--- title: Elm Wealth Research | Investing 101 (2) description: Investing 101 | Regular Elm Posts (2) --- [![Elm Partners](https://insights.elmwealth.com/hs-fs/hubfs/elm%20logo%20mini.png?width=100&height=100&name=elm%20logo%20mini.png "Elm Partners")](http://elmwealth.com/) Open main menu Close main menu # Elm Wealth Research Select Category Featured Insights How Elm Works In the News Investing 101 Risk and Return Tax Matters Uncategorized Posts about: ## Investing 101 (2) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/049-brainteaser-banner.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [A Brainteaser Double-Feature for the Holidays](https://insights.elmwealth.com/elm-wealth-research/brainteaser-double-feature-holidays) Dec 20, 2017, 12:00:00 AM December 20, 2017 Investing 101 ## A Brainteaser Double-Feature for the Holidays *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-1775) Here are two little puzzles that we discussed at an Elm dinner last week in London, at our favorite local Chinese restaurant. Our guests were sufficiently tickled that we thought we’d write them up to share with you. ### Ali and Hassan: A parable from Vic’s dad Ali and Hassan are antique dealers in the bazaar. Hassan notices a beautiful antique glass bowl in Ali’s shop, which Ali claims he was given by an itinerant dervish in return for a cup of rice. Hassan asks Ali for a price and buys the antique bowl for 10 Rials. The next day, Ali drops by on Hassan for tea and expresses regret at having sold the bowl, and buys it back for 20 Rials. Then Hassan, wishing he hadn’t let it go, buys it back for 30 the next day. This goes on day after day until 47 days later Ali visits Hassan intending to pay 500 Rials to get the bowl back. He looks high and low in Hassan’s shop, but he doesn’t see it anywhere. Hassan explains that a client came in and bought the bowl for 500 Rials. With disgust, Ali curses Hassan: “You donkey! Why did you sell our bowl – we were making such good money from it every day!” *How much money do you think Ali and Hassan individually made, or lost, from all the action? Assume Ali got the bowl for free (a bowl of rice was inexpensive back then).* *How much would each of them have made, or lost, if instead of Hassan selling the bowl to a client, it had fallen off his shelf and shattered into pieces? Assume any debts between Hassan and Ali are paid in full.* *Answers in footnote 2 below.*[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-1775) --- ### The Two-Envelope Conundrum: Stick or Switch We had fun playing this game for real at our dinner. We brought two envelopes, pre-stuffed with cash (Pounds, not Rials) and blank paper so the envelopes looked the same. We explained to our guests that in one envelope was a certain amount, and in the other was ten times that amount. We’d choose someone to play the game and let them select one of the envelopes and take a look inside, and then they’d be given an opportunity to stick or switch to the other envelope. *What would your strategy be? Would you always switch, or always stick, or follow some other strategy?* Before we played the game out, a quick poll suggested most were thinking their strategy would be to always switch, based on the ‘quick’ intuitive logic that a 50% chance of a 10x gain seems pretty good, regardless of the potential loss. However, when we then played the game and the situation became concrete, it turns out our dinner guests thought about the problem quite differently. They saw the cash in the envelope our player opened (20 Pounds, in this case), and compared that to their expectation of the total value they thought we would reasonably stuff in the envelopes. Most players reasoned that we would put 100-200 Pounds in the two envelopes combined, so for an opened envelope with 20 Pounds they would switch, but if there were say 100 Pounds in the opened envelope, they would stick with it. What this shows is that the more thoughtful line of analysis uses the fact that in practice we will have some prior expectation regarding the distribution of the value of the game – that is, how much money might be in the two envelopes combined. In this case, a profitable strategy does exist, which is to switch only if the money found in the first envelope is low enough relative to our prior expectation.[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-1775) And, as always, the investor’s individual risk aversion comes into play in that switching also has to be attractive enough to compensate for the risk involved. Conversation around the table went quickly from these two brainteasers to a puzzle on the minds of many: Bitcoin, crypto-currencies, and the fascinating problem of putting a value on them.[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-1775) The two envelope problem seemed to be relevant to how some of our party were thinking about Bitcoin, in that their plan was to hold on until the chance of another big upward multiple was unlikely. Even if you don’t find either of these two puzzles of relevance to your future investing, we hope they give you and your family some fun around the table this holiday season. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest.   Thanks to Vic’s dad for the Ali and Hassan parable and to Jeff Rosenbluth for his guidance on the two-envelope problem, which he used as an illustration while teaching at the NYU Courant Institute of Mathematical Sciences. 2. The answer to the first question is that together they made 500 Rials, 250 Rials each. Perhaps easiest to see if you think about Hassan selling it for 20 Rials after the first exchange, and then both of them would have made 10 Rials of profit from it. The answer to the second question is that when the dust, and payments between them, settled, Ali would have made 250 Rials and Hassan would have lost 250 Rials. 3. We encourage you to read [this Wiki entry](https://en.wikipedia.org/wiki/Two_envelopes_problem) which provides an excellent treatment. Another path to greater intuition about the problem is to set up a Monte Carlo simulation of the game. 4. Some, like Professor Aswath Damodaran of NYU’s Stern School, argue that Bitcoin can be priced but not valued ([here](https://aswathdamodaran.blogspot.co.uk/2017/10/the-bitcoin-boom-asset-currency.html)). [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/brainteaser-double-feature-holidays) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/047-sharpe-ratio-banner.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [A Brief History of Sharpe Ratio, and Beyond](https://insights.elmwealth.com/elm-wealth-research/a-brief-history-of-sharpe-ratio) Nov 26, 2017, 12:00:00 AM November 26, 2017 Investing 101 ## A Brief History of Sharpe Ratio, and Beyond *By James White and Victor Haghani* [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-2882) Early in the 1950s, academics and investors started proposing in earnest a variety of summary statistics to capture in a single number the quality of an investment. It was recognized that expected return wasn’t quite enough, because two investments with the same expected return could have dramatically different levels of risk. Pretty much everyone agreed that the quality statistic should be something like “expected return/risk”, but the devil was in the details, and especially in the definition of risk. In the 1960s, William Sharpe was a graduate student working with Harry Markowitz on Modern Portfolio Theory and the Capital Asset Pricing Model, work for which they’d later share a Nobel Prize along with Merton Miller. In 1966 Sharpe proposed a risk/reward ratio which he called the “reward-to-variability ratio,” or “R/V Ratio” [2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-2882) defined as: Expected Return – Risk Free Rate Standard Deviation of Return The name didn’t quite stick. Thirty years later, in a paper cheekily titled “The Sharpe Ratio”, [3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-2882) Sharpe himself concedes that his original term, which doesn’t exactly roll off the tongue, never gained popularity. Once he himself suggested referring to the measure as the “Sharpe Ratio,” the term as we know it today fell into common usage. Though the original name wasn’t a hit, the concept was: a measure originally coined in the very specific context of a theoretical model came to be the de-facto standard amongst academics and investors for measuring the risk/reward quality of a wide variety of real-world investments. Today use of Sharpe Ratio in both language and practice is ubiquitous, and naturally critiques of its use are nearly as ubiquitous. Some of the core critiques are: - If Risk is taken to mean Risk of Loss, Standard Deviation and Risk are synonymous only when returns are Normally distributed. Many investments, such as corporate bonds, have asymmetric or fat-tailed return profiles, causing Sharpe Ratio to significantly mis-state the true riskiness of the investment.