--- title: Elm Wealth Research (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 ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/075-taking-stock-banner.png) [Risk and Return](https://insights.elmwealth.com/elm-wealth-research/tag/risk-and-return) ### [Taking Stock](https://insights.elmwealth.com/elm-wealth-research/taking-stock) Mar 19, 2020, 12:00:00 AM March 19, 2020 Risk and Return ## Taking Stock *By James White and Victor Haghani* [1](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-1-3253) The longest bull market in US stock market history is over. Uncertainty over the public health and economic impact of the coronavirus pandemic will keep markets extremely volatile, making it likely we’ll touch a wide range of price levels in the months ahead.[2](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-2-3253) Amidst such uncertainty, it’s a particularly good time to take stock of long-term return prospects. In doing so, we’ll present an often-overlooked perspective on the market’s attractiveness which is both intuitive and technically sound. We hope long-term investors will find it useful in deciding how much stock market exposure they want right now, and at other levels the market may visit in the future. One popular way of thinking about equities is that they have an ‘average’ or ‘fair’ earnings multiple to which they tend to revert, making them cheap below that multiple and expensive above it. We don’t subscribe to this view, as we discuss in our note [“Market-Multiple Mean-Reversion: Red Light or Red Herring?”](https://elmwealth.com/market-multiple-mean-reversion-red-light-red-herring/) But we do think there are times when it makes sense to own a lot of equities, because they offer high expected returns relative to other places you can put your money, and other times when relative expected returns warrant a small equity allocation. This perspective requires two measures: 1) a forecast for the expected return of the equity market, and 2) an appropriate ‘benchmark’ investment against which to measure equities’ relative attractiveness. ### Getting Real The most widely used forward-looking indicator of the stock market’s long-term expected return is the Cyclically-Adjusted Earnings Yield (i.e. 1/CAPE).[3](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-3-3253) Importantly, it’s a forecast for what economists call the *“real”* return of equities, which means the return *in excess* of inflation. Increasing our wealth in real terms improves our well-being, increasing it in nominal terms alone does not. Next, we need to identify the appropriate benchmark investment against which to measure equities’ relative attractiveness. Owning equities is risky, and so it’s pretty intuitive to measure the expected return on equities relative to the return offered by a risk-free asset.[4](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-4-3253) We probably wouldn’t want to own any of a risky investment with a 10% expected return if the risk-free rate was also 10% – why take extra risk for no extra return? The same investment with a 5% expected return and 0% risk-free rate might look great. It’s the *excess* return – often called the equity risk premium – we should care about when thinking about the attractiveness of equities.[5](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-5-3253) Our return forecast for equities is both long-term and real, and so the appropriate benchmark for the risk-free rate also needs to be long-term and real. Most suited to this role is the yield on long-term US Treasury Inflation Protected Securities (TIPS).[6](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-6-3253) ### Fifty-Year Historical Perspective on Equity Market Risk Premium Taking the difference between the long-term expected real return of equities and the real risk-free rate gives us the Equity Risk Premium chart below. It offers our preferred perspective on the current and historical attractiveness of US and Global (US plus non-US) stock markets for long-term investors who do not hold strong near-term views. The chart ends on March 18th, 2020. One reason you may not have seen a chart like the one above before is that the US Treasury only began issuing TIPS in 1999. To produce this chart, we had to construct a proxy series for the long-term risk-free real rate from 1970 – 1999, inferring what the long-term TIPS rate would likely have been had it existed, which can be seen in the lower panel of the chart.[7](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-7-3253) We see periods of generous equity risk premia (1975 – 1982), and also periods of low and even negative risk premia (1987 – 2002). An investor looking at CAPE alone might find US equities relatively unattractive right now: the current CAPE of 22.5x[8](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-8-3253) is higher (less attractive) than it’s been 80% of the time over the past 120 years. We think the chart above paints a very different picture, suggesting that today’s US and global stock market risk premia are attractive, in both absolute and historical terms. For example, the current global equity risk premium of about 6%[9](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-9-3253) is higher (more attractive) than it’s been 80% of the time since 1970, and it’s higher now than it was during the entire period from 1985 up to the financial crisis in 2008. While equity risk premia cannot tell us the future path of equity prices, especially in the short-term, they do suggest that current long-term return prospects for global equities are attractive and consistent with an above-average level of exposure.[10](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-10-3253) ### The History of Real Rates Risk premia and real rates have both had a wild ride over the period shown in the chart above. One distinctive feature of this chart is that real rates are *really low* right now. This flies in the face of classical economic theories of interest rates that posit positive real interest rates are necessary to induce people to save for the future, rather than consuming “too much” in the present. It’s surprisingly hard to find deep historical context, beyond living memory, to inform thinking about real rates. The reference work on the long-term, 2,000-year history of interest rates, Sydney Homer’s “A History of Interest Rates,” mentions real interest rates just once in 700 pages. This isn’t especially unusual; in the financial press it’s much more common to read about nominal rates, and investment returns are nearly always quoted in nominal terms. Market-quoted real-return instruments such as US TIPS and UK Linkers are still in early middle age, and have not really penetrated the popular consciousness yet. However, a 2019 paper by Yale economic-historian Paul Schmelzing, *“Eight Centuries of Global Real Interest Rates,”* has shed valuable light on the history of real rates. Here we reproduce a chart from the paper showing the core findings: A few takeaways from this chart: 1. Periods of negative real interest rates, such as much of the developed world is currently experiencing, are relatively common and can be protracted. While negative nominal interest rates historically have been difficult to impose on investors who have the option of keeping cash “under the mattress” rather than in a bank, negative real rates don’t run up against any such hard barrier. 2. There does not appear to be an average or “natural” level of real interest rates around which actual rates fluctuate. 3. There appears to be a downward trend in the level of real rates, estimated at 2bp / year. However, we caution that this trend-line does not have strong predictive power. ### Technical Sidebar We see nothing in the historical data which makes us disagree with the market’s current expectation of near-zero real rates – but what should an investor (we’ll call her Tipper) do who doesn’t share that view, believing instead that risk-free real rates will rise and TIPS prices will fall? A full treatment of this question merits its own note, but for a sense of how one might approach it consider a simplified world with three available investments: TIPS, the stock market and T-Bills, with TIPS being the minimum-risk asset for Tipper, an investor with a long-term horizon.[11](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-11-3253) Tipper has her equity return forecast, expressed relative to TIPS as we’ve been discussing, and because she thinks TIPS prices will fall, she’s also forecasting a high return for T-Bills relative to TIPS. She now needs to decide the optimal combination of equities and T-Bills to hold, based upon their expected excess return relative to TIPS, their risk and their correlation to each other. If we assume that they are uncorrelated, as suggested by both data and a desire for simplicity, then we can determine the optimal allocation to each of the trades separately, driven by their own expected return and risk relative to TIPS and Tipper’s personal level of risk aversion.[12](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-12-3253) In this case, Tipper’s desired equity exposure is still driven solely by their expected return relative to TIPS. Her real rate view makes her want to hold more T-Bills, not less equities, and if her desired equities plus T-Bills exposure is greater than 100% she’ll need to have a negative (short) allocation to TIPS to bring the sum of the allocation weights to 100%. If however she can’t or won’t short TIPS (and we too are generally opposed to shorting any asset), then she wouldn’t be able to hold all the equities and T-Bills she wants and would optimally reduce both her desired equity and T-bill exposures instead. ### Conclusion For an investor who accepts as fair the market real rate offered by TIPS, should the absolute level of real rates impact the equity allocation decision? All else equal, our answer is no. Lower risk-free rates imply lower absolute expected returns for risk-free and risky assets. This is an unfortunate fact for any investor, but in deciding how much to invest in equities, investors should want to scale risky investments proportionally to the risk premium, not the absolute expected real return. Of course, ‘all else equal’ is just the starting point for a fuller assessment. For example, lower real rates means more of the value in equities comes from longer-dated cash-flows, which may increase the long-term riskiness of equities and impact how much an investor should want to own for a given level of expected excess return. And of course, investors taking a long-term view of equity market attractiveness will still want to make adjustments for identifiable near-term impacts to earnings streams, such as those arising from the current coronavirus pandemic. We hope the framework presented in this note gives you a fresh perspective for evaluating the attractiveness of the broad stock market to a long-term horizon. Indeed, if we accept that today’s low real rates represent a fair expectation of the future, P/E ratios which seem otherwise elevated may join low and negative interest rates as part of the ‘new normal’ investing landscape. --- ### Further Reading and References - Campbell, John, and Robert Shiller. *“Stock Prices, Earnings and Expected Dividends.”