Episode 350: Scott Cederburg: A Critical Assessment of Lifecycle Investment Advice

24:19And then what do you want to do at age 36? You just have to kind of iterate through until it converges to an optimal solution. When we do that, it ends up being largely similar to our fixed weight approach. You're 99 % in equity on average across all the ages, and then 1 % in bonds and bills. And if you look across time, basically up to retirement, it's 100 % equity. There's a little blip around retirement. So at age 65, the investor puts 27 % in bills and then mixes the rest of it in domestic and international stocks. But it's relatively short-lived. I think by 68, they're back over 90 % in stocks.

25:03And basically by age 70, they're basically 100 % stocks for the remainder of their life. So it's just kind of this short-lived blip of getting some money off the table right around the retirement period is kind of the only difference between our full life fixed weight design and then this age-based design. That's a big deal though, man. From a financial planner's perspective, the difference between having a client 100 % in stocks forever, the difference between that and somebody who's going to be 27 % in bills at retirement and then holding bills until age 70, there's no joke. If we're talking to a client, that's a very significant difference.

25:39That's a super interesting finding. So how significant were the gains or the benefits from the optimal time-varying strategy that you just described? If we go back to this kind of equivalent savings rate, so we have a 10 % savings rate with the optimal fixed weight strategy. If you do this age-based strategy, you can reduce your savings all the way down to 9.93%. For every$1 ,000 you're going to save, you can buy a cup of coffee at Starbucks with the amount that you can reduce your savings by. It's a relatively low economic significance. That's interesting in two different ways, because it's interesting that it doesn't change things much, but it's also interesting that if somebody really wanted to hold cash early in retirement because it made them feel better, it doesn't have necessarily a huge detrimental effect, it doesn't sound like.

26:23They are picking this as the optimum, and so it is increasing their utility by holding that cash there. But for us, it was a reassuring result where it's very difficult in this setting. Given that we have the bootstrap, we can't do some of the traditional methods of dynamic optimization. We went through and looked at different elements of, hey, what if we let them choose an optimal retirement age, for example, or different things like that, just to see whether we had sensitivity basically to, if we have static optimization as our base case, how bad of a base case is that effectively? Everywhere we look, it's like, it's not that bad.

27:04The fixed weight strategy is so close to this age-based strategy, for example. It makes that initial analysis valid in some sense. How does this time-varying optimal portfolio, how do those allocations change when you abandon the block bootstrap and just assume that returns are independent and identically distributed? It definitely becomes a bigger role for bonds and bills in retirement. They're still choosing all equity up to retirement. And I believe in those specifications with the IID, kind of ignoring the long-term return properties, I think they get back to all equity in late retirement, 90 years old or something like this.

27:46They're kind of back to the all equity strategy. Interesting. So it's equities, adding bonds at retirement and then decreasing bonds slowly back to 100 % equity later on? Yep. Interesting. How does that change if only domestic assets are allowed? Just looking at effectively excluding international stocks from the analysis, if we want to diversify away from domestic stocks, now we have to go to fixed income. So that also increases the role for bonds and bills. In those analyses, you have some fixed income allocation throughout your entire retirement. The working years, we're still seeing 100 % equity, even with just access to domestic stocks.

28:28But once retirement hits, you're always going to have some portion in fixed income. And if you combine these two things and imagine that you're looking domestic stocks, bonds and bills, and then you're also going to say IID, and this is a little bit similar to the setup of a lot of academic papers anyway. You have pretty sizable fixed income exposure throughout retirement at that point. So at age 65, for example, you go from when you're working years, you're 100 % equity. And then at age 65, you switch to 60 % in bonds and bills and just 40 % in equity. So that really swings the analysis quite a bit.

29:06Takes you back to the status quo, I guess. In some sense, it's like, yes, our results are sensitive to this block bootstrap assumption. and the assumption of putting international stocks in, but I have access to international stocks. And we know that returns aren't IID. I feel like those are pretty easy assumptions to get behind. Yeah, it's sensitive to the assumptions, but if they're the right assumptions, then people should be sensitive to them. We had the time-varying optimal portfolio that loads up on bills for 27 % at retirement. And that was with a 4 % constant spending. So they have a million dollars and then adjusting that for inflation every year.

29:46How does the optimal portfolio change when you switch from the constant spending to a proportional spending strategy? We're using 4 % of wealth, but if you just spend 4 % of your current wealth at all times, that's going to fluctuate your consumption around a lot. But your optimal strategy at that point is 100 % equity for your entire life. And it's almost completely flat in terms of the domestic international allocation. So it's nearly identical to our fixed weight optimal strategy. So the blip is gone. What is the interaction between that, the spending strategy and the optimal portfolio? What does that say about sequence of returns risk?