[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-2882) - Limited historical data can result in a Sharpe Ratio estimate which is significantly biased.[5](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-5-2882) Here we’d like to focus on a separate issue which arose from our note [“Some Clarity on Risk Parity.”](https://elmwealth.com/clarity-risk-parity/) In that note, we said that if unlimited leverage is available to the investor at the risk-free rate, then the optimal portfolio from a risk-adjusted return standpoint will be the one with the best Sharpe Ratio, levered to give the optimal amount of expected return appropriate to the investor’s degree of risk-aversion. For many investors though, unlimited leverage on good terms isn’t feasible,[6](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-6-2882) either because the cost is higher than the risk-free rate, or because the investor just wants to avoid leverage.[7](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-7-2882) For the leverage-constrained investor, is Sharpe Ratio still all we need to look at to determine the best portfolio? As you’ve probably guessed, the answer is no: in the presence of leverage constraints, both Sharpe Ratio and the level of expected return are material factors in determining the portfolio with the best risk-adjusted return. In the chart below, we illustrate this in a simple two-asset case, showing the Sharpe Ratio and Risk-Adjusted Return from each possible combination of stocks and bonds, assuming the investor has a “typical” degree of risk aversion[8](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-8-2882) and her wealth is fully invested:[9](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-9-2882) We can see that the portfolio with the best Sharpe Ratio is about 20%/80% Stocks/Bonds, but the portfolio with the best risk-adjusted return[10](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-10-2882) is about 45%/55% Stocks/Bonds.[11](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-11-2882) We believe allocating assets proportionally to risk-adjusted return is sound investing practice, and in the case of assets which follow a random-walk,[12](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-12-2882) risk-adjusted return is fortunately easy to calculate: Risk-Adjusted Return = Expected Return – 1 2 γσ2 where *γ* is the investor’s level of risk-aversion and *σ* the asset’s volatility. This relationship also gives us a formula for the trade-off between Sharpe Ratio and level of return given a leverage constraint. Consider our 45%/55% optimal un-levered portfolio from above – if instead of investing in this portfolio we were able to earn a higher expected return, but with a lower Sharpe Ratio, how much lower Sharpe Ratio could we bear and still be no worse off in terms of risk-adjusted return? The answer is:   SR\* = R √ γ 2δ + γσ2 where *SR\** is the Sharpe Ratio which gives a fully-invested portfolio having return *R\* = R + δ* the same risk-adjusted return as a portfolio with expected return *R* and volatility *σ.* For a brief thought experiment, consider an asset with expected excess return of 4% and risk of 4% , for a (very good) Sharpe Ratio of 1. The risk-adjusted return of this asset is 3.78%[13](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-13-2882), and optimally, our portfolio allocation would greatly exceed 1, i.e. we’d optimally be highly levered. However, we have a leverage constraint, so instead we just hold our entire portfolio in this asset. Now we’re given the chance to switch into an alternative asset with a somewhat higher expected return of 4.5% – how much lower a Sharpe Ratio would we tolerate to still make the switch? The result is pretty surprising: Here we have a list of hypothetical assets, all of which have the same risk-adjusted return, and we can clearly see the Expected Return/Sharpe Ratio trade-off at work – we’d switch to being fully invested in the 4.5% asset if its Sharpe Ratio is better than 0.62, a material discount from the reference portfolio Sharpe Ratio of 1. ### Conclusion As we can see from our thought experiment, in the presence of leverage constraints two portfolios with dramatically different Sharpe Ratios can be equally desirable. In the case of our stylized stock/bond example, the difference between the highest-Sharpe portfolio and the optimal portfolio is material but not too extreme – only about 0.25% per annum in risk-adjusted return. But this difference can be much bigger depending on your assumptions, especially if some of the assets involved have levered, asymmetric, or structured payouts. Our general point is that for most investors, and especially those with a desire to limit leverage, Sharpe Ratio is a useful and important metric, but doesn’t deliver the full-credit answer. To achieve the best expected risk-adjusted returns, investors with capital or leverage constraints need to think a step further, taking both Sharpe Ratio and the absolute level of their investments’ excess return into the mix.[14](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-14-2882) --- 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. Sharpe, William F. *[“Mutual Fund Performance”](http://finance.martinsewell.com/fund-performance/Sharpe1966.pdf)*. Journal of Business, January 1966, pp. 119-138. (p. 123 in particular) 3. William F. Sharpe, [“The Sharpe Ratio”](https://jpm.pm-research.com/content/21/1/49), Journal of Portfolio Management, 1994. 4. Even relatively “vanilla” markets, such as the Broad US Equity market, can display markedly non-Normal behavior, especially over short to medium time-periods. Over longer time-periods this non-Normal behavior tends to lessen, though there’s still disagreement over whether Normal distributions are a sufficiently good model for long-term returns. 5. Due to sampling error, survivorship bias and the critique above. 6. Or accessing such leverage requires investing through 3rd-party managers with their own fee structures and potential agency issues. 7. Consistent with a focus on capital preservation. 8. We’ll define “typical” here as that degree of risk aversion that would maximize expected utility by investing 100% of savings in a stock/bond portfolio with a 60/40 mix. With our example numbers, this implies a coefficient of risk aversion in the Merton model of ~3 (2.7 is what we use in numerical examples throughout). For readers familiar with the Kelly Criterion, this means our investor is ~3x as risk averse as a Kelly bettor. 9. We’re making a material assumption here that, in the absence of leverage, the investor optimally wants to be fully invested, vs. keeping part of her wealth in cash. That’s definitely not true in general, but in the case of our specific 2-asset example here, it is in fact true. 10. In this context used interchangeably with “Expected Utility.” 11. We assume that stocks and bonds can be described by un-correlated geometric Brownian motions, with stocks having 4% expected excess return and 16% volatility, and bonds having 1% expected excess return and 4% volatility. 12. And investors with Constant-Relative-Risk-Aversion (CRRA) utility. 13. Using the same risk-aversion as above. 14. Your authors like the expected-utility framework for unifying these considerations within a single user-friendly toolkit, but we feel the specific method is less important than the general idea of translating expected returns into risk-adjusted returns before making your investment decisions. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/a-brief-history-of-sharpe-ratio) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/033-best-way-banner-1024x487.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [What’s the Best Way to Get Invested in the Market?](https://insights.elmwealth.com/elm-wealth-research/whats-the-best-way-to-get-invested-in-the-market) Mar 8, 2017, 12:00:00 AM March 8, 2017 Investing 101 ## What’s the Best Way to Get Invested in the Market? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-417) A few friends recently asked me how to go about putting more of their savings into the stock market. Is it better to jump in all at once, to average-in over time, or to wait for a market correction? They’ve been held back by a litany of worries—the durability of this eight-year bull market, the distortionary effects of Quantitative Easing, technological disruption, populist political movements (Trump, Brexit, Le Pen), the potential dissolution of the Euro, pension deficits and demographic time-bombs, to name just a few. I wondered if some of Elm’s recent research might offer fresh perspectives, beyond the useful axiom that “time in the market is more valuable than timing the market.” ### Step 1: Determine your desired long-term allocation One of my father’s favorite jokes was about the village simpleton, Mullah Nasruddin, who was out one sunny morning searching for something in front of his house. A passer-by asked him what he was doing. “Looking for my watch,” he said. After some time looking around, the perplexed onlooker asked him if he was sure that he lost it there, to which Mullah Nasruddin replied, “No, I lost it in my shed, but it’s too dark in there to find it.” In that spirit, let’s think about stock market returns where we have the clearest view – in the long term. With a long enough horizon, equity returns primarily boil down to earnings and dividends, which are easier to predict than sentiment-driven changes in valuation. The cyclically-adjusted earnings yield of the global stock market today is about 5%, and the dividend yield is about 2.5%, which suggests a long-term expected compound real return of about 4 – 5%.