* Journal of Finance. July 1988. - Haghani, Victor and James White. *[“Market Multiple Mean-Reversion: Red Light or Red Herring?”](https://www.bloomberg.com/opinion/articles/2017-10-02/what-if-high-stock-values-revert-to-normal-levels)* Bloomberg. October 2017. - Schmelzing, Paul. *[“Eight centuries of global real interest rates, R-G, and the ‘suprasecular’ decline, 1311-2018.”](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3485734)* SSRN. 2019. - Homer, Sidney and Richard Sylla. *“A History of Interest Rates, Fourth Edition.”* Wiley Finance. 2005. --- 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. For example, based on current market volatility (VIX at 85% volatility pa), there’s about a 50% chance the market drops 25% from today’s level at some point over the next two months, a hundred-fold increase in that probability versus three months ago. 3. CAPE stands for the Cyclically Adjusted Price Earnings multiple, popularized by Yale Professor Robert Shiller. It is a Price/Earnings ratio where Earnings are calculated as the average of the past ten years’ inflation adjusted earnings of the index. You can read more about why we like 1/CAPE as a predictor of long-term equity returns here: [The Most Important Number Not Printed in the Wall Street Journal](https://elmwealth.com/the-most-important-number-not-printed-in-the-wsj/) 4. We recognize there is no such thing as a truly risk-free investment, but we use the conventional term ‘risk-free’ to refer to the minimum risk asset for a given investor. 5. In general, we should also care about the risk premium and other return characteristics of all the risky assets we could own, such as real estate, commodities or ‘alternative’ investments, and for taxable investors, it’s after-tax returns that matter. In this note, we will assume a non-taxable investor who can only invest in the stock market or the risk-free asset. 6. For a US investor, although inflation-protected bonds in most developed markets tend to offer similar yields. 7. From 1970-1985, we use the difference (smoothed) between ten-year US Treasury nominal bond yields and expected ten-year inflation as collected in US Federal Reserve surveys, and from 1985-1999 we use UK inflation-linked bonds (“Linkers”). 8. Using the March 18th S&P 500 close of 2398. 9. To be precise, 6.2% as of March 18th. 10. In our note [*“Measuring the Fabric of Felicity,”*](https://elmwealth.com/measuring-the-fabric-of-felicity/) we discuss a simple formula – the Merton Rule – for computing an optimal allocation to equities as a function of the expected excess return and risk of equities, and investor risk aversion, assuming a stylized two-asset world: *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. Our survey of 30 financially-sophisticated and affluent investors suggested an average level of risk aversion about 2.5 times that of a Kelly (log-utility) investor. Ignoring issues such as subsistence consumption and hedging demand, our typical investor facing a 6% equity risk premium combined with a long-term expected risk of equities of 18% per annum, would have an optimal equity allocation to equities of 74%. See Merton’s 1969 paper, *“Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case”* (page 253, equation 29). 11. For long-term investors, TIPS may even warrant the status of ‘numéraire,’ meaning the unit of account for measuring wealth. 12. The general result that optimal allocation to uncorrelated assets can be separated into individual allocation decisions is a special case of the “Portfolio Separation Theorem.” [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/taking-stock) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [How to Fund Your Elm Account](https://insights.elmwealth.com/elm-wealth-research/funding-your-account) Dec 19, 2019, 12:00:00 AM December 19, 2019 How Elm Works ## How to Fund Your Elm Account ### If the ultimate source of funds is currently invested in brokerage assets: - You can transfer assets to Elm through the inter-brokerage ACAT network. We’ll take care of liquidating the assets and getting funds invested on the same day, reducing timing risk. If you hold broad-market ETFs or mutual funds, it’s possible we’ll be able to use some or all of these instruments instead of liquidating them. - This will generate realized gains or losses in a taxable account. If you share an account statement with us, we can help estimate the tax impact of liquidating your assets.The ACAT transfer can take between 2 days and 2 weeks. We initiate this through Fidelity and you will receive approval paperwork to eSign. - You can liquidate assets yourself and transfer cash to your Elm Fidelity account (see below). This allows you to control the liquidation directly, but requires taking market-timing risk between when you liquidate the assets and when we re-invest them. --- ### If the ultimate source of funds is currently in cash or cash proxies: - **For Non-retirment accounts:** - If funds are currently outside Fidelity, you can wire funds into your Elm Fidelity account (same-day delivery). Wire instructions can be found on [Fidelity.com](https://www.fidelity.com/cash-management/information-needed-wire-to-fidelity-account). - If funds are currently outside Fidelity but at another brokerage, we can pull the funds into your Fidelity account through the ACAT network (1-3 days typical processing time). We initiate this through Fidelity and you will receive approval paperwork to eSign. - If funds are currently in another Fidelity account, you can instruct Fidelity to transfer the funds into your Elm Fidelity account ($200k/day limit online, no limit over the phone), or we can prepare a Journal Request form for your signature (1 day processing time). - **For Retirement accounts:** - If funds are currently outside Fidelity but at another brokerage, we can pull the assets into your Fidelity account through the ACAT network (1-3 days typical processing time). We initiate this through Fidelity and you will receive approval paperwork to eSign. - If funds are currently in another Fidelity account, you can instruct Fidelity to transfer the funds into your Elm Fidelity account ($200k/day limit online, no limit over the phone), or we can prepare a Journal Request form for your signature (1 day processing time). [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/funding-your-account) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/header-image.png) [Risk and Return](https://insights.elmwealth.com/elm-wealth-research/tag/risk-and-return) ### [Mind the Gap: Inequality and Diversification](https://insights.elmwealth.com/elm-wealth-research/mind-the-gap) Dec 11, 2019, 12:00:00 AM December 11, 2019 Risk and Return ## Mind the Gap: Inequality and Diversification *By Victor Haghani, Jeffrey Rosenbluth and James White* [1](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-1-3088) ### Introduction Understanding the origins of wealth inequality is critical in the debate over what, if anything, to do about it. In this note, we propose a simple model which is still rich enough to reproduce observed patterns of wealth inequality. We call it the Concentrated Asset Betting (CAB) model. A key element of CAB is a phenomenon known in the gambling world as “over-betting the edge.” Our approach was inspired by Bruce Boghosian’s Scientific American article *“Is Inequality Inevitable?”* which provides an introduction to a straightforward model of wealth inequality called the “Yard Sale Model” (YSM). In a Yard Sale model, it is assumed that people enter into repeated exchanges with each other. In each exchange one party is chosen at random to be the “winner” and one the “loser.” The absolute size of the exchange is determined by the assets of the less wealthy party. As the number of exchanges increases, the model converges to one person having all the money in the economy. To match observed levels of wealth inequality in different countries at different times, the YSM is then extended to include wealth redistribution and a couple of other enhancements. ### Model Description The model we propose is based on the observation that a high fraction of investors have experienced sub-par growth in their savings, after allowing for consumption and philanthropy, relative to the tremendous long-term growth in the public stock market. Victor presented some anecdotal evidence of this in his TEDx talk, [*“Where Are All the Billionaires and Why Should We Care?”*](https://www.youtube.com/watch?v=1yJWABvUXiU) Some of the reasons put forward to explain the shortfall in investor returns include investment fees, commissions and taxes. Our model suggests there may be something even larger and more insidious at work – pervasive and systematically poor money management. Here, money management means the task of sizing and diversifying the risks of a portfolio of investments. Numerous academic studies have documented the tendency of investors to hold significantly undiversified portfolios, especially in the pre-Vanguard era up to the early 1990s. With commissions of $70 or more per trade, investors had an incentive to minimize the number of individual stocks they held.[2](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-2-3088) A study by Vanguard observed that from the 1950s through the 1980s investors’ equity exposure came almost entirely through directly-held stocks, and the median investor held only two stocks.[3](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-3-3088) The most basic version of our model begins with a population of households all with the same initial wealth. Each household starts off fully-invested in one stock.[4](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-4-3088) If their wealth increases, they increase the number of stocks they own, thereby increasing their diversification. We add one stock to their portfolio each time their wealth doubles. Each portfolio is split equally among however many stocks they own, rebalancing monthly. Every stock has an annual expected return of 6%, which roughly matches the US stock market’s annual price appreciation over the past hundred years.[5](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-5-3088) We assume a 19% standard deviation of monthly returns, consistent with Hendrik Bessembinder’s large-scale study *“Do Stocks Outperform Treasury Bills?”* For simplicity, we assume the stocks are uncorrelated with each other.[6](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-6-3088) In our simulation, we flip a coin for each stock every month. If heads, the stock in question gains 19.5%. If tails, it loses 18.5%. This gives us the desired 19% standard deviation, with monthly expected return of 0.5% (6% annualized) for each individual stock.[7](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-7-3088) The chart below shows the ending wealth distribution after running this simulation for 100 years on 1000 families. Like the YSM, our model predicts a high level of wealth inequality. Unlike the YSM, our model features a growing economy. ### Interpreting Model Results All families have identical prospects starting out, yet high levels of wealth inequality naturally arise anyway. What’s at work here? First, with portfolios concentrated in just a few individual stocks, chance creates a lot of inequality in wealth outcomes.