30:22So 4 % rule is kind of as exposed to sequence of return risk as you can potentially be. I think the entirety of that blip where you're getting money into bills for the beginning of your retirement is just to reduce your exposure to that sequence of returns risk. You're trying to make a sudden drop in stocks less damaging to your full retirement. I think that's driving the entire allocation to fixed income in the base case. Michael Kitsy has had an article out a number of years ago about a bond tent, and it sounds like that's kind of it. It's just basically play defense for a couple of years in case you get really, really unlucky, but then the kind of glide path resumes back to 100 % equity.

31:01So sequence of returns risk, if I've understood you correctly, is largely solvable by variable withdrawals. There's a range of hybrid things that people have done where you try not to have the extraordinary volatility of if your portfolio goes up 30 % to you, withdraw 30 % more, but you also don't have such a rigid rule as is implied by the 4 % rule. Presumably there's a degree to which sequence of returns risk exists in things that are closer to the 4 % rule, and it's probably going to be very muted in the things that are closest to the totally variable rule. How do the optimal portfolio allocations change when you allow the couple to condition their investment strategy on the domestic stock valuations on the price to dividend ratio?

31:48It's pretty common in this literature to think about time varying expected returns and how would market conditions affect things. So our approach to it in the simulations is to basically give the couple information every month about is the valuation higher or low currently in the market that they're investing in. And we break it up into quintiles of the price dividend ratio, like the domestic price dividend ratio. So the lowest quintile with the low prices is roughly less than 20 for a price dividend ratio. And then the highest is roughly greater than 50 per price dividend ratio. So the US right now is in the highest valuation bucket.

32:29I think a lot of the rest of the world is not right now. In the middle three buckets, like the middle three quintiles, we get all equity strategy that's pretty close to the unconditional base case, 33%, 67%. So it's really on these two ends. So if we look at the lowest valuation bucket, domestic stock prices are low, the couple chooses to do 65 % domestic, 35 % international. So basically buy the cheap stuff locally and just reduce international allocation. In the highest bucket, I believe the number is it's 75 % international. So you're really upping your investment internationally. And then it's 16 % domestic stocks and 9 % bonds.

33:13So that's where the bonds finally sneak in. We see a little bit of bonds if your domestic stocks are very highly valued, you get this modest allocation to bonds. So that kind of speaks to some of the criticism from the first draft of writing this paper when US stock valuations are as high as they are, it doesn't make any sense, but you kind of address that now. Do you think that this analysis also addresses the idea that expected stock returns are just generally a bit lower now than they may have been in the distant past because markets have gotten safer or whatever? To the extent that the price dividend ratios now are directly comparable to what they have been.

33:49I mean, obviously we've had some shifts away from dividends towards repurchases and things like that. So if we had all the data, we could probably turn it into like a payout ratio sort of thing. But I think it's probably the case that we're going to hang out a little bit more in the top three quintiles than in the bottom three quintiles, or at least hopefully to some extent. To get into that lowest quintile is not good times. Post-financial crisis type of stuff was probably getting towards that lowest quintile. in some of the countries. So when you offer this conditioning based on valuations, how significant were the gains for the optimal portfolio?

34:25If we go back to the optimal savings rate, so if we have 10 % saved in the fixed weight strategy, we've now given the couple more latitude to optimize. So it's going to be better. And so they can get down to about 9.7 % savings. So they get a decent gain. Think out of that. We do some additional analysis just on, is it the bonds that are coming in and saving it? Or is it that domestic versus international allocation? And about 80 % of the gain comes from switching across domestic and international, basically in those two extreme states, betting a lot on domestic when prices are low, getting the heck out of domestic when prices are high.

35:05That's where about 80 % of that economic gain is from. What's the advice here, I guess? Should people actually be conditioning their domestic allocations on domestic valuations? I'm right now about 50-50 US international. I guess I just haven't really changed since our first draft that had a 50-50 rule of thumb. So that means I'm underweight the US relative to market weights. I think I'm perfectly comfortable being underweight in the US given US prices versus European prices right now. On the other hand, you look at all the academic evidence and institutional performance management around trying to time the market.

35:46It's not easy to do. You've sorted valuations into quintiles based on the full set of available information. Yeah. But any investor today does not have the full set of available information. They have past valuations. They don't have future valuations. Your investors have past and future valuations. Is that right? At any given time, we're just telling the investor, this is your price dividend ratio right now, it will end up kind of mattering how you're investing at age 75. And the utility that you're getting does depend on the wealth that you built up over time. It depends on your strategy performance and such up to that point.