[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-417) This is consistent with a [survey](https://elmwealth.com/blog/what-our-market-return-forecasts-really-mean-equity-convexity-and-investment-sizing/) we recently conducted of 120 financially sophisticated friends-of-Elm who on average expected a compound return of 4.2% above inflation for US equities. Given the substantially cheaper valuation of non-US equities, I suspect the survey average would have been 5% if we’d posed the question for global equities. Once you’ve decided on your forecast, the next step is to think about how much you’d like to have allocated to equities given that forecast. To do this, you’ll need to consider the risk of equities and your personal degree of risk aversion.[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-417) We’ve recently circulated three short notes on this topic,[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-417) but it’s also just fine to think about the problem more holistically and intuitively, and arrive at an optimal allocation that feels right without getting too technical. By way of illustration, I expect global equities to deliver a long-term compound expected return of about 5% above inflation, resulting in my personal optimal allocation to equities of about 70%.[5](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-5-417) It’s important to realize this is not a binary decision; your optimal allocation will be higher or lower depending on your forecast of the return of equities, and only if your expected return is zero (or negative) would you want to have no equities at all. ### Step 2: How much to worry about the short term? Unfortunately, there’s a lot of evidence warning us that it’s very difficult to forecast short-term equity returns.[6](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-6-417) It’s true that when equities are cheap, measured by any of the common valuation multiples, their returns over subsequent periods are higher than when they are expensive by those same measures. Although we’re already taking account of this in our long-term forecasts, some investors worry that in the short-term the performance is more exaggerated from the effect of valuation reverting to “fair” value. While we don’t have enough historical data to draw precise conclusions, what we do have suggests that the commonly used valuation multiples don’t give us much extra predictable valuation change in the short term. For example, if we look back over the past 130 years of US equity market experience (using Yale Professor Robert Shiller’s dataset), when PEs were in the highest decile, subsequent one-year real returns were lower than average, but still had a mean positive annual return of 3.4%.[7](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-7-417) This is not to say that you can’t have an expectation that equities are going to go down 10% next year, in which case you really shouldn’t own any equities at all. It’s just that if you do happen to think equities are going down next year, based primarily on equities being over-valued, it’s useful to know that history is not on your side.[8](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-8-417) If your short-term forecast is different to your long-term one, it is the short-term one that should primarily drive your decision.[9](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-9-417) For example, if I thought next year’s return of equities was 3% instead of 5%, then my desired allocation would be 50% rather than 70%.[10](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-10-417) ### The Benefits (and Cost) of Wading in Gently Once you determine the allocation that’s right for you, how should you go about getting there? Most people who ask this question probably already know that cold logic dictates that we should immediately make the adjustment and move our allocation to the optimal point. An incremental adjustment over time, i.e. “averaging-in,” is not financially optimal. However, averaging-in does provide a psychic benefit for those of us (most of us) that are predisposed to seeing the glass as half full when it comes to our past decisions. If the markets go up over the period that we’re averaging-in, then we can be glad we got some of our savings invested at the beginning, and if the markets go down, then we can be comforted that we didn’t invest the full amount right at the start. For example, if an investor put money to work in the stock market over the course of a year in four equal allocations, there would be an 80% chance that at least one of those purchases would be in profit when looking back from the end of the year.[11](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-11-417) Viewed from a slightly different angle, there’s only a roughly 1 in 3 chance that the lowest value of the stock market occurred right at the start of the averaging-in period. ### When does ½ = ¾ ? Building up your allocation to the desired level over time does leave some expected return on the table. But, if you subscribe to the expected utility framework that we’ve recently been writing about, you’ll find that the expected cost is quite low. This is because as we increase our allocation to equities, our expected gain goes up in proportion to our allocation, but the cost of risk grows faster than in proportion to our allocation. In the case of the most popular family of utility functions, it goes up quadratically, that is, in proportion to the allocation squared.[12](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-12-417) In other words, we should require four times the compensation to bear 2 times the risk. This relationship between return and risk results in Expected Utility as a function of our allocation taking the shape of a parabola. As you can see in the chart, the curve flattens out as we approach the optimal point, which means that going the last part of the way to the optimal point doesn’t get us a lot of extra expected utility. Thus, moving ½ way to our optimal allocation gets us ¾ of the value of going the whole way, and going ⅔ of the way to optimal gets us about 90% of the value of going the full distance (see chart again). Recall also that at the optimal point, the risk-adjusted return of our investment is equal to half the gross expected return. Combining these two effects means that averaging-in to your optimal allocation costs relatively little in terms of risk-adjusted return. For example, the expected cost of averaging-in over a year from a 0% to a 50% allocation to equities has an expected risk-adjusted cost of only 0.40%. I suspect this is a cost many investors would find worth bearing to get the comfort of wading into the market gradually. Of course, the cost to you of adopting such an approach will depend on your desired allocation and the averaging-in program you choose. ### Warning: not all averaging-in plans are created equal The averaging-in we’ve been discussing is a disciplined program of investing a fraction of your savings into the market regularly, over a pre-defined period of time.