Scott Cederburg is an Associate Professor of Finance and the Sheafe/Neill/Estes Fellow in Finance at the Eller College of Management, 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, Bloomberg, Forbes, and Consumer Reports, among other outlets.
Are stocks and bonds good in the long game? What are the best long-term investment options? In this episode, we speak to Professor Scott Cederburg about the nuance surrounding the stock market, bonds, and other investment types in the long term. He has a Ph.D. in Finance from the University of Iowa and is currently the Associate Professor of Finance at Eller College of Management at the University of Arizona. His research focuses on the long-horizon performance of a range of asset classes and investment types and has published in high-ranking academic journals, making him the perfect person to speak to about the subject. We discuss the topic through the lens of several papers he has written on stocks, bonds, retirement savings, and return predictability. In our conversation, we unravel the nuance of the returns on long-term stocks and bonds, hear details about his research design, and learn how unanticipated events can affect the market. He also provides insight into the different biases surrounding long-term investments, the block bootstrap approach, reasons why the block bootstrap approach is needed, and why bonds and bills may not be the long-term investment you were hoping for. We also discuss the best options for investors regarding pre-tax and post-tax accounts and the differences between high-beta and low-beta portfolios. He also shares some basic steps for investors to help them protect their investments. Join us as we dig into the past to uncover the financial future with Professor Scott Cederburg.
Key Points From This Episode:
We begin with Professor Cederburg describing his research design for his work investigating long-term returns on stocks and bonds. (0:04:20)
Hear examples of how unanticipated events lead to impacts on stocks and bonds. (0:08:08)
What the overall trend in the data was from his research on stocks and bonds. (0:11:05)
Why considering different biases is essential for financial decision-making. (0:11:45)
How the historical experience in the US stock and bond markets compare to other developed markets. (0:12:45)
Details about the data he collected regarding domestic stocks and investors. (0:13:55)
Learn how probable it is that domestic stocks will deliver losses in the long term. (0:16:41)
Outline of the factors which tend to cause long-term stock losses. (0:17:36)
What potential losses are in the long-term for international stocks. (0:18:58)
How likely stocks will deliver catastrophic losses as opposed to traditional forms of loss. (0:22:15)
Find out how much the probability of loss decreases with longer horizons. (0:23:59)
The contribution of currency and domestic inflation to the trends in the data. (0:24:52)
We compare how well international stocks hedge against long-term real losses in domestic stocks. (0:25:25)
He shares how he thinks investors should approach the home country bias. (0:26:34)
A rundown of the expropriations that exist in Professor Cederburg’s data. (0:27:34)
We talk about long-term stocks and their implications on asset allocations. (0:28:48)
How wide the distribution of long-run stock payoffs are. (0:29:28)
Discover how likely bonds and bills are to real losses over a long period. (0:30:16)
Breakdown of what the distribution looks like for bond returns. (0:31:52)
Whether bonds act as a hedge against poor stock returns. (0:33:24)
Common economic conditions that explain the poor long-term returns for stocks and bonds. (0:34:58)
Ways in which the results can be used to make predictions for the economic future. (0:38:36)
Professor Cederburg tells us if stocks are safe or risky in the long term. (0:40:23)
He unpacks mean reversion in the full-time series compared to the block bootstrap approach. (0:41:27)
Why emerging markets were not considered in the study. (0:43:55)
Advice for investors given the findings of his study. (0:45:00)
We discuss the applicability of the findings within a contemporary market setting. (0:47:04)
Which variables need to be considered when deciding between a pre-tax or post-tax savings account. (0:49:19)
Factors that make a pre-tax and post-tax account valuable. (0:50:41)
Hear the investment type most exposed to future tax schedule uncertainty. (0:54:50)
Whether using a post-tax account can build resilience to tax uncertainty. (0:56:29)
Simple rules for listeners to help them optimize the location of their savings. (0:59:08)
How the simple rules compare to the optimization analysis performed for the research paper. (1:01:40)
Risk-adjusted performance for high beta and low beta portfolios. (1:03:02)
We learn what the implications are for someone investing in low-beta assets. (1:05:58)
Professor Cederburg shares his definition of success. (1:09:17)
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 are hosted by me, Benjamin Felix and Cameron Passmore, portfolio managers at PWL Capital.
Cameron Passmore: Welcome to Episode 224. This week, we welcome Professor Scott Cederburg. Ben, this is another really great, as we said off-mic to him afterwards that both you and I have a number of wows since the interview, and that's always a litmus test for how good the conversation was. Such a practical guy with pragmatic research. He tells the story about how he decided to do some of his research and it came from an email from HR. He saw, “What should I do?” That just led to doing some research, which is so fascinating to me. Scott's the Associate Professor of Finance at Eller College of Management at the University of Arizona. He got his Ph.D. in finance from the University of Iowa.
Ben Felix: It is pretty funny though, the story that you just mentioned that it's like, we talked about the pre-tax and post-tax savings accounts, which in Canada, that's the RSP (Retirement Savings Plan) and the TFSA. They have different names in the US. He was for himself, trying to figure out, where should I be contributing? Then that leads to a paper published in a top academic journal. It's pretty funny. It's also, like you said, extremely practically useful for anybody making that decision, and it's counterintuitive, the finding. I mean, I won't spoil it, but should a high-income earner prioritize their RRSP (Registered Retirement Savings Plan) over their TFSA (Tax Free Savings Account)? The obvious answer seems like it would be yes. When you model out the uncertainty of future tax rates, the answer ends up being no. At least not completely. There's a balance there, which is not, as I said during the conversation with Scott, and that's something that I thought about until reading his paper on it.
Cameron Passmore: We talked a lot with him about what I call this archeological dig into the long-run returns of stock markets around the world. Pretty incredible the work. As he said, he was only able to do it over the past 15 years, because the information wasn't available. Now with Google Translate, etc., he's able to do it and piece together what happened in markets around the world going back to the 1840s, I believe he said, which is pretty incredible.
Ben Felix: Yeah. I've got two papers on this. One, I think starts in 1840s and one starts in the 1890s, I believe. The more recent one that looks at stocks, bonds and bills, and then just for stocks. That one's published. The other ones a working paper. Anyway. Yeah, there's just an incredible amount of data that they've pulled together from one data source when they filled in the gaps. He told us a story about finding old German books on Google Scholar and then using Google Translate to find the data points to fill in the gaps for the missing months of returns to complete their dataset.
Like you said, it's like an archaeological project. The result, and this is where we spend a lot of time talking to Scott about, is this unbelievable dataset. One of the main things we talked to Scott about is the probability of real losses for long-term investors in domestic stocks, international stocks, bonds, and bills. We've talked about this before, right? About the risk of stocks in the long run. That's what Scott's data speaks to. Well, I'm not going to spoil the episode. It's fascinating data.
Cameron Passmore: Fascinating data. I'm not going to spoil it by answering this question either. I asked him. I said, a lot of this must be irrelevant, given the change in market structure and competition information technology. I think you'll find his answer quite interesting.
Ben Felix: Oh, his answer to that question was amazing.
