--- title: Elm Wealth Research | James White (5) description: Regular Elm Posts (5) --- [![Elm Partners](https://insights.elmwealth.com/hs-fs/hubfs/elm%20logo%20mini.png?width=100&height=100&name=elm%20logo%20mini.png "Elm Partners")](http://elmwealth.com/) Open main menu Close main menu # Elm Wealth Research Select Category Featured Insights How Elm Works In the News Investing 101 Risk and Return Tax Matters Uncategorized Posts by: ## James White ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/Factor-note-header.png) [Featured Insights](https://insights.elmwealth.com/elm-wealth-research/tag/featured-insights) ### [Smart Beta: The Good, the Bad, and the Muddy](https://insights.elmwealth.com/elm-wealth-research/smart-beta-good-bad-muddy) Jul 16, 2019, 12:00:00 AM July 16, 2019 Featured Insights ## Smart Beta: The Good, the Bad, and the Muddy *By James White and Victor Haghani* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2714) *Abstract:* “Factor investing, or Smart Beta as it’s known in long-only form, has become one of the most popular forms of investing, straddling the active-passive divide. The authors evaluate theoretical and empirically-based arguments for factor investing, concluding that while many of the arguments, particularly the theoretical ones, are sound, there are still reasons for considerable skepticism. They describe the trajectory of the factor investing paradigm, from the cradle of the efficient markets school to its championing by some of the world’s most successful investment management firms. While factor investing is typically discussed using the language and machinery of efficient-markets models, investors are primarily expecting anomalous excess returns more consistent with behavioral explanations and other market inefficiencies. For factors with plausible risk-based explanations, the authors conclude that even in the presence of significant factor premia, the market portfolio is still likely to be optimal for most investors. The authors also provide simple logical arguments to assess claims such as that factor investing delivers gross investment returns similar to traditional active managers, but with lower fees.” Read the full article in *The Journal of Portfolio Management* [here.](https://jpm.pm-research.com/content/early/2020/01/09/jpm.2020.1.126) --- 1. We are grateful for the many helpful comments of Richard Dewey, Chi-fu Huang, Antti Ilmanen, Vladimir Ragulin, Aneet Chachra, John Glazer, Joshua Haghani, Larry Hilibrand, Peter Hirsch, Arjun Krishnamachar, David Modest, Hedi Kallal and Jeffrey Rosenbluth. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/smart-beta-good-bad-muddy) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/066-damodoran-main.png) [In the News](https://insights.elmwealth.com/elm-wealth-research/tag/in-the-news) ### [A Conversation with NYU Professor Aswath Damodaran](https://insights.elmwealth.com/elm-wealth-research/aswath-damodaran-interview) May 6, 2019, 12:00:00 AM May 6, 2019 In the News ## A Conversation with NYU Professor Aswath Damodaran *April 23, 2019 – New York City* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2623) Victor recently sat down with NYU Professor Aswath Damodaran to hear his views on some of the most passionately debated topics in investing today, from the rise of indexing and what it means for market efficiency, to the origins and theoretical underpinnings of factor investing, to why investors ignore momentum at their peril. Aswath Damodaran is Professor of Finance at the Stern School of Business at NYU. He received his Ph.D. in 1985 in Finance from UCLA, and has been making important contributions to our understanding of finance ever since, earning myriad awards for his research and his teaching along the way. His excellence in the classroom has resulted in many teaching awards and has been voted “Professor of the Year” by the graduating M.B.A. class five times during his career at NYU. Professor Damodaran is the author of eleven books, including several widely-used text books on Valuation, Corporate Finance and Investment Management. You can follow Aswath on his [Musings on Markets blog](http://aswathdamodaran.blogspot.com/), his [website](http://www.damodaran.com/), his incredibly popular [YouTube channel](https://www.youtube.com/channel/UCLvnJL8htRR1T9cbSccaoVw/playlists) or [@AswathDamodoran](https://twitter.com/AswathDamodaran) on twitter. --- **Victor Haghani:** Going back 30 years to when you were starting out as a professor, do you feel that there has been a change in the makeup of market participants? I mean, have we seen a change towards people being much better trained in thinking about value? Do you feel like it’s tougher to beat the market today than it was 30 or 40 years ago? **Aswath Damodaran:** Well, let’s start with the easy one: it is definitely more difficult to create a competitive advantage in this market, simply because areas of competitive advantage are slipping away. I’ll give you a simple example: thirty-five years ago, if you were an investor, you had an advantage just being in New York City over being in Des Moines, Iowa. Why? Because the SEC offices were here, and if you wanted to look up a filing by a company, you could physically go to the SEC offices and check out that filing. You had a competitive advantage based on location. And if you worked at a major investment bank, you had access to a computer. Most people in the world did not – so if you had access to computing power and you had access to data, it gave you a leg up. Now the investing world has become a lot flatter, especially in the US. I can’t think of too many competitive advantages that you would have at Goldman Sachs as an equity research analyst over some person sitting at their own computer. If you’re going to create value in this business now, you’ve got to think of what else you bring to the table. It can’t be that you have better data, it can’t be because you have a more powerful computer – it’s got to be something else, and that’s made investing a lot more difficult than it used to be. --- **VH:** A lot of people are worried about the rise of indexing. Do you think that indexing has gone so far as to make markets less efficient? Robert Shiller has said that indexing is un-American, that we’re losing the ability to value and to price assets. Others have compared indexing to Marxism, arguing that indexing is worse. What do you think? **AD:** Well, let’s start out by noting that many of these people who critique indexing have a very selfish reason for doing so – it’s taking away their living. And that’s for a very good reason, which is they’ve not been very good at what they do for a living and indexing has exposed that. If I thought more of equity research analysts, I would worry more about indexing. If I really thought equity research analysts actually went out and collected information and did research and unearthed stuff about companies we did not know, then I’d be worried about indexing taking away that research. But unfortunately, that’s not what I see equity research analysts doing. They listen to management spout platitudes about the company, and mostly they take them at face value. They take an adjusted EBITDA, they slap a pricing multiple on it, they call it research. That’s not digging up anything about a company, so nothing is lost by those equity research analysts being pushed out of the business. And let’s face it, most active investing is built on mean-reversion. It’s very lazy investing, there is no research that goes in. You just buy stocks with low PE ratios and high growth. Again, we have this vision of analysts as being people who dig for the truth – and that is still there. In fact, I would argue the payoff to doing research is probably greater with indexing than without it. I think there is this false vision of indexing becoming 100% of the market, and I refer people to the Grossman-Stiglitz Paradox proposed in their 1980 paper, [*On the Impossibility of Informationally Efficient Markets*](http://www.dklevine.com/archive/refs41908.pdf),[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2623) which states that because information is costly to obtain, if the market were informationally efficient there’d be no compensation for obtaining the information needed to make it informationally efficient in the first place. That said, there is a potentially dark side to indexing. It has made momentum much stronger, because the nature of indexing is you pile on to whatever’s going up. --- **VH:** Gene Fama has said that momentum is the “premier anomaly.”[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2623) Do you agree with him, and why do you think momentum has historically worked so well across so many asset classes, both cross-sectionally and in time series? **AD:** Because it reflects the reality of pricing, in that the biggest factor in pricing is what other people are doing. Investing has always been a momentum game, at least on the pricing side, and it’s about momentum and momentum shifts. Pretty much all of trading can be summarized into those two groups: you can either be a momentum player or a player who detects shifts in momentum and tries to go against momentum just before it changes. So, all of trading is built around momentum or anti-momentum. When Gene calls it an anomaly, what he means is we cannot explain it using fundamentals. It’s an anomaly – **VH:** Right. So is that to say that there’s not a good risk argument behind it? **AD**: No, there’s not a risk argument – but that raises a broader question of how the pricing process can be very different than the value process. The pricing process is all about mood and momentum. On any given day, it is the biggest explanatory variable for why price is moving. It’s not that cash flows change, or growth rates change, or the price of risk changes – it’s just momentum shifts. **VH:** It does feel like if you were going to base a trading strategy on any one thing… **AD:** It’s got to be momentum. In fact, you cannot devise a trading strategy which ignores momentum. It’s impossible. You can create an investing strategy that’s momentum-free – but that basically means you value something and then you sit there and pray and hope that, eventually, momentum fixes the gap for you. Even those people who believe they’re value players are far more dependent on momentum than they realize, because ultimately, for them to make money, the price has to move to its value. And that may require a momentum shift, which is what we call the catalyst, something that changes the momentum of the game. --- **VH:** Do you think there’s a distinction between momentum – which has a clear definition and has been found to be very helpful in investing – versus return chasing, which has a really bad name and is often put forward as the reason that investor returns are so much lower than fund returns. On the surface, both of them are buying something that’s gone up and selling something that’s gone down – but there’s got to be an important fundamental difference between the two things that allows one to be the best thing that you can do, and the other to perhaps be the worst thing you can do? **AD:** Because, in a sense, momentum has a light side and a dark side. The light side is when you’re riding momentum, you make a lot of money. The dark side is, eventually, momentum does shift – and if your entire investing was built on riding momentum, and the momentum shifts, you can essentially lose everything you gain plus more. I don’t have a problem with the return chasing, if you know when to stop. And I think part of the problem is if all you do is chase returns, and you don’t even think of it as momentum, you’ve forgotten that momentum does shift. That’s why I have more respect for pure traders than I do for portfolio managers who claim to not be traders who chase returns, and then say, “Look, I don’t play the momentum game.” If you’re going to play the momentum game, play it. Play it openly. Return chasers are more delusional. They’re delusional because, while they’re playing the momentum game, they keep telling everybody that they’re not playing the momentum game, that they’re really investors. So what they do is they chase returns and they dress it up as a value strategy, that they’re doing it because of X, Y and Z, because these companies are going to be the forefront of future growth, etc. If you’re going to chase momentum, just chase it. Be open about it. If you’re going to chase momentum, you’ve got to get the timing right, and the problem with return chasers is they don’t realize that. --- **VH:** Let’s talk more generally about the world of factor investing – or smart beta, as some refer to it. Can you give us your perception of the history, and what Fama and French were doing back in the late 80s and early ’90s, and how a few trillion dollars have come to be allocated to this type of investing? **AD**: I think it’s interesting. There is no way that you could have sat in on Gene Fama’s class and walked out of his assessment of factors saying, “That’s a way of making excess returns,” because I can guarantee you Gene would not have framed it as such. He’d have said, “Look, we found price-to-book and market cap as factors that drove past returns,” and the way he’d have concluded would be something like, “That must mean our risk-and-return models are flawed, that price-to-book and market cap are proxies for risk, that this is not something you’re getting an excess return for.” I like to think of the roots of factor analysis as following two different pathways. One is that when you find a factor, what you found is not a way of making excess returns, but it’s a missing