36:24But I don't think we have a pure look ahead bias necessarily in terms of we don't tell the investors that prices are going to get higher than they currently are. We're just trying to think through that. If the valuations are organized into quintiles, they don't know which quintile they're in? They know which quintile they're in. We're letting them optimize their asset allocation within that quintile. If they're in that bucket, this is what they're choosing. They also know if in other years they fall in one of the other quintiles, they know what their strategy would be if they move from quintile three to quintile five and get into high price territory.

37:02They know that they're going to back away the domestic stocks a little bit. We do the joint optimization across the five strategies. So they know how they will dynamically react, but they don't know what the future is going to look like. That's a cool piece of analysis. One of the other things that I've gotten kind of pushback on when I say that your methodology with the bootstrap makes a lot of sense is that some random small country that gets pulled into the bootstrap to represent a domestic country like Canada or the U.S., then it just doesn't make sense. How important is the inclusion of small countries or countries with small stock markets to the main results in the paper?

37:41I guess we've heard this before too. We had a reader pretty recently that seemed pretty offended about Iceland being in the sample. So one of the things that we've done, we've looked at, say, just include large population countries as one way of splitting on this. And we've looked at 0.2 % of the world and 0.5 % of the world. And so for context, Canada is exactly 0.5 % of the world. So it's basically like Canada and bigger countries. And if we just throw out all the smaller countries than that and redo the analysis, we'd get 27 % domestic, 73 % international, 0 % bonds, 0 % bills. And some of the narrative around this too is, well, of course, somebody from a small country is going to want to get most of their money in international.

38:26The numbers, if we just look at the analysis, It actually is going the opposite direction where it's like the larger the countries, they're actually trying to do more international. That sort of narrative doesn't really hold up in the data. The other thing that we've done, there are differences across countries and how important the stock market is or the breadth of industries in the stock market. We can condition on the stock market capitalization being at least half of GDP in a country. The US actually doesn't hit that until the 1990s. It's a fairly stringent thing. And I think these screens do the things that we're trying to do if we look at which countries are in the sample for which times.

39:06And that's also 27 % domestic, 73 % international, 0 % bonds, 0 % bills. We've tried a lot of stuff and people seem to think just this little tweak of the data and everything's going to fall apart, but it just doesn't seem to fall apart. What happens if you take out Germany? Germany is another one of these little stories. Germany has hyperinflation following World War I. So 1920 to 1923. 1923 in particular, bond returns look weird. There was whatever it was, trillion percent inflation or something like this. Summary stats on Germany look weird. And it makes our overall sample summary stats, if you did a standard deviation, it makes bonds look risky because we had really extreme returns in a couple of months in Germany.

39:53I kind of had the stance, It's obviously not one out of the 2 ,650 years worth of data driving our thing. And then Ben was like, well, I've heard it said by a lot of people, so you might as well just run it. So I went ahead and ran it, and it's 34 % domestic, 66 % international, 0 % bond, 0 % bills. If we just throw out all the data from Germany through the entire sample, just purge it from the sample. Virtually no change. Yeah. Yeah, that's crazy. If you just change this one thing, I bet you the results will change. Pretty funny that it doesn't. Not funny. It's fascinating. Also funny though, because people are so sure this is going to change your result.

40:29What about all pre-World War II data? The pre-World War II, there's two concerns. One, we have some data from 1890. And is that comparable to today? And then the second, people seem to think that war risk has gone away. Apparently, they're a little more optimistic than I am. But we can just drop everything World War II and before. I think it's 31 % domestic, 69 % international, 0 % bonds, 0 % bills. It's just the same thing. Crazy. So nothing changes virtually. Yeah. The big thing in terms of sample period is you need to have a long enough sample period where you're including bond market cycles.

41:12Interest rates go up, interest rates go down. Interest rates after World War II are roughly what interest rates are now. And we've had a couple of different interest rate cycles where interest rates go up, interest rates go down. If you were to say, start the sample in 1980, when all the bond yields are at whatever, 15 to 20%, bonds had good returns in the 40 years following 1980, because you get this enormous capital gain from yields falling from 15 % to 5%. And so that's the data that a lot of people are used to looking at on bonds. Well, the 80s was a good decade. The 90s was a good decade.

41:48The 2000s was a good decade. The 2010s was a good decade. Well, the 1970s were terrible. and the 2020s have been terrible. If you're including a full bond market cycle, you have enough of the terrible bond stuff going on. We just can't get the same bond performance as we had since 1980. If we're starting at 4 % now, we have to go to like negative 11 % or something to get that same set of capital gains. For international stock portfolios, how important is the inclusion of the US market? If my domestic market is not the US and I'm outside the US? How important is the US inclusion in the international component for those investors?