[8](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-8-3088) Second, good luck, measured by the number of heads flipped, translates into increasingly large incremental gains in wealth. That means wealth as a function of luck is highly convex in the long-term, as good or bad luck compounds multiplicatively rather than additively. This can be seen in the dramatic curvature of wealth plotted against number of heads flipped over 100 years in the chart below. The third force leading to extreme inequality causes many families to wind up with near zero wealth despite investing in stocks that are all expected to rise 6% a year, as can be seen in the chart above. Over the 1,200 months of the 100-year simulation, the expected number of heads is 600, half of the total flips. Yet, the chart shows that if a household experienced 600 heads, they’d wind up with close to 0 wealth. In fact, they need to get 642 heads just to break even.[9](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-9-3088) This results from “over-betting the edge,” defined as taking so much risk that you lose money in the central case of flipping an equal amount heads and tails. If a single stock portfolio gains 19.5% one month and then loses 18.5% the next month, the total return over the two months is not the +1% you’d get from two months of +0.5% expected return per month. Rather, it is -2.6% as illustrated in the diagram below.[10](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-10-3088) In addition to being able to generate different levels of inequality to a given horizon, we can also influence the degree of wealth mobility in our system by choosing how quickly we allow families to diversify their portfolios by adding more stocks with increases in a household’s wealth. Through this mechanism, the winners get more diversification, lessening their over-betting and increasing the chance of keeping and growing their winnings. An important parameter in the basic form of our model is the number of stocks initially held. The chart below shows how greater initial diversification, and thus less over-betting, dramatically lessens wealth inequality. For each distribution of wealth curve, we calculate the Gini coefficient, a popular summary metric of inequality.[11](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-11-3088) Holding 100% of wealth in an 8-stock portfolio represents the acceptable amount of risk for a gambler who bases her risk-taking on the Kelly Criterion, a commonly-used metric which gamblers generally agree sets an upper bound on how much risk to take for a given opportunity.[12](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-12-3088) Even though an investor with an 8-stock portfolio in our framework can no longer be accused of over-betting, she could still improve the quality of her portfolio dramatically with more diversification. If we had investors start off with portfolios of 1,000 stock holdings, we’d get very little wealth inequality, which is what we’d expect if most families held the market portfolio through an index fund. The chart below displays the actual distribution of wealth in the US in 2000,[13](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-13-3088) which is a good fit with our model using a 9-stock initial portfolio for each investor. ### Conclusions and Future Research While we recognize that there are many causes of wealth inequality, the CAB Model provides a simple and empirically-supported explanation for how the level of wealth inequality seen today came about. Some of the assumptions we’ve made may seem extreme by today’s standards, such as using a 19% monthly standard deviation of stock returns, but the CAB results are robust to more moderate assumptions. Indeed, if the US investing scene for most of the 20th century resembles developing markets today, then a recent paper by Campbell et al, *“Do the Rich Get Richer in the Stock Market? Evidence from India (2018),”* provides direct support for the CAB explanation of wealth inequality resulting from pervasive under-diversification.[14](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-14-3088) We hope this short note will spur further research focused on understanding the properties of this model of wealth inequality, and on refinements to make the model more realistic while still retaining its parsimonious structure. In particular, we hope to explore its ability to match observed levels of wealth mobility, the impact of a wealth-redistribution tax, and how to incorporate non-participation and underinvestment in risky assets as another important cause of long-term wealth inequality. The CAB model provides an alternative to that proposed by Thomas Piketty in *“Capital in the 21st Century”* (2014), which assumes that equity returns are high and constant, so once a household gets rich enough to have significant investable wealth, they’re going to get richer and richer.[15](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-15-3088) Unlike Piketty’s Capital model, CAB tells us where the “missing billionaires” may have gone, incorporates pervasive sub-optimal risk sizing, and predicts the frequently observed downward mobility of the undiversified wealthy. It also points the way to a more level potential distribution of wealth in the future, due to the growth over the past 20 years of index funds and other diversified mutual funds.[16](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-16-3088) Unlike the Piketty and the Yard Sale models, the CAB paradigm does not see extreme wealth inequality as an inevitable and convergent feature of “pure” capitalism absent specific offsetting policies such as wealth redistribution. Rather, it shines a bright and hopeful light on one possible path to less wealth inequality in the future, which is for investors to think more carefully about diversification and investment-sizing, thus improving their chances of participating in the long-term expected wealth creation opportunities offered by public markets. --- ### Further Reading and References - Angle, John. *[“The surplus theory of social stratification and the size distribution of personal wealth.”](https://www.jstor.org/stable/2578675?seq=1)* Social Forces, pp. 293–326. 1986. - Barber, Brad, and Terrance Odean. *[“Trading Is Hazardous to Your Wealth:The Common Stock Investment Performance of Individual Investors.”](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=219228)* Journal of Finance. April 2000. - Bessembinder, Hendrik. *[“Do Stocks Outperform Treasury Bills?”](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2900447)* Journal of Financial Economics. 2017. - Bessembinder, Hendrik, Te-Feng Chen, Goeun Choi and K.C. John Wei. *[“Do Global Stocks Outperform US Treasury Bills?”](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3415739)* SSRN. 2019. - Boghosian, Bruce. *[“Is Inequality Inevitable?”](https://www.scientificamerican.com/article/is-inequality-inevitable/)* Scientific American. November 2019. - Calvet, Laurent, John Y. Campbell and Paolo Sodini. *[“Down or Out: Assessing the Welfare Costs of Household Investment Mistakes.”](https://www.nber.org/papers/w12030)* Journal of Political Economy, Vol. 115, No. 5, pp. 707-747. 2007. - Campbell, John Y., Tarun Ramadorai and Benjamin Ranish. *[“Do the Rich Get Richer in the Stock Market? Evidence from India.”](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3141759)* SSRN. 2018. - Chakraborti, Anirban. *[“Distributions of money in model markets of economy.”](https://arxiv.org/abs/cond-mat/0205221)* International Journal of Modern Physics, pp. 1315–1321. 2002. - Clarke, Andrew, Michael Nolan and Tyrone Sampson. *[“What is a Mutual Fund Worth?”](https://personal.vanguard.com/pdf/what-is-a-mutual-fund-worth.pdf)* Vanguard Research. October 2019. - Davies, James, Susanna Sandström, Anthony B. Shorrocks and Edward N. Wolff. *[“The Level and Distribution of Global Household Wealth.”](https://www.nber.org/papers/w15508)* NBER Working Paper No. 15508. 2009. - Haghani, Victor, Jeffrey Rosenbluth and James White. [Concentrated Asset Betting.](https://github.com/jeffreyrosenbluth/Yardsale) 2019. - Hayes, Brian, *[“Follow the Money.”](https://pdfs.semanticscholar.org/0703/1121910a2103729e43789a8864db00cc9d6b.pdf)* American Scientist 90, pp. 400–405, 2002. - Li, Jie, Bruce M. Boghosian and Chengli Li. *[“The Affine Wealth Model: An agent-based model of asset exchange that allows for negative-wealth agents and its empirical validation.”](https://arxiv.org/pdf/1604.02370.pdf)* arXiv.org. 2016. - Wood, Geoffrey and Steve Hughes. *[“The Central Contradiction of Capitalism? A collection of essays on Capital in the Twenty-First Century.”](https://policyexchange.org.uk/wp-content/uploads/2016/09/the-central-contradiction-of-capitalism.pdf)* Policy Exchange. 2015. - US Wealth Distribution Data from Federal Reserve: [Distributional Financial Accounts.](https://www.federalreserve.gov/releases/efa/efa-distributional-financial-accounts.htm) --- 1. This not is not an offer or solicitation to invest. **Past returns are not indicative of future performance.**   Thank you to John Campbell, Larry Hilibrand, Steven Landsburg, and Vlad Ragulin for their very helpful comments and guidance. 2. [Schwab historical commissions.](https://www.wsj.com/articles/schwab-leaves-san-francisco-for-texas-11574900348?mod=itp_wsj&mod=&mod=djemITP_h) 3. Clark et al, 2019: *“In the early 1950s, 4.2% of the U.S. population participated in the stock market, almost entirely through directly held stocks (Federal Reserve Board, 2019). These investors held undiversified portfolios – a median of two stocks. Half held one stock…Stock investing resembled a game of portfolio roulette. In today’s terms, one spin of the wheel might come up Amazon. The next might be Enron. This approach predominated until the 1980s.”* 4. We assume there are enough stocks so that each household owns different stocks. 5. We are in effect assuming that each household spends the dividends they receive on their stock portfolio. 6. It may appear that the assumption that the individual stocks are uncorrelated, and hence all have a Beta of 0, is unrealistic. Relaxing that assumption, for example by giving all stocks a Beta of 1, does not materially change our results. 7. As will become apparent below, even if we had chosen a single stock risk level half of the Bessembinder estimate, the model would produce a similar pattern of results. 8. The wealth inequality among families generated in our simple model is a direct reflection of the highly unequal long-term performance of individual common stocks, which is partly a result of the compounding effect we described above. Bessembinder (2017) observes that: *“…approximately 26,000 stocks that have appeared in the CRSP database since 1926 are collectively responsible for lifetime shareholder wealth creation of nearly $32 trillion dollars. However, the eighty six top-performing stocks, less than one third of one percent of the total, collectively account for over half of the wealth creation. The 1,000 top performing stocks, less than four percent of the total, account for all of the wealth creation…The positive skewness arises both from the fact that monthly returns are positively skewed, and from the possibly underappreciated fact that compounding introduces positive skewness into the multi-period return distribution even if single period returns are distributed symmetrically…which contributes to the concentration of wealth creation.”