risk factor that’s going to be built into your expected return analysis. The other school of thought is, if you found a factor, that’s a way in which you can build a portfolio and deliver – at least on the surface – higher returns and essentially you can attract more money. And I think we go back and forth between these two groups, and sometimes I think we pick and choose what we want out of those. I think people have to decide what factors really are. Are they really just missing risk variables? The other school of thought basically says, “We’re going to assume that any factor that has delivered more than required is, in fact, something I can make excess returns on.” But you can’t have it both ways, and it becomes interesting when you get a paper that treads in that grey area. One such paper, for instance, is the AQR paper on the size factor: that even though the small cap premium has disappeared over much of the last 37 years, if you screen it for really bad companies, what they call junk, then small cap companies still have excess returns. Now we’re dancing on the head of a pin, because if I really treat it as a factor in the spirit of Fama-French, there’s extra risk associated with it so here’s what I should be doing: when I value a small company I should first assess whether it’s a high quality or low quality company. And then for the high-quality companies, I should use a higher cost of capital than in discounting the cash flows for low-quality companies. That’s a really tough intuitive sell. That if I get a bad company, I should use a lower required return – but this is what happens when we don’t draw the line, when we use those factors to build this premium into a cost-to-capital. This is why I’ve never used the small cap premium in 35 years of valuation practice – because I think the minute you do that, you’re opening the door to including things in your cost-of-capital that really should not be included in there. --- **VH:** If you were given a choice between either investing in an equity portfolio that was built around five or six of the most popular factors today, or you could invest in a portfolio that’s chosen by a hundred of your favorite valuation students selecting individual stocks, which would you prefer? Assuming all the costs are the same for both. **AD:** I’m a great believer that the less activity you need to put into creating a portfolio, the better. To the extent that there are 100 different people involved, no matter what I think about them – I worry about all that activity that they did, and I’m not sure that those things are going to actually pay off in returns, because the good stuff and the bad stuff might all get averaged out. So given the binary choice I would go with the factors, but you know what? I’d go with a pure index fund over the factor one. Because here’s the thing about factors: they have existed, obviously, over the last hundred years. We can see it in the data…but I really think the world is shifting under us. There is a point to make about mean reversion: mean reversion works until it doesn’t. And much of what we do in investing now, we learned in the US on data from the second half of the 20th century. And in that time period the US market was a unique market. If you look at the history of markets over time, it was the most mean reverting, stable market of all time. And when you take the most mean-reverting, stable market of all time, all kinds of mean reversion are going to work for you. So my concern is that maybe we’re taking rules that were developed for the most mean-reverting, stable market of all time and trying to apply them in a new world order where markets might be reverting, but we don’t know to what. And so, I have a concern with any kind of tilted approach where you’re tilting based on past data. I’m not sure the payoff is there. Maybe twenty years ago, my answer would have been different. For me, 2008 was the dividing line where I think there was a structural break in the global markets. I am less and less trusting of mean reversion on a daily basis. --- **VH:** You write annually about long-term expected returns of the market as a whole. Can you give us a brief description of how you come up with your long term expected return for say, the US equity market, or the global equity market? **AD:** I do it on a monthly basis, and I think again this goes back to what I said earlier about mean reversion. In the past the way I would compute those future expected returns was to look backwards: look at the Ibbotson data to 1926, and look at what stocks made on average over T-bonds, and make a leap of faith: if that’s what I made over the last 75 years, that’s what I should expect to make over the next seventy-five. But as I said, so much of what we know came from the US in the 20th century, but starting about 25 years ago my faith in using historical returns started to get shakier and shakier, so I said we’d be much better if I could get a forward-looking expected return for the market. So I stole from the bond market an idea that’s been around forever: that yield to maturity is basically an internal rate of return. You take the price of the bond today, you take future cash flows, you solve for what kind of expected return you’re going to make, given what you pay. So at the start of every month I take the S&P 500 and I look at what people are collectively paying for stocks. I do have to make projections of expected cash flow, but that’s not difficult because these are, after all, the 500 largest market cap stocks. So I solve for an internal rate of return every month, and that becomes my expected return for stocks. --- **VH:** What do you think about what’s often described as the ‘Equity Risk Premium’ puzzle, i.e. that some econometric models suggest that the equity risk premium should be much smaller than it seems to be? **AD:** I love Jeremy Siegel’s work, but I think his basic notion that ‘stocks always win in the long run’ is at the basis of this puzzle. Because if stocks always win in the long term, you know what should happen to your equity risk premium as your time horizon extends? It should go to zero. We know stocks don’t always win in the long term, that there is this catastrophic risk. But then people point to the US and say, “Show me where it is.” You’ve got a survivor market, you take the most successful market of the 20th century and you ask me, “Show me the evidence of catastrophe.” You’re not going to find it. You’re going to have to go look at the Austrian market to find it. We think of one hundred years as a lot of data. But in the longer scheme of history, when looking at the US we’ve just caught a very, very unusual country in an unusual period of time, and we’re extrapolating from there. --- **VH:** We only have time for one more question, so I’ve got to ask you: how you have been so prolific? Eleven books, I lost count of all the articles you’ve had published, a massive online presence, trying to get ideas and valuation techniques democratized, and hundreds of thousands of people reading and watching your teaching. And then on top of it, being a professor and getting all these awards for best professor at NYU, best business school professor in the whole country. It’s really remarkable, can you give any tips for people that are trying to be more productive? **AD:** I have to tell you, I’m a pretty lazy person, I don’t work more than 40 hours per week. What I’ve discovered helps me is to not compartmentalize – because if I thought of my life as, “there’s teaching, there’s research, there’s writing on my blog, there’s X, Y and Z…” then you very quickly run out of hours in the day. But almost everything I do spills over into almost everything else I do. So I’m constantly looking for ways to take whatever I do and get it to serve three or four or five purposes. I’ll give you an example: about five years ago I read The Wall Street Journal post on Uber. It was a Thursday afternoon, and I said, “This will be an interesting company to value.” I did a very rudimentary valuation, because I knew very little about ride sharing; it took me about three hours to do the valuation, about three hours to write the blog post. I put it up on Friday afternoon. That blog post took a day and a half of work, but it essentially became part of my classes, it became an entire seminar that I do on valuing young and startup companies, it became a book called “Narrative in Numbers.” **VH:** Thank you so much for making time to share your clear and insightful thoughts with us. **AD:** You’re welcome! --- 1. This not is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. **Past returns are not indicative of future performance.** 2. American Economic Review (70); pp393-408. 3. Fama, Eugene and French, Kenneth, [Dissecting Anomalies](http://schwert.ssb.rochester.edu/f532/ff_JF08.pdf), The Journal of Finance (August 2008). [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/aswath-damodaran-interview) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/64-pays-to-pay-banner-1024x487.png) [Tax Matters](https://insights.elmwealth.com/elm-wealth-research/tag/tax-matters) ### [When it Pays to Pay Capital Gains](https://insights.elmwealth.com/elm-wealth-research/when-it-pays-to-pay) Mar 11, 2019, 12:00:00 AM March 11, 2019 Tax Matters ## When it Pays to Pay Capital Gains *By Victor Haghani, Lawrence Hilibrand and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2546) US taxable investors know the importance of managing their investments tax-efficiently. A standard approach to the management of capital gains and losses is to defer realization of gains for as long as possible, while aggressively realizing losses,[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2546) particularly short-term losses, a strategy often referred to as “tax-loss harvesting”. However, upon closer examination, this can be significantly improved upon for investors who tend to have a steady stream of short-term capital gains – and in a seemingly counter-intuitive way. Instead of trying to defer realizing a long-term capital gain as long as possible, it can make sense to realize the gain shortly after one year has passed since purchase and the gain becomes subject to the preferential long-term tax rate. If the asset is sold and repurchased, the basis in the asset and the “basis clock” are both reset, thereby creating the option to realize a valuable short-term capital loss if the asset falls in the year ahead. This sounds good, but does it actually add net expected value? We need to compare the expected value of a short-term loss “option” to the expected cost of giving up deferral of a long-term capital gain.[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2546) We value a realized short-term loss at 17% of the loss amount, which is the difference in Federal tax rates for short-term versus long-term capital gains. The value of deferring a capital gain is primarily a function of the expected horizon of the deferral – all else equal a longer deferral period has greater value.[4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2546) We set up a Monte Carlo simulation to estimate the expected value of the accelerated realization approach compared to both a buy-and-hold approach and to the standard tax-loss harvesting approach. The results and assumptions of the simulation are laid out in the table below. What we find is that an investor following the accelerated realization approach would have an expected pre-tax equivalent return about 1.3% pa higher than a simple buy-and-hold approach,[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2546) and 1% higher than the standard tax-loss harvesting approach. The results appear quite robust. For example, taking a shorter horizon of ten years, the difference between the approaches changes by only about 0.15% pa, with the buy-and-hold looking a bit worse and the standard tax-loss harvesting looking a bit better (both compared to the accelerated realization strategy). Higher tax rates, maintaining the same difference between the short-term and long-term rates, don’t have much impact on the difference in expected returns either.[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2546) The accelerated realization approach may be more valuable for some investors and portfolio strategies than for others. It will be especially effective for those who regularly incur short-term capital gains and highly value short-term capital losses,[7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2546) who have relatively static or slow-moving portfolio allocations,[8](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-8-2546) and who can trade their portfolios with low transaction costs. The approach we describe keeps the portfolio more “evergreen” from a tax perspective, in that it slows the build-up of large long-term gains which can then unduly bias allocation decisions. While there will be variability in the tax advantage an investor experiences depending on the path the asset takes, it is an added bonus that the realized tax benefit will tend to be higher the worse the asset performs and the more volatility the asset experiences. That’s to say, you get some extra tax benefit in environments which are otherwise not so great. So it looks like in certain situations, paying your taxes early and often might be a surprisingly tax-efficient way to go. If you’d like to learn more about our approach to delivering tax-efficient returns, or more about our investment approach in general, you can request more info on our home page [here](https://elmwealth.com/) or schedule a call [here](https://elmwealth.com/contact-us/schedule-a-call/) with James, our CEO. --- ### Further Reading and References: - Constantinides, George, [“Optimal Stock Trading with Personal Taxes: Implications for Prices and the Abnormal January Returns”](https://www.nber.org/papers/w1176) NBER Working Paper No. 1176, (1983) - Dammon, Robert, Dunn and Spatt, Kenneth, [“A Reexamination of the Value of Tax Options”](https://doi.org/10.1093/rfs/2.3.341), The Review of Financial Studies, Volume 2, Issue 3, (July 1989), Pages 341–372. - Andrew Kalotay has written extensively on this topic. You can find his research on [Kalotay.com](https://www.kalotay.com/). This idea was described by Joseph Stiglitz as a strategy of “immediate realization” in his paper, [“Some Aspects of the Taxation of Capital Gains”](https://www.nber.org/papers/w1094.pdf). Journal of Public Economics, pp 2, 5-7, (1983) --- 1. This not is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. **Past returns are not indicative of future performance.