[13](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-13-417) Some investors are attracted to the idea of contingent averaging-in, where they plan to increase their allocation to equities only if they fall below some target price level. The problem here is that the investor is taking the risk of the market going up and never (or at least for generations) coming back down again to the target level, and thereby incurring a very significant opportunity cost. To illustrate, let’s consider an investor who adopts a plan of setting a target 10% below today’s market to take his allocation to equities from 0 to 50%. Assuming an expected compound return of 5% above inflation, and evaluating this to a 10-year horizon, there’s a roughly 1/3 chance that he never gets a chance to invest, and the result is he is incurring an expected, risk-adjusted opportunity loss of about 12% of his savings. This is the expected outcome. For an idea of a worst-case outcome, we need only think about an investor who in early 2009 set a target 10% below the level of the markets, and is still waiting for Godot while investors who averaged-in to the equity markets nearly tripled their investment. ### Conclusion Once you’ve decided on your target allocation to equities, perhaps with greater weight on the long-term return driven by earnings than on predicted short-term expected changes in sentiment, the next step is to decide how to get to that target. Choosing a plan is ultimately a matter of personal preference, as any approach other than moving straight to your optimal allocation is financially sub-optimal. However, some plans are less sub-optimal than others. For example, averaging-in over one year has quite a low expected cost. More efficient still would be to immediately move about 50% of the way to optimal (thereby getting 75% of the benefit) and then moving the rest of the way over the course of a year. At the other extreme, following a contingent plan that only goes into action when the price of equities drops by some threshold amount is a risky approach with a high expected cost. In the end, any plan is a good one if it overcomes the inertia and anxiety that hold us back from our chosen investment destination. And, once we’re in for a while, another powerful human trait, forgetfulness, will make us wonder why we spent as much time as we did contemplating the plunge. --- 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 Jeff Rosenbluth, Vlad Ragulin, Andy Morton, James W. White, Amir Mossanen, Arjun Krishnamachar, Josh Haghani and my colleagues at Elm Partners for their useful comments on this note. 2. Many observers feel the US dividend yield is an under-estimate of the true dividend yield, in that US companies make heavy use of stock buybacks in lieu of traditional dividend payments. For more discussion of the expected return of equities, see our video: [The most important number you won’t find in the Wall Street Journal](https://elmwealth.com/blog/video-the-most-important-number-you-wont-find-in-the-wall-street-journal/). 3. You also need to consider other investment opportunities that are different than equities. For this note, we will assume that the only two assets are equities and some risk-less asset (e.g. US T-bills). 4. [Here](https://elmwealth.com/blog/how-much-of-a-good-thing-is-best-for-you/), [here](https://elmwealth.com/blog/a-sharper-lens-for-sizing-up-nickels-and-steamrollers/) and [here](https://elmwealth.com/blog/what-our-market-return-forecasts-really-mean-equity-convexity-and-investment-sizing/). 5. Using our modified Merton rule, my 70% optimal allocation is consistent with an expected compound real return of 5%, risk of 18% and a coefficient of risk aversion of 3 (i.e. 1/3 the risk tolerance of a Kelly bettor). 6. See, for example, Morningstar and Dalbar’s research showing that time-weighted returns have exceeded dollar-weighted returns of US mutual funds by several percent per year over long horizons. 7. The dispersion around that mean estimate was 18%. There were 160 monthly data points in the richest decile of monthly CAPE. We used overlapping data which further reduces the precision of the forecast, as does our belief that these draws do not come from a stationary distribution. 8. While it is a small dataset, it is interesting to note that in 111 out of the 160 months in this richest decile of CAPE, momentum as measured with reference to the one-year moving average was positive, and in those cases, the average return was 8.1% pa. In the 49 cases of negative momentum, the next year’s return was -7.3%, suggesting that momentum is more powerful a predictor than valuation in the short-term. 9. Under assumptions of stocks following a random walk and an investor with constant relative risk aversion, the asset allocation decision is completely myopic (determined by the short-term expectation). In cases where equities are mean-reverting, or display momentum, the results are different. See work by Merton, Campbell or Kritzman for further discussion. 10. Using the modified Merton rule again. See footnote 4, and substitute 3% for 5%. 11. Calculated via simulation, using the risk and return assumptions previously stated. The four allocations would take place at the beginning of the year, and then every 3 months thereafter. 12. The family known as constant relative risk aversion functions, or CRRA for short. 13. There are several ways to average-in: depending on whether the focus is dollars, fraction of savings or number of shares. In this note, we use fraction of savings as the variable. The other approaches to averaging-in do not materially change the conclusions we reach. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/whats-the-best-way-to-get-invested-in-the-market) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/030-sharper-lens-banner-1024x487.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [A Sharper Lens for Sizing Up Nickels and Steamrollers](https://insights.elmwealth.com/elm-wealth-research/a-sharper-lens-for-sizing-up-nickels-and-steamrollers) Jan 24, 2017, 12:00:00 AM January 24, 2017 Investing 101 ## A Sharper Lens for Sizing Up Nickels and Steamrollers *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-387) In a world of low rates and high stock prices, it’s natural that many investors are looking for ways to earn a good return with limited exposure to equities. However, many candidate strategies have return distributions which are significantly different from the Normal and Log-normal distributions that serve as reasonable approximations for the return profile of most typical portfolio asset classes. They require an upgraded set of tools to analyze and incorporate into our portfolio, maintaining a good balance of risk and reward. As an example, one strategy that we’ve been hearing about a lot recently is buying short-term, high-yielding bonds, particularly financial issues.[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-387) On the face of it, this strategy is appealing: these bonds have 4 – 5% yields, seem unlikely to default, and don’t come with a lot of daily market risk. For investors who feel, as many do, that equities are expensive and will generate relatively meagre returns, these bonds appear to provide a lower-risk alternative without sacrificing yield. However, these bonds are quite different animals from the diversified debt/equity portfolios most investors normally think about, and provide an excellent practical illustration of the shortcomings of the most commonly employed investment analysis heuristics. The first problem is our well-documented tendency, when thinking fast and intuitively, of putting too much weight on highly likely “headline” outcomes and ignoring ones that are very unlikely but extreme.[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-387) We are apt to see the promised return of a 5% bond as the expected return, effectively setting to zero the probability of loss from default. Of course, we know there’s no such thing as a free lunch; 5% bonds can’t be risk-free in a world of 0-1% interest rates. Assuming a 3% probability of losing 65% in a default or restructuring brings the resultant expected return on these bonds to 3%, below the headline yield of 5% but still a healthy 60% of it.[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-387) Using the heuristic of expected return, or even the ratio of expected return to risk (aka Sharpe ratio), can lead to a significant mis-evaluation when applied to a case like this. Neither metric gives us an adequate way to weigh the small risk of a large loss, nor do either tell us how much of these bonds we should optimally hold. What’s needed is a more fundamental and versatile tool, a sharper lens for sizing up the proverbial nickels and steamrollers. Expected Utility fits the bill. It’s a concept that’s been around for a long time, but surprisingly is hardly used by present-day analysts and investors. Tellingly, professional gamblers rely on it heavily (well, those who don’t tend to change profession quickly). It’s the general framework behind the “Kelly Criterion,” a betting and investing guideline used to good effect by Ed Thorp, a pioneer in applying probability theory to gambling and investing, and others such as Warren Buffet and James Simons.[5](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-5-387) The basic idea is that instead of thinking of our wealth in terms of dollars, we’re going to think in terms of how much our wealth is really worth to us, which we call its *utility*. For most of us, increasing the dollar value of our wealth delivers less and less utility. A consequence of this decreasing marginal utility of wealth is that we are risk averse: a loss hurts more than the same gain, and we need to be paid to take symmetric risks. Each person’s risk aversion is a matter of individual preference. Starting to think in terms of utility instead of dollar value can be challenging, but we have no choice: to make better decisions we have to get our arms around it.