April 22, 2021

Advanced Topics, Expected Returns, Historical Data

Episode 146: Do Expected Stock Returns Wear a CAPE?

April 22, 2021

Advanced Topics, Expected Returns, Historical Data

As many of you already know, we have been working hard to figure out the best way to model expected stock returns for financial planning and asset allocation. It has a lot of history in financial literature, which is to be expected, given the importance of the figure. In today’s episode, we’re looking all the way back to 1985, when Rajnish Mehra and Edward C.Prescott called the equity premium a puzzle, through to the present day, when the equity risk premium has only gotten larger. We dive into some of the theories for resolving the equity premium puzzle, explain why US stock market data isn’t the best way to estimate future premiums, thanks to its survivorship bias, and some of the general issues with interpreting past returns. Benjamin also gets into predictability, which is not as obvious as it seems, and highlights some of the information from the simulation he performed, and the big breakthroughs from running the numbers. All this and more in today’s episode on expected stock returns, so make sure to tune in today!

Key Points From This Episode:

Kicking off with the fallout from the collapse of Archegos Capital, the death of Bernie Madoff, and the story of the $100 million New Jersey deli. [0:06:35]
Reflecting on the recent article, ‘Could Index Funds be ‘Worse Than Marxism’?’. [0:11:05]
On to today’s topic: do expected stock returns wear a cape? [0:13:05]
Theories for resolving the equity premium puzzle; either the model is wrong or the historical premium was higher than it will be in the future. [0:14:14]
Hear John H. Cochrane’s theory from his 1997 paper, ‘Where is the Market Going?’ [0:14:42]
Why we can’t use historic US stock market data to approximate future premiums. [0:14:57]
Other issues with looking to past returns, like no proof that the equity premium was stationary. [0:15:23]
Why time periods characterized by decreasing risk should effectively see decreased discount rates too. [0:16:04]
Dimson, Marsh, and Staunton (DMS) on expected stock returns using out of sample data. [0:16:40]
Hear some of the equity risk premium stats from their world index versus the US. [0:19:38]
How annual returns have been relatively unaffected by global financial crises. [0:21:15]
From looking back, to what to expect going forward: the issues with interpreting past returns. [0:22:10]
Why, according to DMS, expected returns equal the growth rate in dividends plus the dividend yield. [0:25:26]
Hear the actual figures, which reflect the minor contribution of multiple expansion. [0:26:49]
What a company is worth if it doesn’t distribute capital to shareholders. [0:29:03]
Find out why the expected geometric equity risk premium works out to 3.5 percent. [0:30:13]
While the DMS approach is reasonable, it still doesn’t account for whether expected returns are constant through time or if they vary. [0:32:21]
Predictable stock returns dictate that changing risk aversion over time measurably affects risk premiums after good and bad events. [0:34:45]
Diving into the vast literature on return predictability, including a paper by Goyal and Welch. [0:35:12]
Why predictability is not as obvious as it seems, thanks to our sample data. [0:36:15]
What we can learn from ‘Long Horizon Predictability’ by Boudoukh, Israel, and Richardson. [0:39:30]
R-squared and market timing decisions; why it would need to be higher than it was historically. [0:40:32]
Hear about the world index analysis Benjamin performed and what it proves about risk premiums over 30 and 60 year periods. [0:42:31]
Bootstrap simulations and why they are criticized; because they ignore mean relationship, you get a much wider distribution of outcomes. [0:44:50]
Big breakthroughs from running through these numbers, like noting the upward bias and tighter distribution in long-run historical data. [0:50:34]
How to apply this on your own, using the 3.5 percent risk premium in the long run. [0:52:23]
Some of the other interesting things we noted during these simulations. [0:53:10]
We pull two cards: choosing between a holiday and a pet, and borrowing money with interest. [0:53:56]
Bad advice of the week: a free lunch-esque article on investing in private credit. [0:55:53]

Read The Transcript:

Ben Felix: This is the Rational Reminder podcast, a weekly reality check on sensible investing and financial decision making for Canadians. We're hosted by meet Benjamin Felix and Cameron Passmore, portfolio managers at PWL Capital.

Cameron Passmore: So welcome to episode 146. I thought we could kick it off this week with some nice reviews that we got. And I thought we'd talk about a little bit of the reviews. Anyways, for example, DragonFB in his reviews said that the interviews always remind him of a famous Miles Davis quote. "It's not the notes you play. It's the notes you don't play." And he highlighted that the hosts don't interview with guests, but when they do jump in, they enhance the guest's message. Thought that was really kind of that person because you and I deliberately do not try to say too much in those interviews, get to the guest giving their answers.

Ben Felix: It's true. Also, when you think about the guests that we have, it would be hard to try and butt in considering who they tend to be and the things that they tend to have to say.

Cameron Passmore: But we have had lots of different opinions on recent guests, both in the YouTube comments as well as in the community board. And we just like to hear what people have to say. And I think everyone that we've had on, we have learned something from that people may choose to disagree or have strong feelings about what is said.

Ben Felix: The most recent guest, we knew it was going to be different in how it would be received because it was a very different topic and it was intentionally thought provoking, but also intentionally uncomfortable, which is kind of the whole idea with Jen Richard's book. And I think it was successful in making people feel uncomfortable. And a lot of people said that, but at the same time, the comments within the Rational Reminder community were actually really thoughtful. I think it provoked a lot of really good quality discussion. So from that perspective, I think it was successful. Definitely a different type of episode. And as some people pointed out in the comments, not the kind of thing that they want to see from podcast discussions every week, but to have stuff in there every now and then I think is valuable. And the discussion that it provoked proved that.

Cameron Passmore: I agree and Elamzz wrote, "Always end up feeling like I've learned something that I can apply to my life." That is one of our goals each week. And then Borwaka said, "I'm very interested in a career relating to finance. Having the privilege of even crossing paths with you or I or anyone at PWL Capital would be astounding." And I know you and I do a fair amount of talking to new people in the industry. I always welcome people that do reach out and I've talked to people all over the world through this who are just getting into the industry. And if they find some value in connecting for 15 minutes or half an hour, I welcome that. I know you've done a lot of that also.