42:25This might be about the biggest change that we saw on any of them. So obviously, the US has been a big part of the international portfolio for quite a while and has had that good performance. So if you completely exclude the US from the entire analysis, you get 45 % domestic, 55 % international, 0 % bonds, 0 % bills. International stocks don't become so bad that you're going to go to bonds. You still want to diversify with international stocks, but instead of the base being like 33 % domestic, it's like 45 % domestic. If you just take out the ex-post winner of stocks over our sample, if you take that out, then the international stocks don't look quite as rosy, but they're still preferred to bonds.

43:08It's still crazy though, because that's another one where people are like, well, of course, international stocks look good when you're including US and international. That's true to an extent, but it's not that sensitive to that. Yeah, it's kind of eye of the beholder whether the 45-55 result is very different from our base case or whether it's the same thing. Because in some sense, it's kind of the same thing. It's a different allocation, but it's 100 % equity with a lean towards international. You talked earlier about how the utility is fairly flat within a pretty big range. So it doesn't sound like this is a huge deviation from that.

43:39Another one that comes up a lot, when I've talked about any of your research, like when I make a video about it, there's certain parts of the internet that get extremely upset with me because they think that the US is special. Hear that all the time. And therefore treating it like every other domestic country, the way that you do in your sample is a mistake. How do your data change if the US is in fact special? there's certainly a view that the U.S. is special and that the U.S. being special is going to manifest in the U.S. continuing to have high returns. The way that we can try to model this is we have on the one end of the spectrum, we're not treating the U.S.

44:17any differently. And that's our base case where we just throw it in there with all the other developed countries. So we're going to view this as a 0 % view on the U.S. being special in this particular way. And so that's our base case analysis, 33 % domestic, 67 % international. On the other extreme, the US is special, 100 % guaranteed, and future returns in the US are going to look like past returns in the US. So then we just use 100 % the US sample to do the analysis. If you run that through, you get 100 % domestic, 0 % international, 0 % bonds, 0 % bills. You just throw it all in US stocks and you're good to go.

44:55So then what we can do in the middle of these two is basically mix the two. If you think about running a million simulations, you can run it where 90 % of the simulations come from the U.S. and 10 % come from our full developed sample. We're giving you a 90 % belief at that point that the U.S. is just going to be special and earn higher returns than the rest of the world. And so if you do that, you're already backing off just a little bit on the 100%. You're at like 96 % domestic, 4 % international. And then as you go, if it's 50-50 on whether the US is special or not, then it's 60 % US and 40 % international.

45:33That's about the market weights right now, the world market weights. So in order to have a home bias, as a US investor, to have a home bias, you have to have more than a 50 % belief that the US is going to continue to earn higher returns than the rest of the world, effectively. which there are certainly people who have more than a 50 % belief that this is true just from casual observation of things on the internet and conversations with various people. I know you didn't run it, but could you do the same thing for Canada up until 2009? Canada and the US were pretty close. If we made a Canada special case, would it have a similar effect, you think?

46:12Or Australia? I would guess so. We haven't run it country by country. is potentially something to do to just see how much variation there is across those things. I think to say that that means more to countries or to investors in that particular type of country, I think we would tend to argue against getting too granular in that, yeah, this country got unlucky, but is it a country that just gets unlucky or did it just get unlucky? You said earlier that people have to believe that the US is special and that that's going to manifest as higher future returns. How else could that manifest? If the US has structural advantages and people will talk about innovation and different institutions and all this stuff, an alternative is that we just have higher prices.

47:00And if anything, lower risk premiums, so lower future expected returns, that would be consistent with, there's evidence by Fama and French and Avnis and Walker that a lot of the couple percent of the historical US average return was just the increase in valuations that we had. And it's possible, there's a paper that's now forthcoming at the Journal of Finance by Binsberg and Hua, Peters and Walker. In their model, we have a theoretical model, their investors are learning about the probability of crashes, essentially like disasters in each country. Over the sample, they become convinced that the U.S.

47:40is different from many of the other countries. But now those investors would just price the U.S. higher and have a lower risk premium because it's not as risky. The investors in their model would believe that the U.S. is special, but they believe that that warrants a higher price and lower returns because of the higher price. That seems like an easier equilibrium argument to make to say that all the institutional investors in the US think that the US is special and they're all overweighting the US and then that doesn't have an impact on the valuations that's going to hurt future performance. I think the rationale for the US is always going to earn higher returns is just pretty tough to figure out how that's going to work.