* 9. But if they get just 18 heads more than that, for a total of 660 heads, their wealth will have grown more than one-thousand-fold, catapulting them into the ranks of the super-rich. Unfortunately, there is only 0.03% probability of getting 660 or more heads. 10. By contrast, a one-stock portfolio with just 15% invested in the single stock would make money in the central case of flipping an equal number of heads and tails, i.e.. *(1 + 15% \* 19.5%) (1 – 15% \* 18.5%) – 1 = +0.07%* . The Kelly Criterion calls for 14%, rather than the 15% in this example, and anything over 28% (i.e. twice the Kelly bet) would be over-betting as we’ve defined it here. 11. [The Gini Coefficient on Wikipedia.](https://en.wikipedia.org/wiki/Gini_coefficient) 12. [The Kelly Criterion on Wikipedia](https://en.wikipedia.org/wiki/Kelly_criterion). 13. Davies, James, Susanna Sandström, Anthony B. Shorrocks and Edward N. Wolff. *“The Level and Distribution of Global Household Wealth.”* NBER Working Paper No. 15508. 2009. 14. The authors conclude: *“Return heterogeneity increases the inequality of account size through two main channels, both of which are related to the prevalence of undiversified accounts that own relatively few stocks. The first is that some undiversified portfolios randomly do well, while others do poorly. The second is that larger accounts tend to earn higher average log returns. They do so not by earning higher average simple returns, but by limiting uncompensated idiosyncratic risk which lowers the average log return for any given average simple return.”* (p15). 15. See this paper for a set of essays evaluating the Piketty model: *“The Central Contradiction of Capitalism? A collection of essays on Capital in the Twenty-First Century,”* Edited by Geoffrey Wood and Steve Hughes (2015). 16. See Calvet et al (2007) for how Swedish households at the turn of the 21st century were making better investment decisions, but still with room for material improvement, than Americans were for most of the 20th century. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/mind-the-gap) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/us-consol-840x420.png) [Risk and Return](https://insights.elmwealth.com/elm-wealth-research/tag/risk-and-return) ### [Negative Interest Rates and the Perpetuity Paradox](https://insights.elmwealth.com/elm-wealth-research/perpetuity-paradox) Nov 19, 2019, 12:00:00 AM November 19, 2019 Risk and Return ## Negative Interest Rates and the Perpetuity Paradox *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-1-3043) *“We are actively competing with nations who openly cut interest rates so that now many are actually getting paid when they pay off their loan, known as negative interest. Who ever heard of such a thing? Give me some of that. GIVE ME SOME OF THAT MONEY. I WANT SOME OF THAT MONEY.”*   – President Donald Trump, Economic Club of New York, November 12, 2019 If President Trump had his way, the US would be sporting significantly negative rates right now. While there is wide-ranging disagreement on the long-term impact of negative interest rates [2](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-2-3043) – good, bad or neutral – there is growing acceptance that negative interest rates are the ‘new normal’ with 30% of the world’s government bonds trading at sub-zero yields, as illustrated in the table below. ### Negative Rates and Ultra-Long-Term Bonds For Wall Street’s bond-pricing models, negative interest rates mostly have been no big deal; the same code usually works just fine when yields are negative instead of positive.[3](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-3-3043) But there is at least one exception, a bond type that cannot abide a negative yield: the Consol bond.[4](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-4-3043) Even though governments don’t issue them anymore, they’re one of the simplest and oldest of all bonds. Also known as Perpetuities, these bonds provide the holder with a fixed interest payment each year in perpetuity. They were issued and re-issued by governments such as the UK, France and the US, and were often the market’s largest and most actively-traded issues. The UK retired their last Consol bonds in 2015, and today there are virtually no government-issued perpetual bonds outstanding. However, there are plenty of other perpetual or near-perpetual cash flow streams investors can buy, and recently issued sovereign bonds with maturities of 50 to 100 years may feel like near-perpetual offerings to many investors. The basic formula for the price of a perpetual is simple: p = c y where symbols represent **p**rice, **c**oupon and **y**ield, for *y \> 0* . Two noteworthy aspects of the formula: 1) for any positive coupon and positive finite price, the perpetuity cannot have a negative yield, and 2) price approaches infinity as the yield of the perpetuity approaches zero. The chart below illustrates the relationship between the price and yield of a perpetuity and annuities with different maturities. Notice how extremely convex these curves become at very low interest rates. This kind of convexity is generally an attractive characteristic for buyers of such investments, and a terrifying one for short-sellers. To avoid having to deal directly with infinity – clearly a price that no-one would be willing or able to pay – we’ll consider a 1,000-year annuity paying $1 per year, rather than a Perpetuity. If we know interest rates are fixed for the next 1,000 years, we can easily calculate and see the annuity’s price on the chart above, but what’s a reasonable fair price given some uncertainty in interest rates? Let’s approximate this value by imagining 1,000 different interest-rate scenarios. Let’s say that, in 999 scenarios, interest rates will equal 2%. But in just one scenario, we’ll assume rates will instead average -1%, in the spirit of the ‘new-normal’ for interest rates and the possibility that interest rates can be negative for sustained periods of time in the future. The Expected Value of the annuity is the probability-weighted average of the Values of the annuity that result from those scenarios, producing a result which is pretty remarkable: | 99.9% probability of 2% rates; annuity value of $50 | | --- | | 0.1% probability of -1% rates; annuity value of $2,316,257 (!) | | Expected Value of the annuity is $2,366, which is a yield of -0.15%.[5](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-5-3043) | ### A Potential Perpetuity Paradox What we’re calling the Perpetuity Paradox is the conundrum facing a person who simultaneously believes that there’s a small chance negative interest rates can persist for long periods of time, but would not pay a price anywhere close to the $2,366 Expected Value of the annuity for more than a de minimis amount. We are not claiming that most people hold these beliefs…but if you do (and we don’t think it’s unreasonable to do so) then you’ve got a paradox on your hands. One solution to this potential paradox is suggested by the resolution to [the St. Petersburg Paradox](https://en.wikipedia.org/wiki/St._Petersburg_paradox), proposed by Daniel Bernoulli in 1738. The St. Petersburg Paradox involves a game that no one would pay much to play, despite the game having an infinite Expected Value. The common thread in both the Perpetuity Paradox and the St. Petersburg Paradox is that what someone will be willing to pay is, in the absence of riskless arbitrage, often determined by their Expected Utility and not the Expected Dollar Value of the gamble.[6](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-6-3043) In working with Expected Utility, we’re going to assume a level of risk aversion typical of 30 of our investors we [surveyed](https://elmwealth.com/measuring-the-fabric-of-felicity/) a year ago. We find that even at a price of just $51 for the annuity a typical investor would optimally invest only 1/2000th (0.05%) of her wealth, even though the price represents a 98% discount to Expected Value.[7](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-7-3043) Much closer to the Expected Value of $2,366, a price of $2,100 merits an optimal investment of only 1/10,000th (0.01%) of wealth. Thus, we can see the Expected Utility line of reasoning presents one resolution to the ‘paradox’: even though the small possibility of negative rates makes the ‘gamble’ on the annuity highly valuable, an ordinary investor wouldn’t bet more than a tiny fraction of wealth on it. Sadly, the UK government can forget about issuing one 1-Pound-per-year inflation-indexed Perpetuity to pay off the entire national debt! ### Conclusion We can’t say how long the new-normal of negative interest rates will continue – but given the negative long-term nominal and real rates we see in a number of major economies, it seems difficult to dismiss negative rates as just a fleeting phenomenon. That means it’s worth seriously thinking through the issues involved in valuing and investing in long-lived cash-flow streams, whether arising from government bonds, real estate or equities, near and below the zero interest rate frontier. Regardless of your position on negative interest rates, we hope this note has illustrated two important and intriguing considerations that impact many important investment decisions under uncertainty: - *Convexity matters:* The Expected Value of long-term cash flows is highly convex, especially in the region of low discount rates. It’s noteworthy, in this case, how only a tiny assumed probability of negative rates has such an enormous impact on Expected Value. - *Utility matters more:* Supply and demand is what sets prices, and in the absence of arbitrage, Expected Utility trumps Expected Value in assessing how much demand investors will have for an investment. --- ### Appendix: Using a Probabilistic Interest Rate Model to Put a Value on a Near-Perpetuity It’s hard to describe how far-out the idea of negative interest rates has been to economists and market participants throughout history. What would Sidney Homer, co-author of the 4,000 year survey *“A History of Interest Rates”* and Salomon Brother’s first director of Bond Research, have made of UK investors’ locking in a 65% loss in the purchasing power of their savings by buying 50-year inflation-linked bond at a yield of -2.03%? [8](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-8-3043) Influential economists and philosophers through the ages, including Marshall, Fisher, von Mises, Hicks, Hayek, Knight, Keynes and Friedman, all wrote books and articles proposing differing theories of interest rates. One common thread was that none of them envisioned negative interest rates as a realistic phenomenon they needed to explain. It wasn’t until the late 1970s that economists started to directly embed uncertainty and randomness into interest rate models, thereby taking account of the convexity of discounted cash flows so central to the Perpetuity Paradox we’re discussing. Since then, many stochastic interest rate models have been proposed, including those by Vasicek (1977), Cox-Ingersoll-Ross (1985), Heath-Jarrow-Morton (1989), Black-Derman-Toy (1990) and White-Hull (1990, 2006). For the case at hand, simplicity and familiarity persuaded us to use a model similar to one that we used at Salomon Brothers, called the 2+ model, in the days when banks were allowed to invest their own capital in proprietary trading.