Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
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=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=Transcript of the talk, from the video's captions. Auto-generated: speaker names in particular are unreliable.
=

# Purifying the Equity Premium

Authors:   
Discussant: None  
Video: https://www.youtube.com/watch?v=CQWpmyRN5qQ&t=0s


## Talk (00:00:00 – 00:19:07)

[00:00:00] Great. All right, so many thanks for putting the paper on the program. Uh this is joint work with Tuomo. As you know, he's here.  
[00:00:07] And uh our piece hopes to provide a a fresh perspective on one of the oldest puzzles in finance. That is, of course, the equity premium puzzle.  
[00:00:17] Let me describe our two big ideas uh and summarize our results, and then I'll provide some detail for you. And so, first in terms of the economics, uh the equity premium is conventionally defined as the excess return of stocks  
[00:00:31] over nominal short-term bills. And of course, this is ubiquitous in practice and in academic research.  
[00:00:37] We think that that's an apples-to-oranges comparison.  
[00:00:40] One thing, stocks are real assets, and the T-bill is nominal. And so, also, stocks are long-lived assets, and of course, the T-bill is explicitly short-term.  
[00:00:50] So, what what what we want to do is make an apples-to-apples comparison. In particular, construct what we think is more likely to be the risk-free investment for a long-horizon investor, so the sort of search the sort of investor that this conference is aimed at, uh that we're going to call the real  
[00:01:04] term premium. We're going to duration match a position in the real bond to the stock market.  
[00:01:10] Once you take that out of the conventional equity premium definition, what's left over we're going to dub the pure equity premium, uh hence the title of the paper. Then, of course, with these two components in hand, what we're going to do is go to the vast literature on the equity  
[00:01:24] premium and see which interesting aspects locate in which piece.  
[00:01:29] We're going to pair this economics idea uh with an idea in econometrics, and it's one in part because of necessity.  
[00:01:36] And that is the inflation-indexed bond markets that we're going to be studying uh are relatively young, and so at most four decades of data. That sounds like a lot of data, but as we know, if you're trying to estimate Sharpe ratios precisely, it's  
[00:01:51] not enough, right? Here is Andy Lo's uh formula for the the error of a Sharpe ratio. You can see if you have a sharp ratio of around .2, which is the ballpark we'll be playing in, you need a century of data to reject a null of zero. And so what we're going to  
[00:02:06] do is introduce an estimator that's going to provide a substantial improvement on the sample mean.  
[00:02:12] So in particular, what we're going to do is make what we think is a reasonable assumption that the constant maturity inflation index bond yield, in our case the 10-year yield, is stationary. We're going to use changes in that yield as a control variant. So we're going to  
[00:02:26] regress that out of our premia and see what's left over.  
[00:02:29] Uh that's going to answer the question, what would the average premium have been if yields hadn't changed? We're going to find that the resulting control various estimators quite robust across subsamples, which is going to be important. And moreover, it's going to  
[00:02:42] have a much more precise estimate. We're going to cut standard errors in half.  
[00:02:47] So, let me summarize what we find when we focus on this pure equity premium piece, there is no puzzle. And so compare compared to the conventional equity premium, our pure equity premium has a lower mean,  
[00:03:02] high volatility, and thus a lower sharp ratio, also higher correlation with consumption growth.  
[00:03:09] And so what this means of course is that the equity premium puzzle is in said actually, we think a real term premium puzzle.  
[00:03:15] For example, we're going to find some other interesting results that this pure equity and real term premium piece pieces are quite negatively correlation, have a quite negative correlation, minus .9 in the US and minus .7 in the UK. We're going to  
[00:03:30] characterize this to some degree and find that it reflects what we think is extreme flight to safety behavior that's unrelated to underlying news about fundamentals in the stock market.  
[00:03:41] Where the safety of course is the long maturity inflation index bond. I have safety in quotes of course because if you can infer what I said at the first bullet point, we're going to find that the real term premium has a positive mean, which is somewhat inconsistent  
[00:03:54] with this idea of safety. All right, so let me go ahead and get started. I'm not going to do a literature review because of time constraints. I'm not going to talk too much about the data. I think they're relatively straightforward. Two asset classes and two countries.  