Ben Felix: Yup.

Cameron Passmore: In the merch shop, very exciting and people on YouTube can see. Someone suggested we get the red t-shirts in with the logo on the back. The stock ticker symbols in the box, they're going to be in the store this week and also we've expanded our team. So Lisa Brown, part of our group here at PWL is going to be joining to help take care of the inventory and the merch shop and the shipping. So that's great to at Lisa on the team.

Ben Felix: Because you were literally doing all of the packaging and shipping from your basement before.

Cameron Passmore: Yeah, after hours. It's something I enjoy doing. I'm a bit of an nerd on stuff like that, though. They're kind of fun.

Ben Felix: It's also kind of cool the fact that people up until this point have been receiving things wrapped up by hand by you. It's good. It's kind of cool.

Cameron Passmore: It is actually my signature on the postcard and then I basically do my best imitation of your signature.

Coming up in next week's interview as Paul Merryman is here. And then of course, he's here the week after on May 4th at 3:00 PM for his AMA, with two of his research colleagues. Last week, we interviewed Robert Novy Marx. That will be coming up two weeks after that phenomenal interview. And then after that will be Brad Cornell.

Ben Felix: Yeah. I think Brad Cornell is going to be... Novy Marx is fantastic. I listened to about half of it this morning and it's as good as I remember it from the actual conversation. And then Brad Cornell I think, is going to be really, really interesting because he, on a lot of the stuff that we talk about, he takes a counter position. That's going to be a really, really interesting conversation. He's takes a counter position, but he's written hundreds of published academic papers. So it's a very informed counter position, which I think is going to be healthy for everybody listening.

Cameron Passmore: Any comments on Larry Swedroe being in the community?

Ben Felix: Well, I reached out to Larry and just said, it'd be great if you wanted to check out the community. And he said, he doesn't really have time with all the other commitments that he's got. I was just like, listen, no problem. But he made an account and started answering people's questions. And so everyone was pretty excited to see him in there. His answers are amazing as people would know to expect. So he's not super active in the community. For a couple of days he was, but he's in there, which is pretty cool. Even I think yesterday, he was still putting some content up, which is very exciting for our community.

Cameron Passmore: Speaking of the community, Angelica has launched our Instagram page Rational Reminder. So if you want to see a video of, for example, your bots, they're on the Instagram page, which is kind of cool.

Also received last week, a really nice email from a, just a terrific long-time client about the talking sense cards. And he just said in an email that he liked the idea so much. He went and bought the cards on his own without waiting for us to get them in our own merchandise store. And he said, he'd been using them sporadically with his teenage kids at the kitchen table after a meal. He said, it's usually one or two at a time. He said the kids were super reluctant at first. It sounds boring, but he persisted and he's found them to be great conversation starters. He said they over really well now. They've kind of got into a rhythm with the kids. So he keeps the deck on the counter, near his kitchen table. And he says he pulls it out when the time seems right. So he just reached out to say, thanks for that idea. And it's working really well.

And we are still working with the Institute to try and get the price point a little bit lower. They think they found a solution for us to print in Canada because it's the duties on that really make them cost prohibitive. So more to follow on that. Anything else before we jump in?

Ben Felix: Nope, let's go.

Cameron Passmore: Kick it off with that followup to the Archegos story.

Ben Felix: Yep.

Cameron Passmore: Just a wild story. So we talked about this two weeks ago where basically a family office back I guess imploded. $20 billion has evaporated in no time at all. So news was that Credit Suisse, which is one of the lenders into the family office has taken a $4.7 billion US hit for the client's inability to meet its margin requirements. Morgan Stanley announced almost a billion dollar hit. And then Nomura Bank is somewhere, the loss is expected to be somewhere between the one and $4 billion. So three massive losses for three very large banks. It's just incredible.

Executives, including the CEO of the investment bank, as well as chief compliance officer are stepping down because of this. So like this is big time story that goes back to the financial crisis of 2008. And it all started with a single family office getting access to a ton of credit and having trades that did not go their way to say the least.

Ben Felix: And I think we said the first time we talked about this, that it'll be interesting to see the fallout. And here it is.

Cameron Passmore: And speaking of 2008, many may have heard that Bernie Madoff passed away last week. And he's the person who masterminded the biggest investment fraud in US history, ripping off tens of thousands of people for as much as $65 billion. That's how big the Ponzi scheme was. So he was serving 150 year sentence for the scheme, which they said defrauded as many as 37,000 people in over a hundred countries, including Steven Spielberg, Kevin Bacon, former New York Mets owner, as well as a Nobel Peace prize winner, all had losses.

However, I found an article that talked about how most investors recovered 80% of their losses. And even in the article said, because this all happened, he got caught in late 2008, so the article made reference to how many people actually may have come out better than what they would have invested in as an alternative, because so many things did so poorly at that time in the markets. So they say, well, because you got 80% of your money back, you actually did better off than you would have done had you been left alone. I couldn't find actual data behind that. That was commentary in the article, but there was a lot of money that's taken over a decade to recover a lot of those funds. And if you're interested, PBS FRONTLINE's show did an excellent story on the Bernie Madoff scandal.

And the last story, this one just blows my mind. And so many people commented on it. Just thought we throw it in here was this story about this New Jersey deli? Did you see the story?

Ben Felix: I've read it. Yeah. It's unbelievable.

Cameron Passmore: It's a deli in Jersey called Your Hometown Deli, which is the single location for the over-the-counter publicly traded company called Hometown International, which get this, has a market cap of 101 million US dollars today when we're recording this April 19th, even though this restaurant had sales over the past two years because of COVID, but still had sales over the past two years at $37,000 of sales. Now it's not actively traded. So take that for what it is, but just that's how much the market cap is right now. And it was this article talking about the lawyer who set up, who created the company, formally pled guilty to a Shell company scheme back in 2014. And the CEO of the company is a high profile wrestling coach. I mean the wrestling coach right now in paper towards something like $30 million, but shares a year ago were about $3 per share. And now they're over $13. So it was the famous hedge fund manager, David Einhorn that basically called this out some sort of rampant speculation.

