Episode 397: Hendrik Bessembinder - Constant Leverage & Measuring Investor Outcomes

Hank Bessembinder is a professor and the Francis J. and Mary B. Labriola Endowed Chair in Competitive Business. He returned to Arizona State University in 2015, after holding positions at Emory University and the University of Utah. Prior to his first assignment with ASU, Professor Bessembinder taught at the University of Rochester. His research focuses on market design and trading, including stock, foreign exchange, fixed income, futures, and energy markets, as well as on measuring long term investment performance. He has published numerous articles in the Journal of Finance, Journal of Financial Economics, and Review of Financial Studies, among others. 

A frequent speaker at conferences, financial markets, and universities around the world, Professor Bessembinder has more than 25 years of successful consulting experience, providing strategic advice and analysis for major firms, financial markets, and government agencies. 

In this episode, we welcome back return guest Hank Bessembinder for a deeply analytical conversation spanning leveraged ETFs, volatility, and the future of performance measurement. Hank walks us through his latest research on leveraged single-stock ETFs, clarifying the misunderstood concept of “volatility decay” and decomposing returns into rebalancing effects and frictions. The results are striking: meaningful underperformance relative to simple levered benchmarks, driven by both embedded costs and the mechanics of daily resets. In the second half, we shift gears to a more foundational question: What is a return, really? Hank challenges the dominance of arithmetic averages and even geometric means, arguing that neither truly captures the long-term investor experience. He introduces the concept of the sustainable return—a measure based on the cash flows an investment can support without depleting capital—and outlines how it could reshape academic finance and real-world financial planning.

Key Points From This Episode:

(0:01:03) Welcome back to Hank Bessembinder and overview of his recent research.

(0:06:16) What “volatility decay” really means—and why the term may be misleading.

(0:09:16) Why volatility does not necessarily reduce mean returns in constant leverage ETFs.

(0:10:11) Ex-ante decision-making and the wedge between mean and median outcomes.

(0:11:26) Single-stock vs. index leveraged ETFs: Similar mechanics, different magnitudes.

(0:12:52) Why past research has been so cautionary about long-term use of leveraged ETFs.

(0:15:53) How rebalancing costs differ for long and short leveraged products.

(0:16:57) The benchmark: Levered buy-and-hold versus constant daily rebalancing.

(0:19:46) Empirical results: Long funds underperform by ~0.8% per month; short funds by ~1% per month.

(0:21:10) Decomposing underperformance into rebalancing effects and frictions.

(0:24:15) The real (though rare) possibility of returns below –100% in leveraged products.

(0:27:04) Simulation results over 50 years: Skewness, negative medians, and rebalancing drag.

(0:28:38) Why volatility tends to coincide with reversals—and why reversals drive rebalancing costs.

(0:31:15) Practical guidance: Who, if anyone, should use leveraged single-stock ETFs.

(0:34:58) The limitations of arithmetic means and single-period models.

(0:36:55) Why aggregate investors are not buy-and-hold investors.

(0:39:17) The shortcomings of arithmetic averages, alphas, and Sharpe ratios for long-horizon measurement.

(0:42:38) Why log returns don’t solve the core measurement problems.

(0:44:56) The case for dollar-weighted returns and the limitations of IRRs.

(0:48:18) Modified IRRs and their role in capturing aggregate investor outcomes.

(0:50:14) Introducing the sustainable return: Measuring what can be withdrawn without depleting capital.

(0:53:22) Expected sustainable return and its close relationship to the geometric mean.

(0:56:09) Proportional sustainable return and withdrawal-based performance measurement.

(1:00:00) Individual stock returns through the lens of sustainable returns.

(1:00:53) Nudging academic finance beyond the “econometric streetlight.”

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, and Cameron Passmore, Chief Executive Officer at PWL Capital.

Cameron Passmore: Welcome to episode 397. Nice to be back with you, Ben. It's been a while since I've been on the pod. 

Ben Felix: Been a while, yeah. Good to have you back.

Cameron Passmore: I think it's actually my first time this year to be on and pretty exciting to be talking with today's return guest, Hank Bessembinder, which is a name most listeners certainly are aware of. 

As I said, a returning guest, phenomenal guest, so well-spoken, so thoughtful. I don't want to kind of spill the candy here in the lobby because you're going to do a great intro, but wow, so many interesting things. It kind of links back to your recent podcast and YouTube on ETF slop and kind of the things that are happening in the marketplace. With that, Ben, you have to queue this one up.

Ben Felix: Yeah. We had Hank on back in episode 346 last time and that was actually with Mark and I interviewing Hank. We talked about a bunch of his research then, but he had a couple of new papers out that I thought were really, really interesting. 

As you mentioned, I included one of them in the video that I did on ETF slop. He has a paper out on levered single stock ETFs, which I think are kind of ridiculous. I think Hank does a very good job delicately explaining when they could be useful for someone if they really had a very, very specific hedging or view that they wanted to express in the market. 

I suspect that he agrees that for most people, and I think this comes out in the conversation for most people, they're probably crazy investments. Anyway, so he's got that paper, which was just fascinating. It's kind of an extension of his research on individual stock returns. 

He's kind of said like, okay, we know how skewed individual stock returns are. How does that change when we introduce 2X or 3X long or short leverage? He does a paper on that, which we discussed at length. 

In that conversation, we also discussed the concept of constant leveraged index ETFs because you can get like a 2X or 3X S&P 500 ETF, which you'd expect to perform quite differently from a leveraged single stock ETF. We talked about how those two things might be different. You'll hear Hank say in the conversation, I think I piqued his interest in that he may consider including some index ETFs in his future analysis, which I would be personally very interested to see and I think listeners would too. 

We spent a good amount of time on that. One thing I wanted to point out on the single stock paper is that Hank talks about the costs of these ETFs relative to a benchmark. He describes the benchmark during the conversation, so I won't go into detail on that, but it just jumped out of me after we got through the section that I should have highlighted this during the conversation. 

He talks about the costs of these funds being quite high, but he quotes them in monthly terms. I just want to emphasize that the annual costs, so if we look at long leveraged stock ETFs and then his sample, they're issued since 2022. I think he says 34 single stock ETFs, so it's not huge, but he finds that they underperform a simple frictionless leveraged benchmark by an average of 0.79% per month. Now that is more than nine percentage points per year. That's the point I wanted to highlight. 0.79%, that's not that bad. That's a monthly. That was for long-levered, for short-levered, he finds a 1% underperformance. That's again monthly, so that's 12 percentage points annually of underperformance relative to his benchmark. 

I just wanted to highlight that so it's clear for listeners as they're listening to that section. Those are big numbers.

Cameron Passmore: You said there's hundreds more that have arrived to the marketplace, right?  

Ben Felix: This is my ETF slop video. This has become the thing that all the issuers want to get into the market for these leveraged single stock products. We talked about this during the conversation.

Investors are overconfident, they're distracted by shiny things and ETF issuers are like, hey, this is a great way to make money. People want this stuff. People do, they want it. 

People want prediction markets too. They want to gamble. If you're an ETF issuer and the regulators are giving you the thumbs up, it's a market, why not? 