[00:04:07] Uh I do want to mention that when we duration match the real bond to the stock market, since the stock market has a longer duration, typically, I'm going to choose the longest maturity real bond at any point in time. And so, when I talk about the real bond, I'll be  
[00:04:20] talking about that portfolio that rotates into the longest maturity bond along the way.  
[00:04:26] Let's get started with some plots. And so, here are the cumulative excess returns for these two assets in these two countries.  
[00:04:35] Um you know, you I think you can see several things from these plots. For example, in the US, stocks outperformed real bonds starting in 2013.  
[00:04:44] In the UK, however, uh real bonds outperformed stocks until right near the end of the sample.  
[00:04:49] And then, in both countries, you can see this crash where there was dismal performance of real bonds after 2021.  
[00:04:57] And so, I want to note that because it's going to be relevant later on in the talk.  
[00:05:03] Okay, so we want to measure the duration of the stock market to construct this real term premium uh component.  
[00:05:09] We're going to use a valuation model, not a simple regression.  
[00:05:13] And as will soon be clear, a regression approach is plagued by an extreme omitted variables problem. We definitely don't want to do that. We argue that you shouldn't be doing that going forward given our results.  
[00:05:25] Uh we're going to measure stock duration using a very standard straightforward Gordon growth model to um uh measure that. Uh and in particular, in such a model, it's the inverse of the forward dividend yield. And so, we're going to proxy for that using the  
[00:05:39] trailing 12-month dividend yield in each of these two markets.  
[00:05:42] Now, of course, we're going to grant that other interesting methods could be developed to measure valuation-based duration, but I will say that all of our findings are robust to reasonable variations in the way that we  
[00:05:54] implement this valuation based estimate of stock duration.  
[00:06:00] So, here's what they look like. So, the red line are the stock markets in these two countries. The black line is the real bond. You can see it jumps when we move into the longest maturity bond as I mentioned.  
[00:06:11] Um you can see in the US and I'm summarizing the tables at the bottom that the duration is about three times longer and and varies a lot. That's in contrast to the UK where on average you can see  
[00:06:24] the ratio is one. And so, this is one of the many good things having the UK data in our sample brings to the table. You know, it's a different country. It starts earlier and if you're worried about our duration matching exercise, here since it's one on average, we're basically just sort of  
[00:06:39] fine-tuning, right? And also, we're going to find, of course, that in both countries, broadly speaking, we see the same results.  
[00:06:48] So, let me remind you of those premia definitions and in particular, the real term premium is going to be the product of two things. It's going to be the excess return on that real bond multiplied by that scale factor from the previous slide. And so, that's an ex  
[00:07:02] ante beginning of period measure. And so, this is a implementable portfolio that one could run.  
[00:07:08] So, we're going to measure that and then what's left over will be our pure equity piece.  
[00:07:14] All right. Now, some numbers. So, this is for the US sample.  
[00:07:18] Uh in our sample, the equity premium, the conventional equity premium, was 8.5% roughly speaking.  
[00:07:25] You can see in the green box that for these two pieces, they both equally, roughly speaking, contributed to that experience. Uh you can also see that they have much higher volatility. Of course, we'll come back to that in just a moment. But as a consequence, their  
[00:07:38] Sharpe ratios are much lower than the sum.  
[00:07:41] All right. And indeed the sharp ratios are statistically insignificant.  
[00:07:48] Here's the UK experience. Uh in our sample, the UK had a much lower conventional equity premium for UK. As a consequence in part, you see the real term premium is a much larger component relatively speaking.  
[00:08:01] Now given these these facts, uh one can guess the next slide when we look at the correlation between these two components. Here are the relevant uh correlations.  
[00:08:12] And in the red box is this quite strong negative correlation between these two pieces. And so, they're quite negatively correlated in our sample. And that's also the case in the UK as well, even though it's a different country, different sample  
[00:08:24] period, uh etc. And when you look at these correlations, you might wonder if there's any interesting time variation. Is this driven by some extreme events or what have you?  
[00:08:34] Here we're going to plot time-varying correlations. These are rolling two-year windows using uh at the daily frequency to measure the correlation between these two components of the conventional equity premium.  
[00:08:46] And you can see that though there is some variation perhaps, it's always deep in negative territory.  
[00:08:52] Always statistically significant. All right. Well, what drives this extreme negative correlation?  