However, in their SEC filings, the company said our financial situation creates doubt whether we will continue as a growing concern. The company suggests it needs to find an acquisition target or additional financing to maintain operations. Do you think a hundred million dollar company with $37,000 of revenue? Anyways.

Ben Felix: You got to wonder what's going on there.

Cameron Passmore: How do you go public with one restaurant? I don't know.

Ben Felix: Oh, there's clearly more to the story.

Cameron Passmore: Yeah. The last thing I thought we'd touch on is the article that was in The Atlantic. Had a lot of people DM me on Twitter, just asking for our feedback on this article called Could Index Funds Be Worse Than Marxism? And the point was that there's many companies that have over 20% of their shares that are held by the big three indexers and that index funds now control so much the American marketplace. The article is wondering if there's too much power in too few companies. And if this is a bad thing, so too much power in too few asset managers, and they're wondering what might've been good for investors, low cost index funds may not be great for financial markets. And they argue that index funds may be degrading the information content in the markets.

Ben Felix: We we asked, not about this article, but about just this general concept, because this is not the first time it's come up, but we asked Adriana Robertson in episode 133 about this, because she's at that intersection of law and financial expertise. And she basically said that she's not really worried about it and that there's not enough evidence to suggest that this is actually a problem. So she said, I mean, to quote, she said, "No, I'm not terrified that it's going to destroy liquidity in the markets or it's going to mean that we don't have price efficiency anymore. Or corporate governance has gone out the window. None of these things, I think. I haven't seen any evidence to make me worry." I mean, I would tend to believe Adriana Robertson over another article like this. That's kind of my opinion on that.

Cameron Passmore: I'm not sure it got shared a lot last week.

Ben Felix: It's pretty sensational. But I think because index funds have become a popular investment vehicle that are attracting assets and attracting media attention, bashing them is a pretty good way to get clicks, I would say.

Cameron Passmore: I agree. Okay. So let's jump into the beef this week.

Ben Felix: Yeah. So I titled this topic, do expected stock returns wear a CAPE. I thought it was funny.

Cameron Passmore: Look at you for clickbait title.

Ben Felix: As people know, and we've talked about it a little bit on the podcast. We've talked about it in the community a fair amount. We've been working quite hard, Braden and I, to figure out the best way to model expected stock returns for financial planning and asset allocation. It has a lot of history in finance literature, which makes sense. It's obviously a pretty important number. What do we expect stocks to return or what risk premium do we expect stocks to return over treasury bills? There's a fairly famous, at least famous when you get into this part of the literature paper from 1985 by Mara and Prescott, and they called the equity risk premium a puzzle because it's historically been a lot higher than what any standard economic model would predict. So it's unknown why stocks have returned as much as they have when models would predict something much lower. And that was 1985. Since then the equity risk premium's only gotten larger. So the puzzle has maybe gotten bigger. Lots of people have tried different ways to resolve the puzzle, but there's no consensus, I don't think.

There are two main possible explanations for why the equity premium has been so much bigger than the standard models would predict. One is that the models are wrong. The other one is that the historical premium has been a lot higher than we should expect it to be in the future, which obviously has some important implications. John Cochran in a 1997 paper, he did some serious modifications to the economic models. And he found even with that, the degree of risk aversion that would be required to justify the historical premium was unrealistic.

One of the obvious issues when we're talking about why is the historical risk premium been so high, is that the US stock market suffers from a massive survivorship bias. It has been the most successful market in history, and we know that now, but looking at the US historical data and using that to approximate the future premium or even using that to study what the equity risk premium is, is probably not the best approach.

And then the other big problem with looking at past returns is that we don't really know if the equity premium is stationary. We don't know if it's the same always, and therefore, looking at the long-term history is the best approach, or if it's different through time. If you think about any historical period, there could have been changes in risk and in actual economic risk, there could have been changes in risk aversion, there could have been changes in the ability of investors to diversify their risk. All of those things can affect the equity risk premium over different periods.

Cameron Passmore: It's so interesting to think about, because every one of those points affects your discount rate, and that's what's potentially shifting around through time.

Ben Felix: Correct. Now, if there's a time period that's characterized by a decreasing risk, like if financial markets are getting safer and more liquid and people can diversify their portfolios better and all that stuff, we would expect the discount rate to decrease. And this is, I think the point that you were getting at, Cameron. If the discount rate decreases over a period of time, that pushes prices higher, so it makes a historical return look higher, but what else does it do? It decreases the future expected returns, so that's an obvious problem if you're looking at historical data, especially in a successful country like the US.

So Dimson, Marsh and Staunton, they had a 2007 paper, and they asked two big questions about expected stock returns using out-of-sample data to try and find the answer, and this is the key. I mean, Dimson, Marsh and Staunton have made quite a name for themselves with their data series. They have data going back to 1900 for, at this point, 23 countries, which is, if we're going to look at the historical data, that takes away some of that survivorship bias. They call it two things. There's survivorship bias because some markets don't survive, like Russia and China had market failures at a point in time, but then they also call it an unsuccess bias. So some countries have stock markets that exist for the full sample, but produce very, very low realized returns, so getting this global data set is a big thing. So in this 2007 paper, they asked two questions: how large has the equity premium actually been historically, not just in the US, but in all markets, and then, how big is it likely to be in the future?

Luckily for us, well actually, anybody can access through the Credit Suisse Global Returns Yearbook summary edition. We also subscribed to the DMS data, so we have the annual return series that we can play with, which is one of the things we're going to talk about soon. But in this 2007 paper, they use the data series that they had at that time to decompose the historical return so that they can estimate which components of the historical return, of the global return, were due to luck and repricing resulting from changes in the risk premium. Pretty cool.

Cameron Passmore: That's very cool.