Cameron Passmore: Yeah. How's that for a teaser? There's our clickbait.
Ben Felix: Yeah. Scott's research has been published in all the top journals in financial economics. You go down the list. He’s been in the journal the paper that we mentioned, ‘Tax Uncertainty and Retirement Savings Diversification’. He won a big award for that in 2018. He's done just phenomenal research. We also talked about the low-beta anomaly, or non-anomaly as Scott would call it. Anyway, fascinating conversation with clearly, a very dedicated researcher.
Cameron Passmore: For sure. With that, let's go to our conversation with Professor Scott Cederburg.
Scott Cederburg, welcome to the Rational Reminder Podcast.
Thank you. Thanks for having me.
All right. Scott, you've co-authored some incredible – I mean, it really is incredible empirical work on the long horizon returns of stocks and bonds. Can you describe your data setup for that research?
Yeah. This is joint work with Aizhan Anarkulova, who's my Ph.D. student here at Arizona, and Mike O’Doherty at Missouri. We've put together a data set that has – we have monthly returns on domestic stocks, international stocks, government bonds, and government bills. All told, our dataset is covering 38 developed countries, and we have a sample period in this study starting at 1890. We're covering both a broad set of countries and some long historical time periods. In total, we have about 2,500 years worth of monthly return data from these developed countries.
There were two main things that we were trying to keep in mind when we were putting our dataset together. The first was, we wanted to be really careful when we were classifying what countries were developed. There's always this potential. If we just took, say, the countries that are currently in the OECD, we might at that point be conditioning on things having gone relatively well, in both the economy and the markets in those particular countries. We do an approach where in the early part of the sample, we're defining countries as developed when their agricultural labor share drops below 50%.
The UK in 1841 is the first example of this, where there starts to be industrialization in the UK, and we started having just more manufacturing and services activity, and not everybody has to grow food anymore. Then it geographically spreads to Netherlands and Belgium and France, and then US, Canada, Australia, New Zealand, as we approach the 1900 or so. Then later on, we use OECD membership once that fits.
We're doing measures to get countries into our sample that are based on things that we knew at the time. I think an interesting example of this and why we think it's – for forming expectations of what could happen going forward, is if you look at Czechoslovakia coming out of the Austro-Hungarian empire, it breaks up after World War I. Czechoslovakia is one of the countries that comes out of that. At that point in time, Austria and Czechoslovakia would have been very comparable in terms of per capita GDP. Prague and Vienna are going to be pretty similar; just very developed places.
Then you move through certain time a little bit, and Germans occupy Czechoslovakia in 1938. That's obviously a big hit. In May of 1945, they shut down the stock market in Prague, when the Soviet Red Army came in to basically push out the Germans. One of the former presidents of Czechoslovakia, Edvard Beneš, comes back in with the government. It's like, the government that they're used to, but then they immediately started nationalizing a lot of the publicly traded — the industry traded companies.
Then, in 1946, they permanently closed the stock market in Prague. Not all bad news. Because if you did own stocks in this thing, we're now going to give you some shares in this new public company that we've created, and you're going to get some dividends off of this. Maybe you're going to still get something out of it. Then in 1948, they have a communist revolution, and they no longer recognize personal property rights. It's just bad event after a bad event. Czechoslovakia is an example of a country where we really wanted to have it in our data, because in 1925, you're probably pretty optimistic as a long-term investor. Those are just the series of events that the stock investors didn't anticipate, that ends up taking out maybe 90%, 95% of their total value.
That's wild.
Yeah. There have been a lot of different things that have happened throughout the world and things that were probably very unanticipated. When we're doing the development of classifications, we try not to be conditioning on anything. We're really conscious of this survivor bias. The other type of bias that we're thinking about is what's been termed an easy data bias by Dimson, Marsh and Staunton. This is just like, we're professors, we're writing papers, it's really convenient if I just have a set of monthly returns from a country with no gaps or anything like that.
In reality, we've had five Stock Exchange closures that happened during our sample period. One example of this is during World War I in the US, they closed down the stock market. I think it was August 1914, they shut down the NYSE. Interestingly, Bill Silver has some work on this. There was this black market that popped up a few days later called New Street, and people were trading stocks on the black market. It had maybe 10% of the volume that the NYSE had when it was reopened. Then the US opens its market backup in December of that year, but there are these periods where we just don't have continuous data.
We've gone through and looked at all these periods and tried to really carefully treat these periods. We don't want to just drop these from the data, because that can typically happened around bad events. Then the basis for our data is a database called The GF database from Global Financial Data. That gave us a lot of good data for these long countries and periods. Then we've gone back anywhere where there was a gap in the data, we've been able to fill that doing books in German from 1923. I don't speak German and it's a 1,200-page document and you just go through and with Google Scholar and some time, you can figure it out. Or a dissertation from the 1950s, from a guy in Argentina, that details a bond exchange where they exchange a 3% bond to an 8% bond. He gives all the details on how this exchange actually happened.
You’re like an archaeologist, almost.
It's been a really interesting set of projects to work on because I feel like I've learned more about history and geography doing this stuff than I ever did in the actual classes. Yeah, and thinking back I don't know that any of this would have been possible 10 or 15 years ago. Because now we can just – I'm sitting here in Arizona, and I can find things from all over the world in any language. Then Google Translate has gotten really good at helping us out with all these languages that we don't know. It's been really interesting set of projects to work on.
Crazy. Would it be safe to say that most data like yours, but that doesn't make all the adjustments that you just talk through is upward biased?
That's what we've found. Yeah. We've done a couple of — where we purposefully put back some bias into something. If we just condition on which countries are currently in the OECD, that has some effect on our estimates. Then even more importantly, is if we dropped everything that was a gap period in the data, or before, I forget what the exact numbers were, but it roughly cut the probability of loss in half, if you introduced this bias back into the data.
Why do you think having data like yours that corrects for the easy data bias and the survivor bias, why do you think that's important for financial decision-making?
Yeah, I think it's really important for any forward-looking thing. I mean, in one sense, we're obviously looking backwards and we're looking at all these historical periods. When I'm thinking about this stuff, I'm always trying to think about, the reason that we got into this in the first place is very practical. What could happen to my investments over the next 30 years? The focus that we've been doing and with most [inaudible 0:12:10, papers] so far, is distributions of returns at a long horizon, a 30-year horizon. If I'm sitting here in 2022, and I'm thinking about what's going to happen to me over the next 30 years, we've seen just a lot of paths that countries and markets have taken, historically, that I don't think would have been anticipated at the beginning of those periods. I think, just trying to get as much of an ex-ante view of the world as possible. It's helpful.
Further to that, Scott, in your data, how does the historical experience in the US stock and bond markets compare to other developed markets?
It's interesting, if you look at a monthly level, there's not enormous differences in the average stock return, or the average bond return, or standard deviations of these things. If you do look over the extended holding periods, the US – you've always done pretty well with a 30-year investment in stocks. Jeremy Siegel has stock home-run view on this. Every time the market has dipped down, it bounces back up pretty quickly. When you look at some other countries, that hasn't necessarily been the case. Sometimes there's a crash, and it's not followed by such an enormous rebound. I mean, in the US market, obviously, 2008 and COVID, we had really steep declines, but then really steep ascents fairly quickly after that. That just hasn't occurred in some of the other countries.