[9](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-9-3043) We’ll use this model to generate 1,000 possible paths for future interest rates, which in turn produce bond prices and corresponding yields. We’ll parameterize the model so that the expected bond prices are roughly consistent with the pricing of German bonds with maturities of 1, 5, 10 and 30 years, taken from Table 1. Below is a description of the model. An important feature is that it allows the short-term interest rate to go as negative as h:   *dx = ƛ dt + 𝞂1 dw1   dy = -ɣ y dt + 𝞂2 dw2   dz = -k (z – x – y)dt   r = ez – h* The chart below shows the value of a $1 a year 1,000-year annuity for each of 1,000 paths we generated with this model, arranged from smallest to largest value, and plotted on a log scale since some of the values are so large. You can see how the Expected Value of the annuity is heavily influenced by a small number of very large expected dollar values, just as we suggested in our two-scenario analysis in the body of the note. This is the distribution of values of the 1,000-year annuity which are consistent with the current market pricing for German government bonds, taking into account the uncertainty around future interest rates and the possibility that interest rates stay negative for prolonged periods, consistent with the new-normal perspective. As noted above, we are using a no arbitrage model of interest rates for this analysis. This means that in theory, if the 1,000 year annuity were trading at a price below the model price, an arbitrageur could buy it and hedge it with other bonds and make a riskless profit equal to the difference between the market and model price of the annuity. There are significant limitations involved in doing this in practice for such a long horizon asset, including transactions costs and frictions in holding the required highly leveraged long and short positions of the hedge portfolio, the necessity of the particular interest rate model chosen to have a form and parameterization which accurately describes how interest rates evolve in the future and the extremely long horizon involved in forcing convergence to the model. Alternative interest rate models will produce charts that can look substantially different than the one above. For example, models that assume interest rates will mean-revert to a fixed and pre-known positive level will not produce paths that put such high values on the annuity, but then we’d suggest that such models are not really in the spirit of the new-normal for interest rates. As discussed above, we believe that Expected Utility analysis is the best tool for figuring out what an individual would be willing to pay for this distribution of outcomes, and thereby resolves the apparent paradox of perpetuity pricing in a future that may experience negative interest rates for sustained periods. --- ### Update: Bloomberg author Brandon Kochkodin wrote a great piece in response to our post on negative interest rates, which you can read by clicking the link below: [***How Negative Rates Can Send Bond Prices Soaring***](https://www.bloomberg.com/news/articles/2019-11-21/ltcm-co-founder-finds-infinite-value-in-bonds-on-negative-rates) Victor also took a moment to talk about negative rates on BloombergTV, watch the full interview below: --- ### Further Reading and References - Black. F.. E. Derman and W. Toy. *“A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options.”*  Financial Analysts Journal. 1990. - Cochrane. John. [*“A New Structure for U.S. Federal Debt.”*](https://www.hoover.org/sites/default/files/research/docs/15108_-_cochrane_-_a_new_structure_for_us_federal_debt_0.pdf)  Hoover Institution. working paper. May 2015. - Cochrane, John. [*“Why Stop at 100? The Case for Perpetuities.”*](https://johnhcochrane.blogspot.com/2019/08/why-stop-at-100-case-for-perpetuities.html)  The Grumpy Economist. August 2019. - Cox, J.C., J.E. Ingersoll and S.A. Ross. *“A Theory of the Term Structure of Interest Rate.”*  Econometrica. 1985. - Dybvig, Philip, Jonathan Ingersoll and Stephen Ross. *“Long Forward and Zero-Coupon Rates Can Never Fall.”*  Journal of Business. 1996. - Heath, David, Robert Jarrow and Andrew Morton. *“Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.”*  Econometrica. 1992. - Homer, Sidney and Richard Sylla. *“A History of Interest Rates.”*  Wiley Finance. 1963. - Hull, John and Alan White. *“Pricing interest-rate derivative securities.”*  The Review of Financial Studies. 1990. - Vasicek, O. *“An equilibrium characterization of the term structure.”*  Journal of Financial Economics. 1977. - Saeedy, Alexander. [*“100 Year Bonds? Why ‘Ultra-Long’ Bonds Have Caught on in 14 Countries and Counting.”*](https://fortune.com/2019/08/23/ultra-long-century-bonds/)  Fortune. August 2019. - LePan, Nicholas. [*“The History of Interest Rates Over 670 Years.”*](https://www.visualcapitalist.com/the-history-of-interest-rates-over-670-years/)  Visual Capitalist. November 2019. --- 1. This not is not an offer or solicitation to invest. **Past returns are not indicative of future performance.**   Thank you to Simon Bowden, John Cochrane, Emanuel Derman, Rich Dewey, Ian Hall, Larry Hilibrand, Costas Kaplanis, Bob Kopprasch, Vlad Ragulin, Jeff Rosenbluth, and Rob Stavis for their comments and suggestions. 2. We’ll use the term ‘interest rates’ to refer to both nominal and real (inflation-adjusted) interest rates, except where we think it’s useful to make a distinction. And, we’ll use ‘yield’ and ‘yield to maturity’ to refer to the IRR which discounts a set of bond cash-flows to a given price. 3. Negative interest rates do imply an arbitrage for investors who can keep cash under the mattress, but this generally doesn’t apply to institutional investors. For investors lacking sufficient mattress space, simple interest rates also need to be greater than -100%, or else borrowing money would be an arbitrage – you would get paid today to receive $1 in the future. Interest rate derivative models have also required modifications to allow for negative interest rates. 4. Originally short for ‘Consolidated Annuity.’ 5. Notice the big difference between the Expected Value of the annuity, and the value of the annuity at the Expected Yield. The Expected Yield of the annuity is 1.997% (99.9% chance it’s 2% and 0.1% chance it’s -1%). The value of the annuity at the Expected Yield of 1.997% is $50, whereas as shown here the Expected Value of the annuity is $2,366. The difference is due to the convexity of the price as a function of the yield of the annuity. 6. This puzzle is also reminiscent of the [Mega Millions lottery](https://elmwealth.com/reflections-on-the-lottery/) that we discussed about a year ago, when we suggested that, ignoring the fun value involved, even a ticket with an Expected Value far in excess of its price warrants only a tiny investment by a risk-averse investor. 7. We assume the risk-free asset earns 0%, and that the investor views owning the perpetuity as a risky gamble to be determined by which interest-rate environment is ‘drawn’ from the distribution. If the investor viewed the 1000-year annuity as her minimum-risk asset of choice, she would want to own substantially more than suggested by this analysis, and we’d need to look elsewhere to resolve this paradox.   We assume the investor displays Constant Relative Risk Aversion (CRRA) with a coefficient of risk aversion of 2.5, about average from our survey. Such an investor would be indifferent to a gamble with a 50/50 chance of a 40% gain or 20% loss in wealth. In the Appendix, we present a slightly expanded analysis using a term-structure model, but we feel that what the above analysis lacks in rigor, it makes up for in simplicity. 8. Very roughly, assuming the bond has a 0% coupon (it actually has a 0.125% coupon), the calculation is *1 – (1 – 2.03%)50 = 64%* . 9. A 1996 paper by Dybvig, Ingersoll and Ross, titled [“Long Forward and Zero-Coupon Rates Can Never Fall,”](https://www.jstor.org/stable/2353247?read-now=1&seq=3#page_scan_tab_contents) discusses the asymptotic behavior of interest rates as time to maturity goes to infinity, and makes a case based on no arbitrage for why long forward rates cannot continually fall. We believe the behavior of long forward rates arising from the 2+ model presented here does not violate the no arbitrage constraint. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/perpetuity-paradox) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/oz-840x420.png) [Featured Insights](https://insights.elmwealth.com/elm-wealth-research/tag/featured-insights) ### [There’s No Place Like Home: The Case For and Against Extreme Home Bias in Equity Investing](https://insights.elmwealth.com/elm-wealth-research/no-place-like-home) Oct 30, 2019, 12:00:00 AM October 30, 2019 Featured Insights ## There’s No Place Like Home: The Case For and Against Extreme Home Bias in Equity Investing *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-1-3002) If you’re a US investor, international equity exposure has never been so readily available at such a low cost. Nonetheless, surveys indicate US investors typically allocate 80 – 85% of their equity holdings to US equities, much higher than their proportion of global market value. [We recently wrote](https://elmwealth.com/home-biased-more-indexing/) about how this kind of “Home Bias” can impact expected returns. Here we turn to evaluating 10 arguments often heard in support of high levels of Home Bias.[2](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-2-3002) ### 1. US equities have outperformed non-US equities by 170% over the past 10 years Ironically, we really couldn’t make the point for international diversification any better than this. Ten years ago, few would have or did put forward this magnitude of US outperformance as a likely scenario, but it happened.[3](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-3-3002) Over long periods of time, individual equity markets can significantly outperform or underperform in ways which are very difficult to predict, though easy to explain ex-post with the benefit of hindsight. Ten years sure feels like a long time, and it’s tempting to conclude that it’s long enough to draw some conclusions about what the next ten years will hold, but if ever there was a place to say it, it’s here: *past performance is not indicative of future returns.* *Sources: Bloomberg, MSCI, FTSE. Emerging Market equities included from December 1989.* ### 2. Over the past 10 years, an internationally diversified portfolio wasn’t anywhere near optimal The theory of diversification is *not* that a diversified portfolio is likely to ever look optimal in hindsight, but rather that it has superior risk/return characteristics looking forward given an uncertain future. A concrete example may be helpful: Over the last 10 years, the portfolio that had the highest realized return-to-risk ratio (i.e. Sharpe Ratio), was a portfolio that had about 20 stocks in it, chosen from all members of the S&P 500.