Why wouldn't you issue them? We talked about that, about constant leverage ETFs, both in the single stock and index format. I hope some future interesting research comes out of that. 

In the second half of the conversation, we talked about measuring investor outcomes. He's got two recent papers out on that. One is measuring investor outcomes. 

The other is how should investors long-term returns be measured. We spent a whole bunch of time talking about just the concept of what is a return? Who is the investor that we are measuring the return for and how does the measurement differ depending on who they are?

How does return measurement change when you introduce spending, which is relevant for pretty much every investor at some point? Institutions, individuals, everyone has a spending need. That's really why they invest, to fund future consumption or whatever the cash flow needs are. 

He's got a new measure that he introduced in a paper called the sustainable return. He's got the proportional sustainable return, which are very, I think, financial planning relevant and friendly return measures. We talked about that and he's hoping that academic research moves more in this direction, which I think is really interesting because you can see this convergence of financial planning oriented research and academic finance research arriving at a point where they're relevant to each other, which I think is pretty cool to see. Any other thoughts?

Cameron Passmore: No. Great setup. Great interview.

Ben Felix: We'll link the papers in the show notes. There are three papers we talked about. Lots of interesting stuff. Pretty nerdy episode. Hopefully, people enjoy it.

Cameron Passmore: No doubt. Okay. Good to roll.

Ben Felix: Let's go to the episode with Professor Hank Bessembinder. Hank Bessembinder, welcome back to the Rational Reminder Podcast.

Hank Bessembinder: Well, thanks, Ben. I'm happy to be back. Looking forward to talking about these newer papers.

Ben Felix: Two really interesting papers that we're going to talk about. To start, we're going to talk about constant leverage ETFs, which you've looked at for single stocks in a new paper. Can you talk about what volatility decay is with respect to constant leverage ETFs?

Hank Bessembinder: I should probably start by saying volatility decay is not my favorite expression here because it has this aura of inevitability about it. I think also in some cases, it's been misinterpreted. Let me tell you what I see as the role of volatility. 

There's definitely a role of volatility here. Also, one of the points we got to keep clear, we don't get to live in history. We have to make decisions in real time before we know how things are going to turn out. 

So the discussion for the moment, what we want to focus on is making decisions without knowing how, say, the underlying asset is going to perform. Ex-ante. We're operating ex-ante. 

Volatility matters in two ways. First of all, and part of the reason I got into this project, my prior work about long-run stock returns highlighted the role of skewness in the distribution. When you have a positively skewed distribution, your median outcome is below your mean outcome. 

That same issue comes up here. What was driving that is compounding, the compounding of random returns. Of course, we still have that with levered ETFs, in a sense, on steroids.

When we go to individual stocks rather than indices, of course, volatility is a bigger thing. The skewness issue is there. What drives the skewness in the compound returns is the volatility of the short horizon returns.

With leverage and individual stocks, there's more volatility. So you're going to get a bigger gap. Volatility gives you a bigger gap between the mean outcome and the median outcome. 

You could call that volatility drag if you want, but I'm not sure that's how people have used the term. But anyway, it's a reality. The more volatility there is, the bigger gap you're going to get between the mean outcome and the median outcome. 

That's one important role of volatility. The second role is what does volatility do to the mean outcome, the average outcome? The point I wanted to make that I think has maybe not been fully appreciated is the answer might be nothing at all. 

Volatility does not have to affect the mean outcome on a levered ETF, but it could. How will it? The thing to recognize about rebalancing trades in a levered ETF that's keeping constant leverage is they're basically momentum trades. 

If the underlying went up, you're buying. If the underlying went down, you're selling. So it has this momentum-like strategy. 

So from that, it's really easy to see what's going on here. If you get continuations, you actually do better. If you get reversals, you do worse. 

What volatility does is amplify that effect. If you have reversals and high volatility, it's going to pull down your mean return, your average return. If you have higher volatility and continuations, it'll actually pump up your mean return. 

I don't know if volatility drag really captures all of that, but that's what I see is the role of volatility in these constant leverage products.

Ben Felix: For context for listeners, constant leverage is like a 2X leveraged ETF. They're typically rebalancing daily to maintain that 2X leverage, which means that they're placing trades, buying or doing whatever they have to do to maintain that constant leverage ratio based on what happened the previous day. Sounds like what you're saying is based on the specific series of returns that happen following rebalancing or when they have to rebalance, you're going to get either a drag or maybe not. 

It could be a negative or a positive having the daily rebalancing depending on what happens. But it's not necessarily true that volatility on its own is a bad thing for a constant leverage ETF. Does that make sense?

Hank Bessembinder: Yep. Not necessarily a bad thing in terms of pulling down your mean or average outcome. It will create this wedge between the mean and the median outcome.

Ben Felix: You talked about ex-ante decision-making. How concerned should investors in constant leverage ETFs be ex-ante about volatility decay?

Hank Bessembinder: I don't know if concern is the right word as you just want to understand it. It is going to create this wedge between the mean and the median. Of course, the median by definition is half the outcomes are above, half the outcomes are below. 

The more volatile the situation, the bigger this wedge between the mean and the median is. If you just think of it in terms of a batting average, to use the baseball analogy, volatility is going to reduce your batting average, your win rate. Just be aware of that. 

On the other hand, volatility is the underlying issue of skewness. The thing about skewness is there's some possibility of a home run. Volatility also increases the chances of a home run.

That's how you want to think of it. Volatility, compound levered product is increasing your chance of a home run but also reducing your batting average.

Ben Felix: That's true. Whether you do daily reset leverage, whether you have constant leverage or any other type of leverage, you're going to increase your volatility regardless. With the constant leverage, it's really that I think what people get worried about with the volatility decay concept is that daily reset. 

I think what I found really interesting in your paper is that that daily reset is not necessarily a bad thing.

Hank Bessembinder: That's correct. Any levered product will have the properties that I just described. Then the daily rebalance then either makes things better or worse depending on whether you had continuation or reversals.

Cameron Passmore: Now, your paper focuses on single stock ETFs. I'm curious to know what you think about constant leverage index ETFs as a form of long-term leverage for investors.

Hank Bessembinder: It's essentially the same issues for an index ETF as for a single stock ETF. It's kind of what caught my eye about single stock ETFs is the volatility and skewness is going to be greater. Those were things that I was already interested in. 

The underlying issues are the same, just a little bit muted because the index is going to be less volatile than the individual stocks on average. We already touched on the fact that it's going to make a difference whether you end up having continuations or reversals in the underlying. It's probably the case that individual stocks have more reversals, a liquidity thing, especially in historical data. 

So to the extent that the index has less reversals on average, then the cost of the daily rebalances is not going to be as high for an index, but only if it doesn't have the reversals.

Ben Felix: Yeah. So it's really dependent on the time series of returns that you end up getting, which you can't know in advance. I found your discussion, like you say this in the paper, that you're addressing this issue in a way that maybe has been overlooked in the past. 

Some of the past research on this concept on constant leverage ETFs has really been cautionary against using these products as long-term holdings. Why do you think past research has been so cautionary?