48:25It's like the opposite of what people think. People think that it's special, therefore it'll have high returns, but in reality, it may be special and therefore have lower returns because it's a safer, higher quality market, which is true, but that doesn't mean it's going to have higher future returns. I got it from you, Ben, I think a while back or from maybe one of your guests, but yeah, if it's the biggest, safest market in the world, why would you expect higher returns from that? How important are the relatively low historical correlations between domestic and international stocks? How important is that to the performance of the optimal portfolio?

48:53We've seen the domestic international stock correlation vary across time. It's gone up. It's gone down. It's gone back up. It's relatively high right now. If you look over shorter periods, and I haven't done this super formally, but it tends to be the case if you're looking at the U.S. correlation with international stuff, it tends to be pretty high most of the time. And then there are just these little periods where it's 0 % correlation or negative correlation for just a short period of time. And then it kind of goes back up to very high correlations. It'll be interesting to see whether we're just in a high correlation regime now, and it's less likely that we do that kind of switch or it's just one of those hadn't happened in a little while.

49:33But one of the things that we can do, we do this split where you take your retirement periods. I think we focused on retirement periods, but you take the retirement periods and you can split that into quintiles based on the realization throughout your retirement of how high is that correlation between domestic and international. And then you can look at the low correlation regime versus the high correlation regime, the stock strategy of the strategies that we consider, it's still the best strategy across all five buckets. One of the things that we see is that we're looking specifically at the probability that you run out of money in retirement.

50:11And in that high correlation bucket, so this is very high correlation across all world markets, all of the strategies have very low ruin probabilities. In the low correlation, we see much more spread. Ours is the least sensitive to the correlation, but some of the other strategies get really bad when the correlations are low. My guess is that the correlation across markets is some sort of proxy for whether it's worldwide macro stuff or whether it's war stuff or whether it's trade stuff. There's all kinds of things that could be going on to kind of drive wedges between different markets in the world.

50:50But I think most of those wedges are probably bad wedges. There may be a degree to which high correlation is going to hurt the diversification benefit of domestic stocks versus international stocks. But that may be the state of the world where there's not as bad of a set of risks. And then in the times when the world is a little more risk-laden, there's going to tend to be lower correlation and you get more of the diversification across international markets. It's a little tough to exactly tease that out on what's driving that result. but that's kind of my sense. Those are the two probably like most intelligent pushbacks that I've seen against your paper.

51:31Current valuations are higher than a lot of the sample, therefore it's not valid or correlations, valuations, correlations. You've addressed both of them, I think pretty well in this version. What about labor income? How does an increase in correlation between labor income and domestic stock returns affect the optimal portfolio? There's a lot of disagreement in the literature on exactly the extent of this correlation. So we've had everything from some of the older literature was basically saying that there would be effectively zero correlation between labor income and stock returns. There's others that depending on kind of how you're splitting workers on education levels, income levels, things like this, there's a set of workers and probably realistically, the most likely retirement savers are probably on the higher end 0.3 correlation or something like this between the labor and the stock market.

52:23We look at a range of everything, 0 % in the base case, but everything up to 0.5%. And basically you do that, the investors are going to get away from domestic stocks a little bit because they're already exposed to that correlated risk with their labor income. They never run to bonds. They just put more internationally and diversify a little bit more that way. So effectively their labor income becomes a little bit domestic stock like, they already have a bit of that exposure. And so then they just go more towards international stocks. But the pattern turns out to be reduce the weight in domestic stocks by 3 % for every 0.1 of correlation.

53:01So your paper talks a lot about leverage as well. So I'm going to switch gears a little bit and talk about leverage. The base case has a no leverage constraint. How do the optimal portfolio results change when you allow for leverage? We've kept no leverage as a base case because outside of some of your listeners, I don't know a lot of people who are levering up their retirement savings within the actual retirement accounts, you're typically restricted from doing a lot of this stuff. So we're kind of trying to write to just the average person who's picking a default fund in their retirement account and probably isn't trading futures or anything.

53:36But if we do introduce leverage, it tends to be the case depending on risk aversion and depending on how expensive the leverage is, we do see our investors wanting to take on some leverage. So one of the issues around leverage is figuring out what's the cost of leverage. We do three different approaches. One's like very high cost of leverage, but I have an E-Trade account after about 15 different mergers or something like that. And I looked it up yesterday and they would charge me, I think, 12 % per margin. And so there's that on the one extreme. We have kind of a middle ground of 1.4%. That's the lowest margin rates that we could see.