[4](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-4-3002) The reason everyone doesn’t now own just those 20 stocks is that many investors have an accurate sense that it will be a *different* small group of stocks doing the best over the next 10 years. And indeed, the best risk-adjusted “hindsight” portfolio from 1999-2009 is completely different than one from 2009-2019. The idea behind diversifying to own 500 stocks is not that 500 stocks will beat every combination of 20 stocks over any given period. Instead, the problem is we don’t know which will be the best 20 stocks looking forward, and without this knowledge, the diversified portfolio looks better than choosing a more concentrated portfolio. But, if you know the big winners with hindsight, they’ll always look a lot better than owning the diversified portfolio. So too with international diversification. Over any given period, there’s very likely to be one or two markets which significantly outperform the globally diversified portfolio, and in recent years amongst major markets, that outperformer has mostly been the US. That doesn’t reflect a flawed theory of diversification, just a recognition that – in both theory and practice – the benefits of diversification are to be seen through the windshield looking at the road ahead rather than in the rear-view mirror. ### 3. Investors favor the familiar This is completely understandable, but it’s a cognitive bias that can potentially come at a high cost. For most people still in their earning years, their human capital is often their largest asset, and domestic markets are much more highly-correlated with that human capital than are foreign markets. All other things equal, we’d be better off owning things less correlated with our primary asset, the very opposite of this bias. US investors may be especially unaware of this subtle cost of concentration because the history of US equity markets has been so benign in our investing lifetimes. However, US investors in the 1930s or 1970s, Japanese investors in the 1980s, or Russian investors in the early 1900s and late 1990s all received a first-hand lesson in the value of international diversification. ### 4. International equities don’t offer much diversification, because whenever US equities experience a large correction, international equities usually go down as much or more Over short horizons of days, weeks, and months, large moves are indeed typically shared by nearly all public equity markets. This is also true of equities within the same market, yet we intuitively understand that despite this, owning a portfolio of 500 stocks spread out over all sectors of the economy provides meaningfully more diversification than owning just a handful of stocks. While individual equities may often be highly correlated during large moves over short time periods, such as during the 2008 financial crisis, most investors have longer horizons over which these correlations tend to dissipate. This is true of the correlation between US and international equity markets as well, as we see in the chart below: *Sources: Bloomberg, MSCI, FTSE. Emerging Market equities included from December 1989.* A number of studies support the view that international diversification works over the long term as differences in underlying economic, demographic, political, social and regulatory fundamentals between countries and regions make themselves felt in equity market returns. For example, see *[International Diversification Works (Eventually)](https://www.aqr.com/-/media/AQR/Documents/Insights/Journal-Article/International-Diversification-Works-Eventually.pdf)*  by Asness, Israelov and Liew (2010): *“Over longer horizons, underlying economic growth matters more than short-lived panics with respect to returns, and international diversification does an excellent job of protecting investors.”*  Increased globalization has likely led to higher correlations among regional equity markets, but it’s far from clear whether this globalizing trend will continue or start to reverse. There’s also an important point to make about the limits of the historical record: even a long past fails to plumb the depths of possible futures. Many events are possible which have never happened before and don’t show up in any data series. Diversification offers an effective first line of defense against low-likelihood but large-impact scenarios. ### 5. US companies earn a meaningful fraction of revenue internationally, thus investors get international diversification just from US equities US equities do have substantial international earnings. However, all US companies share exposure to a long list of significant US-specific risks — economic, political, financial, regulatory, tax, labor, etc. These are important risks, and non-US stocks can provide diversification from them in a way that US stocks with significant international earnings streams cannot. According to [Morningstar](https://www.morningstar.com/articles/949609/investing-close-to-home-is-overrated), 35% of the revenue of US public market companies came from outside the US in 2018. While this may seem to provide broad exposure to international economic activity, it offers less diversification than it seems. US companies’ international revenues come from big companies in a concentrated set of industries. For example, in 2018, 60% of the revenues of the information technology sector came from non-US markets while the utilities, real estate and financials sectors received just over 10% of their revenues from overseas.[5](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-5-3002) And there are many segments of the non-US economy which US companies hardly touch at all, particularly in less open economies in the developing world. ### 6. Non-US equities are riskier than US equities International equity market returns measured in dollars have been more volatile than US market returns. For example, since 1990, the volatility of US equity returns was 14.5% compared to 17% for non-US equities.[6](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-6-3002) However, this by itself is not an argument against diversification. The three main inputs into the “portfolio optimization” problem are volatility, return, and correlation – and all three matter. There is still a significant benefit from a large non-US allocation if non-US equities are more volatile than US equities, but also offer a higher expected return and diversification benefits through imperfect correlation. The “extra” volatility of non-US equities is known and should already be incorporated into market prices and thus into expected returns. ### 7. US investors spend their savings in dollars, and so they should only invest in dollars to avoid the currency risk associated with non-US equities It’s a useful simplification to split investment assets into two buckets: minimum-risk assets (risk-free assets, in theory) and risky assets. An investor’s base level of expected future spending in retirement should ideally be supported by minimum-risk assets. To the extent that spending is going to be in one’s home currency, then the minimum-risk assets must also be in that currency.[7](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-7-3002) For a risky asset though, the main things that matter for how it fits in a portfolio are its expected return, volatility, and correlation with other investments. For a given level of volatility, return and correlation, it doesn’t matter that some of that volatility comes from currency risk rather than some other source. Hence, US investors should not shun foreign equities just because they are not denominated in dollars, as long as their expected return is sufficient given their contribution to overall portfolio risk.[8](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-8-3002) Additionally, although it may be difficult for US investors to imagine, there are circumstances when being diversified away from one’s domestic currency can be beneficial. ### 8. The US is the greatest place on Earth to invest We agree that the US has been a terrific environment for business and this is likely to continue, but sadly this is no secret and so should already be reflected in the pricing of US equities. If anything, there’s little room for this common view to be strengthened over time, and significant room for it to be weakened. ### 9. Investing in non-US equities is difficult and expensive This certainly used to be the case, but not so much anymore. The expense ratio of Vanguard’s non-US equity index fund (VXUS) stands at 0.09% down from a 0.45% initial average expense ratio for their European, Asian and Emerging Market equity index funds, launched in 1990, 1990 and 1994 respectively. While Vanguard’s US equity index funds with an expense ratio of 0.03% are cheaper than their non-US equity index funds, the gap is quite narrow at just 0.06%. There is still a tax wedge between US and non-US dividends as a smaller fraction of non-US dividends have the preferred “qualified” status, which, for high marginal rate US taxpayers, gives them a roughly 20% lower tax rate than non-qualified dividends. We estimate that the total of expense and tax differences adds up to about a 0.15% extra cost for holding non-US equities. In a simple mean-variance framework, this changes their optimal portfolio weight by about 5%, providing justification for a bit of Home Bias.[9](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-9-3002) ### 10. US equities are about 55% of the MSCI global equity index, so isn’t owning 80-85% of US equities a pretty minor deviation? The major index providers, MSCI and FTSE, include significant “investability” and free-float adjustment factors in their market weights. These adjustments make sense in the context of creating an index which can accommodate the benchmarking of trillions of dollars of investment, but they do have the effect of exaggerating US market weights. The raw, unadjusted global market value weight of US equities is closer to 35%, and it is expected to decline in the future as the developing world catches up with the US, so an 80-85% US allocation represents a dramatic departure from global market-value weights today, and in the foreseeable future. The chart below illustrates the expected gain possible from different levels of international diversification from a US investor’s perspective. It assumes 40% in US equities is the optimal weight, based on unadjusted global market value weighting[10](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-10-3002) while also taking account of the extra expense and tax costs of owning non-US equities. Moving from 100% in US equities to 85% captures only about 40% of the benefit of optimal diversification. Moving further to 55% in US equities captures more than 90% of the total diversification gain available. Notice that the closer we get to the optimal point, the gain curve becomes flatter and there’s less available gain from each 1% change in allocation. ### Conclusion You’ve probably gathered that we don’t find much merit in most of the arguments supporting a high degree of Home Bias in global equity investing. However, as seen in the chart above, there’s a relatively broad range of choices around the optimal allocation which are reasonable and which involve little sacrifice in portfolio quality. Indeed, Elm’s offerings use a Baseline US equity exposure of about 50%, significantly higher than the 35% raw market-value weight while still delivering the vast majority of expected diversification benefits. Some of this adjustment from 35% to 50% comes from the small extra cost associated with holding non-US equities, as described in \[9\] above. Most of it, though, comes from taking into account investor preferences, happily in a way which isn’t significantly sub-optimal. This note reflects how we think about determining our “Baseline” allocation to US and non-US equities. This Baseline serves as the starting point for our dynamic asset allocation approach. Depending on the level of current expected returns for each asset bucket, we vary allocations away from the Baseline.