[00:08:59] Uh you know, I'm sure there's a lot more research can be brought to bear on this question. We're going to try to at a high level distinguish between two possibilities. Uh one uh is something that we'll call the cash flow news hypothesis. And that is that fundamentals arrive and they drive both  
[00:09:13] the realized pure equity premium, perhaps by a habit formation, and the realized real term premium, perhaps via precautionary savings.  
[00:09:22] That's one possibility. The other possibility we'll consider and try to distinguish between these two is what we're going to dub the endogenous flight to safety hypothesis, where preference shocks unrelated to underlying news about fundamentals are responsible for  
[00:09:36] that negative correlation. So, what we will do is use uh the method and news terms from a recent paper with John and Stefano to try to test and discriminate between these two hypotheses.  
[00:09:50] So, here on the slide you can see at the top those three components of the conventional equity premium. Together, they would sum up appropriately signed to the unexpected conventional equity premium realization.  
[00:10:02] You can see at the bottom of the slide the correlation between these news terms. And as you can see, the negative correlation that we found in previous slides is clearly a discount rate news phenomenon. You can stare at these numbers and and sort of back it out, but  
[00:10:16] let me make it easy for you. What we'll do on the next slide is take the realized returns on each of these two components, the There we go. The real term premium and the pure equity premium, regress  
[00:10:29] them against cash flow news. You can see that the R squares are relatively low, suggesting there's not much of a role for our cash flow driven hypothesis. When you look at the cross regression residual correlation, you can see that that negative correlation that  
[00:10:43] we found before, that's present in the discount rate news terms, is unrelated to cash flow news.  
[00:10:50] All right. So, in some sense, we could argue that we've solved the equity premium puzzle. That it's not a puzzle if you remove the real term premium because it reduces the mean premium.  
[00:11:02] It increases the variance of the premium. And as I'll show you now, also makes that pure equity piece more correlated with US consumption growth.  
[00:11:11] I'm going to show you the US results here. We also have the UK results in the paper. They're broadly similar, but there's some caveats that one might be cautious in interpreting.  
[00:11:22] All right. So, here we go. Here we have the consumption growth beta of the conventional equity premium in the first row.  
[00:11:30] As we take away the real term premium component, what's left over, the pure equity piece, has a much higher consumption growth beta.  
[00:11:39] As we move right across the slide, we're going to do what others have done. I'm thinking of Daniel and Marshall or Jonathan Parker's work. As we look at lower frequency estimates of these betas, you can see it strengthens. And so, we're going to find here that the pure equity premium's consumption beta  
[00:11:52] is much larger, especially at longer horizons.  
[00:11:57] You can think about other ways to try to measure the consumption risk in these uh these premium.  
[00:12:02] Here is one way to look at what happens in extreme events.  
[00:12:07] We're going to study consumption crashes. In particular, we'll look at the two that occur in our sample, the GFC and the COVID experience. The top you can see the realized return on the sum in these two pieces. The realized return on the conventional equity  
[00:12:21] premium is minus 5% give or take. Um once you take out the real term premium piece, the pure equity piece has a really large negative response during these consumption crashes. Again, consistent with it being quite  
[00:12:34] reasonable to understand in the context of consumption based asset pricing. Here we also see the event time experience of the pure equity piece during these two uh consumption crashes.  
[00:12:47] Right now, so it seems like the pure equity premium appears much less puzzling to even the simplest sort of consumption based asset pricing model, power utility. So, we're going to use some Hansen Jagannathan bounds to measure exactly how much less, right?  
[00:13:00] So, we're going to show you three estimates. Gamma 1 is going to assume correlation of 1 and uses Annette's uh result from her a piece looking at the consumption growth volatility of stockholders.  
[00:13:11] Uh Gamma 2 is going to use aggregate consumption growth, which mixes both stockholders and non-stockholders, of course. And Gamma 3 is going to use the actual measured correlation between returns and consumption growth. You can see on the slide the improvement that we  
[00:13:26] make in this regard. And so, at the top, as you move from the left to the right, you can see that these bounds these estimates of gamma become quite unreasonable, over 100. But, once we take out the real term premium piece, what's left over is  
[00:13:41] actually quite reasonable. And so, for example, with gamma 1 a bound of 2.1 is a quite reasonable estimate of risk aversion. Now, certainly 22, as we go to the right, may not be that reasonable, but we've made substantial progress in going from 100 and  
[00:13:55] to 22. You can see similar improvements in the bounds in UK data.  