** Thank you to our friend and accountant David Untracht for his helpful comments. Of course, any errors are our own. 2. Subject to wash-sale rules. 3. We also need to take account of transaction-costs and the risk associated with complying with the wash-sale rule when realizing a loss. 4. The value of deferral is also greater the higher the effective tax rate and the higher the expected rate of return on the asset. Deferral is also more valuable if the investor expects to avoid capital gains tax completely by donating or bequesting the appreciated asset in the future. Expected changes in tax rates and tax rules also impacts the value, or potential cost, of deferring capital gains. 5. A simple back-of-the-envelope estimate for this difference, if we could only trade once at the end of every year and using the other assumptions in the table, would value the option to realize a short-term loss at the end of the year as 4.7% (the value of a one-year at-the-money put option with 16% volatility and a 4% risk-free rate) times the value of converting a short-term gain into a long-term gain of 17%, which gives a value of 0.80% after-tax. The value of a 30-year deferral is the difference between the return of investing for 30 years at 4% and paying tax at the end versus paying the tax every year, which is 0.33% after-tax. So, the net benefit is 0.47% (*0.80% – 0.33%* ) after-tax, or a pre-tax equivalent of 0.62% pa. We find a much higher benefit of 1.3% in our simulation primarily because we can trade once every month, which is of significant incremental value. 6. Choosing to not realize long-term gains if they were particularly high improved results, but only marginally. 7. For investors who do not expect to have short-term capital gains every year, the incremental value of this accelerated realization approach will be eroded, or even erased. For example, if we assume the investor has only a 50% chance of having short-term gains in a given year, and will only find out whether he has gains after the year ends, the extra expected return from accelerated realization compared to standard tax-loss harvesting drops from 1% to about 0.25% pa (assuming that if the investor doesn’t have short-term gains in a particular year, short-term losses can still be offset against long-term gains). Also, the value will be impacted negatively for investors who are more likely to have short-term capital gains in years when the stock market has risen. 8. Not having any tax-lots with a long-term basis can be inconvenient for dynamic strategies which may need to sell and would like to avoid realizing short-term gains. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/when-it-pays-to-pay) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/costanza-840x420.png) [Risk and Return](https://insights.elmwealth.com/elm-wealth-research/tag/risk-and-return) ### [If George Costanza Were a Hedge Fund Manager](https://insights.elmwealth.com/elm-wealth-research/george-costanza-hedge-fund-manager) Jan 14, 2019, 12:00:00 AM January 14, 2019 Risk and Return ## If George Costanza Were a Hedge Fund Manager *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2429) It’s only a small over-simplification to say that investing is about predicting how things will turn out in the future, and placing your bets accordingly.[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2429) If your prediction is right, you generally expect your bets to make money and you are happy. But there are some relatively common types of investing strategies in which your predictions about future price moves can be correct, but you lose money anyway. Here’s an example: let’s say at the start of 2007 you have $100 of capital, and you use it to put on a trade of long $100 of Goldman Sachs (GS) and short $100 of Morgan Stanley (MS). You do this because you expect GS to outperform MS. Each month, you re-balance your trade so that both the long and short leg are equal to your current total capital, which has grown or shrunk from $100 based on the relative moves of the stocks. Rebalancing like this is not the only way to hold a long-short position, but it’s rightly popular as it significantly reduces the chance of losing more than 100% of your starting capital. So, how did you do? The total return of GS to the end of 2018 is a loss of 3%, but MS is down 29%. You were right, GS outperformed. You made a good prediction of the future. But how much money did you make? Maybe a profit of $26, arising from the 26% by which GS outperformed MS? Unfortunately, a $26 profit isn’t the right answer. It’s not even close. The actual outcome is you’d have lost $24! [3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2429) Before trying to explain, we want to tell you that there’s nothing unusual about these two stocks and the paths they took.[4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2429) The crux of the explanation is that being short a stock is not the opposite of being long it. Imagine you open a brokerage account and put in $100 which you use to buy a stock. This is going to sound really obvious, but at all points in time in the future, the current value of your brokerage account will be equal to the current value of the stock. Let’s compare that with being short a stock: you again open a brokerage account, put in $100, and go short $100 of stock. If the stock goes up by 10%, now the value of your brokerage account is $90, as you have an unrealized loss of $10 on your short, but the value of your stock short is $110. Not good, and it’s not advisable to simply do nothing. If you don’t cover at least $20 of your short to bring it in line with your capital, you can find yourself running a heightened risk that you could lose your full $100 and the broker will cover your short for you.[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2429) Keeping our focus on the short stock trade, let’s assume you initially shorted the stock at a price of $100, and then the price goes up or down each month by $10, fluctuating around $100, and at the end of the year, it’s right back to $100 where it started. Here’s where there is a big difference between being long that stock or short it. If you were long the stock, the value of your account would be the $100 you started with. But if you were short, and if your policy is to equalize the value of your short position to the value of your account once a month, you’d lose about 1% per month from rebalancing that short position.[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2429) It’s tough to make money being short a stock: you don’t just need to be right, you need to be very right\![7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2429) Now here’s where things get even more interesting, and where George Costanza makes his appearance. If you were long GS and short MS, we’ve seen that you lost money. But what if you had the GS-MS trade the other way around, long MS and short GS? You’d lose even more money, 34% of your starting capital to be precise! What kind of devilish trading strategy loses money both ways around? Well, it’s the kind of trade that George Costanza would probably have chosen, if the producers of *Seinfeld* had him working for a NY hedge fund instead of the NY Yankees. It always hurts to lose money, but it really stings when it happens despite our investment thesis proving correct, as in the case of the GS versus MS trade we started off with. In the *Seinfeld* episode titled [“The Opposite”](https://www.youtube.com/watch?v=1Y_6fZGSOQI) George complains to Jerry that every decision that he has ever made has been wrong, and that his life is the exact opposite of what it should be. Jerry, who clearly is unaware of the nature of long-short trades, tells George “if every instinct you have is wrong, then the opposite would have to be right.” Wouldn’t it have been just perfect if George, true to character, proved Jerry wrong by finding an investment that would lose money both ways around? That’s why we’re pretty sure that if George Costanza were a hedge fund manager, long-short would be his trade. --- ### Appendix I: A More Formal Treatment --- ### Appendix II: Historical Price Series of GS and MS, and Calculation of Long-Short Strategy Returns with Monthly Rebalancing (data from Yahoo Finance) --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest.   Thank you to Jeff Rosenbluth, Chi-fu Huang, Larry Hilibrand, Andy Morton, Vlad Ragulin, Vladimir Piterbarg, Derek Smith, and Garth Friesen for their thoughtful help with this note. 2. We are devotees of thinking about investing in terms of probability distributions, scaling functions, and risk-adjusted returns, but for this note we’ll put that aside for simplicity. 3. Ignoring transactions costs, borrow fees, and interest earned on your capital. 4. You’d get these same results if we simulated a random walk for stocks A and B, such that one was down 3% and one down 29% over the horizon, and they had annual standard deviations of returns of 31% and 37%, and a correlation of 0.75 as GS and MS did over the period. We also confirmed this result more generally in the pool of the roughly 400 stocks that were continuously in the S&P500 from 2007 to through 2018. 5. The situation with levered longs is essentially identical. The similarities between holding a short and holding a levered long position run deep. 6. And all that rebalancing generates a lot of turnover, which often involves other costs and frictions. For example, in our illustrative GS versus MS trade, turnover averaged $245 per year on a starting trade size of $100. 7. We hope someone will pass this note along to Elon Musk, to help him find some sympathy for Tesla short-sellers, or at least to help him feel better to know how poorly many Tesla short-sellers have been doing given Tesla’s (and Musk’s) high (44%) volatility. Even if you shorted $1mm of Tesla stock at its all-time high price of $385 per share on September 18, 2017, by the end of 2018 you’d have lost 10% of your capital, even though the stock finished the year trading at $333, down 13.5% from that all time high. See the third bullet point in Appendix I for an explanation of this 23.5% difference. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/george-costanza-hedge-fund-manager) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/moe-840x420.png) [Risk and Return](https://insights.elmwealth.com/elm-wealth-research/tag/risk-and-return) ### [When They Won’t Accept That You Really Don’t Know, Tell Them About Mo](https://insights.elmwealth.com/elm-wealth-research/tell-them-about-mo) Dec 18, 2018, 12:00:00 AM December 18, 2018 Risk and Return ## When They Won’t Accept That You Really Don’t Know, Tell Them About Mo *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2377) Most of us working in the finance industry are used to being regularly called on to predict where different assets are heading. We figure out pretty quickly that it’s impossible to know where anything is going with the degree of certainty that our inquisitors often seem to expect. But there are occasions, like a holiday dinner at your in-laws, when it just won’t do to answer with “I really have no idea” and then proclaim your belief in the Efficient Market Hypothesis. In this note, we’ll propose a solution: move the discussion to momentum (or “Mo” for short), and the light it sheds on the question being asked. The harder it is to pin down the fair value for an asset, the handier momentum seems to be. Take Bitcoin, the epitome of an asset whose value is difficult to establish. Is it going to rival the value of dollars in circulation and gold above the ground, or is it headed to zero? You’d have been a hero if you’d told family and friends to buy some Bitcoin about six years ago when it traded at $20.[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2377) It’s gone up about 150-fold since then, for an annual return of about 140%, or 8% a month. That seems about as good as it gets, but actually it’s not quite. If you were a Bitcoin know-nothing (like us) but you believed in momentum in asset prices, and especially in ones that are hard to value, then your advice would have made you an absolute legend. Owning Bitcoin only when its price exhibited positive momentum would have resulted in a 500-fold investment multiple with about the same volatility of returns as a buy and hold strategy.