Okay. Now, in your paper, you look at domestic stocks, and I just want to make sure that I'm clear and that our listeners understand. When you're looking at domestic stocks, you're looking at the experience of a domestic investor in each country in your sample, investing in domestic stocks. Is that right?
Yeah. The broad assumption that we're making in this paper is that domestic country returns, or domestic country returns, like a domestic country periods and domestic country period and it's informative about what can happen to domestic country investors. Then the methodology that we're going to use, I can describe a little bit too, so we're going to use what's called a block bootstrap simulation approach. This is basically, you can think of all the country returns, there's a big urn and we're just going to be drawing historical returns out of this. Then we can compound those up and create 30-year buy and hold returns.
Then, there are a couple of important aspects of how we're going to set this up. One is that every time we draw something from the urn, it's going to be a set of a domestic stock return, an international stock return, a bond return and a bill return from this same country month. We're going to do that to preserve cross-asset dependencies that are in the data. Then the other thing that we're going to do, rather than just taking say, one month at a time from different countries, we're going to tend to be taking pretty long chunks of consecutive data from inventory as we're drawing something. This is the block bootstrap approach.
On average, we take 10 years of consecutive data from a given country. We're trying to do that to maintain the time series dependencies. Mean reversion would be a really important example of this, where relatively high stock returns tend to be followed by relatively lower returns going forward, and vice versa on the other side. Then persistent volatility and things like that. We want to try to preserve as much of that as we can in the data.
A reason that sort of thing that makes the bootstrap approach necessary in this context is if you go back to the Czechoslovakia example, they were developed for less than 30 years, before basically, everything was gone. If we were just straight up trying to pull 30-year periods from the actual data, we would reintroduce the survivor bias into the analysis. Also, I mean, more a minor point, but it's under beginning of period and end period of performance, if you just take the periods that have actually happened in the data. We do use this block bootstrap analysis that this is going to produce distributions of returns, and we do everything from one month returns to 30-year buy and hold returns.
Yeah. It’s super interesting. If you're using rolling historical periods, what you're saying is that you would end up with many overlapping periods where Czechoslovakia in the example wasn't in the data, which is having survivorship bias. Yeah, okay. That's interesting. Okay. in terms of findings, how likely are domestic stocks to deliver real losses at long horizons?
Yeah. We are estimating at a 30-year horizon in domestic stocks in developed countries of 13% loss probability. For some context, if we were to use the US data for this analysis, you end up with about 1% chance. That's the safe data that we've learned from his you're going to win if you can invest for 30 years. Yeah, 13%. Another way of thinking about that, 30 years is roughly the viable savings period for somebody saving for retirement. If you're really starting to make some money at 30, or 35, this is your one shot, and there's a one in eight chance that you would lose relative to inflation. It is important that – I'll point out that everything that we're doing is going to be relative to inflation, so I'm going to be talking about real loss problems.
What tends to cause long-term real losses in stocks?
We were able to decompose the return realizations into three different components. One is just that you're going to get some dividend income, which is important for determining kind of, it's an important part of the returns that you're earning over time. That tends to not really vary across the gain and loss type of periods. The second thing is a valuation change. It could be the case that just price dividend ratio rockets, and we all make a lot of money. That's really important at a one-month horizon. That's much more than half of the volatility of stock markets at a short horizon. It's just changes in valuation. Then as we go out to a 30-year period, it becomes less and less important to your eventual outcomes. We actually don't even see huge differences between gain and loss periods for changes in valuations.
The biggest thing is the third component that's just real dividend growth. Your long-term stock market outcome is basically just, do you get a lot of cash flow growth, or do you not get a lot of cash flow growth? There's this enormous difference where in the gain periods, you get pretty good positive real growth. Then in the loss period, it tends to be large, negative growth in the real dividends that are coming off of stocks.
Wow. Okay, so you said 13% is the probability of real loss in domestic stocks. What is it for international stocks at the long horizon?
We're estimating that the international stocks are doing a lot better. They have about the same average performance and about the same standard deviation of performance. We're only estimating a 4% probability of loss for international stocks, which is at least much, much better than what we're seeing in domestic stocks. Even the left tail just isn't nearly as nasty for the international stocks. There's two really important components of international stocks. One, so we're doing all the currency conversions that you would need to do in order to invest in this. Our international stock portfolio, basically, from the perspective of an investor in any one country, we're going to be evaluated investment in all the other countries, other than that one.
Then there's two main components of the international stock return over the long run. The first is you just get a weighted average of the real returns across all the markets that you're investing. That's an incredibly diversified thing. Some countries are going to do well. Some countries are going to do poorly. You just get this really nice, super safe diversified component there. Then currency conversions are always on the top of people's mind, when they're thinking about investing internationally. What's interesting is if you look at a one-month horizon, or a one-year horizon, these currency fluctuations make stocks pretty risky. Your currency may appreciate in your home country, and that hurts your investment in the international stocks.
What's really interesting is as you increase the horizon, the changes in your exchange rate tend to offset the local inflation stuff. If you have a bad local inflation shock and inflation is high, there's a tendency for your currency to depreciate relative to the other currencies that – that offsets that local inflation risk. We're finding, everything longer than a four-year horizon, you're actually better off keeping the currency risk in your portfolio. If you were going to compare perfectly currency hedged returns versus unhedged returns, as long as you're thinking in real terms, like after inflation, you're actually better off being unhedged, because there's this natural hedge of exchange rates, versus this local inflation component that you have.
This ends up being, I think, one of the very important diversification aspects of international stocks is that they end up being almost completely unrelated to your domestic inflation. The real returns on international stocks have basically zero correlation with your domestic inflation, because of that currency hedge.
Wow. If you're going to invest internationally currency hedging, maybe not a good idea if you're a long-term investor.
Yeah, exactly. If you hold for a few months, then definitely, it takes out a bunch of the variance. For the long-term investors, I think you just buy everything and see what happens.
As long as you can behave well, correctly. You mentioned diversification. One of the reasons why we diversifies to avoid catastrophic losses. How likely are stocks to deliver catastrophic losses, as opposed to just garden variety losses?
Yeah. I mentioned that 13% overall loss probability. One piece of context that you can have on larger is if you look at Japan over the last 30 years of our sample period, that's starting in 1990, and then go into 2019. The nominal return in Japan was negative 9% over that period, and the real return was negative 21%. That's already a 20% loss of buying power over a 30-year period. That observation would be in the ninth percentile of our distribution. There's a 9% chance that you would do worse than that. We estimate a 5% chance that you're going to lose at least half of your buying power over a 30-year period.
What?
The 1% tails is nasty. I mean, it's obviously unlikely, but it's basically, minus 80% with a 1% chance.
That is nuts.