54:17And then if you go into derivatives markets, there's a paper by Vinsberg and Diamond and Grateria. They estimate the risk-free rates that are implicit in futures contracts. So what's your implicit borrowing cost if you're trading in futures? And that's about 0.37 % above treasury bills. So that's the lowest spread that we consider. We talked to another large asset manager in Europe about this, and we're asking them what their clients do, and they're talking about like the Lombard loan market. And then we kind of ask the question, what happens around financial crisis or something? And they're like, yeah, that market dries up and you can't borrow.

54:57We're kind of assuming that away and just saying, hey, regardless of the market, you're not gonna have to reverse out of your leverage at the worst possible time. So I think we're given pretty favorable conditions, at least at the lowest leverage cost level. I think it's pretty favorable conditions giving leverage the benefit of the doubt. How important is the cost of leverage to the optimal use of leverage and the optimal levered portfolio when you model it out? It's very sensitive. Nobody wants to pay 12 % margin rates. That couple is 0 % leverage and the no leverage constraint is not binding.

55:32So they pick the same optimal portfolio as in the base case. At the medium 1.4 % spread above treasuries, that's again like the lowest margin rate that you're going to be able to get on your own, that they choose 55 % leverage. And they invest 34 % domestic, 66 % international, 0 % bond, 0 % bills. It's effectively the exact same portfolio, just lever it up. At the very low cost of leverage, like the 37 basis points, they do 100 % leverage. We do cap them out at 100 % leverage. They do 100 % leverage. And I think that one is 15 % in bonds at that point. The rest is split across domestic and international stocks in about the proportion that you would assume.

56:18But at 100 % leverage, they are finally going to start getting some bonds in there. With some of these products that are available out there, there's leverage inside the product itself. And you're going to have to pay a fee on top of the borrowing costs for that. So how do you think the product fee for a fund using leverage should be accounted for in the total cost of leverage? A lot of these funds, they're actually going to be able to access something like this 37 basis point spread. If they're using futures or other ways of borrowing, they're probably within the fund being able to do that. So then there becomes this issue of management fee plus borrowing cost.

56:53And I think a good comparison is I can be unlevered in a passive fund for like two basis points. So then what's it cost me to lever? And as soon as you're doing leverage, now you have to have active management. The leveraged ETFs do daily rebalancing. If you're going to maintain a specific leverage level, you have to trade every day. And so you're going to have to pay somebody to do this. I don't think anybody's doing this on their own. And so if it costs me 1 % to invest in that, and then 37 basis points within the fund for leverage, that's 1.37%. Our middle case is 1.4%. I think it's effectively getting us to about the same place.

57:36In that middle case, it was 55 % leverage or 155 % exposure to the same optimal portfolio as the base case. Does that suggest that at least based on that analysis, people should be optimally using some leverage in their portfolios? I mean, if they have access to borrowing cost, then I think this is going to depend on risk aversion too. At the median borrowing cost, if you have low risk aversion, you're still 100 % equity in there. It just sort of depends. I don't think I am personally going to go out and start levering up. But if somebody has the risk tolerance for it, then I suppose our data are suggesting that there is a strong enough return reward for taking on the risk that you're not crazy for doing it.

58:30It's a dangerous thing to say. We once did an episode years ago on leverage and talking about how a lot of models suggest that it is optimal, particularly for younger investors. And man, people went pretty crazy over it, for lack of a better word. All of a sudden, everybody that listened to our stuff wanted to use leverage. And we're like, whoa, we weren't necessarily saying that you should do that. I think this is one of those things. We all have some prior beliefs on things. And I guess I have a pretty strong prior that I should not be levering up my retirement savings. And that's going to be strong enough to outweigh any of this other evidence.

59:10And then I do think kind of coming back to this unmodeled aspect of it, where what happens if your leverage channel dries up in the financial crisis? I mean, that's what happened in the financial crisis to everybody running these leveraged strategies on mortgage back stuff. This is when credit disappears. And if you have to unwind your two times levered equity position in whatever, late 2008 or early 2009, then you miss out on the bounce back, perhaps as another argument for maybe don't take that part quite so literally. I think that is a risk. And that seems to be a risk that large institutions are internalizing that risk when they're doing arbitrage strategies and things like that, their liquidity dries up and they have to get out at the wrong time.

1:00:00So I think levered investors are going to face that same potential issue. We had talked years ago to an asset manager who was building concentrated portfolios to try and get access to higher expected returns. And their reasoning was that leverage in bad times would be really sucks. So if you have to choose how to get higher expected returns, you're better are concentrating in higher expected return assets than you are levering up lower expected return assets for the exact reason that you just said. So knowing that that is an unmodeled risk to get to that result is a pretty important piece of information for people listening.