[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2377) The momentum strategy that would have produced this return works like this: every month-end, if Bitcoin’s current price is higher than its average price over the past year, momentum is positive and you hold Bitcoin for the next month. Otherwise when its price is lower than its one-year average, momentum is negative, and you hold T-bills for the next month. The simulated returns we show in the chart below do not include transactions costs, but in the case of Bitcoin over this period the strategy would have only demanded a trade once every two years on average. Natural gas is another trade that’s come up frequently over the years and is a good contrast to Bitcoin. What’s generated interest in this trade is the fact that the energy content of 1 unit of natural gas is about 1/6th that of a barrel of oil, and, over the past twelve years, the price of natural gas has traded at an average discount of 68% to this energy content-based “fair value”. [4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2377) That’s about as cheap as an asset gets. In fact, it’s so cheap it strongly suggests an incomplete model. And indeed a little bit of knowledge can be dangerous: the popular natural gas ETF with ticker UNG became available in early 2008, and since then an investment in UNG would have lost 98% if held to the end of November 2018.[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2377) That’s an annualized return of -30%.[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2377) Ouch! Instead, as with the Bitcoin example, if you were oblivious of the “value” of natural gas but only conscious of the tendency of market prices to exhibit momentum, you might have saved your friends a fair bit of change. The same momentum-based approach as applied to Bitcoin, being long natural gas only during the roughly 20% of the time that momentum was positive would have resulted in a small gain over the period instead of a 98% wipeout. So, if you find yourself at your office Christmas party or a family holiday dinner, pressured by etiquette to proffer an opinion about a speculative trade you know nothing about, tell your audience these twin tales of how Mo can make you more dough or save you from woe.[7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2377) In the true holiday spirit, you’ll have made the gift of a fishing rod rather than a fish. ### Charts: --- 1. This not is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. **Past returns are not indicative of future performance.** 2. Six years is as far back as we have data to do this analysis. 3. Measured as annualized standard deviation of returns. 4. US natural gas, which is the type easily traded, also has been priced at a steep discount to natural gas in most of Western Europe and Asia. 5. A more logical expression of the view that natural gas is cheap to oil would have been to go long natural gas and short oil. Indeed, over this period, the largest oil ETF, USO, was down 88%, but the trade of being long UNG and short an equal dollar amount of USO, rebalanced back to offsetting amounts on a monthly basis, would have resulted in a loss of 90%, over the period. A simple momentum overlay applied to this relative value trade resulted in a gain of 4% over the period, ignoring transactions costs and the cost of borrowing USO to be short it. Exploring this surprising result warrants its own short note. 6. This is a Sharpe Ratio of about -0.7, which is pretty good, except for the negative sign in front. What this means is that shorting UNG, or the natural gas futures it is based on, would have been a very high quality trade. Over that period, the spot price of natural gas dropped “only” about 50%, while the rest of the loss came from futures rolls where the market, just like our value-conscious friends, expected the price of natural gas to go up in the future. 7. If your audience rightly isn’t convinced by two cherry-picked examples viewed over relatively short horizons, refer them to this comprehensive piece of research, which also has an exhaustive list of references, on the prevalence of momentum over the past 200+ years: Geczy, Christopher and Samonov, Mikhail, [Two Centuries of Price Return Momentum, Financial Analysts Journal, Vol. 72, No. 5](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2292544) (September/October 2016) [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/tell-them-about-mo) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/060-mega-millions-main-1024x487.png) [Risk and Return](https://insights.elmwealth.com/elm-wealth-research/tag/risk-and-return) ### [Reflections on the Mega Millions Lottery: Can a Lottery Ticket with Great Odds Still be a Bad Bet?](https://insights.elmwealth.com/elm-wealth-research/reflections-on-the-lottery) Oct 31, 2018, 12:00:00 AM October 31, 2018 Risk and Return ## Reflections on the Mega Millions Lottery: Can a Lottery Ticket with Great Odds Still be a Bad Bet? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2312) Last week, two of our favorite financial journalists – the WSJ’s Jason Zweig and Bloomberg’s Matt Levine – covered the Mega Millions lottery featuring an eye-catching jackpot of $1.54 billion.[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2312) Jason’s [What Investors Can Learn from Gamblers](https://www.wsj.com/articles/what-investors-can-learn-from-gamblers-1540572491) suggested that we use this lottery as a case study to help us make better investment decisions more generally, and that’s our intent as well. Matt’s humorous take in [It’s OK to Get Distracted by Mega Millions](https://www.bloomberg.com/opinion/articles/2018-10-22/mega-millions-jackpot-might-correlate-the-stock-market) is to “live a little!” and “If you are a hardworking hedge-fund analyst desperate to quit your daily grind, it’s okay to spend this morning buying lottery tickets and the rest of today and tomorrow fantasizing about what you’ll say to your boss when you win.” He posted a [spreadsheet](https://docs.google.com/spreadsheets/d/1xAcsNkxHUQkHE4ycvYzirI-gOoRfC_sEOq2La8q7T_s/edit#gid=0) that calculated the Expected Value of a ticket, and took a flier himself (boringly, we didn’t). Taken together, these articles suggest that if the Expected Value of the ticket is less than what you must pay for it, then you should pass…unless you get a net hedonic kick from the experience of buying it. But what’s left unexplored is this: what if the Expected Value is actually greater than the cost? This isn’t an entirely hypothetical question, as it’s sometimes the case that the combination of rapid growth of a rolling jackpot and the tendency of many players to crowd around certain numbers and patterns results in the opportunity to play the lottery with a positive edge.[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2312) What should you do then? Well, it depends. Specifically, it depends on how much the odds are in your favor, how much the ticket costs relative to your wealth, and the extent to which increases in your wealth have diminishing marginal value to you. This “diminishing marginal value of wealth,” encoded in what financial economists call your Utility function, is at the crux of the decision, and it’s what makes Expected Utility a better decision-metric than Expected Value. Using Expected Value implicitly assumes that making $10 feels just as good as losing $10 feels bad, which just isn’t how it works for most people.[4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2312) Using utility preferences instead of monetary values takes account of the asymmetry between winning and losing (imperfectly in many cases) but it usually gets us in the ballpark of the right decision.[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2312) Let’s illustrate with an example: say you have $100,000 of savings, and that you’re very tolerant of financial risk.[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2312) To make our point really clear, let’s also say that a $10 ticket gives you a probability of winning the $1.5 billion jackpot 100 times more favorable than the fair odds. In other words, the Expected Value of the ticket is $1,000 but you get to buy it for just $10. You know you’ve got a great deal based on Expected Value, but what about Expected Utility? Well, despite the Expected Value of the ticket being 100x its face amount, the Expected Utility of buying the ticket is negative – in fact, *really* negative.[7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2312) You’d need to be able to buy the ticket for less than $0.65 to have a good investment from an Expected Utility perspective, ignoring its fantasy-fun-value. Even if you had $1 million of savings instead of $100,000, you’d still find buying the ticket for $10 a negative Expected Utility proposition. Is this something we should pay attention to, or is there a problem with Utility theory here? We’re paying attention: Expected Utility puts weights on the almost-certain loss versus the almost-impossible huge gain in a way that is both intuitively appealing (to us, at least) and theoretically sound. Sure, if you could play this lottery at these super-favorable odds ten million times, you’d have a 99.9% chance of winning at least once…but that’s not what you’re faced with here, not to mention a few practical problems like coming up with $100 million of cash to buy the tickets. Also, the utility-based decision rule isn’t saying that you shouldn’t play the lottery when the odds are in your favor, it’s just saying that $10 is too big of a bet relative to $100,000 or even $1,000,000 of wealth. Your optimal bet size, with those great odds and $100,000 of wealth, would be to spend about a dime on a ticket. We agree with Matt that we shouldn’t overthink what we do with $10 for a lottery ticket.[8](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-8-2312) After all, as he put it, “Ten bucks won’t even get you into a movie, and isn’t this more fun to think about?” But there are investments out there that can look like a lot like lottery tickets, with positive Expected Value arising from a small probability of a big payout and a high probability of a relatively small loss. Viewed through the lens of Expected Value, we might be tempted to commit some serious dough to these lottery-ticket style investments. That’s when we need to coolly pull Expected Utility out of our toolkit to get a clearer picture of an investment’s attractiveness and how much of it to take on board. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest. 2. Or a lump sum cash value of $878 million. $1.54 billion was the estimated annuity value. Both are pre-tax figures. 3. For a more detailed description of these positive odds opportunities, or in their words, “fantastic expected rates of return offered by certain lottery drawings”, and also a more detailed discussion of the ideas in this note, see “[Finding Good Bets in the Lottery and Why You Shouldn’t Take Them,](https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Abrams2011.pdf)” by Aaron Abrams and Skip Garibaldi, Mathematical Association of America (2010), which won the Lester R. Ford Award for outstanding papers in mathematics in 2011. 4. We are skeptical of assertions that some people have utility curves that display an increasing marginal utility of wealth arising from small increases in wealth being transformational in terms of a person’s quality of life, at least in the case of the financial circumstances of the typical reader of our research notes. 5. This is all in the literature. For a more in depth discussion, see our note: [A Sharper Lens for Sizing Up Nickels and Steamrollers.](https://elmwealth.com/a-sharper-lens-for-sizing-up-nickels-and-steamrollers/) 6. We’ll assume your utility, or loosely speaking your happiness, goes up with the natural log of your wealth, which is to say you exhibit log-utility, *U(W) = ln(W)* . This is a very risk tolerant utility versus wealth schedule, at least according to a [survey](https://elmwealth.com/measuring-the-fabric-of-felicity/) we recently conducted and wrote about. In our survey, we didn’t find any of our respondents nearly that risk-tolerant. Log utility would suggest that you’d take a 50/50 gamble, where you double your wealth on heads versus losing 49% of it on tails, a gamble which most people wouldn’t think twice to turn down – especially for people who are older and have more financial savings versus their human capital. 7. Here’s the calculation: the utility of his current $100,000 of wealth is *ln(100,000) = 11.5129* . If he wins the lottery, his utility goes up to *ln(1,500,099,990)* and if he loses the lottery his utility goes to *ln(99,990)* . The expected value of a 1:1,500,000 chance of winning the lottery and 1,499,999:1,500,000 of not winning is 11.5128, which is lower than 11.5129, so buying that ticket is a negative Expected Utility decision. In fact, we can figure out just how bad it is, and the answer is that it’s like having $9 less wealth to start with. 8. It’s been observed that people do weird things with small sums. So, someone with $100,000 of wealth might turn down a fair coin flip that’ll win $110 on heads versus lose $100 on tails, even though all that would be needed, even for a pretty risk-averse investor (e.g. the average from our survey), is better than win $100.31 versus lose $100. It’s fascinating that people tend to play the lottery when they shouldn’t, but then refuse symmetric but small favorable bets when they should take them. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/reflections-on-the-lottery) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/annuity-island-840x420.png) [Risk and Return](https://insights.elmwealth.com/elm-wealth-research/tag/risk-and-return) ### [The Annuity Puzzle: How Big is the Free Lunch Being Left on the Table?](https://insights.elmwealth.com/elm-wealth-research/the-annuity-puzzle) Oct 15, 2018, 12:00:00 AM October 15, 2018 Risk and Return ## The Annuity Puzzle: How Big is the Free Lunch Being Left on the Table? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2259) The looming Savings Crisis is usually attributed to people not saving enough and making poor investment decisions with what they do save. We believe there’s another major culprit, which is that due to market inefficiencies too many investors can’t order the free lunch inherent in pooling their longevity risk with others. Franco Modigliani, father of the Life Cycle Hypothesis of Saving, brought attention to this aspect of the savings problem in his 1985 Nobel prize acceptance speech.[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2259) He described what has become known as the ‘annuity puzzle’: *“It is a well-known fact that annuity contracts…are extremely rare. Why this should be so is a subject of considerable current interest and debate.”* Things haven’t changed much since then, with annuities still comprising a small fraction of the US retirement market at less than 8% of total retirement assets of $28 trillion.[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2259) A self-directed investor faced with uncertainty about how long she will live will want to keep some savings in reserve against long life. But, if she converts her savings into an annuity with reasonable terms she should get to spend substantially more, because her longevity risk can be pooled with other people. The puzzle is: why don’t more people convert their savings into a lifetime annuity as they get older, thus enjoying the benefits of being able to reserve less and spend more? Our objective in this note is to show just how big of an opportunity gap exists between managing longevity risk oneself compared to shedding that risk by buying an annuity. We also want to use this note as an illustration of the usefulness of the Expected Utility framework we’ve been writing about recently.[4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2259) Let’s say Jane is a 65-year-old single woman in good health who has $1mm of savings and receives social security income, which takes care of her ‘subsistence’ needs. For simplicity, let’s say she has no interest in future charitable or family bequests,[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2259) so her wealth has no utility to her unless she consumes it in her lifetime. We’ll also assume the only available investment is an inflation-indexed bond that pays a 0% real rate of interest after tax. We recognize this is a highly stylized scenario, but it’s a good starting point for figuring things out and then making things more realistic later. The chart below shows her life expectancy, which indicates she expects to live 20 years, with quite a bit of uncertainty around that:[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2259) How should Jane budget her consumption in excess of her subsistence needs? It seems to us that the clearest way to solve this problem is to find the spending pattern that maximizes Jane’s expected utility[7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2259) over the remainder of her life. We’ll assume Jane already knows her utility function, and that it takes the form that we found most common from the investor survey we recently conducted.[8](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-8-2259) It’s worth pausing here to ask why it’s so important to have a fancy utility function, and not just assume Jane’s happiness is proportional to her consumption? The reason is that if her happiness is directly proportional to consumption, there’s no basis for preferring any one spending plan over another; Jane might as well spend her whole $1mm in the first year, and afterward just live at her subsistence level. Such a plan is not psychologically plausible, and using a concave utility function is our preferred way to ensure that such a solution is not selected. By recognizing that increasing consumption in any given period gives us diminishing marginal gains in happiness, we have a way of preferentially weighing extra consumption now versus less consumption later. Armed with Jane’s utility function and the probability distribution of her life-expectancy, we want to find the consumption rule which optimizes her expected utility over the rest of her life. This optimal rule can be solved both analytically and numerically, and in the chart below we show it in red.[9](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-9-2259) If she lives to 115, she will have spent her entire $1,000,000, but if she dies at a younger age, she will have spent less than that and expire with money in the bank. In blue, we show her planned spending if, instead of managing her savings and life-expectancy risk herself, she bought a zero-fee annuity.[10](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-10-2259) Notice that the annuity would give her just shy of $50,000 per year of spending, which is determined so that the expected payout to her (given her probability of dying each year) equals $1,000,000. You can see this is roughly the right number since she is expected to live 20 more years, and *20 \* $50,000 = $1,000,000* . As you can see, Jane’s optimal spending per year if she chooses to manage her own longevity risk is substantially lower than the annuity payment, because she needs to keep much of her savings as a precaution against living longer than expected. Given her longevity probabilities, she should expect to spend only $627,000 of her $1,000,000 by managing her own savings, compared to an expected spend of the full $1,000,000 if she buys the annuity. If she lives to 115, the annuity would have paid her almost $2,500,000, compared to $1,000,000 from managing it herself. Another way of describing the size of the opportunity gap is that the annuity provider could charge a fee of 3.75% pa on the annuity assets they manage and deliver an annuity of about $28,000 pa that would leave Jane with the same expected lifetime utility as she’d get from managing her longevity risk herself. The fact that people like our hypothetical Jane do not avail themselves of annuities to benefit from this substantial increase in expected spending is the heart of the annuity puzzle that has perplexed many financial economists (and annuity salespeople too), and what Professor Modigliani brought attention to in his Nobel acceptance speech. Of course, many people are not like the highly stylized 65-year old we’ve described here for our illustration. For example, if a person highly values making end-of-life bequests which are large relative to lifetime consumption, then the benefit to purchasing an annuity will be much lower, and possibly insignificant.[11](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-11-2259) More realistic fee structures, investment opportunities, and tax effects than we’ve assumed will also have an impact on our analysis, although we expect the general character of our findings should hold for many people. ### Conclusion While this annuity puzzle has received much attention over the years, we hope that we have added to the discussion by showing the magnitude of the potential opportunity gap. What makes this even more of a puzzle is that unlike taking typical market risks, bearing one’s own longevity risk does not offer compensation in the form of a risk-premium. For many people, longevity risk can be more consequential than the risk they bear in their investment portfolio. So why might annuities have such a low take-up given the significant risk and dollars-and-cents benefits for a large class of investors? Some possible explanations include: existing products which are complex and opaque, visible and hidden fees being too high, investor aversion to giving up control of their savings, investors worrying about the credit risk of the provider, or underwriters being too conservative in pricing longevity risk.[12](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-12-2259) Some wealthier investors may feel they don’t need an annuity as long as they can get by on the income from their investment portfolio without eating into capital, a posture which generally results in lower consumption than that suggested by maximizing lifetime expected utility. Or if some investors just haven’t given enough thought to the reserve they should be holding against their own longevity risk,[13](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-13-2259) there could be a benefit from more financial education. An annuity offering with greater transparency, simplicity, efficiency and security would very likely help. Indeed, in the early 1700s the British government funded itself through the sale of lifetime annuities, and various mutualized schemes and instruments have seen success in the past. It may be just this kind of bold or creative solution that is needed to harvest the opportunity gap posed by this apparent disconnect between financial theory and practice. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest.   Thanks to Larry Hilibrand, Vladimir Ragulin, Chi-fu Huang, Andy Morton and John Glazer for their input. 2. [Life Cycle, Individual Thrift and the Wealth of Nations,](https://assets.nobelprize.org/uploads/2018/06/modigliani-lecture.pdf?_ga=2.120170568.1121429910.1536285213-1476573467.1536285213) 1985. 3. [2018 Investment Company Fact Book,](http://www.icifactbook.org/ch8/18_fb_ch8) figures 8.5 and 8.6. Also this [Thinkadvisor](http://www.icifactbook.org/ch8/18_fb_ch8) survey. 4. See our notes [here](https://elmwealth.com/how-much-of-a-good-thing-is-best-for-you/) and [here](https://elmwealth.com/a-sharper-lens-for-sizing-up-nickels-and-steamrollers/) for a review of the core ideas of the Expected Utility approach to financial decision making under uncertainty. 5. Or that she’s made them already and has no desire to add to them. Or, alternatively, that the estate tax is 100% with no exclusions. 6. Data from the [Social Security System website](https://www.ssa.gov/oact/STATS/table4c6.html). Probability goes to zero at age 115. 7. Specifically, the utility derived from spending her wealth. 8. A Constant Relative Risk Aversion utility function with a risk-aversion parameter of 3. In our note [here](https://elmwealth.com/measuring-the-fabric-of-felicity/), we discuss how she might have found this out. For simplicity, we are also assuming Jane does not exhibit time preference regarding her utility. 9. Robert Merton provided a solution to a stylized form of this problem in [Optimum Consumption and Portfolio Rules in a Continuous-Time Model,](http://www.people.hbs.edu/rmerton/Optimum%20Consumption%20and%20Portfolio%20Rules.pdf) Journal of Economic Theory (1971), pp 399-401. He assumed that the investor faced a constant probability of expiring each year, conditional on reaching that age. While mortality risk in reality takes quite a different form than this, Merton’s formulation has a closed-form solution, which is to spend a constant proportion of wealth each period, with that proportion being a function of the concavity of the investor’s utility curve and the attractiveness of a constant investment opportunity set. Merton concludes: *“Thus, an individual who faces an exponentially-distributed uncertain age of death acts as if he will live forever, but with a subjective rate of time preference equal to his “force of mortality”, i.e., to the reciprocal of his life expectancy.”* To illustrate with a simple example, for an investor with Jane’s utility function, and assuming the only available investment delivering an inflation-adjusted risk-free return of 0% and a 5% annual probability of dying (which gives an expected 20 more years to live), the investor would optimally choose to spend about 3.5% of existing wealth each year. In so doing, over a 50 year period, such an investor would expect to have spent only 43% of starting wealth, an even larger shortfall than in the case discussed in the body of the note, based on more realistic mortality risk. Interestingly, this topic does not pick up much coverage in the Lifetime Portfolio Choice and Consumption literature, and is not discussed in the popular Asset Pricing textbooks of Campbell, Cochrane or Huang & Litzenberger. 10. Priced with no profit for the insurer. 11. In fact, the desired bequest needs to be very large relative to desired lifetime consumption in order for the bequest to serve as a sufficient reserve against living longer to make the annuity of little benefit. For example, let’s say Jane knows she will live exactly 20 more years, and her bequest function is such that her optimal spending would be $40,000 per year, leaving a $200,000 bequest for her family or her favorite charity. Using Jane’s implied preferences for spending versus bequest, and introducing longevity risk, we find that her optimal spending pattern is such that her expected lifetime spending is about $600,000, and her expected bequest is $400,000, roughly twice as big as the bequest she’d like to make. Her bequest would be extremely variable too, ranging from almost $1,000,000 if she dies in one year, to almost 0 if she lives to 105.   Alternatively, she could purchase a lifetime annuity that gives her about $40,000 per year as long as she lives, and she could take the remainder of her savings and make a bequest of $200,000. In fact, by buying an annuity, Jane could get the same expected utility with only $750,000 of savings, using $600,000 of it to buy an annuity of $30,000 per year and leaving $150,000 in bequest. Thus, the gap between managing longevity risk herself versus buying an annuity in this case is still very significant, even though smaller than in the base case we analyzed with Jane having no desire for a bequest. 