That's capturing a little bit more. We have negative 90% returns in Czechoslovakia. Germany and Japan both had about negative 90%. If you lose a world war, it's really not good for your stock market. The revolutions towards governments that are really not favourable to stock markets are also obviously, really, really bad tail events for investors.
Those are domestic tails?
Yeah, so that's all on domestic. The international, I forget off the top of my head what the tails are. But like I said, the probabilities are much lower for international stocks and that left tail just isn't nearly as severe.
We've been talking about the 30-year horizon in the spirit of the Jeremy Siegel stocks for the long run concept. How much does the probability of loss decrease with longer horizons?
It does definitely decrease. A one-month horizon, I mean, it's almost 50-50. It's more maybe 56% positive, 44% negative. Out to a five-year horizon, you're down to 29% probability of loss. It's at least a little over 70% chance that you'd have a positive five-year return. Yeah, positive five-year return. Then out to a 30-year horizon, yeah, we're down to 13%. For domestic stocks, the loss probability just doesn't drop it as quickly as you would want it to with horizon. For international stocks, at short horizons, it's pretty similar loss probabilities to domestic stocks. It's just over the long run, it seems like, that loss probability is dropping a lot quicker for international stocks than it is for domestic.
I think we already talked about this. I just want to make sure I understand. Is a lot of that explained by the currency, or the domestic inflation piece?
Yeah. I think that's a big part of it. Then just being diversified across a broad set of economies, where maybe we have just an awful global recession that lasts forever. There is a lot more country by country variation that didn't go well in a particular place, or there's unfavourable shift in governments, or something like that. If you can just diversify across all that stuff, you're going to be better off.
How well do international stocks hedge against long-run real losses in domestic stocks?
Yeah. There is a positive correlation between the outcomes that you get in the real domestic stocks and the outcomes that you're getting in the real international stocks. There's a positive correlation there. We do see lots and lots of circumstances where the domestic market would lose, but you still get not only just a small positive gain in international stocks, but you still have the potential for getting a pretty good gain. There's at least been some of those that are around different currency reforms that countries have had where their local markets really take a hit but then they depreciate their own currency a bunch, so your international stock portfolio gets a big boost from that sort of an event.
Okay, so we talked about the performance of domestic stocks, the performance of international stocks. International stocks seem to be pretty protective at the long horizon. How do you think investors think about home country bias? For context, we're in Canada, where 3% of where the global market, many Canadians have some home country bias. We think that's not such a bad idea, because there's some tax efficiencies and stuff like that. Given what we just talked about, how do you think investors should approach home country bias?
Yeah. I think, some degree of diversification is, I think, going to be valuable. It just protects against some of the aspects that are going to hit all the domestic markets that just getting some of your money out of that domestic system and into something else, I think has some advantages. Since I started working, I think I've had a little bit more of my retirement in international stocks than most of my colleagues have. I just continued to lose on this. The US market has just continued to go straight up. I have to believe at some point in my 30 or 40 years savings period that this is going to even out, or balance out, or something. I guess, I will continue to hold a decent chunk in international stocks.
We talked to Fama, Gene Fama A while ago, and he's a proponent of home country bias. A big part of his reasoning for that is that there's expropriations that don't show up in the data. Do I understand correctly, though, that those do show up in your data?
With governments that are just seizing assets, so we would capture anything that is like, the nationalization of industries within a country. We would not be capturing if there has been a country that seizes the assets, specifically for foreign investors, we would not be seeing those. It's a really good point. I don’t know that we've systematically looked to see whether that has happened in any of the countries that we have in our particular sample. We have seen the nationalization within countries that affects all shareholders equally. Czechoslovakia, Chile, are both examples of that, with large amounts of nationalization of companies.
Interesting. Okay. Fama’s word of caution could still have some merit there.
Yeah. I think, certainly, depending on I think some of the emerging markets may have more potential for that, than investing in Belgium. That’s, yeah, definitely potentially a risk.
If stocks have a significant risk of real loss over long horizons, can you talk about the implications for asset allocation?
Yeah. To some extent, is going to depend on what other options we have available. We can talk more about funds and bills, but those are not necessarily going to seem like they're the best place to run and hide. We are starting to, I guess, more formally look into asset allocation. That's our next project was actually supposed to be where our last project was going to go. Then it turns out with this much data that you have to get through and all these issues, it just turned into its own project by itself. We're starting to look into the asset allocation stuff using this big data set, and just see where it takes us.
That's super interesting. We talked about the probability of real losses for stocks. How wide is the distribution of long run stock payoffs?
Yeah. It's fairly extreme, because we've been talking about the left tail. Obviously, the right tail is way out there. If you start compounding up a good period after a good period, the overall spread, if you take the middle 90% of the distribution, if you invest a dollar and hold for 30 years, your 90% spread is you get 48 cents worth of buying power out of that dollar, so you've lost a little over half to $24 worth of buying power. It's obviously a great outcome where we're all rich and saying hi to each other from each other’s yachts, and that would be great.
You mentioned bonds and bills. How likely are they to deliver real losses over a long-period?
Bonds and bills are looking worse than stocks on this aspect. Again, I'll stress that we are looking at the real outcomes on these things. Relative to inflation, bonds are losing with a 27% probability over a 30-year horizon. Bills, it's 37%. If you look at the loss probability by horizon, it does drop a little bit for bonds, because it starts out at whatever, and they go up 55% of the time, down 45% time at a monthly level. It drops down a little bit to 27%, but that's still over a one in four chance that you're not going to beat inflation.
The bills, the loss probability is almost constant as a function of inflation. Just a longer holding period just doesn't really help you with bills. With bonds and bills, there's really not much in the way of we're looking all at domestic bonds and domestic bills. There's really not much in the way of defaults on bonds. Obviously, Greece recently, there were – there was something in Germany following World War II. There's a few of these, but mostly, it's just the yields that we're getting on these things don't keep up with inflation, if there is an inflationary period. It's just so easy for a quick bout of inflation to take out any gains that you are going to get from a low, or short-term interest rate over a 30-year period.
Bonds, I was going to say, tend to. But they're more likely to lose in real terms than stocks. What about the size of the distribution? What does the distribution look like for bond returns?
Yeah. If you're looking at 30-year performance, if we're measuring risk by standard deviation, it has a much lower standard deviation of payoffs than the stocks. That's really just because it lost the right tail. Your stocks and bonds are not really that good. The bad outcomes in bonds are actually worse than the bad outcomes in stocks. The same is true for bills. It's not uncommon to lose, or, I shouldn't say not uncommon, but I want to say, there's still a 5% chance that you're going to lose 80-plus percent of your real wealth in bonds, or bills. Just because if you do get inflation for a five, or 10-year period within a 30-year period, the rates just don't seem to pop up so high to offset that inflation. You just end up losing a ton of real buying power.
Makes it sound like bonds are terrible investments for long-term investors.
I mean, certainly the inflation linked stuff that we have now, this is not something that we had access to throughout our whole historical period. I know personally, I've been investing in I bonds in the US that are just inflation linked bonds. I'm setting up my own inflation linked annuity that I can draw out of in retirement.