Hank Bessembinder: Well, there are good reasons for caution. In my prior papers about long-run compound returns in the market, the results seemed surprising to a lot of people. What I take away from that, and I got to admit they were surprising to me at first too until I eventually I think got a grasp as to what was going on. 

The thing is the properties of compound random returns can be a little bit counterintuitive. And then with the levered products, we add in the additional effects of the daily rebalancing, which can also be counterintuitive. And then the third thing is fees and what I call frictional costs are high. 

What it all comes to is you might not get what you naively think you're going to get. If you say, gosh, that underlying produced 20% and I was in a 2X product, where's my 40%? There's a long list of reasons that you might not be at 40%. 

It's not so simple to completely unpack what those are. These products can really catch you by surprise if you don't fully understand them.

Ben Felix: I think the thing that's interesting to think about is that everything that you just said, kind of like we talked about earlier is true. Whether you're in a daily reset leveraged ETF or whether you're going to the bank and taking out a loan or using margin or whatever, those properties are going to be similar. The one difference is the daily resets. 

Hank Bessembinder: The daily reset is the difference that comes from maintaining constant leverage.

Ben Felix: If you have 2X leverage, no matter how you get it, you're not going to get 2X the compound return. That's just true because of the volatility properties that you've been talking about. 

The thing that I think is interesting to think about is maybe the daily reset is not as bad as I think some past papers have made it seem. That's at least my perception from reading your paper after having read those. I made a video years ago about leverage and I talked about how volatility decay, it's a bad thing. 

It's this additional cost that you get from the daily reset so you shouldn't use those as a long-term holding. After reading your paper, I'm kind of questioning what I had said back then.

Hank Bessembinder: Two things in there I think I should respond to. I agree. I don't know if I'd exactly use the words not as bad as it appeared.

What I'm saying is that the daily rebalance doesn't necessarily hurt you. That's why I'm a little resistant to the term volatility drag, especially if people are going to use the volatility drag to refer to the effect of the daily reset because it doesn't necessarily hurt you. It all depends on whether you end up with reversals or continuations.

To the extent reversals are more likely, then on average it'll still hurt you, but it doesn't have this inevitability to it that some of the prior discussions had suggested. One thing I will say though about what's attainable, if you just use a margin account to get to 2X leverage and you don't have any additional trading costs, you actually can get twice the underlying. If there's no frictions, you've got your borrowing costs which are going to pull you down a little bit, but in a hypothetical where if you didn't have the borrowing costs and if you didn't have trading costs, you really could get two times the compound on the underlying. 

Many of the complexities come from the frictions and from the daily reset.

Cameron Passmore: How do the rebalancing costs for long and short lever ETFs differ?

Hank Bessembinder: Well, it's the same underlying issue that reversals, should they show up, will damage your performance. Continuations, should they show up, will improve your performance, but it's not symmetric across long versus short. People who looked at these issues long before I did, worked out the math of how large these rebalancing trades need to be, what drives the size of the trade, first of all, how big is the return on a given day, but beyond that, what shows up in the algebra is the square of your leverage ratio minus your leverage ratio. 

If L is the leverage ratio, L squared minus L, that determines how big your trades need to be. You could just plug some numbers into that and quickly see that for negative leverage, that turns out to be bigger. For negative two, it's bigger than it is for positive two. 

What that all comes down to is that the rebalancing trades are bigger with negative leverage, other things equal. The effect of rebalancing is going to be larger for negative leverage.

Ben Felix: Real quick for listeners, we're talking about looking at leveraged single stock ETFs. Can you talk about how you benchmark returns to constant leverage in your paper?

Hank Bessembinder: It's really not too much different from what prior people had done when they were looking at index products, and I alluded to it a minute ago. Suppose that instead of buying the levered ETF, you simply borrowed, whether it's on margin or you took money, got out a loan from your bank, you simply borrowed to establish a levered position. But then once you had borrowed to establish the levered position, from there on, you're buy and hold, you just leave it there. 

Something that may or may not be obvious is that if you do borrow to get to say 2X leverage and then after that you're buy and hold, you don't stay at 2X leverage as the performance of the underlying changes, your leverage changes. This is why the constant leverage product has to trade every day to keep the constant leverage. This relatively simple strategy of borrow, establish a levered position, and then don't trade anymore is what I use as the benchmark. 

Given how the underlying performs, that turns out to be a pretty simple benchmark to compute. We've also got pretty simple expressions for how the constant rebalance position should have performed every day. We can say, okay, given what the underlying did, how should the constant leverage position have done every day? 

We just compare how you would have done if you had been levered buy and hold to levered constant leverage, and that difference is what I label as the rebalancing cost. But then we can take it a step further. The actual funds trade, so you can compute what the hypothetical performance should have been given the constant leverage. 

Then you can see what the fund actually delivered. It's going to be less, and that's what I label as frictions.

Cameron Passmore: How do you decompose levered ETF returns?

Hank Bessembinder: That was it in essence. You start with the actual return that the levered ETF delivered, the actual compound return that it delivered. Compare that to what constant leverage would have delivered if it delivered according to the formula. 

It just gave you your leverage every day, and there is an allowance in there for interest for borrowing costs. But if the actual performance is less than what the constant leverage strategy would have delivered without any frictions, that difference is labeled frictions. Then the difference between the frictionless daily rebalance and the frictionless buy and hold is the effect of daily rebalancing. 

We can decompose the actual performance against this simple hypothetical alternative of establish a levered position and don't trade anymore. We can decompose it into two parts, a friction piece and a daily rebalancing piece.

Ben Felix: You've got implementation costs, trading costs, fees, and that kind of thing. Then you have the rebalancing piece that we've been talking about empirically. Again, this is for single stock ETFs, not for index levered ETFs. 

Empirically, how do the ones that you look at in your sample perform relative to your benchmark?

Hank Bessembinder: I should first of all clarify the sample that's in the current version of the study, it's 35 levered ETFs for which I could get a reasonably long time series of data. I should mention I plan to update the study probably in the next month or two. There's been literally hundreds of additional single stock ETFs launched that are not included in my study. 

As soon as the database provider updates the data, which should be in a week or two, they should have it updated through the end of 2025. I plan to update the study and there'll be a much broader set. For the 35 funds that were in my study, I found that they underperform.

If we look at a monthly horizon, the levered long funds underperform the simple benchmark by eight-tenths of a percent per month, and the short funds underperform a simple benchmark by one percent per month. Those are fairly big numbers. Now, the underlying stocks did well. 

These products were first launched in 2022 on a few high-flying stocks that have continued to be high-flying. The long funds actually delivered pretty good mean returns, but nevertheless, they were underperforming this simple benchmark by eight-tenths of a percent per month.

Ben Felix: We talked earlier about how you can decompose that performance or underperformance in those cases. Can you talk about how those two components contribute to the underperformance of each, long and short-levered ETFs?

Hank Bessembinder: This was one of the more interesting things because there's asymmetries across the long and the short. For the long-levered funds, about a quarter percent per month was being lost to rebalancing, while more than half a percent per month was being lost to frictions. I probably should clarify just here a little bit about frictions. 