12. See [this working paper](http://www.nber.org/papers/w25067#fromrss) from the NBER for further discussion. They find product fairness to be the biggest driver of investors’ annuity aversion. Insurance companies may be charging an extra risk premium for longevity risk, which is only partially hedge-able with sales of term life insurance. 13. Peter L. Bernstein, “Against the Gods: The Remarkable Story of Risk”, (1996), page 4. One might wonder whether governments expect higher estate taxes from investors who don’t buy annuities, but with the $10mm per person current US government lifetime estate exclusion, there doesn’t seem to be a tax incentive on the part of the government to discourage annuities. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/the-annuity-puzzle) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/fabric-felicity-840x420.png) [Featured Insights](https://insights.elmwealth.com/elm-wealth-research/tag/featured-insights) ### [Measuring the Fabric of Felicity](https://insights.elmwealth.com/elm-wealth-research/measuring-the-fabric-of-felicity) Sep 17, 2018, 12:00:00 AM September 17, 2018 Featured Insights ## Measuring the Fabric of Felicity *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2223) We steer our financial course through life choosing how much to spend and how to invest what’s left, periodically updating our choices as circumstances evolve. This is the essence of financial planning: specifying in advance a desired spending and investment policy conditional on relevant aspects of our life, varying investment opportunities, and our preferences for the benefits derived from our wealth. It’s a pretty simple problem to put into words but finding an optimal solution has occupied some very bright minds for the past 60 years, since Harry Markowitz got the ball rolling with his brilliant but highly-stylized one-period, static portfolio selection paradigm.[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2223) Since then, researchers have made tremendous progress in both specifying and solving increasingly realistic and relevant formulations of this problem, with the goal of maximizing expected lifetime utility at the core of most formulations. In fact, academic research in this area has been so rich that it’s given birth to an entire academic discipline with dedicated university courses and textbooks.[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2223) And yet, even though the study of this problem has delivered novel and valuable insights, we haven’t seen meaningful adoption by the financial planning or wealth management industries. The issue may in part involve the “utility” formulation so common in academia. Utility is a measure of the happiness, or felicity,[4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2223) we derive from using our wealth, and researchers generally presume that an investor knows her own “utility function,” which is to say the relationship between her wealth and utility. Unfortunately, sparingly little has been written about how an individual should calibrate her personal utility function. Financial planners may also worry that these relatively stylized academic models of utility don’t adequately represent investor preferences in the real world and fear their clients will be confused by a process grounded in an unfamiliar abstract formalism. Are these reservations justified? We decided to create a short survey to address this question by testing whether a group of financially-sophisticated investors could comfortably communicate their preferences in a way which we could then translate into utility terms, and whether these preferences are reasonably consistent with core utility concepts. If the responses were affirmative, then we’d have reason to believe that putting the academic research findings into practice could have a big payoff. So, over the past six weeks, we gave the survey to a group of 31 friends and former colleagues from the finance industry.[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2223) We make no claims that results from this selective sample are automatically applicable to broader groups, but we thought it would be a good starting point to see if there’s at least a kernel of people who would be comfortable thinking within this framework.[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2223) Below is the survey.[7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2223) As we’ve done before in our research, we framed the survey questions using coin-flipping thought experiments.[8](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-8-2223) A utility-based framework is built into the structure of the questions, but you’ll see we don’t actually use the word “utility” anywhere in the questions, as we hoped to bring as few preconceptions into the survey as possible. We’d value getting more responses, so please [take the survey here](https://goo.gl/forms/vZ1MlmxUaQ0fG49v1) if you have a few minutes to give it some thought before reading on. 1. Imagine you are presented with a one-time investment opportunity where the outcome depends on whether a fair coin flip comes up heads or tails. The coin flip is uncorrelated with your existing portfolio of investments and consumption and bequest plans. If it comes up tails, you lose 10% of your wealth. Which of the following amounts of upside would make you feel most ambivalent between accepting or declining the coin flip? If you can’t decide between two options, tick both. In case it helps, the Sharpe Ratios of the different options are 0.05, 0.11, 0.18, 0.26 and 0.34 respectively. 1. 11% 2. 12.5% 3. 14.5% 4. 17% 5. 20.5% 2. Same question as above, but now the downside if the coin comes up tails is you lose 20% of your wealth. Which upside would make you feel most ambivalent? Again, if you are finding two answers close, tick both. The Sharpe Ratios are 0.11, 0.25, 0.44, and 0.80 respectively. 1. 25% 2. 33% 3. 50% 4. 175% 5. I wouldn’t risk losing 20% of my wealth for any of these upsides. 3. Still flipping a fair coin. Now imagine that if it comes up heads, your wealth will increase 5-fold. What’s the most downside you’d accept to take that flip? Again, if your answer is between two options, please tick both. 1. 80% 2. 50% 3. 30% 4. 20% 5. 15% Before proceeding, we need to explain a little about how we picked the specific values in answers (a)-(e). The family of utility functions most commonly used in the academic literature is called Constant Relative Risk Aversion (CRRA) Utility.[9](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-9-2223) It’s hard to beat for simplicity, requiring just one parameter: the coefficient of risk aversion. One of the fundamental insights of the utility framework is that an individual’s utility curve defines her risk preferences, and in particular her level of risk aversion. Risk aversion comes from the asymmetry in utility between positive and negative changes in wealth. The parameter which describes the curvature of the utility function (the asymmetry) therefore also describes the level of risk aversion.[10](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-10-2223) Answers (a)-(e) each reflect one particular level (1, 2, 3, 4 and 5) of risk aversion. So, for example, an individual who displays CRRA Utility with a risk aversion level of 3 would choose answer (c) in all 3 questions. Two “ideal” individuals whose preferences are well represented by CRRA utility and who have the same coefficient of risk aversion would answer our survey in the same way, regardless of their wealth.[11](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-11-2223) And now to the survey results. In sum, we were encouraged by the responses. You can find the full response data [here](https://docs.google.com/spreadsheets/d/1dc_a5GwHaPhxHrvrTNe2AFiuKu76E8z1o5Mj_9mNtRw) and summarized in the chart below. Here’s what we take away from the survey data and follow-on conversations: - The style of calibration questions we used appears reasonable and comfortable to answer for our particular group, with not one respondent needing clarification before answering the questions. - The risk preferences of our respondents seem broadly consistent with CRRA utility. Respondents tended to answer the three questions in a consistent fashion. Most selected nearby letters or the same group of letters across all three questions. Had answers been selected at random, the average expected variation per respondent would have been 50% greater across the three questions. - The level of risk aversion evidenced by our respondents is strongly clustered around choice (c), equivalent to a risk aversion level of 3, as indicated in the bar chart above. We think Q2 is the mostly broadly relevant of the three questions, and the average value of answers to Q2 was 3.2, with not one person choosing (a) and only three choosing (e).[12](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-12-2223) The average value for Q3 was 3.0.[13](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-13-2223) We’d like to give a flavor for what’s implied by a risk-aversion level of 3. In line with the survey, an “ideal” investor with CRRA risk-aversion of 3 would never risk more than 30% of her wealth on an even-odds gamble regardless of the upside, and would need at least 50% of upside to risk 20% of her wealth. In an investing context under the most basic set of assumptions, such an investor would optimally invest 50% of her wealth if her only investment opportunity were a risky asset with an expected excess return of 4% and standard deviation of 16%.[14](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-14-2223) We look forward to writing a lot more about this topic in coming notes, using increasingly realistic sets of assumptions. Before concluding, we feel a few caveats are in order. The thinking of our respondent group may not be representative of the broader population. Seven have PhDs in finance, and four have published relevant research papers. Caution is also called for in light of the extensive body of behavioral finance research, much of it in the area of Prospect Theory, which holds that people systematically make choices inconsistent with the classical utility functions that we used in our survey.[15](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-15-2223) Furthermore, psychological studies suggest that most of us are not very good at knowing how we’ll feel in different future scenarios. However, there’s no escaping the type of questions posed in our survey if we want to make sound long-term financial decisions. An imperfect calibration of our preferences is likely better than no calibration at all. An approach that ignores or denies the premise of decreasing marginal utility of wealth will likely find itself trying to maximize expected future wealth, which can produce dangerous and nonsensical policy recommendations.[16](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-16-2223) We’ve been encouraged by the results of this survey and are looking forward to taking the next steps towards applying the valuable and extensive body of academic research to the real world financial planning and investing challenges faced by us all. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest.   Thank you for the helpful comments and guidance of Chi-fu Huang, Jeff Rosenbluth, Andy Morton, Vlad Ragulin, Ben Miller, Ayman Hindy, Larry Hilibrand, Aron Landy and all our friends who generously shared their time with us in taking our survey. 2. Harry Markowitz, [Portfolio Selection](https://www.math.ust.hk/~maykwok/courses/ma362/07F/markowitz_JF.pdf). The Journal of Finance. pp 77–91 (Mar 1952). 3. The discipline is often called Lifetime Portfolio Choice and Consumption. Many consider the seminal paper Robert Merton’s [Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case](http://www.people.hbs.edu/rmerton/Lifetime%20Portfolio%20Selection.pdf), The Review of Economics and Statistics, Vol. 51, No. 3 (Aug. 1969). For a brief overview, see John Campbell, [Strategic Asset Allocation: Portfolio Choice for Long-Term Investors](http://www.nber.org/reporter/fall00/campbell.html), NBER, (2000).   For an in depth treatment, these books: John Campbell and Luis Viceira, [Strategic Asset Allocation](https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Campbell_Viceira.pdf) (2002), John Campbell, Financial Decisions and Markets (2017), Robert C. Merton, Continuous Time Finance (1992), John Cochrane, Asset Pricing (2005). 4. felicity: the quality or state of being happy. The “fabric of felicity” is attributed to utilitarian Jeremy Bentham: *“Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do…The principle of utility recognises this subjection, and assumes it for the foundation of that system, the object of which is to rear the **fabric of felicity** by the hands of reason and of law.”* Introduction to the Principles of Morals and Legislation, Chapter 1, (1789). 5. Our 31 respondents were a pretty special group, intentionally chosen to be highly financially sophisticated. The majority are investors with Elm Partners. All are reasonably affluent too, stating that their current wealth was significantly in excess of what would be needed to support their basic consumption needs. 6. Although our sample represents a small niche of investors as a proportion of all investors, it’s large in absolute terms, and influential. 7. Another approach would have been to ask people about their investment portfolios and their assumptions of expected return and risk of their portfolios in order to back out an implied degree of risk aversion from their portfolio choices. We felt that would be considerably more complex and blurred by other considerations that respondents might bring to their decision making, such as the degree of mean-reversion in equity markets, making it difficult to isolate the characteristics of their utility functions. 