[6](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-6-387) For the rest of this note, we’re going to assume a level of risk aversion that we think may be typical for high net worth investors. It’s a degree of risk aversion that would leave an investor *indifferent* between accepting or declining a payment of 4% of wealth in order to take a 50-50 risk of making or losing 20% of wealth.[7](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-7-387) So, coming back to these short-term bonds – what’s the expected utility of owning them? The answer depends on what fraction of our wealth we invest in them. Let’s look at this chart of expected value and expected utility as a function of what fraction of our wealth is invested: [8](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-8-387) As you can see, if we put 45% of our wealth into these bonds, we’ve increased our expected utility by the same amount as if we had received a risk-free payment equal to 0.5% of our wealth. A greater or smaller allocation to these bonds is of less utility to us, and beyond a 75% allocation, we’d actually be better off doing nothing at all. As is clear from the chart, expected utility not only tells us the “price of risk” – the difference between the Expected Return and Expected Utility lines in the chart – but it also allows us to determine how much of the asset is optimal to hold. Even better, we can compare across assets with very different distributions, knowing we’re pricing risk consistently. The heuristics of Expected Return or Sharpe ratio are silent on these critical questions and do not allow for appropriately comparing assets with dramatically different return distributions.[9](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-9-387) By linking investment inputs and characteristics to optimal size, Expected Utility also gives us an intuitive framework for translating the *uncertainty* in our assumptions into investment-sizing decisions. Our analysis so far has been highly stylized, but using this utility framework is a good starting point from which to build in more complex, real-world factors. For example, we could extend the analysis to look at a portfolio of these bonds or the full menu of alternative investments, rather than just a single bond. For taxable investors, we’d want to take account of interest being taxed at high ordinary rates, while the periodic capital losses cannot be offset or carried back. A robust analysis might also bring in other factors such as the *timing* of potential losses relative to when those losses hurt the most. To a greater or lesser degree, many popular investment strategies, such as selling puts on the stock market, holding concentrated individual stock portfolios or investing in leveraged hedge fund strategies which don’t or can’t employ tight stop-loss limits, are also good candidates for the application of the Expected Utility framework. Our message here is not that utility is the only thing you need – but rather that for enterprising investors looking at potential investments with highly skewed and/or non-linear return distributions, the standard toolbox of Expected Return and Sharpe Ratio is inadequate. Although Expected Utility analysis is rarely seen in the mainstream, we hope we have illustrated that it is both practical and useful. --- ### Appendix: Variation on a Theme An extension to an interesting and related investment challenge is how to scale a Hedge-fund (HF) investment. In the case of a HF that has an expected excess return of 5% and follows a Brownian random-walk with Sharpe Ratio of 1, then for an investor twice as risk averse as Kelly, expected utility is maximized by investing 1000% of wealth in the HF.[10](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-10-387) This doesn’t pass a basic sanity test, let alone one of prudence! So what’s wrong? Is the utility-corrected lens we’re looking through flawed somehow, or is it that we’re looking at an inaccurate representation of the HF return distribution? We think the lens is fine and that an investment that is fully described by a Brownian random-walk with Sharpe Ratio of 1, with no risk of blow-up, is a truly amazing investment. But, as at least one of your authors can attest, HFs *do* have a real risk of blow-up with low recovery,[11](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-11-387) even if the probability is relatively remote. What does our utility framework suggest once we incorporate this tail risk into our analysis? Let’s now assume that most of the time our HF follows the 1-Sharpe random walk as above, but also has a 0.1% / year[12](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-12-387) chance of blowing up with zero recovery. We can see this is just a slightly more complex variation of the short-term bonds example above. As shown in the chart below this blow-up risk, though very small, has a dramatic impact on the optimal scaling recommendation. Including the small chance of a blow-up yields approximately the same scaling recommendation as for a 0.3-Sharpe Brownian random-walk with a 5% expected return, which is similar to the stock-market. In contrast, including the 0.1%/year chance of blow-up only moves the Sharpe Ratio from 1 to 0.83, a *much* smaller difference than suggested by the utility framework. Here again, we see that for highly skewed or non-linear return distributions, the toolbox of Expected Return and Sharpe ratio is inadequate, and an expected utility analysis is both useful and intuitive. --- 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. These bonds are usually subordinated or issued at the holding company level, or may even be preferred stock. 3. Daniel Kahneman, *Thinking Fast and Slow* (2010). 4. For reference, 3% is the fair-market default rate assuming a 4% equity risk premium and a credit β of 50%. 5. See Ed Thorpe’s *Beat the Dealer* (1966). 6. See one of your authors’ notes for more information on calibrating personal utility, available at SSRN: [“Practical Utility, Risk Aversion, and Investment Sizing”](https://ssrn.com/abstract=2867255). 7. There are many models for utility, but here we use the most common model   U(x) = x1 – n – 11 – n and assume a typical value of *n = 2* for our model investor. In general this leads to betting 50% as much as the “classic” Kelly criterion suggests. This form of utility function is wealth-scale independent. 8. Assuming a 5% 1-year bond with default probability 3%, recovery 35%, and a 1% risk-free rate subtracted out so we can just look at excess return. 9. Assets with dramatically different distributions can have very different utility and intuitively very different risk profiles, but identical Sharpe ratios. 10. Assuming the only investment options are the HF and a riskless bond, and the investment is continuously rebalanced to 1000% of current wealth – generally not a realistic option for HF investments. There’s a classic result that the utility-optimal scaling under these conditions for an asset following a Geometric Brownian random walk is:   κ = μ – rnσ2 = 1000% in this case. 11. A result of the leverage typically employed. 12. Chosen not for perfect accuracy, but to demonstrate the impact of even quite a small blow-up likelihood, in this case 1 HF out of a pool of 1,000 each year. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/a-sharper-lens-for-sizing-up-nickels-and-steamrollers) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/026-overvalued-banner.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [Do Index Buyers Make Over-Valued Stocks More Over-Valued?](https://insights.elmwealth.com/elm-wealth-research/do-index-buyers-make-over-valued-stocks-more-over-valued) Dec 2, 2016, 12:00:00 AM December 2, 2016 Investing 101 ## Do Index Buyers Make Over-Valued Stocks More Over-Valued? For more than 60 years, the capitalization-weighted market portfolio has been a cornerstone of the modern theory of investing. As it inexorably takes its place as a cornerstone of investment practice, it has been subject to a litany of increasingly strident criticisms, such as the recent Sanford C. Bernstein paper, “The Silent Road to Serfdom: Why Passive Investing is Worse Than Marxism.” If the purpose of such notes is to get press attention, they are successful, but if the purpose is to help our understanding of how markets function, they generally fall short.[1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-331) In this note, I want to dispel one frequently voiced myth about indexing, namely that when investors put their money into broad, market-cap weighted index funds or ETFs, it has the unintended consequence of increasing the aggregate mis-valuation in the market, by making over-valued equities more over-valued and under-valued ones more under-valued.