The fund will have trading costs. The fund has management fees. On top of that, most funds are using swaps to gain their leverage. 

Those swaps have embedded borrowing rates, and those embedded borrowing rates are higher than you might think. When I built in my frictionless benchmark, I didn't pretend money was free. I said, okay, you have to pay to borrow, but I used the federal funds rate, or I could have used the U.S. Treasury bill rate. It would have been about the same thing. But in any event, to the extent that the funds are paying an interest rate that's higher than the federal funds rate, that's also showing up as a friction. I think that's actually a big piece of what I'm measuring as a friction.

In any event, for the long funds, the underperformance was about two-thirds due to frictions and one-third due to rebalancing. For the short funds, it goes the other direction. About three quarters of a percent per month is due to rebalancing. Only about a quarter percent per month is due to frictions.

Ben Felix: That is so interesting. That was one of the more interesting parts of the paper.

Hank Bessembinder: I found it interesting. I think I'm starting to understand where it's coming from. These higher interest rates embedded in swap terms are mainly relevant on the long side. 

And then the point we brought up a moment ago, that other things equal, your rebalancing trades are bigger for an inverse fund. I think that's probably what's driving things. One thing I might add, I mentioned that so far I've only got 35 funds. 

There's been hundreds of funds launched more recently. The anecdotal evidence, for example, from Jeff Ptak, I hope I said his name correctly, over at Morningstar, he's showing me some data for some individual funds. The anecdotal evidence is that some of these funds are paying much higher borrowing costs. 

In any event, when I get the paper updated in a few weeks, I'll be able to say something more about that.

Ben Felix: You had a great article on that that I included in a video that I did on ETF slop, in which I included these leveraged single-stock ETFs. Would you consider including leveraged index funds, ETFs, in your update?

Hank Bessembinder: I wasn't thinking about that just because other people have been studying the index funds. I was kind of carving out a separate niche. There's a fellow named Baolian Wang, I believe, at Florida, who recently did a relatively updated study on index funds. 

I might just keep this to the individual stocks for the moment. But who knows what will come up for the next project?

Ben Felix: I'll look for his stuff. But just seeing the analysis that you're doing with single-stock leveraged ETFs side-by-side, like the same exact type of analysis and how you're breaking down the underperformance, I think it'd be fascinating to see for index and single-stock side-by-side.

Hank Bessembinder: I think I might put that on my to-do list.

Ben Felix: Seeing how the components of underperformance break down for the two different types of investments, I think it'd be really, really interesting.

Hank Bessembinder: Yeah, I agree. That does sound interesting.

Cameron Passmore: How common is a return less than minus 100%?

Hank Bessembinder: If you look at my paper, it says it hasn't happened. But right after I drafted that, it did happen on a levered ETF. Not one listed in North America, but one listed in London. 

I'm sorry, but I don't remember all the details offhand. But one of the tech companies, maybe Cisco, I don't remember for sure, one of the tech companies went up more than 50% in a day. So the negative 2X product, we should get in here, the target return was less than negative 100% on the negative 2X product. 

It's never happened among ETFs listed and traded in the US, but it could happen. In the paper, in addition to studying 35 leveraged single-stock ETFs that have actually been launched since 2022, I did a hypothetical. What if hypothetically we had had levered single-stock ETFs over the past 50 years? 

This is a little bit of a broad interpretation because we probably even hypothetically wouldn't have had levered ETFs on every stock. But if we had in the past, we would have had cases where a levered ETF had a promised return of negative 100% or worse about five times per day on average.

Ben Felix: Wow. That's wild.

Hank Bessembinder: It's never happened in the actual products, but it certainly could have happened with a lot of frequency in the past. In fairness, that's driven in part by saying, well, if hypothetically there had been levered products on all stocks, there's a lot of micro caps out there. If I restrict it to the larger capitalization stocks, it's considerably less frequent, but it still would have happened a lot of times. 

And even with some household names, Apple had a day during the dot-com bubble where it dropped more than 50% in a day. So if you had had a 2X product on Apple on that date, it would have shot right through negative 100%. A really interesting case study, I think GameStop, when it first hit the headlines in January 2021, there were not any levered products on GameStop at the time. 

There is at least one, maybe more than one on GameStop now. If there had been, I looked at the data, 3X, 2X, negative 1X, negative 2X, they would have all blown up during that month. All four of them would have blown up during the month with a promised return, a target return less than negative 100%.

Ben Felix: Yeah, that's wild.

Hank Bessembinder: This is a real possibility. And I really think it's only a matter of time until it's going to happen with a product listed in the US.

Ben Felix: You mentioned the simulations. Can you talk more generally about how the single stock leveraged ETFs in your simulations perform? And in this case, they don't have the live product frictions, but they still have some of the other rebalancing costs. 

I'm curious how that sort of distribution of returns for leveraged single stock ETFs looks in your simulations.

Hank Bessembinder: As you said, there's no frictions. It's basically just the levered return and the effect of the daily rebalancing. In some sense, it's what you'd expect. 

The long products would on average have made money. The short products would have averaged lost money. The last 50 years in the US markets, the overall market was strongly up. 

In terms of the means, the long products would have delivered good returns. The short products would have cost you money. But the skewness is there, which drives the wedge between the mean and the median. 

For the most part, the median returns are negative. The only exception was for the 2X product. That's where we've got relatively modest leverage in combination with hindsight, a strong equity with premium. 

Even there, the median was considerably below the mean, of course, but it stayed positive. But for the 3X product and for the short products, the median's negative.

Cameron Passmore: And what role did rebalancing costs play in the simulated outcomes?

Hank Bessembinder: On average, for the full set of stocks that I simulated, rebalancing costs dragged down performance. It was costly to have daily rebalance. As we talked about earlier, that's basically a question of whether you had continuations or reversals on average in the data. 

For individual stocks in the US over the previous 50 years, on average, it's been reversals. The daily rebalancing has degraded performance.

Ben Felix: We already talked about this earlier, but maybe just in the context of these simulations, how does the empirical relationship between volatility and serial correlation affect the rebalancing costs that you see?

Hank Bessembinder: I came across something that was surprising to me, or maybe I should just say informative to me, because if you look about what's been written or when politicians weigh in on these levered products, you tend to see a lot of statements that basically say volatility is bad for these products. Volatility is bad for investors in these products. And in part, I was pushing back on that by saying, well, it's not necessarily bad. 

Some things I found in the historical data, some of these other researchers and observers of the market were at least aware of some of these. But one of the things I found is that underlying stock returns differ depending on high volatility periods versus low volatility periods. And it's that underlying stock returns tend to be worse during high volatility periods. 

So that's one part of the mix. But the other thing is that I found empirically, we tended to get more reversals during high volatility periods. Some people might say, well, isn't that obvious? 

And it wasn't obvious to me. It doesn't have to work that way. Think of geometric Brownian motion or random walk or IID, a set of returns that don't have any serial correlation, don't have any memory. 