What about, because these are government bonds in your sample, right?
Yeah.
Do you have any idea what corporate bonds would look like?
We just don't have the data. I can't really speculate.
Do the bonds act at all as a hedge against poor stock returns?
If anything, it goes the other way. For both bonds and bills, conditional on a loss, any asset class, you're over 50% chance of losing. I'll pull numbers out of my head. I want to say, if stocks lose and there's a 61% chance of losing in bonds and a 60% chance of losing in bills, if one of those two loses, there's over an 80% chance that the other one loses, too. Short-term, long-term, everything's pretty linked. If you look overall, there's 13% chance of losing. If you look overall, the odds of losing in domestic stocks, domestic bonds and domestic bills is still six and a half percent. It's a one in 16 chance that all three domestic markets lose over a 30-year period.
Wow. That combined probability is higher than the probability of losing in foreign stocks?
Yeah.
Interesting.
That's saying like, “I'm going to hold on to some international stocks and see.” Hopefully, we're all in the state of the world where the next 30 years is in the nice, middle part of that distribution where you are still doing okay in all these assets, but I think it is worth – as I think about my own retirement, I'm not so concerned about where my expected wealth is going to be, or the median of my distribution. It is, I want to protect myself against that 10% tail of the bad outcomes.
On this big archeological dig, did you come up with common, I guess, economic conditions that might explain long-term poor returns in stocks and bonds?
Yeah. For bonds, it's really easy. It's just inflation. I mean, that's basically, if you don't have high inflation over a period, you're going to be fine as a bond or bill investor. Again, limited upside, but you're going to be fine. It's not a function, it’s just like, there's very little probability that you're going to be fine if there's a lot of inflation, and you're a fixed income investor.
For stocks, I mentioned international stocks provide a really nice hedge against inflation. Domestic stocks also do a pretty decent job of hedging against domestic inflation. If you're looking at nominal stock returns, they are positively correlated with domestic inflation. Now, there's some ideas that you do have a company that has some buildings and some equipment, and they're selling products that maybe the price of the products is increasing with inflation, so that they could protect a little bit from inflation.
Domestic stocks do worse in inflationary periods than they do in non-inflationary periods, but not nearly as bad as bonds and bills. For stocks, there is a tighter link to just macro-economic conditions over the whole period. As an example, we were finding in the gain periods, over 30-year periods, the real per capita GDP growth is 1.9% per year in the game periods. It's only 1% per year in the loss periods. There's a tendency for the loss periods to contain one of these big economic disasters that, like Robert Barrow and some others have been studying the consumption shocks, consumption disasters that you lose 15% of GDP in just a handful of years.
Those tend to happen a little bit more in the loss periods. They tend to happen in those loss periods. We're still even finding, there's about a third of these 30-year losses in domestic stocks would occur simultaneous with above median GDP growth. You can see this in the data, there have been countries that have lost and actually, had pretty good economic growth over a 30-year period and will end up realizing a negative 30-year real return.
We thought this was a little bit. It was in some ways, a little bit unexpected, after we had already looked at the real dividend growth, because losses in stocks, it's just terrible real dividend growth. Then you're thinking like, “Oh, it's got to just be the case that there's these terrible economic conditions.” There are some periods even when dividend … GDP growth is okay. We're trying to link to a recent literature that there's a macro literature on labour share. If we're thinking about total output, then there's the share that goes to the labour, share that goes to capital. Then, maybe there's just a leftover share for profits for the publicly traded firms.
That proportion of the total economy that's just going out to shareholders in the form of profits, seems to fluctuate a bit, potentially. Some folks have been attributing the last 30 or 40 years in the US to a shift away from labour share and towards just this profit share thing. It seems like, there are other times in other countries where maybe this is all circumstantial evidence, but maybe the labour share, it really increases in a country and there's just not that much leftover for the shareholders. The companies just become a little bit less profitable if that happens.
Interesting. We can't really look at, or can we look at current economic conditions and make any slight predictions about what the future might look like?
Yeah. The most obvious one, I think, is inflation on the fixed income side. If we're starting here – I mean, in the US right now, you look at lagged inflation versus where the short-term rates are, I mean, it's a negative 5% real return. I think last year’s real return in bills would have been negative 7%. If you have any years in the 30-year period, where you have a negative 7% return in bills, you're not going to make that up during that. Inflation tends to be persistent enough that it's just not going to be a good spot to be in.
In some earlier analyses that we did, they're not currently in any of our papers, we tried to look at conditional distributions of returns, conditional on either the short-term interest rate, like valuation ratios. For the short-term interest rate, if you're in a low interest rate environment, I remember the loss probability on bills, if the short rate was between zero and 2%, the loss probability on bills was 83%. If you're in a low-interest rate environment, you're just not going to make positive real returns on bills, even over a long horizon. I guess, interest rates have popped up a little bit over real interest rates, I don't know necessarily have.
The valuation stuff, it wasn't as stark as maybe I would have initially expected. I want to say, the most extreme thing if you had a really high price dividend ratios, so just prices are high, I think that 13% baseline probability for losing in stocks was something like 18% if you were in the highest bucket of valuation, which is it's bad. Don't get me wrong. It wasn't like it was 30%, or 40%, something like that.
Based on all of your work, do you think stocks get riskier, or safer over long horizons?
Yeah. I think objectively, they do seem to get safer. Your last probabilities are dropping as the horizon grows. We seem to be seeing that, pretty good evidence of that. There are some nuanced ideas that was an important paper by Lubos Pastor Robert Stambaugh, where they're trying to say, “If I'm sitting here in 2022, looking forward, I have additional sources of uncertainty that we might want to take into account that I don't know exactly the structure of the world and all this stuff.” They're actually coming up with a result that stocks are riskier for a long-horizon investors than they are for short-horizon investors. It's a complex issue and there's nuance to it. It's certainly the case, if we look backwards, the longer the holding period, the safer stocks were.
You talked about how you use block bootstrap for this analysis. I know we talked about the survivorship bias if you just used the historical fold time series. Do you have a sense, though, for is there more mean reversion in the full-time series than in your block bootstrap setup?
Yeah. We've done a couple of things on that. One is just robustness on what the length of our block bootstrap is. If we take 20-year blocks on average, the loss probabilities are still all within 1% of our case. We're getting basically the same thing. It might be 12% in domestic stocks instead of 13%. Maybe that's a little bit of additional mean reversion, the longer ends.
The other thing, you can just look at the data. There are these issues with we didn't have a 30-year block for Czechoslovakia, or Argentina, and some of these other issues. It was still just if you take all the 30-year periods, it's from the raw data. I think, there's about nine and a half of the 30-year periods that actually existed in countries ended up in losses. That, again, leaves out Czechoslovakia and Argentina, that they have real losses over the periods that we have, and Czechoslovakia, you're not going to recover from that. Those things would be increasing that probability, I think, getting us fairly close to what our estimates are from the bootstrap.
Interesting. Okay.