Ben Felix: Because once you strip those two pieces out, those are unreliable. Obviously luck, we can't count on repeating, and likewise, repricing. Like if discount rates declined over a period of time, you don't really expect that portion of realized returns to repeat again in the future, so that's not really part of the equity risk premium. I guess it's a component of luck, specific to that historical outcome.

So when they wrote this paper, they had 17 countries in the database, and like I mentioned, we have 23 countries in the database now, including the Russia and China failures and including, I think the big unsuccess additions that they added were Austria and Portugal, and those are quite recent additions to the overall data series. So now, when we're looking this whole thing, we're not just looking at the one successful market obviously, which is important. So it's 23 countries back to 1900, but then as more available data comes in more recent years, they add countries. So the full series for their world index includes 90 countries in the current iteration for the most recent data in the series.

So for the annualized equity risk premium ... this is geometric terms ... for the world index from 1900 through 2020, the risk premium was 4.4% over US treasury bills. Now, the US premium over the same period was 5.8% over treasury bills. Those were geometric mean risk premiums. So geometric, meaning annually-linked return, so that gets biased downward from volatility relative to if we just took the average of each single year on its own, which would be the arithmetic average.

Now, I think an important observation there, two observations, one is that the US equity risk premium has maybe not been as high as a lot of people tend to think, and that it's been a lot higher than the world risk premium. If we take real returns instead of risk premiums, the world index geometric return was 5.2% over this period and the US was 6.6%. So that's the inflation-adjusted return for US stocks, 6.6%. Now, people will, often enough that it's alarming, will say things to me like, "I'm using 10% for my financial planning projections because that's what the S&P 500 has done." It's like, "Yeah, well not really. It's actually not."

Cameron Passmore: Literally, not really.

Ben Felix: Yeah, it's been a lot lower than that. And the world, which takes away some of that success bias, has been a lot lower even still. Now, if you think about this historical period that we're talking about, it contains World War I, the 1929 crash and depression, World War II, 1973 oil shock and recession, the tech bust, the global financial crisis, coronavirus. Doesn't really affect things negatively because the one year return ended up being not so bad in the end.

That's a crazy thing to think about too, is that if you just look at annual returns of the market, a year like 2020, you wouldn't even register as exceptional. So weird to separate what happened in history from the stock market performance in that year. It's weird to think about. And now we're sitting here 120 years in the future. We have no ... I mean, we could go read a book I guess, but much less historical context as to what happened in each year. Anyway, that's totally separate topics. Just interesting to think about.

Okay, so we have an idea from the DMS data now what the historical risk premium and real return looked like, but we have to think about now, what do we expect going forward? So this is where Dimson, Marsh and Staunton are stripping out those less likely to repeat components. And they make the point that if you put yourself in the shoes of somebody in 1900, there were a lot of reasons to be optimistic at that time, but over the next 50 years, there were unexpected civil and global wars, the 1929 crash that we mentioned, the Great Depression, periods of hyperinflation around the world, the spread of communism, conflict in Korea and the Cold War. And what ended up happening over that period, that there were reasons to be optimistic in 1900, from 1900 until 1949, the annualized real of return on the world index was 2.7% for 50 years, 2.7% real return.

And then they make the point that, "Okay, now step into 1950. Things seem pretty bad." Market returns have been bad for the last 50 years and there's lots of reasons in 1950 to be pessimistic, but then the outcome that we got was different. There was no third World War, the Cuban Missile Crisis was diffused, the Berlin Wall ends up falling, Cold War ends, productivity and deficiency accelerate, technology progresses, stock market function improves, decreasing discount rates. And then again, we look at the realized outcome for that next 50-year period, from 1950 to 1999, the annualized real return on stocks was 8.6%.

Cameron Passmore: Amazing.

Ben Felix: Right. So you started off in this period of what seems like an optimistic period and ended up with a really bad outcome, and you started off with what seems like should be a pessimistic period and you end up with a really good outcome. And so over that period, and then even more so ... they're talking about ending 1999, but even more so since then, valuation ratios have expanded a lot, I mean, especially right now, and particularly in the US, reflecting some combination of lower risk, increased optimism, political risk declined, mutual funds became common, which allowed people to diversify, again, effecting discount rates, global portfolio allocations became more common, which previously it was very hard to access foreign markets. And it's also plausible with things like the ability to diversify and maybe even just experience investing in stocks, and investors became more tolerant to risk. So this is one of the challenges with interpreting past returns, and we've alluded to this earlier in the conversation. Looking at past returns are not necessarily indicative of the future.

Ben Felix: It's similar to the point that Cliff Asness was making in his recent paper, The Long Run Is Lying To You, which we talked about on a recent episode. If risk is declined, risk tolerance has increased, we expect higher prices, driving up past returns, but we don't expect higher returns. The same thing we mentioned a minute ago. You actually expect the opposite, but it can be very misleading to look at the high realized returns and make assumptions about what it looks like for the future.

So Dimson, Marsh and Staunton decomposed the components of the historical world equity risk premium into the sum of the geometric growth rate of real dividends, the expansion of the price dividend ratio and the mean dividend yield. They take the geometric average of all those things, sum them up, take away the risk-free rate and that adds up to the realized equity risk premium. But if we're going to take out price multiple expansion, we're going to say, "Let's not bet on that happening again," under that assumption, the expected returns just equal the growth rate in dividends plus the dividend yield, which in the very, very long run, I know we're talking about 121 years and it's not even true in that sample, but in the very, very, very long run, returns should just equal dividend yield or earnings yield plus the growth rate in ...

Cameron Passmore: In the dividend.

Ben Felix: ... earnings.

Cameron Passmore: Yeah.

Ben Felix: Right. Shareholder yield. I mean, it's dividends plus share repurchases. And they do talk about repurchases because in the US, they've been more substantial, but they show that in their sample, you would have had a little bit of an increase in total yield if you included buybacks in the US and globally, and it didn't actually make much of a difference, so they just stick with dividends. So the actual figures here, the return going back to 1900, breaks down roughly as 4% in dividend yield, 0.7% in real dividend growth, 0.5% in multiple expansion.