8. We continue to like posing the questions in terms of ambivalence or indifference between accepting or declining a gamble, as we discussed in this note: [How Much of a Good Thing is Best for You?](https://elmwealth.com/how-much-of-a-good-thing-is-best-for-you/) 9. *U(W) = (1 – W1-ƞ)/(ƞ – 1)* for *ƞ* ≠ 1, and *U(W) = ln(W)* for *ƞ = 1* , where *ƞ* is known as the coefficient of risk aversion. See this [Wiki article](https://en.wikipedia.org/wiki/Isoelastic_utility).   In addition to the simplicity, plausibility and tractability of CRRA Utility functions, a line of reasoning known as Portfolio Turnpike theory states that for long-term horizons, investor preferences are likely to converge to CRRA utility. See Mossin, [Optimal Multi-period Policies](http://web.math.ku.dk/~rolf/Mossin) (1968) or Cox and Huang, [A Continuous-Time Portfolio Turnpike Theorem](https://www.sciencedirect.com/science/article/pii/016518899290046H?via%3Dihub) (1992). 10. The degree of curvature of one’s utility function is also at the center of the spend-now versus save-and-spend-more-later decision. The greater the curvature, the greater the inducement required to defer consumption. We expect to delve deeper into the mechanics of this in upcoming notes. 11. Assuming their “subsistence” spending needs are a small fraction of total wealth. 12. A choice of (a) is equivalent to “log-utility”, the most commonly used level of risk-aversion amongst academics, and of interest to gamblers through the original statement of the Kelly Criterion. 13. We also expected to find that respondents would evidence a higher level of risk aversion for smaller gambles than larger ones, and indeed we found this to be the case. The average coefficient of risk aversion to Q1 (10% downside) was 4.0, while for Q2 (20% downside) it was 3.2. It is worth noting that for very small gambles, investors should logically be willing to accept a very small edge, as the price of risk should be proportional to variance, or bet size squared.   So, for an investor with coefficient of risk aversion of 3, say with $1mm of net worth, she should be indifferent to a fair coin flip of lose $10,000 versus gain $10,300, but we’ve observed that in practice most people demand a much bigger edge than that for small gambles. We are not overly disturbed by this tendency, as what really matters for the Lifetime Portfolio Choice and Consumption problem we are concerned with is risk aversion to more substantial risks. 14. As per the Merton rule: *µ / (ƞ σ2)* , where *µ* is the expected excess return over the risk-free rate, *σ* is the standard deviation of returns, and *ƞ* is the coefficient of risk aversion. See this [Wiki article](https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem), or Merton’s original 1969 paper, [Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case](http://www.people.hbs.edu/rmerton/Lifetime%20Portfolio%20Selection.pdf) (page 253, equation 29′). 15. Behavioral finance mostly focuses on the question of what people actually do, not on questions of what people should do. The idea that behavioral heuristics, like those arising from classical utility functions, could help reduce inherent bias and produce more optimal outcomes is not inconsistent with behavioral finance generally. Other criticisms of the classical utility framework argue that people systematically display internally inconsistent preferences, for example as suggested by the [Allais paradox](https://en.wikipedia.org/wiki/Allais_paradox). 16. Even with technical constraints such as an arbitrary threshold on the probability of going broke. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/measuring-the-fabric-of-felicity) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/tax-cake-840x420.jpg) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [Tax Efficiency and Dynamic Asset Allocation: Can We Have Our Cake and Eat It Too?](https://insights.elmwealth.com/elm-wealth-research/tax-efficiency-and-dynamic-asset-allocation-can-we-have-our-cake-and-eat-it-too) Sep 4, 2018, 12:00:00 AM September 4, 2018 How Elm Works ## Tax Efficiency and Dynamic Asset Allocation: Can We Have Our Cake and Eat It Too? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2199) We are frequently asked about the tax efficiency of our dynamic value-and-momentum investment approach. The concern is often that with estimated turnover of 50% – 100% per year, returns might be less tax-efficient than a simple static, buy-and-hold type of approach, which is generally recognized as the gold-standard of tax-efficient investing.[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2199) As we’ll explain below, we believe our dynamic approach is expected to be, and has been, as tax-efficient as a static one. In this note, we will: - describe the historical tax-efficiency of our approach, as experienced by an actual investor for the past six years. In the Appendix, we show simulated results for the past 11 years, and… - explain why we expect to continue to deliver tax-efficiency in US taxable portfolios, particularly through the inherently favorable tax characteristics of momentum-induced rebalancing and from the account-by-account, tax-aware portfolio-rebalancing tools we’ve developed in-house. ### Tax-Efficiency of an Elm Investor (2012-2017) While tax performance in a particular instance will strongly depend on the specific path of the market and the investor’s entry and exit point(s),[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2199) the actual experience of one of our early investors may be a useful illustration of the degree of tax-efficiency we can deliver.[4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2199) The example below is from an investor in our Delaware Fund. While our Fund is different in a number of material ways from an SMA account, we chose this example as it allows us to share a history twice as long as what we have for SMAs.[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2199) We have also run longer-term comparative simulations based on investment start dates from 2007 to the present, with results consistent with the example we show here – see the Appendix for details. As always, we emphasize that even ten years of historical experience, in and of itself, cannot tell us much about what to expect in the future.[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2199) In the table below, we compare the income and its tax character from our chosen investor versus a simulated fixed-weight portfolio with the same Baseline weights as Elm’s strategy,[7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2199) and rebalanced back to those weights each month. | | Actual Investment in Elm Fund | Static Fixed Weight Asset Allocation | Tax Rate: Approximate Allocation | | --- | --- | --- | --- | | Start Value: Jun. 1, 2012 | $10,000,000 | $10,000,000 | | | End Value: Dec. 31, 2017 | $15,540,340 | $15,095,500 | | | Increase in Investment | $5,540,340 | $5,095,500 | | | Unrealized Capital Gains | $3,644,880 | $3,164,590 | 15% | | Total Realized Capital Gains | $298,700 | $291,924 | | | Short-term Capital Gains (Losses) | ($459,360) | $45,243 | 41% | | Long-term Capital Gains | $758,060 | $246,681 | 24% | | Qualified Dividends | $867,580 | $848,738 | 24% | | Int Inc & non-Qualified Dividends | $610,850 | $629,692 | 41% | | Tax-exempt Income | $118,330 | $160,556 | 0% | | Blended Tax Rate on Investment | **17.1%** | **18.8%** | | | Past returns and tax characteristics may not be indicative of future returns and tax character. Note: summarized k-1 data: e.g. foreign tax credits and misc deductions are not shown separately. | | | | The right-most column displays the assumed Federal tax rate applied to each type of income. Notice that we use 15% for unrealized capital gains, 9% lower than the 24% for realized long-term capital gains, in recognition of the benefits of deferring capital gains tax.[8](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-8-2199) If we applied an 18% rate to unrealized gains for the dynamic strategy and 15% for the static strategy, to reflect the higher expected turnover of the dynamic strategy in the future, this would increase the blended tax rate of the dynamic strategy by 1.9%, putting it roughly in line with the static approach. Bottom line: not only did our chosen investor do over 4% better than a simulated static weight investor on a pre-tax total return basis (with about 10% lower risk),[9](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-9-2199) but, over a reasonable range of assumptions, he experienced an effective blended tax rate that was attractive in absolute terms, and also was roughly equal to, or possibly even lower than, that of a static weight investor.[10](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-10-2199) ### Elements of a Tax-Aware Approach Over this period, if our Fund had rebalanced exactly back to our desired asset allocation each month, turnover would have averaged about 80% per year, while the static, fixed weight approach would have experienced turnover of just 14% per year. However, in practice, both turnover rates would be lower as neither strategy would be rebalanced exactly back to target each month. Despite the higher turnover of Elm’s strategy, there are several subtle but significant effects that together yield high expected (and so far, realized) tax-efficiency for our dynamic approach. First, the momentum overlay is what generates most of the additional turnover compared to a static approach. Its nature is to generate frequent but small short-term capital losses punctuated by less frequent but large long-term capital gains. Second, our portfolio turnover generally takes the form of buying and selling a small ‘top’ slice of the portfolio, which typically has relatively low built-up gains or losses. Beneath this ‘top’ slice, there will tend to be a more static base layer of the portfolio that can hold a buildup of unrealized long-term capital gains. Keeping track of specific tax lots also contributes to greater tax efficiency. Finally, a substantial fraction of total income is generally in the form of tax-preferred Qualified Dividends and tax-exempt municipal bond income, a benefit enjoyed by both the dynamic and static-weight strategies.[11](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-11-2199) In addition to the features described above, which relate to Elm’s core asset-allocation strategy, we apply additional tax-aware portfolio management techniques at the execution level. Our rebalancing algorithm recommends the transactions that will achieve the best trade-off between minimizing realized gains, minimizing transaction costs, maximizing realized losses, and staying close to our asset-allocation targets.[12](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-12-2199) Because many of the dozen or so markets we invest in are related, and several different instruments are generally available per market, we can often achieve a much better tax result for our investors than if we naively re-balanced each market exactly to target without thinking about taxes. Our taxable investors also benefit from periodic tax-loss harvesting, and our system automatically works to prevent tax-adverse wash sales between groups of linked accounts. ### Conclusion We hope this admittedly-limited treatment of this important topic sheds some light on our ability to deliver tax efficient returns through a systematic, dynamic and tax-aware asset allocation approach. We put a lot of focus on tax-efficiency, just as we do on efficiency in fees, as both are risk-free improvements to investor returns worth more than the same amount of expected but uncertain extra return we could try to earn by taking more risk. To paraphrase Ben Franklin: *“A risk-free penny saved is worth two expected but risky pennies earned.” [13](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-13-2199)* --- ### Appendix: Simulated Experience for Global Balanced Taxable SMA over a Full Cycle (2007-2017) The chart below provides a summary of the tax efficiency of our dynamic Global Balanced asset allocation strategy for the 11 full years to the end of 2017, in both absolute terms and relative to a static-weight Baseline strategy. This analysis provides a picture over an entire economic and financial market cycle, including the recession and bear market of 2008-2009. In the bottom section of the chart, the lines show the tax benefit (or cost) of realized capital losses net of realized capital gains. Realized short-term and long-term capital losses (and gains) are valued at tax rates of 41% and 24% respectively. The simulation of our dynamic asset allocation approach was calculated by running our current tax-aware rebalancing algorithm over the historical period 2007-2017, but it does not include the further potential benefit of doing tax-aware “harvest” transactions at times other than on our 40-day rebalancing cycle. For the static-weight portfolio, the simulation assumes that we rebalance the portfolio back to the Baseline weights every 40 days in a tax-aware manner, also without any extra “harvest” transactions. The chart shows that not only did Elm’s dynamic asset allocation approach provide a significantly higher pre-tax total return over the period, 110.5% versus 72.2%, but also until the end of 2015 it achieved this with greater tax efficiency too. By the end of the 11-year period, the total tax benefit delivered by our dynamic strategy falls just slightly below the net tax benefit enjoyed by the static-weight strategy, which is partly a result of the higher return of the dynamic versus static strategy during the period. The salient feature of the cumulative tax benefit of our dynamic strategy occurs in the period of late 2008 and early 2009 during the bottom of the market when our rebalancing strategy realized substantial short-term and long-term capital losses, which resulted in a long-lasting cumulative tax benefit of about 2%, or roughly 0.2% per annum amortized over the full 11-year period. In sum, and keeping in mind the usual caveats about the past not necessarily being indicative of the future, this historical backtest does not contradict the proposition that Elm’s dynamic asset allocation strategy can deliver tax-efficiency comparable to that of a static, buy-and-hold style approach. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest. 2. And far more tax efficient than most hedge fund and other alternative investments, as discussed [here.](https://elmwealth.com/us-tax-reform-leaves-even-less-pie-investors-alternatives/) 3. Half of our SMA investors who have been with us for more than six months have added to their SMA portfolios at least once. Additions tend to improve tax efficiency of returns. 4. There are many other limitations to the usefulness of our example, such as the short period of time covered, the relatively benign market environment over that period, and the recognition that tax rates and law will change over time in ways that are impossible to predict. 5. See [here](https://elmwealth.com/how-to-invest-with-elm-fidelity-smas-vs-fund/) for some of the salient differences between an investment in our Fund compared to an investment in an SMA managed by us at Fidelity. 6. Please see our note [“What’s Past is Not Prologue”](https://elmwealth.com/whats-past-is-not-prologue/) for more on the limits of historical data in investing. 7. You can find our latest Baseline weights in the second table in our latest investor report [here.](https://elmwealth.com/wp-content/uploads/2017/12/Dec-2017-Monthly-Performance-Report-for-Elm-Partners-Portfolio-LLC-1.pdf) 8. This is roughly in-line with an expectation of deferring capital gains for about 20 years with an equity nominal return of about 7%. 9. The annualized standard deviation of monthly pre-tax returns of the Elm Fund was 6.0% compared to 6.9% for the static Baseline portfolio over period. 10. Some of the difference in blended tax rate comes from the short-term capital losses that were generated, which we assume investors can make use of to offset short-term capital gains elsewhere in their investment portfolio. Even without that benefit, our dynamic approach still achieved a slightly lower blended tax rate than the naive static weight approach.   We also note that the static approach could have achieved a lower blended tax rate if we had applied some of the same tax aware portfolio management strategies, but our purpose here was to illustrate the potential benefits of all that we can bring to bear in delivering tax efficient returns versus. a “vanilla” static-weight investment approach. 11. Our Delaware fund structure also benefits, in a rising market, from new investors coming in to the fund, allowing us to buy new higher basis tax lots, and investors redeeming and taking capital gains allocations with them. 12. With short-term gains weighted significantly more heavily than long-term gains. We discuss how tax considerations impact portfolio rebalancing in more detail in this note [here.](https://elmwealth.com/how-much-should-the-tax-tail-wag-the-asset-allocation-dog-a-rule-of-thumb-for-weighing-capital-gains-taxes-in-portfolio-rebalancing-decisions/) 13. See [here](https://elmwealth.com/a-penny-saved-is-two-pennies-earned/) for more on Ben’s maxim, and [here](https://elmwealth.com/us-tax-reform-leaves-even-less-pie-investors-alternatives/) for a more general discussion of tax efficiency in long-term equity investing versus alternative investments. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/tax-efficiency-and-dynamic-asset-allocation-can-we-have-our-cake-and-eat-it-too) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/most-important-840x420.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [The Most Important Number Not Printed in the WSJ](https://insights.elmwealth.com/elm-wealth-research/the-most-important-number-not-printed-in-the-wsj) Aug 30, 2018, 12:00:00 AM August 30, 2018 How Elm Works ## The Most Important Number Not Printed in the WSJ *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-1-2191) We are often asked for our estimate of the long-term return of the equity market. Our framework currently indicates 5.3% above inflation for global equities, which we know strikes many investors as high. This is understandable, given that the most available and frequently cited valuation ratio – the S&P500’s CAPE[2](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-2-2191) – currently stands at about 30, which is higher than it’s been 96% of the time since 1900 and far above its average level of about 17.[3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-3-2191) How do we arrive at our estimate of 5.3% real return? First, we need a simple and fundamentally sound predictor for each major regional equity market. One such measure is the Cyclically Adjusted Earnings Yield, i.e. 1 / CAPE, as suggested 30 years ago in a seminal paper by Shiller and Campbell.[4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-4-2191) While there isn’t enough historical data to statistically derive a high level of confidence in this predictor, such evidence as there is combined with its fundamental economic rationale supports its use as a reasonable indicator.[5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-5-2191) By way of anecdotal context, the Cyclically Adjusted Earnings Yield in 1968 was 4.6% for US equities, and the actual real return over that period has been 5.8% – not spot on, but not too bad either given all that’s happened over those 50 years.[6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-6-2191) Next, we need a good decomposition of the global equity market. The table below presents current data: | Region | CAPE | Earnings Yield (1/CAPE) | Market Cap. Weights | | --- | --- | --- | --- | | US | 28.4 | 3.5% | 37% | | x-US Developed | 18.5 | 5.4% | 31% | | Emerging Markets | 13.9 | 7.2% | 32% | | Global Earnings Yield | | 5.3% | | | **Source:** World Federation of Exchanges, Bloomberg, MSCI.[7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-7-2191) | | | | As you can see, non-US equities offer a much higher earnings yield than US equities. This has a major impact on our return estimate given non-US equities represent almost 2/3rds of the global equity market on the basis of pure market capitalization. There is good evidence that investors, and particularly US investors, tend to significantly over-weigh the US in their thinking about global equities. Even though the US represents less than 25% of global GDP and less than 5% of global population, many investors think of the US equity market as a proxy for the global market, which just isn’t the case. The big index providers, MSCI and FTSE, are also partly to blame for this biased perception, as they assign a weight of over 50% to US equities as a result of adjustments they make for free-float and investability factors. They do this so that their indexes can be investable on a massive scale with minimal distortions, but at the cost of rendering their indexes less representative of the global market. Fortunately, investors who are not constrained to track MSCI or FTSE indexes can achieve a truer and more balanced representation of the global equity market, particularly on a forward-looking basis, by using un-adjusted market cap weights as presented in our table – so long as not everyone tries doing this at the same time.[8](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-8-2191) Another reason that our estimate may strike some investors as high is that we do not make an adjustment for the reversion of CAPE to its historical mean level. In a recent Bloomberg [note](https://elmwealth.com/market-multiple-mean-reversion-red-light-red-herring/), we explained why deviations from the mean for CAPE don’t actually tell us much about expected market returns above and beyond what the absolute level of CAPE already tells us. Hence, including mean-reversion does not improve CAPE as an indicator of long-term return.[9](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-9-2191) We don’t include market momentum in our estimate, as we are focused on long-term returns and the effects of momentum average out to zero over long time horizons. We also stopped short of making an adjustment for taxes, as this will vary according to personal circumstances.[10](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5#easy-footnote-bottom-10-2191) As a general matter, equity investing is among the most tax-efficient forms of long-term investing, given the ability to defer capital gains and the preferential treatment of dividends in many tax regimes. The simple framework we’ve described in this note is not meant to have near-term predictive power. Instead, we hope it provides a useful starting point for thinking about the long-term return of equities, which is one of the most critical inputs into lifetime decisions about how to invest, save, and spend. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest. 2. Cyclically Adjusted Price to Earnings ratio, which is the current equity index price divided by the past 10 years of inflation adjusted earnings. CAPE was first suggested by Graham and Dodd (1934), but popularized by Professor Robert Shiller. 3. Using Robert Shiller’s [reference data.](http://www.econ.yale.edu/~shiller/data.htm) 4. Campbell and Shiller, [“Stock Prices, Earnings and Expected Dividends”.](http://www.nber.org/papers/w2511.pdf) 5. We have presented our views on this several times in the past, such as in this Elm video from three years ago: [The Most Important Number You Won’t Find in the Wall Street Journal](https://elmwealth.com/video-the-most-important-number-you-wont-find-in-the-wall-street-journal/) (2015).There is a plethora of literature on this subject, presenting sometimes opposing perspectives, and we recognize that it is more the topic of a book than a one page note. A variety of simple structural corporate-growth models can produce the result that real equity returns will be centered around the earnings yield.   One basic condition under which real returns will equal the earnings yield would be if company earnings can grow with inflation with all earnings paid out currently to shareholders. While these models are all caricatures of the real world in a variety of ways, they nonetheless provide a solid starting point for making sense of long-term historical data. For a more up-to-date evaluation of CAPE as a predictor of real equity returns, particularly assessed in non-US equity markets, see [Keimling and Huber](https://www.starcapital.de/fileadmin/user_upload/files/publikationen/Research_2016-01_Predicting_Stock_Market_Returns_Shiller_CAPE_Keimling.pdf) (2016). They conclude: *“Existing research indicates that the cyclically adjusted Shiller CAPE has predicted long-term returns in the S&P 500 since 1881 fairly reliably for periods of more than 10 years. Furthermore, the results of this paper indicate that this was also the case for 16 other international equity markets in the period from 1979 to 2015.”* 6. Again Robert Shiller’s [reference data.](http://www.econ.yale.edu/~shiller/data.htm) 7. CAPE figures are based on an average of MSCI and Bloomberg historical earnings numbers for major regional markets. For non-US markets, historical earnings are converted to US dollars at historical exchange rates and the current index price is converted to US dollars at the current exchange rate. 8. See our [note](https://elmwealth.com/our-asset-allocation-methodology/) here for a fuller discussion of how we arrive at our regional equity market weights in our Baseline portfolio, which are in between the unadjusted market cap weights from the table and the MSCI and FTSE adjusted weights. 9. The main points in our note were that much of the apparent mean-reversion in CAPE is explained by cyclically adjusted earnings catching up with stock prices, rather than the other way around, and the fact that a random walk will give the illusion of mean reversion when looking backwards, but in reality we won’t know the mean of the distribution in advance. 10. For the sake of clarity, in this note we’ve put to the side a further consideration in thinking about equity returns, which is the “convexity” effect, stemming from equities having the attractive characteristic of unbounded upside and bounded downside.   Our return estimate is a central estimate of the long-term return, but if the actual long-term compound return turns out to be 2% better than the estimate, that results in a much larger gain than the loss for a return 2% lower than our estimate. This convexity effect can have a material impact on asset allocation decisions, depending on the magnitude of return variability. See our paper on this topic [here.](https://elmwealth.com/what-our-market-return-forecasts-really-mean-equity-convexity-and-investment-sizing/) [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/the-most-important-number-not-printed-in-the-wsj) [3](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/3) [4](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/4) [5](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/5) [6](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/6) [7](https://insights.elmwealth.com/elm-wealth-research/author/james-white/page/7)