[11](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-11-3002) Some of the above arguments for US Home Bias have been famously made by Warren Buffett, who has received a lot of attention for taking a strong “no-place-like-home” position. Indeed, he’s instructed his heirs to avoid non-US equities completely by taking all their equity exposure through a low-cost S&P 500 index fund. Perhaps he’ll reconsider his advice after reading this note. --- ### Further Reading and References - Asness, Clifford, Roni Israelov, and John Liew. [*“International Diversification Works (Eventually).”*](https://www.aqr.com/Insights/Research/Journal-Article/International-Diversification-Works-Eventually)  Financial Analyst Journal. 2011. - Brinson, Gary and Roger Ibbotson. *“Global Investing: The Professional’s Guide to the World Capital Markets.”*  McGraw-Hill. 1993. - Bryan, Alex. [*“Investing Close to Home is Overrated.”*](https://www.morningstar.com/articles/949609/investing-close-to-home-is-overrated)  Morningstar. 2019. - Dimson, Elroy, Paul Marsh, and Mike Staunton. *“Triumph of the Optimists: 101 Years of Global Investment Returns.”*  Princeton University Press. 2002. - French, Kenneth, and James M. Poterba. [*“Investor Diversification and International Equity Markets.”*](https://www.nber.org/papers/w3609)  NBER. 1991. - Haghani, Victor, and James White. [*“Do US Industry-Sector Weights Explain the Higher Valuation of US vs non-US Equities?”*](https://elmwealth.com/sector-weights-us-vs-nonus-equities/)  Elm Partners. 2019. - Scott, Brian, Kimberly Stockton, and Scott Donaldson. [*“Global equity investing: The benefits of diversification and sizing your allocation.”*](https://www.vanguard.com/pdf/ISGGEB.pdf)  Vanguard Research. 2019. --- 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 Gary Brinson, Jeffrey Rosenbluth, Larry Hilibrand, Antti Ilmanen, Vladimir Ragulin, Rich Dewey, Aneet Chachra and Joshua Haghani for their insightful and helpful comments, and to Paul White of Vanguard for providing us with information about the history of Vanguard’s international equity index offerings. 2. We specifically focus on Home Bias as it relates to equities, as there are very different issues related to international fixed-income markets. We also assume the perspective of a US-based equity investor, though much of what’s said is relevant for non-US investors, especially given that no other market has nearly as large a weight in the global portfolio as the US. 3. Indeed, many financial commentators were even expecting the US would experience a ‘lost decade’ of low or negative equity returns. 4. From 2009-2019, the mean/variance optimal portfolio had 22 stocks in it and a realized, backward-looking Sharpe ratio of 2.4, vs 0.92 for the portfolio of all stocks in the S&P 500 present in the index over the entire period. 5. From Factset report [here](https://www.factset.com/hubfs/Resources%20Section/Research%20Desk/Earnings%20Insight/EarningsInsight_102519.pdf). 6. Annualized volatility calculated from monthly dollar returns. 7. By this criterion, non-US bonds denominated in foreign currency would not be a suitable holding for this bucket. 8. How much expected return one should demand or be willing to give up relating to currency risk depends primarily on the degree to which currency risk impacts the risk of international equities measured in dollars. There are good reasons to expect foreign equity markets to rise when their domestic currency falls, dampening the volatility in dollars, and we tend to see this in normal times. A very mild correlation in the range of 0.15 to 0.25 in this direction is enough to make the impact of currency fluctuations on non-US stock returns in dollars close to zero. However, over the past twenty years, that normal relationship has been overwhelmed by global investors treating the US dollar as a safe haven and flocking to it in times of crisis. If global investors continue to behave in that way, then US investors in non-US equities should expect to earn some compensation for bearing the risk of non-safe-haven currencies. 9. Using a correlation of 0.7 between US and non-US equities. 10. We selected parameters of volatility and correlation of US and non-US equities that would make the unadjusted market value weights be the optimal mean-variance weights. 11. For each asset bucket, the expected return forecast has a long-term component based on valuation, and a medium-term component based on momentum. You can read more about our asset allocation methodology [here.](https://elmwealth.com/about-elm/how-we-invest/) [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/no-place-like-home) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [A Few Quick Responses to Michael Burry’s Index-bubble Remarks](https://insights.elmwealth.com/elm-wealth-research/michael-burry-index-bubble) Oct 4, 2019, 12:00:00 AM October 4, 2019 Investing 101 ## A Few Quick Responses to Michael Burry’s Index-bubble Remarks Burry: “This is very much like the bubble in synthetic asset-backed CDOs before the GFC in that price-setting in that market was not done by fundamental security-level analysis, but by massive capital flows based on Nobel-approved models of risk that proved to be untrue.” - Is there any market in the which the ‘normal’ state is for the marginal buyer to be a value-focused fundamental securities analyst? Even long before ETF and index funds, we’re pretty sure that’s not how most markets ever functioned - Credit ratings agencies made a business decision to rate large swaths of the sub-prime and alt-A CDO market AAA, then used a useful model to justify that decision. We know of no models approved by Nobel prize-winners supporting the idea that home-prices can’t go down, or that mortgage defaults should be uncorrelated in all states of the world - Money being allocated to broad equity ETFs (or active managers, or equities generally) isn’t largely being driven by false belief in any particular model (faulty or otherwise) nor an idea that there’s no risk in equities, it’s being largely driven by cash real rates at 0 and investors making a knowing decision to take more risk vs holding cash Burry: “And now passive investing has removed price discovery from the equity markets. The simple theses and the models that get people into sectors, factors, indexes, or ETFs and mutual funds mimicking those strategies – these do not require the security-level analysis that is required for true price discovery.” - Active managers are still more than 50% of equity funds - Private-equity funds are larger than ever and can take under-valued public firms private - HF long-short funds are larger and more active then ever and can make market-neutral bets of almost unlimited size - If there was truly not enough price discovery, you’d expect large mis-pricings that sophisticated investors could capitalize on: so long-short funds should be having a field day, and private equity funds should find an incredible target-rich environment of great companies under-valued by the public markets. But neither seems to be happening - If passive vehicles were really distorting markets, you’d expect significant discrepancies between public and private valuations, and if there’s a public-markets bubble you’d expect the public market valuation to be much higher. But in fact, many companies are choosing to stay private because they’re getting higher private-market valuations, in an environment where in theory all the private investors are sophisticated securities-analyst types. By way of example, Wework’s latest private valuation was $47B, while now they’re talking about an IPO at more like $10B because the public markets are so much more skeptical of Wework’s fundamentals than the private markets have been Burry: “In the Russell 2000 Index, for instance, the vast majority of stocks are lower volume, lower value-traded stocks. Today I counted 1,049 stocks that traded less than $5 million in value during the day. That is over half, and almost half of those – 456 stocks – traded less than $1 million during the day. Yet through indexation and passive investing, hundreds of billions are linked to stocks like this.” - He seems to be arguing that investors in aggregate should hold a lot less of these small/less liquid stocks than they do, but doesn’t that seem to cut against the idea that these smaller, less liquid stocks are significantly under-valued because of passive investing? Burry: “Potentially making it worse will be the impossibility of unwinding the derivatives and naked buy/sell strategies used to help so many of these funds pseudo-match flows and prices each and every day. This fundamental concept is the same one that resulted in the market meltdowns in 2008.” - We have no idea what this means Burry: “The bubble in passive investing through ETFs and index funds as well as the trend to very large size among asset managers has orphaned smaller value-type securities globally,” - We’d think the proliferation of value and small-cap funds would make investing in smaller value-type securities easier and more widespread than it ever has been, far from orphaning them. Micro-cap names may be getting excluded, but it’s not like micro-caps were easy or common to invest in prior to passive investing either [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/michael-burry-index-bubble) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/home-bias-v2.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [Home Biased: A Case for More Indexing](https://insights.elmwealth.com/elm-wealth-research/home-biased-more-indexing) Sep 25, 2019, 12:00:00 AM September 25, 2019 How Elm Works ## Home Biased: A Case for More Indexing *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-1-2930) Home Bias refers to the tendency to invest more heavily in one’s domestic equity market than global market-value proportions would suggest. When Warren Buffett advises his heirs to put 90% of their inheritance in the S&P 500 and the rest in US Treasuries, that’s an (extreme) example of the kind of Home Bias we’re talking about. At the other end of the spectrum, an investor from Switzerland investing even 10% of her wealth in Swiss stocks would be showing a high degree of Home Bias as well. Whether or not home-biased investing makes sense, the fact is that people in pretty much every country do it. Our question is: if everyone’s doing it, does it matter? Or if everyone equally over-weights their domestic market does it all pretty much wash out, with the over-weights cancelling out the under-weights? Let’s address the question with a stylized thought experiment, based loosely on Home Bias surveys. Such studies indicate that US investors invest 80% – 85% in the US market. In smaller markets, such as the UK and Canada, investors allocate about 50% of their equity investments domestically, an even larger divergence from market capitalization weights, as can be seen by comparison with the chart below.