[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-331) For example, Timothy O’Neill, the global co-head of Goldman Sachs’ investment-management division, called indexing *“a bubble machine”* which *“guarantees that the most valuable company stays the most valuable, and gets more valuable and keeps going up.”*[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-331) It’s a good story, but on closer inspection, it’s not true. To see why, think of the equity market as being owned by two kinds of investors: a) market cap indexers, who own every equity in the market in proportion to its market capitalization, and, b) active managers, each of whom owns a portfolio of equities that matches his or her assessment of which are the best ones to own or avoid. We can see that while each active manager will own a portfolio that diverges from market cap weights, the holdings of the active managers in aggregate must by definition be in proportion to market cap weights. As William Sharpe explained in his seminal 1991 note, “The Arithmetic of Active Management”:[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-331) by definition, since the portfolio representing the total market and the portfolio of indexers are both capitalization weighted, it follows that active managers have to be capitalization weighted in aggregate too.[5](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-5-331) Let’s dig deeper into these flows that worry the indexing critics. There are two ways that an investor can buy an index fund: a) with fresh money, for example from a pay-check, or b) from the sale of an actively managed holding of equities. In the case of a fresh money purchase, if the seller of the index fund is an indexer too, then the whole index as a package changes hands, and that shouldn’t have any impact on relative prices of individual equities. Furthermore, since it’s spread out over the whole market, an index trade should also have less price impact than an investor buying a concentrated subset of the equity market. If, however, the sale comes from a cross-section of active managers, then the new indexer needs to buy five times as much of a stock that has five times the market cap compared to another. There are two reasons why this should not increase aggregate market mis-valuation: 1) to the extent that this buying has price impact, wouldn’t our best guess be that a stock that is five times as big as another can absorb five times the buying with the same percentage price impact? And, if you don’t agree with that, then 2) assuming that many stocks are mis-valued, why should we expect that big companies are more over-valued in percentage terms than small companies? Isn’t it more plausible that *some* large companies are over-valued and some are under-valued, and likewise for smaller companies? While it is true that an over-valued company has a market value that is larger than its fair value, for any given equity we don’t know a priori whether it is over-valued or under-valued, a subtle but critical distinction. This reasoning was explained in greater depth by Harvard Professor André Perold in a 2007 note defending market cap weighted indexing: “Holding a stock in proportion to its capitalization weight does not change the likelihood that the stock is overvalued or undervalued. The notion that capitalization weighting imposes an intrinsic drag on performance is, accordingly, false.” [6](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-6-331) Let’s turn to the second case, that of an investor who decides to sell his actively managed holdings and move into an index fund. We should only be concerned here if we believe the investor somehow manages to sell the active managers who hold relatively under-valued equities. Even though all active managers think they own under-valued equities, we’ve already shown this cannot be the case in aggregate, because active managers as a group can’t do anything other than own the market index. The intransigent critic of indexing might counter that that the investor who moves into an index fund will tend to sell his active holdings that have performed the worst recently, which would have the effect of pushing those stocks down even further. This argument requires us to believe that the active manager who is doing the worst is also somehow most likely to be the best at identifying under-valued equities. If we believe that investors in actively managed portfolios tend to chase returns (and we do[7](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-7-331)), then the effect of the return chaser moving into an index fund results in less of the pressure that the critic of indexing is concerned about. This is because the return chaser is doing half the chasing by not buying the actively managed portfolio that has done well recently. Better still, by giving up return chasing by becoming an index investor, he will be less likely to cause mis-valuation in the future. In this note, we have used a simplified representation of the marketplace to explain why the argument that investor flows into broad, market-cap weighted indexes make misvalued equities more mis-valued is not correct. Of course, the real world is not so simple; investors frequently use index funds and ETFs to get exposure to narrowly defined indexes, such as utilities or REITs, or as part of active asset allocation approach (see our recent note on [Active Index Investing](https://elmwealth.com/whats-all-the-hoopla-passive-indexers-are-still-a-rare-breed/)). These uses of index products are worthy of attention (and are the main focus of our business at Elm Partners), but they don’t turn the fallacy into a truth in the case of broad, market cap weighted index funds, which has been the focus of this note, and represent the vast majority of index fund and ETF assets. --- 1. See this WSJ [article](http://www.wsj.com/articles/is-indexing-worse-than-marxism-1479857852) (Nov 24th, 2016) by Burton Malkiel (Princeton professor and author of “A Random Walk Down Wall Street”) for a critique of the Sanford C. Bernstein note. 2. In the case of flows into narrowly defined “index” baskets, such as utilities or REITs, as we pointed out in our note [“What’s up with REITs?”](https://elmwealth.com/whats-up-with-reits/) in July, this is better thought of as active management rather than broad market cap indexing and as with all actively managed investing, it can indeed impact relative valuations. 3. James Ledbetter, “Is Passive Investment Actively Hurting the Economy?” The New Yorker, March 9, 2016. 4. William Sharpe, “The Arithmetic of Active Management,” Financial Analysts’ Journal, 1991: *“Each passive manager will obtain precisely the market return, before costs. From this, it follows (as the night from the day) that the return on the average actively managed dollar must equal the market return. Why? Because the market return **must** equal a weighted average of the returns on the passive and active segments of the market. If the first two returns are the same, the third must be also.”* 5. Lasse Pedersen, in “Sharpening the Arithmetic of Active Management”, SSRN.com, (2016), argues that Sharpe’s equality does not hold in general. In the case of a well-constructed, well-managed index, the effects that Pedersen lists are small enough to ignore for the purpose to which we are applying Sharpe’s equality. 6. André Perold, “Fundamentally Flawed Indexing,” Financial Analysts Journal, volume 63, number 6, November/December 2007. Professor Perold was responding to the theory proposed by Robert Arnott (and others, including Jeremy Siegel) that, *“No longer must investors suffer a performance drag by settling for an index that inherently overweights every overvalued company and underweights every undervalued one. With due respect to the pioneers in finance theory and the cap-weighted indexers, there is a better way.”* Page 41: Arnott, Robert. 2006. “An Overwrought Orthodoxy.” Institutional Investor (18 December):36–41. 7. For a more detailed discussion of return chasing, see our research paper on [SSRN.com](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2718428) and this blog post: [Return Chasing Can Be Hazardous to Your Wealth](https://elmwealth.com/return-chasing-can-be-hazardous-to-your-wealth/). [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/do-index-buyers-make-over-valued-stocks-more-over-valued) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/024-biased-banner.