In those models, you can turn volatility up or down without creating any reversals or continuations. So they didn't have to come together. But empirically, high volatility periods have also been reversal periods. 

So maybe now that we're starting to make some sense out of why so many observers say that volatility is bad for these products, that they've observed that at least on average, high volatility periods tend to be reversal periods. That's where I'm shining the spotlight. Reversal periods are where your returns get dragged down by the rebalancing.

Ben Felix: That's so interesting. So the concept of volatility decay is really kind of an observation that reversals spike up when volatility is high. But it's really reversals that are driving that wedge, not the volatility.

Hank Bessembinder: Yeah. Think of the volatility as strengthening or being an amplifier for whatever sort of serial correlation you have. The technical term that some of your audience might be okay with, what matters is the serial covariance, which is the product of the volatility and the serial correlations. So they both matter.

Ben Felix: That's super interesting. Back to what we were talking about earlier with index versus single stock, it would be interesting to see the difference in reversals in those two with individual stocks versus indexes. I wonder if indexes have less aggressive reversals during times of high volatility.

Hank Bessembinder: You're piquing my interest.

Ben Felix: I'm glad.

Hank Bessembinder: Might be good to see those results side by side.

Ben Felix: Yeah, I think so.

Cameron Passmore: How do you think most investors should approach the use of single stock levered ETFs?

Hank Bessembinder: I think most investors should be hesitant. And the reason I say that is these are complicated and can be counterintuitive products. And I think the first hurdle is you really shouldn't be dabbling in these unless you really understand them, which is kind of a high hurdle. 

But for those that get across that hurdle and kind of know what they're getting into, if you use them on a daily basis, you just be in for a day and you're out, which is at least officially how the companies that create these products say this is how they should be used. It's all about having either you got something you want to hedge for a day or you have a strong directional view and you think today's the day. If that's you, you have the need to hedge something for today. 

You have a strong directional view for today. The product is designed to give you a way to deal with that, a way to take advantage of that. Where things get trickier is the possibility of entering one of these positions and staying there. 

To their credit, the vendors generally warn this is complicated. Things might turn out different than you thought. I understand the motivation. 

Somebody sees how well NVIDIA has done in the last three years and says, wow, wouldn't it have been great to have 2X on that? I understand where the motivation is coming from. Another possible motivation, you know, it's kind of, econ speak, but we talk about skewness preference. 

I think the truth is some people like the idea of skewness. They like the idea of the possibility of really big payoff. I think that's showing up in a lot of places in the financial markets. 

I'm kind of a fan in principle of prediction markets, but I think prediction markets are starting to be used that way by some players as well. But in any event, if you're doing it because you want the chance of a really big payoff, well, skewness does give you the chance of a really big payoff. But I'm just saying go in with your eyes open. 

Skewness means your batting average is not as high as you might think it is. Should it turn out that there's reversals, maybe NVIDIA got a big return, but you're not going to get twice NVIDIA's return if it turns out there were reversals on the way. And then there's this question of how high the fees are, the fees and frictional costs. 

To me, numbers like three quarters of a percent or 1% per month loom large. Maybe if you're really sure you're going to get 40%, you don't worry about that. But on average, those are going to catch up with you.

If you know what you're doing, and either you have a really strong directional view or you have the skewness preference, the product is there. Just recognize the complexities and the cost.

Ben Felix: These are single stocks, so it's like we talk about skewness. You're more likely to lose than to win, but if you win, you could win really big. I think last time we had you on, we talked about basically that concept and how skewness isn't a bad thing.

It means that you can win really big if you're smart. I can't remember what I asked you, but you said something about how people should review literature on overconfidence if they think that they're going to be the one that picks the big winner.

Hank Bessembinder: That's an issue, all right. I think I, a few moments ago, used the phrase, if you have a strong directional view, just remember there's somebody else on the other side of that trade. What's their view?

Ben Felix: Yeah, I think a lot of people have strong directional views that they maybe shouldn't have. These tools make it really easy for them to speculate on those views and charge some pretty meaningful fees for the privilege.

Hank Bessembinder: Behavioral psychologists have done a lot of research and the fact that most of us tend to overconfidence is one of their more solid findings, something to keep in mind.

Ben Felix: Makes it a profitable business if you're an ETF issuer. The other couple of papers that you had recently that I thought were really interesting were on measuring investor outcomes, measuring long-term returns for investors. Where do you think academic research has fallen short in its measurement of long-term returns for investors?

Hank Bessembinder: I should maybe preface this a little bit. Some of what I'm going to say is a little bit critical, but frankly, I'm criticizing myself as much as anybody. I'm relatively new to these thoughts that are in these papers here. 

I should also say, I'm not arguing we should burn down the house. There's a lot of tools that have been developed and they are informative tools and we're going to continue to use them. With those caveats in place, I just don't think we have been serious about trying to measure long-run investor outcomes. 

Most of what we do is arithmetic means, which we can talk a little bit more about, but arithmetic means don't capture. You've got a series of monthly returns or annual returns and then you just take the average of them. That doesn't capture a long-term investor's experience. 

Arithmetic means are not even an attempt to capture a long-run investor's experience. The one thing we do sometimes is compute buy and hold returns or geometric means and then you compound them, you get buy and hold returns. That's at least a good faith attempt to try to capture a long-run investor's experience.

I'm going to borrow a phrase here. I think it was actually originated by Edward McQuarrie. I don't know if he's on your radar screen. 

If not, I think your audience might enjoy hearing from him. He's made some good arguments lately, but he uses the phrase, "the return that nobody ever got." That's what comes to mind for me when we compute geometric mean and buy and hold returns. 

It's a good hypothetical. It's informative. What would you have earned if you had just bought this investment, reinvested your dividends and other than that, just held it?

It's informative, but nobody does that, especially over really long horizons. Think of the sort of data that's in Jeremy Siegel's book. He computes the buy and hold returns over 100 years or so. 

Nobody was buy and hold for 100 years. I don't think we have been serious to date about actually trying to measure outcomes for long-term investors. We're not serious enough.

Cameron Passmore: What problem do dividends introduce for measuring aggregate shareholder returns?

Hank Bessembinder: The first thing I should talk about a little bit is aggregate versus non-aggregate or representative versus non-representative. There's a lot of perspectives that can be brought to bear. You can talk about a hypothetical investor who used a given trading strategy. 

How did they do? You can talk about an actual investor who used the trading strategy they used. How did they do? 

But I think at least in some contexts, it's interesting to ask, well, how did investors overall do? How did the group, the body of investors do overall? In my earlier papers, I had this wealth creation measure, which was an attempt to go that direction to try and capture the aggregate experience. 

I think particularly for economists who study the markets, not necessarily as much for an individual investor or an investment manager, but for economists that study the markets, I think we should be paying more attention to this idea of the body of investors, the aggregate investor. That's the preface. Here's the deal on comparing the aggregate investor to what I just laid out, the buy and hold investor. 

The aggregate investor is not a buy and hold investor. How do we know that? First of all, dividends. 

Companies pay dividends. The aggregate investor does not reinvest the dividend. Individuals can. 

I do. Maybe you do. A lot of people do. 