Cameron Passmore: Wow.

Ben Felix: Right. That is interesting, right, that the contribution of multiple expansion is so small: .5% of the return over the full period. Most of it is coming from dividend yield. Now, I think some insights that come just from those pieces of data are that, what we were just saying, in the very, very long run, dividends or shareholder yield, like we mentioned, are the biggest driver of returns. And as much as year-to-year capital gains seem like such a big deal, in any given year, capital gains dominate the realized outcome, and that's what we deal with every day, speaking with clients about, "How did things look last year? How did things look over the last few years?" Most of that's dominated by capital gains, but in the very long run, they actually make a pretty modest contribution.

Now, very long run, we're talking about 121 years in this case, which is longer than most people's investment horizon. The realized outcome over a shorter period of time is likely going to have a contribution from capital gains, but because we can't really bank on that, Dimson, Marsh and Staunton are saying, "Well, we shouldn't bank on it." So what do we expect if we don't get that piece?

Cameron Passmore: You're talking about shareholder earnings, not just the payment of dividends, correct?

Ben Felix: They use "dividends," but they make the point that cash distributed to shareholders through repurchases or dividends, that's the shareholder yield item that I mentioned, but they looked at, how much does that affect things. And in the US, I think it added 30 basis points or something. Globally, they said it didn't make much of a difference at all, so they just used the dividend yield going back for the full sample. Yeah, this is mostly dividends here.

Cameron Passmore: And how would a company be treated if it paid no dividends and did no share buybacks but had capital appreciation?

Ben Felix: How would it be treated?

Cameron Passmore: Yeah, how would it be treated in this formulaic view of the world?

Ben Felix: It raises that interesting question of, is a company worth anything if it doesn't distribute capital to shareholders? There's a long discussion about this in the Rational Reminder community if you search, "What is the asset value of a stock?" Someone asked that question and it was a very detailed discussion that I don't think I can recount the whole thing right now, but it almost becomes a philosophical discussion. But in the very long run, yeah, dividends become extremely important to their realized outcome.

Another interesting point that comes out of their analysis is that dividends have historically grown only slightly above inflation. We sometimes hear that dividends outpace inflation over the very long run. In this case, well, at least we had the real dividend growth rate of 0.7%, so that's real above inflation, so slightly outpacing inflation. They said, I think, that in half the countries in the sample, dividend yields in those countries did not outpace inflation. Just kind of an interesting side note. The capital gains contribution being so small as another really interesting point. Now, if we take that out, so this is what Dimson Marsh and Staunton do, they take out capital gains so we lose 50 basis points off of the historical return. They also make the point that dividend yields are a lot lower now than they've been. We saw the 4% yield historically. So we need to reduce that a little bit to figure out what a more realistic estimate is forward-looking. So with those adjustments... Oh yeah. They make the point that a lot of the dividend yield in the full sample comes from what they attribute to good luck in the post 1950 period.

So if you correct for that, look at what yields are today, and then account for the price multiple increasing piece, they suggest that the expected geometric equity risk premium is closer to 3.5% going forward. So when you take out those less likely to repeat or less reasonable to count on components, then we're looking at an expected geometric premium of 3.5%. That's the number. The geometric number is what you would use if you were doing just a basic single number, like straight line projection, because the 3.5% takes into account volatility. And that's also a risk premium, so you'd be adding back the risk-free rate to the 3.5%.

The other thing that they do is look at the historical comparison between the arithmetic average and the geometric average. That difference, for the full sample, is 1.5%. So for their forward-looking estimate, they add 1.5% back to the 3.5 to give you the arithmetic expected return. And that's relevant because if you're doing Monte Carlo, so I just said 3.5%, you would use as the single number to project forward, but the 5% is what you'd use to put in the Monte Carlo, including modeling the standard deviation.

Cameron Passmore: Fascinating.

Ben Felix: Right. And that would give you something closer to the 3.5% because of the volatility captured in the Monte Carlo simulation. I think that's a pretty reasonable approach, what they've done. Let's look at the full country experience for everything that we have data for, including failed markets, strip out the stuff that we don't really expect to repeat, or at least we don't want to count on repeating and developing expectations, and use that as an expected risk premium. I think that's pretty reasonable. But I mentioned earlier that we don't really know if expected returns are constant through time or if they vary.

So 3.5%, we can maybe use that as a... There's one equity risk premium, and it doesn't change over time. It's not obvious though that expected returns are constant. If they're time varying, then there's a chance that economic indicators like earnings to price or dividend to price might give us information that we can use in asset allocation spending and saving decisions, financial planning, I guess. Generally speaking, a time varying equity risk premium would change over time, I guess, obviously, based on a risk and risk aversion, which happened to tend to move together. If you think about it just logically, forgetting about what the data say for a second, just think about it logically, after a market decline, investors have less wealth and they'll tend to be more averse to risk, which should increase the equity risk premium. Otherwise, investors wouldn't want to own stocks.

They need a higher expected return to invest in stocks when they're more risk averse and have less wealth. And then after a bull market, the opposite will be true. That, I guess, economic logic would predict that stock returns should mean revert over time because there's this self-regulating mechanism through changes in risk aversion over time.

Cameron Passmore: It kind of reminds me of the conversation we had with Lubos Pastor around elections, same sort of logic.

Ben Felix: Yeah. And Lubos Pastor's research comes up in this too, because he talks about that mean reversion piece. Lubos says that there's this common belief that stock returns are mean reverting in the long run, which makes people think stocks are less risky in the long run. But he counters that with a couple of points that I'll touch on in a minute. Lubos argues that stocks are riskier in the long run than many people like to believe. So in that changing risk aversion over time dynamic that I just mentioned, after good times, the risk premium is lower, after bad times, it's higher. Now, if this is true and if stock returns are mean reverting, another way to describe that is that stock returns are predictable, because if they get way above the mean, they should predictably revert to the main.