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [Lessons from Betting on a Biased Coin: Cool heads and cautionary tales](https://insights.elmwealth.com/elm-wealth-research/lessons-from-betting-on-a-biased-coin-cool-heads-and-cautionary-tales) Oct 26, 2016, 12:00:00 AM October 26, 2016 Investing 101 ## Lessons from Betting on a Biased Coin: Cool heads and cautionary tales *By Victor Haghani and Richard Dewey* [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-306) ### Introduction You’re invited to a talk by a former hedge fund manager who was a partner at a fund that famously flopped about twenty years ago. You turn up, hoping to hear some valuable insights (or at least some entertaining tales) but instead you are offered a stake of $25 to take out your laptop to bet on the flip of a coin for thirty minutes. You’re told the coin is biased to come up heads with a 60% probability, and you can bet as much as you like on heads or tails on each flip. You will be given a check for however much is in your account at the end of the half hour.[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-306) That’s it. Would you feel it was worth your time to play, or would you walk out? How would you play the game? What heuristic or mental tool-kit would you employ? These questions led us to conducting the exact experiment described above. By having participants engage in an activity as simple as flipping a coin, the betting strategy and its evolution are easily isolated for observation. This simple game also turns out to have properties that are similar to investing in the stock market as well as implications for finance and economics education. Below we’ll describe the experiment, how our subjects played the game and the conclusions we draw from the experiment. ### The Experiment Our coin-flipping experiment was played by 61 subjects, in groups of 2 to 15, in the quiet setting of office conference rooms or university classrooms. The proctor for the game outlined basic principles, such as no talking or cooperation and that subjects were not to use the internet or other resources while playing the game. The experiment began when subjects were directed to a URL that contained a purpose-built application for placing bets on the flip of a simulated coin. Participants used their personal laptops or work computers to play the game. Prior to starting the game, participants read a detailed description of the game, which included a clear statement, in bold, indicating that the simulated coin had a 60% chance of coming up heads and a 40% chance of coming up tails. Participants were given $25 of starting capital and it was explained in text and verbally that they would be paid, by check, the amount of their ending balance subject to a maximum payout. The maximum payout would be revealed if and when subjects placed a bet that, if successful, would make their balance greater than or equal to the cap. We set the cap at $250, ten times the initial stake. Participants were told that they could play the game for thirty minutes, and if they accepted the $25 stake, they had to remain in the room for that amount of time.[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-306) Participants could place a wager of any amount in their account, in increments of $0.01, and they could bet on heads or tails. Participants were asked a series of questions about their background before playing and about their experience when they finished. The sample was largely comprised of college-age students in economics and finance and young professionals at finance firms. We had 14 analyst- and associate-level employees at two leading asset management firms. The sample consisted of 49 males and 12 females. Our prior was that these participants should have been well-prepared to play a simple game with a defined positive expected value. ### Optimal Strategy Before continuing with a description of what an optimal strategy might look like, perhaps you’d like to take a few moments to consider what you would do if given the opportunity to play this game. Once you read on, you’ll be afflicted with the curse of knowledge, making it difficult for you to appreciate the perspective of our subjects encountering this game for the first time. So, if you want to take a moment to think about your strategy, this is the time to do it. If you’re a professional gambler, chances are you’ve heard of the Kelly criterion, a formula published in 1956 by John Kelly, a brilliant (if somewhat eccentric) researcher working at Bell Labs. The formula provides an optimal betting strategy for maximizing the rate of growth of wealth in games with favorable odds, a tool that would appear a good fit for this problem. Dr. Kelly’s paper built upon work first done by Daniel Bernoulli, who resolved the St. Petersburg Paradox – a lottery with an infinite expected payout – by introducing a utility function that the lottery player seeks to maximize. Bernoulli’s work catalyzed the development of utility theory and laid the groundwork for many aspects of modern finance and behavioral economics. Dr. Kelly’s paper and the eponymous formula caught the attention of gamblers and investors. It was further developed and applied to casino games and financial markets by Ed Thorp in a series of papers and popular books, most notably *Beat the Dealer* and *Beat the Market.* Following Kelly and Thorp’s initial work, many others – including Murray Gell-Mann – have further developed the theoretical foundations, while notable investors such as Warren Buffett, Bill Gross and James Simons have all reportedly made use of the Kelly formula. The basic idea of the Kelly formula is that a player who wants to maximize the rate of growth of his wealth should bet a constant fraction of his wealth on each flip of the coin, defined by the function *2 \* p – 1* , where *p* is the probability of winning. The formula implicitly assumes the gambler has log utility. It’s intuitive that there should be an optimal fraction to bet; if the player bets a very high fraction, he risks losing so much money on a bad run that he would not be able to recover, and if he bet too little, he would not be making the most of what is a finite opportunity to place bets at favorable odds. While it’s true that the expected value of the game goes up the higher the fraction the player bets, the outcomes become so skewed that a player who exhibits risk aversion will find an optimal betting fraction well below 100%. The odds themselves play a role in the optimal fraction to bet; the more favorable the odds, the higher a fraction one ought to bet. Finally, as the flips are independent random outcomes, the strategy should only depend on the player’s account balance, and not on the pattern of previous flips.[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-306) In our game, the Kelly criterion would tell the subject to bet 20% (*2 \* 0.6 – 1* ) of his account on heads on each flip. So, the first bet would be $5 (20% of $25) on heads, and if he won, then he’d bet $6 on heads (20% of $30), but if he lost, he’d bet $4 on heads (20% of $20), and so on. ### Findings: How Well Did Our Players Play?? *“How did you go bankrupt? Gradually, and then suddenly.”*   – Ernest Hemingway, *The Sun Also Rises*, 1926 Our subjects did not do very well. While we expected to observe some sub-optimal play, we were surprised by the pervasiveness of it. Sub-optimal betting came in all shapes and sizes: over-betting, under-betting, erratic betting and betting on tails were just some of the ways a majority of players squandered their chance to take home $250 for 30 minutes play. Only 21% of participants reached the maximum payout of $250,[5](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-5-306) well below the 95% that should have reached it given a simple constant percentage betting strategy of anywhere from 10% to 20%.[6](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-6-306) We were surprised that one-third of the participants wound up with less money in their account than they started with. More astounding still is the fact that 28% of participants went bust and received no payout. That a game of flipping coins with an ex-ante 60/40 winning probability produced so many subjects that lost everything is startling. The average ending bankroll of those who did not reach the maximum and who also did not go bust, which represented 51% of the sample, was $75. While this was a tripling of their initial $25 stake, it still represents a very sub-optimal outcome given the opportunity presented. The average payout across all subjects was $91, letting the authors off the hook relative to the $250 per person they’d have had to pay out had all the subjects played well. The chart below summarizes the performance of our 61 subjects, who in aggregate wagered on 7,253 coin flips, 59.6% of which were heads. Only 5 of our 61 financially-sophisticated students and young investment professionals reported that they had ever heard of the Kelly criterion. Interestingly, having heard of Kelly did not seem to help two of them: one barely managed to double his stake, and the other one only broke even after about 100 flips. In post-experiment interviews, we found that the notion of betting a constant proportion of wealth seemed to be a surprisingly