[00:14:02] Okay, great. Now to be honest, of course, we didn't really solve the equity premium puzzle.  
[00:14:08] What we've done is instead just sort of quarantined it safely within this real term premium bit.  
[00:14:13] And so, there's lots of questions one wants to ask. Uh some of these we'll leave to future research, but I'll talk about the the first one there. How large is the true mean real term premium?  
[00:14:26] Now one of the reasons I showed you this cumulative excess returns is because in these data, the sample period really matters.  
[00:14:33] So, when Tom and I first started working on this project back in early 2022 the bond market trailing returns looked very different. Uh as you can see and remember from that graph um at that point in time, more than 100%  
[00:14:46] of the in-sample uh equity premium was due to the real term premium.  
[00:14:51] Thanks. And so, in indeed, taking on pure dividend risk had earned a negative premium in both countries since the inception of these real bond markets.  
[00:15:00] Uh now, Jules has a paper that ends exactly at the end of 2021.  
[00:15:06] And though he is mainly focused on comparing equities and nominal bonds, he also finds equally extreme results. And so just adding 3 and 1/2 years really changes what's going on in in these data. Let me show you that explicitly.  
[00:15:20] And so um these red boxes compare these two components if we were to have written this paper as we didn't in early 2022 versus now. Okay, and you can see the the change, the incremental change  
[00:15:34] that occurs in that three and a half year period. And you know, we don't want to write papers that are going to change after just three years of data. And so, we were worried about this. And so, in response what we did is come up with a better way to estimate these premium to give you more assurance that what we're  
[00:15:48] finding is robust and will for the most part stand the test of time. And so, we have two equations here. The first equation is the traditional sample mean estimate. The second is our control various estimate where this on the right hand side of the  
[00:16:02] regression this variable D is has a mean zero.  
[00:16:07] Now, the unexpected, I'm sorry, the unconditional mean of both of those equations is what we want to see, but the second equation's intercept is going to be much smaller in terms of its standard error as long as D is highly correlated with U. Not very negatively auto correlated. In the paper we have  
[00:16:22] some simulation to flesh all this out. And so, you can take a look at that if you're interested. We think that this sort of setup in our in our case is perhaps the near ideal real data use case. So, what we're going  
[00:16:36] to do is estimate real bond term premium using that constant maturity real yield change as our control variant D. So, let me make sure everybody understands and so in population yields won't trend up or down by  
[00:16:49] assumption. In any particular finite sample they may trend up by chance, may trend down by chance. What we want to do is estimate what would the premium have been if that by chance trend didn't occur. Okay? And if the method works,  
[00:17:02] hopefully, fingers crossed, you'll see much more robust estimates across these subsamples and much smaller standard errors. So, let me show you that.  
[00:17:12] So, here, I apologize for all of the data, but I want to have it all on one slide.  
[00:17:17] And so, we have the conventional equity premium, the real term premium, and the pure equity premium for the full sample, the sample that ends in 2021, and then for both countries. Focus for now on the the red  
[00:17:31] and green boxes. The red box is the standard error of the conventional sample mean estimate. The green box is the standard error of our control variates estimate. What you can see is that the numbers inside the green boxes are always much smaller than those in  
[00:17:44] the red box. And so hopefully um we have more precision uh about just what these premium might be.  
[00:17:53] Next, let's move to the estimates themselves. Now the relevant comparison is within a country across these two samples. You can see for the red boxes across these two samples, for example, in the US  
[00:18:04] moves around a lot, 4.52 to 12.21. However, in the green boxes, our control variates estimate, which takes out the by chance movement in yields, is much  
[00:18:15] more stable across these two subsamples. So I think I'm doing well on time.  
[00:18:21] I'm going to go ahead and conclude, give us lots of time for questions.  
[00:18:24] Uh so what we did, we decompose the conventional equity premium into two components, the real term premium piece and the pure equity premium piece.  
[00:18:35] We also introduced a novel control variates statistical technique for estimating mean premium.  
[00:18:40] And we found that the pure equity premium is not that puzzling.  
[00:18:44] Of course, that uh hides the fact that the real term premium is extremely interesting, and as we say on the side here, screams for additional research because of its role in the equity premium puzzle.  
[00:18:56] It's positive sample mean, uh it's negative consumption beta in the US, and its negative correlation with this pure equity premium piece.  
[00:19:04] All right. Thank you.