And there's this vast literature in financial economics on return predictability. And that's what it's referred to as when you're reading about it. And the first time I saw that, I was kind of like, "Predictable? Stock returns aren't predictable." But there's a pretty substantial body of literature suggesting that they might be, and then a whole other body of literature countering that. I said to someone recently that academic finance is like people having rap battles with each other. I guess that's why, when we spoke with Robert Novy-Marx, I said that he has mic drop papers. Maybe I was thinking of that.

There's one paper that cited a lot in the predictability literature. It's kind of like the ultimate throw down showing that returns are not predictable, by Goyle and Welsh. It's a comprehensive look at the empirical performance of equity premium prediction. And what they find in their research is that the predictability models would not have helped an investor with access only to information available at the time, to time the market. And that becomes important. Basically what they're saying is that predictability looks obvious when you consider the full sample of data, but it's much less obvious when you only consider the historical data at each point that you would have been making a prediction. And you can see this in the very long run returns in the DMS data series too, which is really cool to look at. But if you sort all five-year historical returns in the DMS series by the starting years return, so we're taking all five-year periods and sorting them by the first year's return, there's a monotonic, it's perfect, it's a beautiful relationship between low starting years and high subsequent five-year returns.

So this seems to kind of go in the face of the buy the dip analysis that we talked about recently. But you did not have that information. At each of those historical points in time, you didn't have the full series of data to rank your given year relative to all of the past and all of the future. You only had the past. If you make that correction and only look at the past data at each point in time that you would have been ranking, how was this first year in the five-year sample, the relationship completely breaks down completely. It's not like it gets a weaker. It's just gone.

It's crazy when you see it in a chart. You go from this beautiful monotonic relationship to no obvious relationship at all. And then the way that the predictability literally talks about this as an out of sample test. Because in sample, you have all these data. Out of sample, you're just looking at the history that you have available at that time, and then testing the strategy out of sample, and it completely goes away.

Another place this gets really tricky, and it's the same bias, it's the same in sample bias is that if you run regression on earnings to price, so the Shiller PE, for example, the Shiller earnings yield, and try and use a regression to see how well does that predict the realized ten-year returns following a given evaluation, it seems obvious that there's a relationship. The R-square in that regression, the explanatory power of the earnings yield over realized returns is somewhere between 30 and four 40% in the US data, which is very high, very high. And Vanguard had a paper a while ago citing the same statistic, which, for a long time, really led me to believe that it's quite useful in predicting returns. Cliff's done a paper on earnings yield too. It's a very common relationship to observe.

One interesting observation that I made when I was preparing for this topic was that the relationship does not hold in countries. Now, lots of different reasons that could be true, one of them being that there's not as much data, not nearly as much data. I only have a test starting in 1981, the relationship between CAPE and realized returns in a bunch of different countries.

It's not reliable. It's not consistent. Like in Canada, for example, it had no explanatory power at all whatsoever. The R-square was zero. So that knocks my confidence a little bit, but again, not that much data. But then there's this other paper, Long Horizon Predictability: A Cautionary Tale, from Boudoukh, Israel and Richardson. And they explained that that type of regression that I just mentioned has an effectively small sample size because you're using overlapping observations, which results in overstated T statistics. And based on that, there's way less statistical evidence of long horizon predictability than that regression that I just mentioned would suggest. So then R-square shows up with a high T statistic in the regression because of the overlapping data, not because it's a good predictor of future returns. So that's another knock to that idea. And when you think about it, we don't have very many... I just mentioned from 1981 until now, that's 30 years. So if we're looking at 10 year periods for predictability, that's three non-overlapping samples.

Cameron Passmore: Four.

Ben Felix: Four non-overlapping samples, which is obviously not a ton of data. Now, even if we assume that that R-square is that high, we'll just forget about the paper that I just mentioned and say, "Okay, maybe the R-square is 0.4," like it is in the US or has been periods in the US. In other countries, I think Germany was quite high. Europe as a region it's quite high in those regressions when I looked at them. Dimensional had a paper a while ago, looking at what would the R-square need to be in those regressions to be able to use the information in making market timing decisions or asset allocation decisions, same kind of thing. And in their analysis, they found the R-square would have to be much higher than it has been historically to actually be useful in market timing decisions, just because there is still so much uncertainty.

Now, this gets kind of tricky. Because the results are somewhat mixed, I kind of lean toward, there's probably not predictability that we can use, but there's some relationship between price and expected returns. So one of the things that Braden and I have done recently, which was a pretty cool exercise, is we useD the DMS data to model different approaches to estimating expected returns. We used rolling historical periods, which are interesting because they capture actual historical periods in the sequence that occurred in. But they're problematic for the reason that I was just talking about, because a large portion of the data are overlapping. So we don't actually have that many independent samples. Even though we have 120 years of data, if we're looking at 60 year periods, that's two independent samples. So there's a big smoothing effect that makes the usefulness of the data a little bit questionable.

But the other interesting thing about the DMS I that we have 23 independent country samples. So we have one world index. We also have 23 countries going back to 1900. So we were able to do some interesting analysis with that. And I'm going to talk about that here. So with the world index at the 50th percentile, we see a 30 year average equity risk premium of 5.4%. And at the 60 year, it was 5.7%, pretty good. The 10th percentile outcome for the 30 year horizon was 1.2%. And this is an interesting data point here. For the 60 year horizon, it was 4.6%, which seems pretty great. And that speaks to that idea that stock returns do mean revert over very long periods of time, but we're looking at two really non-overlapping data points there. So caution is warranted. And I'll talk more about that in a second. At the 90th percentile, in the rolling historical periods for the world index, we get an 8.3% risk premium for 30 year periods, I think I said that, and for 60 year periods, 6.8%.