1:00:33Good point. Okay. So we're talking about this optimal levered strategy, the middle case. I think you said the spread was 1.4 % above treasuries. In that scenario, how significant were the gains of that optimal levered portfolio versus the optimal unlevered portfolio? I don't think we've run that number specifically. I was kind of eyeballing the expected utility. I've got a pretty good sense for these things. I think it would turn out to be around 8.8 % or so for an equivalent savings rate. So I think they're perceiving an economically significant gain from this, but subject to the caveats that we just went through.

1:01:10What about levering up a 60-40 portfolio? How would that compare to levering up the optimal levered portfolio? A common argument is that you shouldn't be 100 % equity. You should do the 60-40 and get leverage. Comparing the 55 % leverage with all equity and the 55 % leverage with 60-40, the 60-40 strategy, you have to save almost 25 % to match the utility of 10 % in the other one. So there's a very large difference. So from there, how does the levered 60-40 portfolio compare to the base case unlevered optimal portfolio? So this is the trade-off between being just 100 % equity or using the 60-40 and getting leverage to try and take advantage of whatever diversification benefits you get with bonds.

1:01:59But when we run that, it's relative to 10 % in the base all equity strategy with no leverage. you have to save 19 % in this levered 60-40 strategy. And it's a little bit counterintuitive. Once you lever up the 60-40, you actually hold almost 100 % of your wealth in stocks and then you own bonds on top of it. It's the rebalancing where throughout your entire life, stocks are giving you these gains and you keep on taking these gains and you just keep on throwing them into bonds. And then the bonds aren't doing anything for you. And so if you were to run just like a no rebalancing, that would just get you back to an equity dominated portfolio pretty quickly.

1:02:41Then that would have like a much lower, I guess, equivalent savings rate. But that's not what the 60-40 strategy is. The 60-40 strategy is, yeah, you got to get away from expensive stocks and into the bonds and everything. Our investors just really don't like the prospect of having 40 % invested in bonds. Yeah, that's a crazy result. Because like you said a minute ago, Scott, that's what people say. You shouldn't be 100 % in stocks. Instead, you should lever up a 60-40 portfolio to get to the same expected return level with more diversification that your findings show, maybe not. What do you think that specific finding says about traditional mean variance, annualized monthly return type thinking where you do want to lever up to the maximum sharp ratio?

1:03:25Sharp ratio has a nice grounding in historical finance and everything. But I think you were talking to Hank Bessenbinder about similar issues recently. He's also thinking about long-term returns. And by the time you get skewness in there and everything like that, it's like, well, sharp ratio is not necessarily telling you the whole story. One way of thinking about it is there's a couple of ways to get into kind of cap M world, mean variance world. One is to have mean variance preferences. Markovitz started us off there. But another way to get into mean variance world is to have normally distributed returns because with a normal distribution, the mean and variance are the only thing.

1:04:04There's no skewness. There's no excess kurtosis. It's only mean and variance. And so in that sense, picking the best set of mean and standard deviation, that gets you the best distribution. Those two things define the distribution and it gets you to the best distribution. So the best Sharpe ratio is the best normal distribution for investing. If we're thinking about our stuff, now we're thinking about long-term return distributions. In some sense, our investors are still just looking for the best distribution. It's just that the Sharpe ratio is not going to define what the best distribution of returns, even our retirement wealth, that's after 40 years of investing.

1:04:43So there's going to be huge skewness. A sharp ratio penalizes the good outcomes on the right tail just as much as it does the bad outcomes on the left tail. It just treats things symmetrically. A sharp ratio doesn't really apply very well over longer horizons. And so I think recognizing that people have tended to apply sharp ratios to monthly return moments. But that gets you back to this problem where at a short horizon, bonds look like they're diversifying you a lot. And then over long horizons, they're really not. And that's just very tough to reflect in a sharp ratio framework. The results throughout the paper, how sensitive are they to risk aversion?

1:05:24The headline results are not that sensitive. So our investors are going to be optimizing utility and utility considers the whole range of outcomes and utility actually really penalizes bad outcomes quite a lot relative to like what a sharp ratio would. But they're just looking for the best distribution and the stocks, the all equity portfolio just has the best distribution. And it's not like, oh, we're doing this trade-off between the upside potential and the downside safety. If it's winning on both, you're just going to get that same result for every set of investors that look at it. They're like, yeah, that's a better distribution.

