 and get leverage. Comparing the 55% leverage with all equity and the 55% leverage with 60/40, the 60/40 strategy, you have to save almost 25% to match the utility of 10% in the other one. There's a very large difference.
Mark McGrath: From there, how does the levered 60/40 portfolio compare to the base case unlevered optimal portfolio?
Scott Cederburg: This is the trade-off between being just 100% equity or using the 60/40 and getting leverage to try and take advantage of whatever diversification benefits you get with bonds. But when we run that, it's relative to 10% in the base all-equity strategy. With no leverage, you have to save 19% in this leveraged 60/40 strategy. It’s a little bit counterintuitive. Once you lever up the 60/40, you actually hold almost 100% of your wealth in stocks, and then you own bonds on top of it. It's the rebalancing where throughout your entire life, stocks are giving you these gains, and you keep on taking these gains, and you just keep on throwing them into bonds. Then the bonds aren't doing anything for you.
If you were to run just like a no rebalancing, that would just get you back to an equity-dominated portfolio pretty quickly. Then that would have a much lower, I guess, equivalent savings rate. But that's not what the 60/40 strategy is. The 60/40 strategy is, yes, you got to get away from expensive stocks and into the bonds and everything. Our investors just really don't like the prospect of having 40% invested in bonds.
Ben Felix: Yes, that's a crazy result because like you said a minute ago, Scott, that's what people say. You shouldn't be 100% in stocks. Instead, you should lever up a 60-40 portfolio to get to the same expected return level with more diversification, but your findings kind of show maybe not. What do you think that specific finding says about mean variants, traditional mean variants, annualized monthly return type thinking, where you do want to lever up to the maximum Sharpe ratio?
Scott Cederburg: Sharpe ratio has a nice grounding in historical finance and everything, but I think you were talking to Hank Bessembinder about similar issues recently. He's also thinking about long-term returns. By the time you get skewness in there and everything like that, it's like, well, Sharpe ratio is not necessarily telling you the whole story. One way of thinking about it is there's a couple of ways to get into CAPM world, mean-variance world. One is to have mean-variance preferences. Markovitz started us off there.
But another way to get into mean-variance world is to have normally distributed returns because with a normal distribution, the mean and variance are the only thing. There's no skewness. There's no excess kurtosis. It's only mean and variance. In that sense, picking the best set of mean and standard deviation that gets you the best distribution. Those two things define the distribution, and it gets you to the best distribution. The best Sharpe ratio is the best normal distribution for investing.
If we were thinking about our stuff, now we're thinking about long-term return distributions. In some sense, our investors are still just looking for the best distribution. It's just the Sharpe ratio is not going to define what the best distribution of returns. Even our retirement wealth, that's after 40 years of investing, so there's going to be huge skewness. A Sharpe ratio penalizes the good outcomes on the right tail. Just as much as it does the bad outcomes on the left tail, it just treats things symmetrically. A Sharpe ratio doesn't really apply very well over longer horizons, and so I think recognizing that people have tended to apply Sharpe ratios to monthly return moments.
But that gives you back to this problem where at a short horizon, bonds look like they're diversifying you a lot. Then over long horizons, they're really not. That's just very tough to reflect in a Sharpe ratio framework.
Mark McGrath: The results throughout the paper, how sensitive are they to risk aversion?
Scott Cederburg: The headline results are not that sensitive. So our investors are going to be optimizing utility, and utility considers the whole range of outcomes, and utility actually really penalizes bad outcomes quite a lot relative to like what a Sharpe ratio would. But they're just looking for the best distribution and the stocks. The all equity portfolio just has the best distribution. It’s not like, “Oh, we're doing this tradeoff between the upside potential and the downside safety.” If it's winning on both, you're just going to get that same result for every set of investors that look at it. They're like, “Yes, that's a better distribution.”
The very risk-averse investors are going to place a ton of weight on that left tail, like the bad outcomes. But they're coming up with the same answer as the very low-risk aversion investors that are like, “Look at all this upside that I can get.” Those two investors are coming to the same decision for different reasons, but they're coming to the same decision. The places that we see risk aversion mattering more as things like leverage. If we start relaxing some of those constraints, you see a little bit more of an effect. But the headline results, the all equity is not really that dependent on risk aversion.
Ben Felix: How has the response been from both academics and practitioners since you released the very first draft of this paper?
Scott Cederburg: I would say that we've had a lot of people very interested. I mean, it is a topic that people are interested in and excited about. We've had a lot of very helpful comments. Nearly everything that we've done is in direct response to somebody's feedback, and the design of some of these things are based on conversations with other professors and Ben. That's been great. On the other hand, it's been a little bit weird where there's been a few folks talking very publicly about the paper with criticisms that we're just not really sure where they're coming from, and it's not clear that they've looked closely at the paper and thought about what we're doing in making some of the criticisms. Ben's been my sanity check on a few of these things as well.
I think people just feel very strongly about this, and they have strong views. We had a recent discussion at a conference that was misreporting numbers that are in the paper to basically try to make the paper look less conceivable or tougher to believe. I think in academia, we're used to arguing about stuff, but it's good to argue about the facts. If you don't like one of my assumptions, that's cool. We can talk about alternative assumptions and everything, but that's where we prefer the conversation to be. Again, we've had lots of good, very helpful people and received unsolicited feedback from John Campbell, which was really cool. We've got lots of really helpful people.