We've also just looked at which countries have these things, and I think we have 11 countries in our sample that have experienced a negative 30-year loss. Then Argentina and Czechoslovakia, you probably want to add to that list. We have a total of 38 countries in our sample, but some of them are Latvia and Lithuania just got into the OECD recently, so we have a year or two of data. Those sort of, they count towards the 38 countries, but they didn't have a chance to lose over a long period.
That out of a baseline of maybe 20 countries that we have a lot of data on, it's then to 13, depending on whether you're counting Argentina and Czechoslovakia have experienced the negative returns.
That's crazy. That's one negative 30-year period over the full sample.
Yeah. Some of the countries have, if you're thinking you can come in as an investor in any one of the months of just doing rolling 30-year windows, there tends to be these periods where it's like, well, “If you would have come in anytime in these five years, you would have experienced the loss over the next 30 years.” It's a little tough to figure out exactly how to count those things. I want to say, Germany had two that were non-overlapping. It's not good to lose world wars. That's bad for the stock market.
Have you looked at all at emerging markets?
No, we haven't. It's partially due to data side of things. Where the first step, when we started doing this project was to define very carefully what periods we wanted to look at. Because we knew once we were doing that, that we were going to have to delve into all these issues. As soon as we expand everything out, then we need to do this for all the countries that we add. I think, it's likely that there's going to just be more systematically missing data that we're not going to be able to find sources for. Even finding some of the stuff for Argentina is pretty tough. If you can imagine really, really tiny markets in some of the less developed countries, I think it's going to be a challenge to do that.
Okay, so given domestic and international stocks have a reasonable probability of losing long horizons, bonds aren't protective of that either. What should investors do with this information?
I hate to be the guy who's always bringing bad news to people. The one thing that we know helped is saving more money. It's not particularly fun to increase your savings level. Saving more money is going to help, even if there are losses, helps you still have something by the time you have retirement.
The other side of this, too, we have another project with Rick Sias, my colleague here at Arizona, where we're looking at withdrawals during retirement. There's a popular 4% rule, where you pull out 4% of your money each year, inflation adjust that. Using historical US data, that seems to be okay, that that has a pretty good chance that you're not going to run out of money.
Using the full developed country sample, I think our baseline is that like a married couple would have a 17% chance of running out of money before the second one dies with the 4% rule. We're estimating a two and a quarter percent rule, basically still gives you a 5% chance of losing all your money. There's a 95% chance that you don't lose all your money. That implies that you have to have a lot of money at retirement if you want to actually be pulling anything out. Then there's the risk that your retirement savings period is not going to be all that great. Everything looks a little bit riskier than maybe we would have thought going into this project.
Is that withdrawal work published anywhere?
It's really a new paper. I think, we have an under submission at a journal right now.
Oh, cool. Because that's awesome. We've talked a lot about that, about the 4% rule and how it doesn't hold up. We've used the Dimson, Marsh, Staunton data to look at it. I would love to see your data. My last question on this section for you, Scott, it's got to do with, you've done all this work over so many years, going back a 100 and plus years, right? I can hear listeners wondering, with all the change in market structure, technology, competitiveness, information, does that change the applicability of this information? How do you think about that?
That's a great point. We've certainly thought about that a lot. There's a couple aspects. One, if you look back at return days, it doesn't look that different in the early part than the later part. You think about the massive changes in the way that everything's traded, and just all the economic developments that have been and technological developments, but it's still some people coming together and trading some stocks that are reflecting some macro-economic conditions and all this stuff.
The other thing that we've done is at least post-war, we can just basically chop off everything World War II and prior. We had pretty similar estimates on loss probabilities. Our earlier paper in the JFE that we just looked at stocks, we had one specification there. We did every starting period from 1841 to 2000 in that one. The loss probability, just using post-2000 data, we were estimating was 19%. It doesn't seem like the more recent data is indicative that there's just no more tail risk.
Wow.
Like Japan, starting in 1980, is another example, where it just sometimes things can happen. Japan and the US were by far the two largest stock markets in the world at that time. It's not even just small markets, and it's not just worse. There's some risks.
That one's crazy, because I think Japan at one point was much bigger than the US, right?
Yeah, it is. The last 30 years of our sample are perfectly timed on that particular thing, just by happenstance. Because I think, even 1989, prices are still running up, and then it was 1990 and beyond was pretty awful.
Yeah. All right, I want to move on to another one of your papers on savings location. This paper changed the way that I think about a lot of these things. I think, I've fell victim to the common ways of thinking about it, that you introduced in your paper. This is talking about which type of account people should ideally be saving in a pre-tax account, or a post-tax account. There are versions of these in the US. Canada, in Canada, we have the TFSA, where you put post-tax money in the RRSP, where you put pre-tax money. Which variables need to be considered in deciding whether to contribute to a pre-tax, or post-tax savings account?
Yeah. If you're just thinking one versus the other, the main thing to think about is just tax rates. It's whatever the tax rate that you have right now on the money that you would be putting in, so that's your marginal tax rate that you're subject to right now. What tax rate are you going to be paying in retirement? With the post-tax types of accounts, you pay your tax today at your marginal rate. With the pre-tax accounts, you're going to pay at least in the US, I'm not sure if the rules are any different in Canada, but you would pay, basically, as ordinary income tax on any withdrawals that you would make from the pre-tax account.
If those two tax rates ended up being – each other. If we have a known constant tax rate, then there's no difference between these two accounts and it doesn't matter which one you pick, at least on the tax side. Maybe there's other random regulatory things. On the tax side, this wouldn't matter. Then, it's really thinking about what's my tax rate now, versus what my tax rate going to be in retirement? The main thing that we were focused on then is how to think about, I know where my tax rate is now, but how do I think about where my tax rate is going to be and just trying to think through the uncertainty around that, was the main part of our study.
What makes a pre-tax savings account valuable?
The pre-tax account, we're going to be putting in money before taxes in the current year, and then we'll take that money out and be taxed on it in retirement. One aspect of this is with a progressive tax system, you might currently be in a high tax bracket for this particular year. If you can pay a little bit into a pre-tax account, end up dropping, going through that high tax bracket, and you can save yourself from paying the high tax rate.
The other thing that we focused on in our paper is, presumably when we get to retirement, there's still a pretty good chance that we're going to have a progressive tax system. If you end up with pretty high income, you'll end up paying higher tax rates. If you end up with lower income in retirement, you'll end up paying lower tax rates. To some degree, these types of accounts almost provide a hedge against, if I ended up doing really well with my career and making a lot of money, I can afford to pay some higher taxes. If I don't end up doing all that, well, then I get to be subject to the lower tax rate.
This also applies to what happens in the market over this time. If the market ends up doing really well, I have a lot of money in retirement. I can afford the taxes. If the market does really poorly, now at least I'm paying low tax rates on that income.
Okay. You introduce the saying that the pre and post-tax accounts are identical if tax rates are constant. With the pre-tax account, you have your current tax rate and your unknown future tax rate, which may give you a penalty, or a bonus depending on how stuff ends up going, but also, what happens in the future tax rates. Okay, on the post-tax account, what makes it valuable?