1:06:00The very risk-averse investors are going to place a ton of weight on that left tail, like the bad outcomes. But they're coming up with the same answer as the very low risk-aversion investors that are like, look at all this upside that I can get. Those two investors are coming to the same decision for different reasons, but they're coming to the same decision. So the places that we see risk aversion mattering more is things like leverage. And if we start relaxing some of those constraints, you see a little bit more of an effect. But the headline results, the all equity is not really that dependent on risk aversion.

1:06:34How has the response been from both academics and practitioners since you released the very first draft of this paper? I would say that we've had a lot of people very interested. I mean, it is a topic that people are interested and excited about. We've had a lot of very helpful comments. Nearly everything that we've done is in direct response to somebody's feedback and the design of some of these things are based on conversations with other professors and Ben. So that's been great. On the other hand, it's been a little bit weird where there's been a few folks talking very publicly about the paper with criticisms that we're just not really sure where they're coming from.

1:07:16And it's not clear that they've looked closely at the paper and thought about what we're doing in making some of the criticisms. Ben's been my sanity check on a few of these things as well. Like, I think people just feel very strongly about this and they have strong views. We had a recent discussion at a conference that was misreporting numbers that are in the paper to basically try to make the paper look less conceivable or tougher to believe. I think in academia, we're used to arguing about stuff, but it's good to argue about the facts. If you don't like one of my assumptions, that's cool. We can talk about alternative assumptions and everything, but that's kind of where we prefer the conversation to be.

1:08:02So again, we've had lots of good, very helpful people and received unsolicited feedback from John Campbell, which was really cool. We've got lots of really helpful people. It is a topic that people, I think this is the right word, they get very emotional about, which is interesting. It kind of flies in the face of a lot of what people intuitively believe. If you think about Ben and I, what we do for a living, maybe just in Canada, but in a lot of places, the sort of glide path portfolio or the 60-40 model. I mean, if you've been doing this for 25 years and you've been putting your clients into that, and then here's this paper that kind of says, well, actually you were wrong.

1:08:35You're probably going to be critical before you actually do the work to do an about face with your clients. Yeah, I think even with professors, when we present this, when you run across the people who are already 100 % equity, it's not trivial, the number, but they all love it because they're like, you know, I was right. But it just goes back to like, everybody already knows that they're right on this thing. It's very difficult to like shift the prior beliefs with new evidence. Confirmation bias all the way down. As you've been taking all this feedback and comments and criticism and kind of refining and improving the paper, has anything about the additional research and findings surprised you?

1:09:12I think it was just the cumulative effect of just how resilient the results are. We just got to a point where it's like, we'll run it. We know what it's going to look like, but we'll run it. Okay. There stopped being surprises pretty early on. It is surprising though, because there's so many things where it's like, I wonder how different it would look without Germany, or I wonder how different it would look excluding everything before World War II. I agree that the resilience of the general findings are pretty surprising. And valuations too, like all those things, that plausibly could change things quite a bit.

1:09:43Very interesting. So what's next for this thing? I know you've been doing conference presentations and stuff like that. Does this go to journals? What happens next? We always kind of had a long runway with this paper. We felt like we wanted to make sure that We got comments and address all the criticisms and everything like this. We've gotten a ton of feedback. We've made a ton of changes. We're ready to start taking our shots. We'll start submitting to the journals. At the end of the day, as academics, the only thing that we get rewarded for is publications and top journals. And so that's what we'll try to do.

1:10:14So you just go submit it to top journals and see what happens? Yeah, we just have to get a set of referees and editors that are not particularly grumpy and see how it goes. So it's pretty brutal just because of the average rejection rates at these journals are all over 90%, basically. You kind of work on a paper for two or three years, and then you have a very limited number of unconditionally small probability things that you're chasing. Crazy. Well, I obviously hope that that all goes well. I personally, I'm not an academic or a referee at a top journal, but I think this is really good paper.

1:10:51Thank you. Cross our fingers. Well, Scott, thanks again for coming back in the podcast. I think, like I just said, it's a really cool paper. The way that you guys have addressed all of the feedback and criticism and questions that have come since the first draft means the right way to address it. You went and modeled all of it and showed that the results are pretty resilient to all of the what ifs. I think that's really cool to see. I think people who are managing their own finances and thinking about this, you've seen the response in the rational-minded community. I think your episodes and any discussion related to your paper are some of the biggest topics in the whole community because it's so practically relevant to somebody who's managing their own money or for Mark and I who are helping other people manage their money.

1:11:28You made a big impact there. It's pretty cool to see the paper continue to get better. Thank you. All right. Thanks everyone for listening.