If somebody's buying the stock to reinvest their dividend, somebody else is selling the stock. Across the two of us, it's not been reinvested. All the secondary market trading in the world will never put that money back in the company. 

The only way it gets back in the company is if they sell some more shares, which brings up another way that the aggregate investor differs from the buy and hold investor. When companies do sell more shares, the aggregate investor funds it. When companies repurchase shares, the aggregate investor receives it. 

The aggregate investor is not a buy and hold investor. One of the things I've tried to bring out, and I'm not the first person to think about this, I've got references in the paper, but I want to try to motivate people to think more about what the aggregate investment experience is. For that, the buy and hold is not the right answer, and the arithmetic mean is not the right answer either.

Ben Felix: Can you talk more about the problem with using arithmetic means? They're so common, as you mentioned before, in academic literature, in mean variance optimization, in Sharpe ratios, which people still today cite all the time. What are the problems with using that measure?

Hank Bessembinder: Again, I should preface this not to get people any more upset than necessary. We only want to get people optimally upset, not extra. There's a lot of information in arithmetic means and Sharpe ratios and mean variance optimization. 

There's a lot of statistical theory we can draw on there, econometric theory, so we can test hypotheses about those things. Those are reasons we're not going to abandon them anytime soon. That said, arithmetic means just add up the returns and divide by the number of observations.

They're not even an attempt to capture what happens over multiple periods. I think it's two things. One, arithmetic means are just really simple and we've all been using them since second grade. 

The other thing is the Capital Asset Pricing Model. We're all aware of the evidence that suggests the Capital Asset Pricing Model probably doesn't work like we wish it worked, but it's a nice, simple, intuitive model. Go back to that model. 

It's a single period model. In single period models, you don't think about long horizon investors. The things you brought up, Sharpe ratios, mean variance analysis, their intellectual roots are very directly in the Capital Asset Pricing Model, a single period model. 

The best thing about an arithmetic mean of a series of returns, let's just say you got monthly returns, you take the arithmetic mean. Under simple assumptions, that arithmetic mean is an unbiased estimate of the expected return in a future month. That's a strong defense for it, but notice the exact phrasing there. 

It's the best estimate of the expected return in a future month. It's still in no way an attempt to go after multi-period long run measures. Even the arithmetic mean itself, if you said, well, could somebody capture the arithmetic mean? 

You cannot capture the compound arithmetic mean. That's one of the first things we learned in Finance 101. The compound arithmetic means higher than the compound geometric mean, and there is no way to capture it. 

What you can do is rebalance every period to keep your investment constant. If your position went up, take some money off the table. If your position went down, put some more money in. 

If you rebalance every period to keep a constant investment, you will earn the arithmetic mean with no compounding, but that's the only trading strategy that the arithmetic mean gives you the answer to, what did I earn? As I said, it's not even an attempt to capture a long horizon investor's outcome.

Cameron Passmore: How do these issues extend to factor regressions?

Hank Bessembinder: Pretty straightforward, actually. One of the main reasons we do factor regressions is to get alphas, the portion of the arithmetic mean return that's not explained by factor outcomes, but alpha is still an arithmetic mean. What it has in common with things like Sharpe ratios and mean variance optimization is it's firmly rooted in the single period Capital Asset Pricing Model. 

Some might remember that alpha was originally called Jensen's Alpha, named for Michael Jensen. If you go back to Michael Jensen's paper, he's very explicit that he's developed this measure as an application of the single period Capital Asset Pricing Model. It's got the same issues and has the same intellectual horizon. 

If somebody wants an unbiased estimate of the non-factor based mean return in a given month, the monthly alpha is an estimate of that.

Ben Felix: Why can't we use log returns to solve some of these issues?

Hank Bessembinder: This is a good question and one I actually run into with some regularity. There's a lot of good things about log returns. I was actually having a, I don't know, I want to call it a debate, I was having a discussion with another researcher about pros and cons of log returns. 

He sent me back an email with about five paragraphs of advantages of log returns, which was clearly generated by AI. But that's okay, that didn't make them wrong. My point is there's some well established advantages of log returns out there. 

The biggest one is that you can sum them, you can sum log returns, you can't sum regular returns, which gets us back to why arithmetic means of regular returns are a misleading number. The problem with log returns is, and I think it's a big one, in my conversation with this person who was trying to convince me to use log returns, he was unable to give any response, a meaningful response to it. It's that a log return is actually misnamed.

It's not a return. What is it? It's a nonlinear function of a return. 

It's a mathematical transformation of a return. One of its nice properties, besides the fact that you can add it up, is that if we're talking about a short interval of time, it's still a really close approximation. But for long horizon investors, talking 10 years, 20 years, 30 years, okay, the good news about log returns is you can add them up. 

The bad news about log returns is they're not returns. You can add up a bunch of log returns and then undo the log, do an antilog exponential, and what you'll get, you probably know this, you'll get the buy and hold return. But you have to undo the log to get the buy and hold return. 

And if you want anything other than the buy and hold return, you're going to have to do something else besides that. The use of logs doesn't sidestep any of the issues. You can do the computation that way. 

You can multiply gross returns to get a buy and hold return, or you can convert to logs, sum them, and then do the exponential. They're identical. No issues are changed by which way you did the computation. 

So anyway, that's the issue. Every complexity that exists with real returns is not avoided. None of the complexities are avoided by going over to log returns.

Cameron Passmore: And what are the benefits of measuring performance using dollar-weighted returns or IRRs?

Hank Bessembinder: I'm growing to be a fan of dollar-weighted returns. I'm definitely not the first person to use dollar-weighted returns. And one of the things I think is interesting is they seem to be used a lot more in investment practice than among academics. 

I can only point to a handful of papers where academics have measured dollar-weighted returns. But in practice, you probably know Morningstar has their series, Mind the Gap. My Vanguard account shows an investment return number. 

I only recently dug into what they were doing. They were reporting a dollar-weighted return. I'm a fan of the dollar-weighted return. 

What I like about it is it tries to take seriously that we are not buy and hold investors. And I just had this conversation with another academic recently, and they said, I just put the same amount into my retirement fund every month. Doesn't that mean I'm a buy and hold investor? 

No, buy and hold is the geometric mean, the buy and hold. It applies to somebody who invests once and does nothing else until the end, except reinvest their dividends. If you're periodically putting money in, you're not a buy and hold investor. 

If you're periodically pulling money out, you're not a buy and hold investor. If you're doing a mix, you're not a buy and hold investor. Anyway, dollar-weighted returns try to take seriously, let's take into account money in and money out of an investment. 

I think it's got tremendous potential. I think it's way understudied. The biggest hurdle, I believe, is that we need our statistical friends, our econometrician friends to help us out so we can test theories about geometric means. 

To my knowledge, we don't have a good body of statistical tools, which we would need. The dollar-weighted return takes seriously the actual cash flows in and out of an investment.

Ben Felix: We've had Ludovic Phalippou who's been pretty critical of IRRs, specific to private markets. But yeah, what are the drawbacks of using IRRs?