Ben Felix: It is a topic that people – I think this is the right word. They get very emotional about, which is interesting.
Mark McGrath: It kind of flies in the face of a lot of what people intuitively believe. If you think about Ben and I, what we do for a living, maybe just in Canada, but in a lot of places, the sort of glide path portfolio or the 60/40 model, I mean, if you've been doing this for 25 years and you've been putting your clients into that, and then here's this paper that kind of says, "Well, actually, you were wrong," you're probably going to be critical before you actually do the work to do an about face with your clients.
Scott Cederburg: Yes. I think even with professors, when we present this, when you run across the people who are already 100% equity, it’s not trivial, the number. But they all love it because they're like, “You know I was right.” But it just goes back to like everybody already knows that they're right on this thing. It's very difficult to shift the prior beliefs with new evidence.
Mark McGrath: Confirmation bias all the way down. As you've been taking all this feedback and comments and criticism, and kind of refining and improving the paper, has anything about the additional research and findings surprised you?
Scott Cederburg: I think it was just the cumulative effect of just how resilient the results are. We just got to a point where it's like, "We'll run it. We know what it's going to look like, but we'll run it." Okay. They're stopped being surprises pretty early on.
Ben Felix: It is surprising, though, because there's so many things where it's like, "I wonder how different it would look without Germany, or I wonder how different it would look excluding everything before World War II.” I agree that the resilience of the general findings are pretty surprising and valuations, too. All those things, that plausibly could change things quite a bit. Very interesting. What's next for this thing? I know you've been doing conference presentations and stuff like that. Does this go to journals? What happens next?
Scott Cederburg: We always kind of had a long runway with this paper. We felt like we wanted to make sure that we got comments and address all the criticisms and everything like this. We've gotten a ton of feedback. We've made a ton of changes. We're ready to start taking our shots. We'll start submitting to the journals. At the end of the day as academics, the only thing that we get rewarded for is publications and top journals, and so that's what we'll try to do.
Ben Felix: So you just go submit it to top journals and see what happens?
Scott Cederburg: Yes. We just have to get a set of referees and editors that are not particularly grumpy and see how it goes. It's pretty brutal just because of the average rejection rates at these journals are all over 90%, basically. You got to work on a paper for two or three years, and then you have a very limited number of unconditionally small probability things that you're chasing.
Ben Felix: Crazy. Well, I obviously hope that that all goes well. Personally, I'm not an academic or a referee at a top journal, but I think this is really good paper.
Scott Cederburg: Oh, thank you. Cross our fingers.
Ben Felix: Well, Scott, thanks again for coming back in the podcast. I think, like I just said, it's a really cool paper. The way that you guys have addressed all of the feedback and criticism and questions that have come since the first draft means the right way to address it. You went and modelled all of it and showed that it was also pretty resilient to all of the what-ifs. I think that's really cool to see. I think people who are managing their own finances and thinking about this, you've seen the response in the Rational Reminder community. I think your episodes and any discussion related to your paper are some of the biggest topics in the whole community because it's so practically relevant to somebody who's managing their own money. Or for Mark and I who are helping out the people to manage their money, you made a big impact there. It's pretty cool to see the paper continue to get better.
Scott Cederburg: Thank you.
Ben Felix: All right. Thanks everyone for listening.
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https://community.rationalreminder.ca/t/episode-350-scott-cedurburg-a-critical-assessment-of-lifecycle-investment-advice/35942
Papers From Today’s Episode:
‘Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice’ — https://
papers.ssrn.com/sol3/papers.cfm?abstract_id=4590406
‘Is The United States a Lucky Survivor: A Hierarchical Bayesian Approach’ — https://
papers.ssrn.com/sol3/papers.cfm?abstract_id=3689958
‘Risk-Free Interest Rates’ — https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3242836
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Benjamin on LinkedIn — https://www.linkedin.com/in/benjaminwfelix/
Cameron Passmore — https://pwlcapital.com/our-team/
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Cameron on LinkedIn — https://www.linkedin.com/in/cameronpassmore/
Mark McGrath on LinkedIn — https://www.linkedin.com/in/markmcgrathcfp/
Mark McGrath on X — https://x.com/MarkMcGrathCFP
Professor Scott Cederburg — https://eller.arizona.edu/people/scott-cederburg
Professor Scott Cederburg on LinkedIn — https://www.linkedin.com/in/scott-cederburg-0917b0121/
Professor Scott Cederburg on Google Scholar — https://scholar.google.com/citations?user=CZKf3WEAAAAJ
Eller College of Management — https://eller.arizona.edu/
Episode 224: Prof. Scott Cederburg: Long-Horizon Losses in Stocks, Bonds, and Bills — https://rationalreminder.ca/podcast/224
Episode 284: Prof. Scott Cederburg: Challenging the Status Quo on Lifecycle Asset Allocation— https://rationalreminder.ca/podcast/284
Vanguard — https://investor.vanguard.com/
‘The Portfolio Size Effect and Using a Bond Tent to Navigate the Retirement Danger Zone’ —https://www.kitces.com/blog/managing-portfolio-size-effect-with-bond-tent-in-retirement-red-zone/