The post-tax account, you're going to pay your taxes upfront, and then under the current laws anyway, you're never going to have to pay taxes on that again. You can lock in a known rate today, and then you never have to worry about tax rate risk again. One of the things that we really emphasized in the study is just the amount of uncertainty that there is over where taxes could go over a 30-year horizon. I always use 30-year horizons for some reason. It's over a 30-year horizon, we just don't really know where the tax brackets are going to be. In this paper, we didn't make any assumption about like, “Oh, we think rates are going to go up, or we think rates are going to go down.”
We took historical tax rate changes in the US and bootstrapped with those and just simulated out where we could end up. You end up with these really wide distributions for what the tax rate could end up being at each income level. There's some chance that we're sitting there at, say, 15%, 20% tax rate, but there's some chance that it's going to be a 60%, or 70% top tax rate. We've been there before in the relatively recent past.
There's a lot of data that we have about where taxes are going to end up. In these post-tax types of accounts, you get to withdraw whatever you can put in. If you can just lock something in right now, you've eliminated this big source of uncertainty. That's entirely unrewarded. At least for stocks, you're getting rewarded for taking on some risk. You know that there's a tail. You know that you're not guaranteed to make money, but on average, you do pretty well on stocks. You're getting no compensation for the tax rate risk. The Roth account in the US allows you to just eliminate that tax risk from your personal problem.
Yeah. That's the TFSA in Canada. This to me was pretty mind-blowing. I guess, I just hadn't thought about it enough. With the TFSA, or the Roth, you're locking in your future tax rates. You’re completely eliminating that risk. With the traditional IRA, or the RRSP in Canada, even if you're in a currently high tax bracket and expect to be in a future lower tax bracket, even if that's the case, there's uncertainty about your future tax rate, both in terms of how the investments performed, but also in terms of what tax brackets actually are in the future. Even if you're in that situation, you may still want to allocate to a post-tax account.
Yeah. It could be the case that the low tax brackets in the future are at higher rates than the higher tax brackets are now. That's definitely possible.
Diversification once again. What investment type is most exposed to future tax schedule uncertainty?
There's definitely young investors who have an awful lot of runway, until they're going to be in retirement. There's just so much that can happen potentially over the next 30 years. Even, we didn't model this thing, but folks have talked about the possibility of a consumption tax. To the extent that you can potentially move away from an income tax and towards the consumption tax, or any number of things, it could be changing. There's just a lot of uncertainty, what can happen over a really long period of time. Then as you're getting closer and closer to retirement, I think you're probably starting to get a better idea of what the tax regime is going to be when you're actually hitting the retirement age.
The other aspect of it, so there seems to be a lot more uncertainty about historically, we've seen much more fluctuation in the top tax rates compared with the bottom tax rates. Wealthier investors who are in higher tax brackets, there's a possibility that the high tax bracket when I retire is going to be 25%. I think there's a possibility that it's going to be 75%. That's a 3X difference on how much money you actually get a take of your account when you retire.
Okay. Now, when people are looking at this decision, if we take the example of the high earner, and they're looking at using their pre-tax account and making some assumption about what their future income is going to be, it quantitatively looks obvious that they should be using the pre-tax account, as opposed to the post-tax account. Given the uncertainty about future tax rates, is it possible to quantify the benefit of reducing uncertainty by using a post-tax account, even though it might seem like using the pre-tax account will be smarter?
Yeah. We ran an analysis where we basically, we could do some optimization, where you were ignoring the uncertainty about the tax rates and just assuming that things were going to be constant. Then allowing the investor to think about this tax rate uncertainty. At a 10-year horizon, we were finding that effectively, the investor would be willing to pay an annual fee of up to seven points a year ahead and switch their allocation to consider the optimal, given all the uncertainty that we have.
Then at a 30-year horizon, it's 2% per year benefit that they're getting from considering this type of information. What's interesting about that is it's actually these highest fees are actually exactly the people that it doesn't seem like, that they're always currently thinking about Roth. It's people who are currently in a high bracket are actually benefiting more from considering this tax rate uncertainty, just because they're so much more likely to be subject to a higher tax bracket – a fairly high tax bracket when they're in retirement. There's so much uncertainty about where those tax rates are going to be that just getting some money out of that system, and into a post-tax account seems to have a really big economic benefit.
That's crazy. Somebody who's currently in a high tax bracket, would be willing to pay a 2% fee to give them the same hedge that they would get from just contributing to their post-tax account.
Yup.
Wild.
Yeah. I think that was the counterintuitive thing that came out of our analysis, where even right now, so US there's some 32% and 35% brackets. In the grand scheme of things, that might not be an overwhelmingly high tax rate. It's perfectly plausible that retirement tax rate is going to be 50%, 60%, something like that. Just a lot of times when we're thinking about these optimal things, just getting away from what we would call the corner solutions where you're a 100% in this one, 0% in this one, or are a 100% in this one and 0% in this one. Just getting yourself somewhere in the middle has such a big benefit. There's not huge differences between 60-40 and 40-60. Just getting yourself away from 0%, a 100% decisions tends to have a big benefit.
That's really interesting. A lot of people may not be able to run a perfectly optimized analysis of all this. Do you have simple rules that people can follow to at least somewhat optimize the location of their savings?
Yeah. I think, I would think of it in terms of a two-step rule. The first would be, if you're currently just not making that much money, maybe you're young, just an entry level job, we have some tax brackets that are 10% to 12%. Anytime you can lock in 10% to 12%, do Roth, lock that in as much as you can. Then beyond that, if you're in some of the higher tax brackets, we came up with a rule of thumb, that you take your age and you add 20 and then try to have that much in traditional and then the remainder in a Roth, the US versions. Yeah, do your age in the pre-tax and the remainder in the post-tax.
When you're relatively young, if you're 30-years-old, that says, 50-50 in these two things. As you get closer to retirement, there's less uncertainty about your future taxes, and you can shift it towards the traditional account. The post-tax account has less of this benefit of locking in a rate if you're already 60-years-old and getting closer to the date. Then we would say, maybe 80% of the pre-tax, 20% of the post-tax.
Can you say the rule one more time? You cut out just a little bit.
We want you to take your age and add 20.
Okay, there it is.
Then do that percentage in the pre-tax and then do the remainder in the post-tax.
Okay. Yeah, that's not something that I thought about before. Even somebody that you would think it would be optimal to contribute to the pre-tax account, to the RRSP in Canada, or the traditional in the US, they should still be contributing the amount that you just said, based on that rule to their post-tax Roth/TFSA. Unreal takeaway.
I think, just getting some of your money out of the system. Again, just 0% is just not going to be the best thing most of the time. We didn't model this particular part two, but when you are in retirement, if you have money in both of these buckets, you can also manage on an annual basis around the different tax brackets. If you need to spend a little bit more on one particular year, you can take money out of the post-tax account that you've already paid the taxes on, get yourself down to a lower marginal tax bracket for the pre-tax account withdrawals. There's, I think, multiple benefits of just having a little bit in each bucket, and you can optimize as you go.