Hank Bessembinder: I think this will overlap with what Ludovic had to say. The thing about an IRR, any of you or anybody who sees this podcast who's come through an MBA program or a corporate finance class has seen IRRs discussed in the context of project valuation. You do net present value, you do IRR. 

The same animal when applied to investment returns and applying it to actual cash flows as opposed to forecasted cash flows, it's the same animal. The reason we like it is it takes all these cash flows into account. Also, it's like an interest rate, which makes it pretty intuitive in a lot of contexts. 

But the thing about an interest rate is it's a percent per period. So it's completely stripped of scale. And it's also stripped of trying to find the correct short version for the issues that Phalippou was getting after. 

If most of your money comes back out of an investment after a year, but the investment continues for a few years, then for most of the time, you were not earning the IRR on your capital. The fact that it's a percent per period can be misleading. And in particular, there's going to be a temptation, you've computed it, comes out to be 1% per month. 

And then somebody says, well, how did I do over the 60 months? There's a temptation to then compound it. And I believe that's one of the things Ludovic was critical of also, and my coauthors and I are also critical of. 

Because when you take that IRR and compound it, you're assuming that the cash flow is reinvested at the IRR rate. And that's typically not available to you. The compound IRR is not a reliable number.

Cameron Passmore: And how does the modified IRR work?

Hank Bessembinder: It keeps what I think is the best features of the IRR, which is that it takes seriously the amount and timing of cash flows in and out of your investment. But then it doesn't make a counterfactual assumption about what happens to those cash flows. You also need to take seriously, okay, if this investment, private equity or other, if this investment threw off some cash, you reinvested it somewhere, what did you earn on the somewhere?  

It gives you a final outcome while also trying to be realistic about your reinvestment rates. And I believe Ludovic has also advocated for use of modified IRRs. I think he's on the right track.

Ben Felix: You talked earlier about the challenges with measuring aggregate investor returns. Can you talk about why the modified IRR is the only measure that has the potential to accurately measure compound returns for the aggregate investor?

Hank Bessembinder: Well, it basically draws on the points we've made in the last 15 minutes or so. The aggregate investor is an active investor. They're not a buy and hold investor because they don't reinvest dividends. 

They do participate in new equity issues and repurchases. So they are an active investor. The money that's put in, say if a company has an equity offering, has an opportunity cost, money that comes out can be reinvested somewhere at some rate. 

So it tries to be realistic about the fact that the investor is active, not buy and hold, and tries to be realistic about opportunity costs and reinvestment rates. So it tries to realistically capture everything that should be captured. Of course, there's practical data limitation issues. 

An individual investor might be able to do this. A family office might be able to do this. For the aggregate, we don't know. 

We don't know where the aggregate share repurchase cash flows get reinvested, so we just have to make assumptions, assuming it was done this way. That's why we only say it has potential to get the right answer without saying that necessarily we've done it in the paper.

Cameron Passmore: How does performance measurement change when there are portfolio withdrawals?

Hank Bessembinder: This is kind of, in my mind, a major philosophical distinction. What we were just talking about with the dollar-weighted return, it does take into account all of the cash flows, whether you're putting more money in or pulling money out. It takes them all into account. 

If you do what I just described and take that modified IRR and then compound it, it's an implicit assumption that any cash that comes out of one investment just gets reinvested in another investment. Then we measure the final outcome by what's your portfolio worth at some date in the future. Buy and hold had the same thing built in. 

It just assumes that you put some money in and you just leave it there and you measure outcomes based on your portfolio value at some future date. John Cochrane, who's another very thoughtful guy, I don't know if you've ever reached out to him as potentially being on your podcast, very thoughtful guy. He had a paper a few years ago where he advocated we should think more about measuring investments based on the series of cash flows that the investment can produce. 

In this second paper, my co-authors and I developed a measure that tries to implement that. It's a change in focus from how big is my portfolio at some future date. Sometimes as a motivator, I say, do we really want to measure our investment success by how big our portfolio is on our last day? 

Is that really what we had in mind? I don't think so. It's a change in focus from what is my portfolio value on a future date to instead how much could be withdrawn from this investment. 

What series of cash flows could this investment have supported? We developed a new measure with that exact idea in mind. We call it sustainable return. 

The reason we call it sustainable is what we work out is how much could you have withdrawn as a level annuity such that the final value of your portfolio is the same as your initial value. This can be inflation adjusted. I think it's more intuitive and more obviously useful if you think about it as inflation adjusted.

You can just think of it as saying how much of the corn could we have eaten each year without diminishing the seed corn. That's what we have in mind with the final value being equal to the initial value. That's why we call it sustainable return. 

I was recently talking about this measure in an audience that included some of the leading scholars on sustainability. They said, are you sure that's the term you want to use? People get confused with sustainability initiatives. 

I said, well, I'm kind of stuck. I already chose the term. I also asked the question, I said, what do you think is the definition of sustainable when people talk about sustainability initiatives? 

I posited that maybe it's not so much different from not eating the seed corn. I'm not sure if it's actually the wrong label or not, but in any event, we chose it. We're stuck with it.

That's what it is. It's the series of withdrawals relative to the initial investment, so it's a ratio. It's a series of withdrawals, periodic withdrawals relative to the initial investment that leaves your final value equal to your initial value.

Ben Felix: Given a specific time series of returns, you're solving for how much could have been withdrawn each period as a percentage of the starting amount?

Hank Bessembinder: Exactly.

Ben Felix: Such that you're left with the same amount of capital as you started with.

Hank Bessembinder: That's what it is. You used the phrase, "for a series of returns," and it is important to recognize this, like the other measures, is an ex-post measure. Like the arithmetic mean or the geometric mean or the dollar-weighted return, it's an ex-post measure. 

You can only see it after the fact. Nothing magic about it here. It's not something that guarantees anything for anybody. 

It's just an alternate way of measuring an investment performance based on the stream of withdrawals that it could have sustained.

Ben Felix: People are familiar with the 4% rule for retirement spending, which is how much you could have spent without running out of money in the worst sequence of returns in whatever time series you're looking at. This is quite different from that.

Hank Bessembinder: Well, I mean, it's related to it. It is an ex-post measure. The 4% rule, I think, to the extent people try to run with it, that you're using it as an ex-ante rule. 

You're saying, I'm spending 4% each year, and we'll see how things turn out. And people have done studies about how often would things have turned out well, how often would they have not turned out well. There is a parallel here. 

We worked out the math. We came up with that your expected sustainable return, in a statistical sense, the average sustainable return. The expected sustainable return is almost precisely the expected geometric mean. 

The expressions differ, but numerically, it's almost exactly the same number. So if you wanted to map it into a spending rule, it would map into focusing your spending on the expected geometric mean. I don't think that's an earth-shaking new insight.

The only thing is, geometric means are less than arithmetic means. It suggests focusing on the more modest geometric mean for your spending as a spending rule as compared to trying to spend the arithmetic mean.

Ben Felix: Even still, just to relate it back to the 4% rule, if you use the sustainable return, the geometric expected return, for example, as a spending rule, there's a pretty good chance that in a given sequence of returns, you'll run out of money. It's not designed to hedge against that bad outcome. It's just the expected outcome.