[2](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-2-2930) We start by assuming a world with no home bias, and eleven national markets with a total value of $100: a Big market weighing in at 50% of the total, and ten Small markets representing 5% each.[3](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-3-2930) We’ll also assume that investor wealth lines up with the size of their respective markets. --- Now we’re going to flip a switch and turn Home Bias on: Big market investors now want to be 80% invested in their domestic market, 30% above market cap weight. The ten Small markets exhibit even stronger Home Bias, wanting to be 50% invested in their home market, 45% above their 5% weight. The table below shows how the numbers play out[4](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-4-2930): | | Big Market | **Small Markets (Combined)** | | --- | --- | --- | | Market Value: | $50 | $50 | | Big Investors’ desired allocation: | $40 | $10 | | Small Investors’ desired allocation: | $13 | $37 | | Excess Demand: | $3 | $(3) | By flipping the Home Bias switch we’ve created a supply-and-demand problem: the Big market isn’t currently big enough to take the $40 from domestic investors plus the $13 from the Small investors, as this adds up to $53 and the market-value is only $50. The Small markets in aggregate will have a corresponding shortfall in demand.[5](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-5-2930) We can see that if Big investors want to own 80% of the $50 of their market, then all that’s left for the Small investors combined is $10 of the Big market, so at most they can have a 20% allocation to the Big market. Any greater desired allocation creates excess demand for the Big market. Ultimately, this conundrum must be resolved by market values changing: specifically the Big market going up in value relative to the Small markets. All else equal it would have to go up quite a lot: 60%, from $50 to $80 if we hold the Small markets constant.[6](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-6-2930) The increase in Big market value could be accomplished either through rising prices or through new issuance. If prices rise, this would mean a reduction in the long-term expected return of the Big relative to the Small market of around 1.5% pa, a very sizable impact assuming both markets had expected returns around 4% without the Home Bias distortion. If instead there’s new issuance, such issuance would represent less attractive investment opportunities at the margin than previously outstanding equity, resulting again in lower expected returns for Big market equities.[7](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-7-2930) ### Conclusion We read so much about how indexing is causing distortions in markets, but we’ve seen here how *not* indexing can itself lead to significant distortions. If there were less home bias and more passive investing in line with global market-value proportions, US equity investors would likely enjoy lower relative valuations and higher expected returns. While we agree with Mr. Buffett’s advice to non-professional investors that indexing is the way to go, we wish he’d have encouraged his disciples to take a more worldly perspective. --- 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 Vlad Ragulin, Nir Kaissar, Aneet Chachra and Jeff Rosenbluth for their helpful comments. 2. Figures vary across studies, and most are based on data which is 15-20 years old. For example, see these articles: [Home Bias in Global Bond and Equity Markets (2006 working paper)](https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp685.pdf), [Forbes 2018](https://www.forbes.com/sites/simonmoore/2018/08/05/how-most-investors-get-their-international-stock-exposure-wrong/#28f112a76aac) and this from Vanguard: [The Role of Home Bias in Global Asset Allocation Decisions (2012)](https://personal.vanguard.com/pdf/icrrhb.pdf).   Also, even the fraction of global market cap represented by the US is debated, with some analysts suggesting that 30%, the raw weight excluding free-float and investability adjustments made by FTSE and MSCI, is the more appropriate weight to use. 3. Equivalently, we could have started out with a world with 100% home bias, in which investors allocate 100% of their equity investments to their domestic equity markets. Relaxing the assumption that wealth is proportional to domestic market value will increase (decrease) the imbalance caused by Home Bias if wealth in the Big market is greater (less) than it would be under the proportional assumption. 4. The Big market investors want to put $40 into their home market, leaving $1 to invest in each of the ten Small markets. The Small market investors want to put $2.50 into each of their home markets, and allocate their other $2.50 of investments according to market cap weights – so $1.32 (50/95) into the Big market for a total of $13, and the rest, $1.18, split equally among the other nine Small markets. 5. More generally, with one Big market making up 50% of the total market, and many small ones comprising the other 50%, the Home Bias deviation from market weight in the Small markets needs to be two times the deviation in the Big market to balance out. Any Small market Home Bias less than that results in excess demand for the Big market (and vice versa). The formula for the balancing amount of Small market Home Bias as a function of Big market Home Bias and the Market Weights of the Big and Small markets is: *HBSmall = 1 – (1 – HBBig)(1-MWSmall)/MWBig* where *HB* is Home Bias, and *MW* is Market Weight. 6. This result depends on the choice of starting point and assumptions regarding domestic wealth. One way we can get this result is by making the simplifying-but-imprecise assumption that domestic wealth moves in line with the value of the home market.   Alternatively, we can arrive at this result with the assumption that investors initially exhibit 100% home bias, and that market weights are $50 for the Big market and $5 for the Small markets, and then investors change to wanting to have 80% in the domestic market for the Big investors and 50% in the Small market for the Small investors. To arrive at balance, holding the value of the Small markets constant, the Big market needs to jump to a value of $80. If we allow both the Big and Small market values to change, there are an infinite set of moves of Big and Small markets that would accomplish the balancing, such as Big up 20% and Small down 25%. 7. Another flavor of this resolution is for equity long-short funds to short the Big market and go long the Small markets, but again, this presumably would require an inducement in terms of a positive expected return spread between the Big and Small equity markets. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/home-biased-more-indexing) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/sector-weights-featured-2.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [Do US Industry-Sector Weights Explain the Higher Valuation of US vs non-US Equities?](https://insights.elmwealth.com/elm-wealth-research/sector-weights-us-vs-nonus-equities) Aug 20, 2019, 12:00:00 AM August 20, 2019 Investing 101 ## Do US Industry-Sector Weights Explain the Higher Valuation of US vs non-US Equities? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-1-2777) Global equity market Investors are acutely aware of the tremendous outperformance of US equities versus non-US equities over the past ten years, as illustrated in the chart below. About 2/3 of this 135% cumulative outperformance is accounted for by higher earnings per share growth of US versus non-US equities.[2](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-2-2777) The remaining 1/3 is attributable to the relative change in earnings multiples, leaving the one-year trailing Earnings Yield of US equities at 4.9%, 2% lower than the 6.9% for non-US equities.[3](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-3-2777) The difference in the 10-year cyclically-adjusted Earnings Yield is even wider, at roughly 3%. In a recent conversation we had with [Seeking Alpha](https://seekingalpha.com/article/4277701-asset-allocator-elm-partners-victor-haghani-active-index-investing-podcast) founder David Jackson, he posed a good question: to what extent could the difference in Earnings Yield between US and non-US equities be explained by US market-cap indices being more heavily weighted towards technology companies with high growth potential, while non-US markets lean towards lower-growth natural resource and financial companies? And if sector differences do explain much of the differential Earnings Yield, might we conclude that non-US equities may not in fact offer substantially higher long-term expected returns? [4](https://insights.elmwealth.com/elm-wealth-research/page/5#easy-footnote-bottom-4-2777) The table below addresses this question. Indeed, the US stock market has a 10.9% heavier weight than the non-US stock market in Information Technology companies, trading at a PE of 23.4x, counter-balanced by a roughly 11% lower weight in Basic Materials and Financial Services, trading at a significantly lower PE of about 15x. However, the differences in weights and PEs aren’t enough to explain much of the total difference in Earnings Yields between the broad US and non-US markets. We arrive at this conclusion by applying US industry-sector Earnings Yields to both US and non-US sector weights, and finding the difference in sector weights only accounts for 0.3% of the 2% difference in Earnings Yields between the broad US and non-US equity markets, as shown in bold in the table below. Of course, it’s possible that a deeper dive into the growth prospects of each US and non-US sector might explain more of the difference in Earnings Yields. But, given that sector-makeup differences don’t seem to materially drive total-market Earnings Yield differences, perhaps it’s more likely that the higher valuation of the US equity market is a consequence of factors such as the much faster pace of US stock buybacks as well as the well-documented powerful home-bias of US investors. Long-suffering investors in non-US equities may well be in for still more suffering, but at least they should be comforted that the higher Earnings Yield of non-US equities is not a mirage that disappears when looked at through the lens of industry-sector weights. --- 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. Earnings growth measured in earnings per index unit. 3. Earnings-Yield is calculated as 1/PE. PE data from [Vanguard.com](http://www.vanguard.com/) for VTI and VXUS ETFs. 4. Based on a view that Cyclically-Adjusted Earnings Yield is a good indicator of long-term expected real returns. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/sector-weights-us-vs-nonus-equities) ![](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/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/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/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/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) [3](https://insights.elmwealth.com/elm-wealth-research/page/3) [4](https://insights.elmwealth.com/elm-wealth-research/page/4) [5](https://insights.elmwealth.com/elm-wealth-research/page/5) [6](https://insights.elmwealth.com/elm-wealth-research/page/6) [7](https://insights.elmwealth.com/elm-wealth-research/page/7)