How does the rule of thumb that you just mentioned compare to the optimization analysis that you did in the paper?
There is fairly minor differences in how well off you are doing the full analysis, versus this. Again, a big part of that is just that so much of the benefit of diversifying comes from even the first 10% or 20% that you shift away from a 100%, 0% of allocation. As long as you can get yourself in the rough ballpark, then you're good. We thought about just using age itself in the pre-tax and the remainder in post-tax. I think, there was enough of a benefit to make it slightly more complicated and say, age plus 20 in the pre-tax, but they're roughly similar. It's just the idea that you're going to be a little more heavy in the post-tax when you're younger and shifting towards the pre-tax as you get older.
Super interesting. That paper was so cool. I guess, in Canada to really replicate the rule of thumb properly, we would have to rerun the analysis with a bootstrap of historical Canadian tax rates.
Yup.
Yeah, interesting.
Yeah, that's a good point.
I don't know how volatile historical Canadian tax rates are relative to US. Good takeaway for us to look into. All right, Scott, I want to finish up with your paper on low beta. This is another fascinating one. What explains the historical, statistically significant differences in risk-adjusted performance for high beta and low beta portfolios?
There's this old result in the finance literature, where the high beta stocks tend to underperform relative to the CAPM. The low beta stocks outperform. If you do a high beta minus low beta strategy, we find over a [inaudible 1:03:18] period that this would have a CAPM alpha of minus 7% per year. There's this just massive difference in the risk adjusted performance of these two things.
What we did in our paper is, if you actually look at the time series, and you're looking at all the stocks in the market, there's actually a lot of variation in the distribution of firm betas that existed at any point in time. There are some periods where there are lots of really low beta stocks and lots of really high beta stocks. There are some periods where everything's clustered much closer to one. There aren't very many stocks with a beta of only 0.2, and there aren't very many with a beta of 2.
One of the implications that this has is as we're forming these beta sorted portfolios to evaluate this strategy, the beta of the portfolio itself shifts around a lot over time. There are some periods when the beta strategy has a lot of exposure to the market, and some periods where it doesn't have really all that much exposure to market. Sometimes the beta of the strategy as we buy high beta stocks and sell low beta stocks, sometimes the beta of that thing is only 0.5, and sometimes it's 2.
It just happens to be the case that systematically throughout the sample period, the beta of the strategy is related to both the expected market return and the market volatility. These two things combined, such that when we just estimate an unconditional CAPM that we would traditionally do, we're going to overstate the amount of risk that we think that we're taking on average, so the beta that we get from this regression is higher than the average beta that we typically have on this strategy.
We're tending to have more exposure to the market when the market returns, or the expected market returns are low. Then you have relatively less exposure when the expected market returns are high. These are a couple of features of the risk of this strategy moves make it so just the expected return on the high beta stocks shouldn't be that much higher than the expected return on lower beta stocks. If we do something called a conditional CAPM, where we model the time variation in the beta of the strategy and we run this regression, now all of a sudden, we find an insignificant alpha on this strategy. It's about 2% per year of alpha, but statistically insignificant. That explains the historical finding that we were finding this huge CAPM alpha from betting against beta.
What are the implications of that for someone who's investing in a low beta ETF?
Yeah. One implication of it anyway, would be, if I were to be taking a strategy where I'm trying to keep my risk roughly constant in this particular thing, so if you're scaling up and scaling down in the low beta stocks that would tend to reverse out these things, the time variation that we saw in the past, and it might end up destroying any apparent alpha that you're going to get. Trying to manage the risk to be relatively constant might end up taking out the source of performance.
Our view on it is that there – I guess, myself and my co-author, Mike O’Doherty, I think our view is that there is no beta anomaly. Because if we know that the risk of this thing is changing over time, then we shouldn't be taking into account that the risk of this thing is changing over time. We would call it a statistical bias when we're looking at the unconditional CAPM that's huge. Our stance on it would be that there just isn't a beta anomaly, but it still seems to be a highly popular strategy.
Then with a low beta strategy, are you just getting time varying risk exposure? Is that what it is in the end?
Yeah. It's just on average, you're going to be getting whatever you're supposed to be getting. There's another piece of evidence that people often throw out there on high beta versus low beta, where if you do a cumulative buy and hold from 1926 until now, people draw these two lines, where it's like, what's my cumulative wealth from investing in low beta stocks? What's my cumulative wealth from investing in high beta stocks? In the low beta stocks, you end up with more in the end, than you did with the high beta stocks. There's an aspect of cumulative buy and hold returns, where it really starts to depend more on variance than it does on the expected returns.
One way of thinking about this, like imagine we go to Vegas, and suppose that Vegas comes up with a new game where there's a 75% chance that you win, but put down your $10. If you win, they give you $10, now you have $20. There’s 75% chance that you win. Now you have to re-bet that $20 and you have to sit there and play it a 100 times. Even though I have this great expected return on this game, and my expected outcome after a 100 times is actually huge and enormous and positive, but there's a 10 to the negative 30th chance that I actually walk away from the table with any money. I almost always just zero, because this is a high variance thing, where if you lose one time, you're done.
To some extent, high beta stocks, the high beta stock portfolio looks like that, where it just has a couple of really big crashes. The cumulative buy and hold performance can't ever recover. I don't know anybody who bought some high beta stocks in 1926 and decided to hold on to those until 2020, without ever rebalancing across anything. As soon as we're willing to rebalance, then this cumulative buy and hold performance is super relevant for us. It becomes more like, what's the annual expected returns, or something like that. Those don't look nearly as out of whack as I think the common perception is.
Super interesting. Scott, our final question for you, how do you define success in your life?
Really saving the tough questions for last. Yeah, I guess as I'm reflecting, it was always a piece approach, whereas you're getting a Ph.D., you're just trying to get some things going and be able to get a job at a good research school and everything. Then you get a job, and then there's a tenure clock that you're on. Then it's okay, I need to work towards this and get tenure. Then post tenure, then you no longer have this set timeframe stuff. I think, as I'm thinking about this, there's still a lot of things that I want to be able to do and there's a lot of parts of the world that I haven't seen and there's places in the world like southern Portugal, I really want to go to again. I think from this point forward, success in my life is just trying to do the things that I need to do really well, in order to give myself the flexibility to do these things that I want to do.
Great answer. Great to meet you, Scott. Thanks for joining us.
Yeah. It was great to meet you as well. Thanks a lot for having me.
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Benjamin on Twitter — https://twitter.com/benjaminwfelix
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Prof. Scott Cederburg — https://eller.arizona.edu/people/scott-cederburg
'Long-Horizon Losses in Stocks, Bonds, and Bills: Evidence from a Broad Sample of Developed Markets' — https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3964908
'Stocks for the long run? Evidence from a broad sample of developed markets' — https://www.sciencedirect.com/science/article/
'Tax Uncertainty and Retirement Savings Diversification' — https://www.sciencedirect.com/science/article/
'Does it pay to bet against beta? On the conditional performance of the beta anomaly' — https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12383