That consistency over 60 year periods is interesting, but like I just mentioned, I think caution is warranted there. So the next thing we did with historical data, and this is the individual country piece, which I thought was really interesting was kind of like, instead of looking at the whole world index, how wide is the distribution of individual country outcomes? And that's going to become important when we talk about the bootstrap that we did in just a second. So we took the individual country outcomes and use that to form the percentile. So we sorted individual country outcomes. At the 50th percentile, the 30 year return was 4.9%. And at the 60 year horizon, it was 5.1%. So pretty close to the world index, which I guess makes sense. And then at the 10th percent, the 30 year horizon was negative 80 basis points.

So 10th percentile of individual country outcomes, negative 80 basis points annualized at the 30 year horizon for the rolling historical periods. And at the 60 year highs, it was 1.6%. So big divergence from the average country. And it just speaks to the fact that we've mentioned earlier that there are unsuccessful markets. Even over very long periods of time, some equity markets have not delivered very strong returns. At the 90th percentile for individual countries, we were, again, pretty similar to the world index with 8.7% for 30 years and 7.3% for 60 years. So the next thing we looked at is bootstrap. And this part gets really interesting because one of the criticisms of bootstrap is that we destroy... If there is mean reversion. If there is, we destroy that completely by introducing bootstrap because it takes away any serial curl. Any relationship in the time series goes away because you're dumping all of the annual returns that we have and you're resampling. You're pulling one out, sticking it in year one, putting it back in, pulling another one out randomly, stick it in year two, putting it back in. And you're creating an independent return series by following that process. But because of that, any relationship that existed between years one and two or one in five or whatever is destroyed. So the criticism is that because it ignores mean reversion or any relationship in the time series, you end up with a much wider distribution of outcomes. Which is true, and we see that, but I'm going to tie that back to the individual country outcomes in a second.

So we did 10,000 bootstrap simulations with the DMS World Index data and compared them to the historical data, killing the zero correlation pretty much knowingly. There are ways around that you can do block bootstraps that try to deal with that, but we didn't do that. We just did a good old fashioned bootstrap. At the 50th percentile at the 30 year horizon, the risk premium was 4.7% in the bootstrap, which is a bit below the rolling historical number. And at 60 years it was 4.7%, which is a full 1% lower than the rolling historical number for the World Index. So that's a big deal. It's a big hit losing 1% per year by doing bootstrap instead of the rolling periods. At the 10th percentile, we get 0.4% for 30 years. So better than the -0.8 that we had in the worst in the 10th percentile of individual countries.

Over 60 years, and this I just find so interesting. It's a random outcome, but still interesting. Over 60 years, the 10th percentile on the bootstrap is 1.6%, which is exactly the same number as the 10th percentile of individual country outcomes. So I was trying to see how crazy are these bootstrap results? You know what I mean? If we look at individual country outcomes and compare that to the distribution of outcomes from bootstrap, is it totally out of whack? And it's not. So I think that argument that bootstrap gives you an unrealistically wide distribution because it ignores mean reversion, I don't know, it's only true if you believe there's mean reversion. And because we've had mean aversion with some of the individual countries, I don't know if it's crazy to assume that that bad of an outcome could happen again in the tails of a distribution.

So I thought that was kind of neat. And then at the 90th percentile bootstrap gave us 8.9% for 30 years, 7.7 for 60 years, which is again higher than the historical World Index, but in line with the individual country experience. I find that just completely fascinating. The range of outcomes for bootstrap is a lot wider than it is for the rolling historical periods, but not out of bounds at all relative to the individual country experiences. Now, does it make sense to accept that the World Index could have the experience of the worst country within the world? Maybe that's unrealistic. It's just interesting to see that it's not totally crazy to have an outcome that bad, at least at the individual country-level.

Now, the next thing that we did was a modification of the bootstrap, because we wanted to see what predictability, if we added some predictability to the model, what does that do to the expected outcome? So we set up a bootstrap that incorporated a predictability model with an R-square that we defined of 0.2, so 20%. So 80% of the outcome is determined by the randomness from the bootstrap. 20% is determined by a predictable model based on earnings yield. I don't know, maybe I'm just being biased. Even though the evidence seems to suggest, or at least it's very mixed on predictability, it just seems crazy to me to completely ignore the information in the price. Maybe I just need to check my biases. I don't know. So when we run this one, this simulation with the predictability built in, the result's pretty much right in between the historical rolling periods and the bootstrap samples, which is kind of what we expected.

The other really interesting avenue that it opens up is that we can define the earnings yield. We can define the price level in the model. So instead of just setting the price earnings to the historical level for the simulation, we can say, "Okay, well, prices are really high right now. So let's put in the current earnings yield as the input in the model." So that 20% contribution from the earnings yield will predict a little or return. It'll give us a downward bias. So we ran that and it was really cool. I mean, that's all I can say about it, but it lets us run a simulation where returns at the start of the period, because prices are high, end up being lower. But then they eventually converged to the expected return. Which in the model, the expected return ends up just being that 3.5% number from DMS. But we're not ignoring the fact that because prices are high, maybe you can argue there's a higher chance that we're going to have lower realized returns in the relatively near future.

I think the big breakthroughs in running through all of these numbers were seeing the upward bias and the tighter distribution in the long run historical data, which you can attribute to smoothing in the limited independent samples. The observation of how wide the bootstrap distribution is compared to the historical data, but then see that that lines up well with the individual country experience, I thought that was just completely fascinating. Makes me think maybe bootstrap's not so bad and maybe you don't need to try and model predictability.

Cameron Passmore: Interesting.

Ben Felix: I thought that was pretty cool. And then that also, to an extent, I mean, with bootstrap, we are assuming unknown mean, but I think that wider distribution of outcomes speaks a little bit to what Lou Bosch Pastore told us about stocks being riskier in the long run. I don't know what the average return is going to be in the future. We don't know what the equity risk premium is today. And we don't know what the parameters of the return generating process. So you don't know any of those things and you've got this volatile asset relying on mean reversion or assuming mean reversion may be a risky assumption to make for long-term from projections.

I did like, in this model that we've created here, I did like that contribution, some contribution earnings yield. Just from an economic logic perspective, even though I said in the data that it doesn't seem to be predictive when you only look at historical data, which is all we have to make a projection today, it doesn't seem to be predictive. But I just can't get over the fact that it seems crazy to completely ignore price in making forward-looking projections.