Hank Bessembinder: Yeah, it's an expected outcome. The paper has the exact formula for the sustainable return, but the numerator of the formula is the geometric mean. We expect geometric means to be positive, but in any given time series, they can be negative. 

If you're trying to pull out the same amount each period in a series of returns that has a negative geometric mean, you're going to run out of money. It's certainly not a guarantee.

Ben Felix: Related to that too, and we'll get there in a second, I just want to mention for listeners, because you brought it up earlier, it's a little bit out of context now. We have had John Cochrane on twice. 

We did one episode on portfolios for long-term investors and we did one episode on fiscal theory of the price level. He was fantastic.

Hank Bessembinder: I need to go find his episodes because he's always worth listening to.

Ben Felix: They're good episodes.

Cameron Passmore: How does the proportional sustainable return work? 

Hank Bessembinder: It kind of naturally flows from the discussion we were just having. Again, sustainable returns is an ex-post measure. We do think it's informative. 

We do think it's creative. Maybe we're patting our own back here. Creative way, alternative way to think about investment performance, but you only see it after the fact. 

If you try to operationalize this in real term, there's a substantial risk of ruin. You could well run your portfolio value down to zero. The proportional sustainable return says, well, instead of specifying a constant dollar amount each period, what is a constant percentage of your current investment that you can pull out subject to the same final condition that your final value is equal to your initial value? 

We also ran out the math on that one and it turns out to be a pretty simple thing. The proportional sustainable return, the rate of proportional withdrawal leaves your final value equal to the initial value is the geometric mean divided by one plus the geometric mean. It's pretty close to just being the geometric mean.

We think that's potentially useful too. That when you're in no danger of exhausting your balance, but you don't have a level annuity, you have just a constant percentage of the value of your portfolio. As long as there's never a negative 100% return, your series of withdrawals never goes to zero. 

An interesting point, Phil Dybvig, another interesting fellow, Nobel prize winner, who I have great respect for, actually developed a very similar spending rule, but with much more complicated setup, much more complicated mathematics. We just got it with a few lines of algebra, basically.

Ben Felix: Wow. Super interesting. People can do some mix of the two approaches. 

There's a lot of financial planning research on this where you can do something like a total proportional spending rule, but you can cap the amount that you increase or decrease your spending each year. So you then introduce a probability of ruin, but you can get somewhere in between a pure constant dollar spending and proportional spending so that you don't have such a volatile income, which many people are averse to.

Hank Bessembinder: Understandably. Much of the work that's been done here has been done with numerical simulations, basically going through the historical data and saying, how would it have worked out? And I respect that. 

What we're hoping, and we can't claim more than baby steps, but with a couple of closed-form solutions, analytical solutions, we're hoping that there's some possibility of reasoning out solutions here, as opposed to doing numerical historical evaluations. We're not there yet, but we're hopeful this can nudge us that direction.

Ben Felix: That's really interesting. It's cool to see serious finance researchers going in that direction. We have James Choi coming back on the podcast in a bit. 

He's done some work on what he calls practical finance, taking financial theory and making it really easy for people to implement with an Excel spreadsheet. And it sounds like you're kind of doing similar stuff, which is awesome.

Hank Bessembinder: Trying to go that direction.

Ben Felix: Yeah. I mean, it's great to see.

Hank Bessembinder: Related to your comment, this area of research, I think, is way understudied by finance researchers. I mean, there are kind of a subset of people in finance departments who do call it pension and financial planning stuff, but I think there's room for a lot more people to be trying to grapple with these issues.

Ben Felix: There's a whole body of financial planning research that kind of gets at these issues, but it doesn't tend to come at it from the perspective that I think that you would, and that James would, applying probably a little bit more theory and analytical methods, as opposed to in financial planning, there's a lot of, I don't know what you call it, empirical stuff, using historical data, testing different things.

Hank Bessembinder: I've done plenty of simulations myself going through historical data and it's definitely informative. If we can make some progress with analytical thought and formulas, that could be good too.

Ben Felix: Yeah, that's very cool. We've talked about your research on individual stocks and listeners will probably remember that from last time that you were on as well. What do individual stock returns look like through the lens of the sustainable return?

Hank Bessembinder: Particularly through the original version where the issue is what level annuity could have been withdrawn. They look about as risky through that lens as they do through the other lenses. I've kind of criticized some of the other measures, but to some extent you get correlated outcomes across measures. 

They do contain some information. More than half of the individual stocks that we studied have negative sustainable returns. You would have had to have been adding money each period to keep its value constant. 

The basic idea that the distribution of individual stock returns is skewed, it shows up again when we use the sustainable return as the measure.

Ben Felix: How do you hope that future academic research will incorporate measures like the sustainable return? I love thinking about this question because it makes it so relevant to our world. We live in wealth management. 

We're helping individuals solve these problems. Seeing academic research really through that lens is just incredible.

Hank Bessembinder: I'm trying to nudge other academic researchers to branch away from their comfort zone of studying arithmetic means and conditional arithmetic means, alphas. I have a pair of papers. One of them is a less formal follow-up that I just completed a couple of months ago. 

I use the phrase that we've been searching under the econometric streetlight. I'm sure you know the allusion to searching under the streetlight. Searching under the streetlight because you can see things and you can do statistical tests there. 

When what people are interested in is not under the streetlight, you see the issue. I'm trying to nudge more people to, first of all, think more about actually measuring a long horizon investor's returns. Arithmetic means don't actually measure it.

Geometric means don't actually measure it. Think about trying to actually measure it. Then also take into consideration this idea that John Cochrane has posited that think more about measuring investments based on the series of cash flows for other purposes, for real purposes. 

We didn't touch on the purposes. Retirement planning comes to mind, but if you're a pension fund manager or you're an endowment manager funding research or arts or charitable products, nudging people to think about the stream of cash flows for real purposes that investments can fund, that's the big picture goal to get more people interested and get the statisticians interested because we're going to need their tools if we're going to do it.

Ben Felix: Super interesting. I guess one of the things John talks about in that paper is that your portfolio should reflect the cash flows that you need to be funding. It's an interesting thing about the sustainable return is a constant spending, but it doesn't touch on a person might have a specific sequence of spending needs.

Hank Bessembinder: I view the sustainable return as a baby step towards this broader idea that John had in mind.

Ben Felix: Very cool. It's cool to see the story arc of John's paper then resulting in other researchers looking at actual ways to put that thinking into practice. Great stuff.

Hank Bessembinder: I hope to pull in more researchers. There's room for more intellectual horsepower here.

Ben Felix: No, definitely. It's great to see. Fun to talk about. All right. We talked about three papers that you have out recently, which was really interesting work and it was great to have you back on the podcast.

Hank Bessembinder: It's been my pleasure. Gratifying that there's some people out there who care about research along these lines. Thanks for having me back.

Ben Felix: We care and our listeners also care. They're going to love this episode.

Cameron Passmore: You bet. No doubt.

Ben Felix: Thanks.

Cameron Passmore: Thank you.

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