Dimson Marsh and Staunton suggest extrapolating from the historical record for the forecast. Which we did in the model, but I think adding a little bit from earnings yield make sense. For somebody to apply this on their own, with or without having the actual return generating model that we've created, you could make maybe do something like the 3.5% risk premium in the very long run suggested by Dimson Marsh and Staunton, then talk on the risk-free rate. And then weight that at 80%, which is what we did in our model. We give the R-squared of 20%, 20% explanatory power. So give the random portion, which the 3.5% risk premium incorporates the randomness because that's the geometric mean. So wait that at 80% and then give the current earnings yield projected return based on that, give that a weight of 20%. The only challenge is that if you do that, the earnings yield piece doesn't update over time like it doesn't in our model, but I think at least gives you a fairly close approximation.

And another interesting thing that we realized as we did all of this is that Raymond, our director of research at PWL, his expected returns model has always been 50% long run historical data and 50% earnings yield, the expected return from earnings yield. And so I've been trying to solve for a better model. And in the end, I'm basically just saying, maybe we should weight the predictive portion a little bit less. I was maybe expecting something more elaborate or a bigger breakthrough, but it ends up being very similar to what we've been doing, just potentially giving less weight to the predictive component.

Cameron Passmore: That's it?

Ben Felix: That's it.

Cameron Passmore: It was awesome. Okay, are you ready to pull two cards, which neither of us have seen before? Card number one, I'll go first, give your voice a break. Imagine you won a game show. By the way, these are cards from the University of Chicago Financial Education Initiative. So imagine you won a game show. So you have two choice for prizes. Number one, an exotic amazing two week vacation, or your choice of a pet with all pet expenses paid for the pet's lifetime. Which would you choose? I mean, I have Oscar behind me who, by the way, Oscar chased a rabbit on the weekend and pulled a muscle in his front leg. So he's limping around. That's why he's been so quiet behind me here. Poor guy is pretty sore. So already having a pet, I would choose an amazing two week vacation. I'm more into experiences now than getting another pet. So that would be my choice. What would your choice be?

Ben Felix: If covering all of the expenses of the pet includes compensation for the mental overhead of having the pet, I'll take the pet. Otherwise, I'll take the vacation. I grew up with dogs. I loved dogs growing up and I always figured I would have a dog, but ever since I started living on my own, I honestly can't imagine, especially now with kids, I can't imagine taking on that additional responsibility.

Cameron Passmore: Number two, would you borrow a $100 if you had to pay a $101 back. And if you had to pay $200 back, or if you had to pay $150 back, would you borrow the hundred dollars?

Ben Felix: Well, it depends what I'm going to use a hundred dollars for, I think is the answer.

Cameron Passmore: Asking what your cost of capital is.

Ben Felix: Yeah, I don't know if I can just answer the question. If I had a scenario, am I investing in something that's going to give me $400 or a chance of $400? Is the interest deductible?

Cameron Passmore: There you go, all kinds of left brain answers. Cool. Okay, so let's get on to bad advice the week. This is not so much the advice that's bad, it's more of the framing of the article that I think is worth commenting on. So this came from our regular listener, Andrew, who actually posted a picture of himself in his hoodie that he got for being kind enough to send us the bad advice of the week. I think it's actually his profile pic on Twitter, for what it's worth.

Ben Felix: Anyway, we came across this article on LinkedIn, and the article is called Investing in Private Credit Bond, Bond Like Stability, Equity Like Returns. I mean, ran out of the gate has got an aura of a free lunch. I understand that might be a click bait type title, and it's actually the fund provider that put the article out there. But the premise of the article is that with historic low interest rates and central banks supporting the economy, fixed income investors will have to temper their return expectations. And instead of investing in government of Canada bonds and GICs and then adding in equities for the higher return that they need, another option would be to add in private.

Cameron Passmore: So we are not professing to be private credit experts. I know a few weeks ago you talked about the sources of the risk factors in fixed income, at least the higher expected returns. In simple terms, the article highlights and does highlight that private credit is a specific lending agreement between a borrower, often a company and a lender. They don't trade in the public market and they typically do not originate from a bank. But why I think it's a good candidate for bad advice of the week is that some of the language in the article is not great. So I'm not making a comment about the asset class. But I tell you, when I hear titles like this, invest in “X” has got bond like stability, but equity like returns. And this brings me back to kind of hedge fund talk pre-Bernie Madoff era, or even long before then, before we moved to index funds 20 plus years ago, this would be a common kind of pitch.

But some of the language in this article, number one, like I said, downplaying the risk, bond like stability, equity like returns. Number two, which we would often hear is highlighting exclusivity. The article says, "You will gain access to this exciting asset class that is generally reserved for larger institutional investors." This pitch of scarcity, very, very popular. In fact, it still is popular, but we just don't look at as many items like this. Third point made, use of leverage. Quote, "As part of the pools conservative strategy, the use of leverage will be limited. While more leverage could potentially augment returns that also increase a downside risk, we do not believe that extreme use of leverage is necessary to achieve our target returns, so we've kept leverage at one X. And there's also a lockup period that the pool requires investors to remain invested for a longer period, 10 years in this case."

Ben Felix: What are the fees?

Cameron Passmore: I couldn't find the fees. I'm sure they would be there. I just didn't dig into what the fees might be. And the article did say, "You must be to an advisor to make sure it fits with your overall plan." So they did cover that. My only issue is that sometimes these things, this kind of loaded language, I think, can wallpaper over some of the underlying potential risk factors.

Ben Felix: I think downplaying risk and highlighting exclusivity, those are probably used to sell lots of products that like you say, we just don't look at. But I doubt that practice has declined since you remember it.

Cameron Passmore: No, and a lockup period. There's your bad advice that weak. Let's hope Oscar's front leg gets better. Anything else to add?

Ben Felix: Nope, I don't think so.

Cameron Passmore: All right. Thanks for listening.