non-intuitive approach to playing this game. Our results do not offer any indication that participants were converging to optimal play over time as evidenced by sub-optimal betting of similar magnitude throughout the game. How subjects played the game in the absence of employing Kelly was illuminating. Of the 61 subjects, 18 subjects bet their entire bankroll on one flip, which increased the probability of ruin from close to 0% using Kelly to 40% if their all-in flip was on heads, or 60% if they bet it all on tails, which amazingly some of them did. The average bet size across all subjects was 15% of the bankroll, so participants bet less, on average, than the Kelly criterion fraction, which would make sense in the presence of a maximum payout that would be within reach. However, this apparent conservatism was completely undone by participants generally being very erratic with their fractional betting patterns, betting too small and then too big. Betting patterns and post-experiment interviews revealed that quite a few participants felt that some sort of doubling down, or Martingale betting strategy, was optimal, wherein the gambler increases the size of his wagers after losses. Another approach followed by a number of subjects was to bet small and constant wagers, apparently trying to reduce the probability of ruin and maximize the probability of ending up a winner. We observed 41 subjects (67%) betting on tails at some point during the experiment. Betting on tails once or twice could potentially be attributed to curiosity about the game, but 29 players (48%) bet on tails more than 5 times in the game. It is possible that some of these subjects questioned whether the coin truly had a 60% bias towards heads, but that hypothesis is not supported by the fact that within the subset of 13 subjects who bet on tails more than 25% of the time, we found they were more likely to make that bet right after the arrival of a string of heads. This leads us to believe that some combination of the illusion of control, law of small numbers bias, gamblers fallacy or hot hand fallacy was at work. After the game concluded, we asked participants a series of questions, including whether they believed the coin actually had a 60% bias towards heads. Of those who answered that question, 75% believed that was the case. ### How Much Should You Be Willing to Pay to Play? Not only did most of our subjects play poorly, they also failed to appreciate the value of the opportunity to play the game. If we had offered the game with no cap, this experiment could have become very, very expensive for your authors.[7](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-7-306) Assuming a player with agile fingers can put down a bet every 6 seconds, that would allow 300 bets in the 30 minutes of play.[8](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-8-306) The expected gain of each flip, betting the Kelly fraction, is 4% and so the expected value of 300 flips is *$25 \* (1 + .04)300 = $3,220,637* \![9](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-9-306) Given the expected value of the uncapped game is about $3 million, how much should a person be willing to pay to play this game, assuming that he believes that the person offering the game has enough money to meet all possible payouts?[10](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-10-306) Just as is the case with the St. Petersburg Paradox, where players are generally unwilling to pay more than $10 to play a game with an infinite expected value, in our game too, players should only be willing to pay a fraction of the $3 million expected value of the game.[11](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-11-306) For example, if we assume our gambler has log utility (which the Kelly solution implies) and has de minimus investable wealth, then he should be willing to pay about $10,000 to play the game (the dollar equivalent of the expected utility), a small fraction of $3 million, but still a very large absolute amount of money in light of the $25 starting stake.[12](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-12-306) With a capped payout (the game we actually offered) a simple (but not strictly optimal) strategy would incorporate an estimate of the maximum payout. If the subject rightly assumed we wouldn’t be offering a cap of more than $1,000 per player, then a reasonable heuristic would be to bet a constant proportion of one’s bank using a fraction less than the Kelly criterion, and if and when the cap is discovered, reducing the betting fraction further depending on betting time remaining to glide in safely to the maximum payout. For example, betting 10% or 15% of one’s account may have been a sound starting strategy. We ran simulations on the probability of hitting the cap if the subject bet a fixed proportion of wealth of 10%, 15% and 20%, and stopping when the cap was exceeded with a successful bet. We found there to be a 95% probability that the subjects would reach the $250 cap following any of those constant proportion betting strategies, and so the expected value of the game as it was presented (with the $250 cap) would be just under $240. However, if they bet 5% or 40% of their bank on each flip, the probability of exceeding the cap goes down to about 70%. ### Similarities to Investing in the Stock Market *“If you gave an investor the next day’s news 24 hours in advance, he would go bust in less than a year.”*   – Nassim Taleb An interesting aspect of this experiment is that it has significant similarities to investing in the stock market. For example, the real return of US equities over the past 50 years was a bit over 5% and the annual standard deviation was about 15%, giving a return/risk ratio of about 0.33. Many market observers believe the prospective return/risk ratio of the stock market is well below its historical average, and closer to that of our coin flip opportunity, which has a return/risk ratio of 0.2.[13](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-13-306) Of course, there are significant differences, from the binary-versus-continuous nature of outcomes, to the question of risk versus uncertainty when investing in the stock market where no one can tell you the distribution from which you will draw outcomes. Furthermore, most investors believe the stock market is not a successive set of independent flips of a coin, but that there are elements of mean reversion and trending in stock market behavior, and of course, outlier events happen with much higher probability than would evolve from a series of coin flips.[14](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-14-306) Most people we discussed this with felt that there is a fundamental difference between flipping a coin 300 times in 30 minutes, and investing in the stock market where we have to wait 30 years to get 30 flips of the coin. In fact, to the extent that stocks follow a random walk, with both return and the risk we care about, variance, both growing proportionately with time, then horizon should not affect our betting strategy, although it does affect how highly we value the opportunity to play.[15](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-15-306) After the experiment, we discussed Kelly and optimal betting strategies with our subjects. We were left with the feeling that they would play the game more effectively if given another chance. We wonder whether any long-lasting impact could be had on investor behavior through similar discussions of sensible approaches to stock market investing. Perhaps investing in the stock market is much more nuanced and complex than betting on a biased coin, or perhaps it’s easy to stick to a sound, albeit boring, strategy for 30 minutes but impossible to maintain that discipline for 30 weeks, months or years. ### Conclusion *“This is a great experiment for many reasons. It ought to become part of the basic education of anyone interested in finance or gambling.”*   – Edward O. Thorp While we did expect to observe poorly-conceived betting strategies from our subjects, we were surprised by the fact that 28% of our subjects went bust betting on a coin that they were told was biased to come up heads 60% of the time. Before this experiment, we did not appreciate just how ill-equipped so many people are to appreciate or take advantage of a simple advantageous opportunity in the presence of uncertainty. The straightforward notion of taking a constant and moderate amount of risk and letting the odds work in one’s favor just doesn’t seem obvious to most people. Given that many of our subjects received formal training in finance, we were surprised that the Kelly Criterion was virtually unknown and that they didn’t seem to possess the analytical tool-kit to lead them to constant proportion betting as an intuitively appealing heuristic. Without a Kelly-like framework to rely upon, we found that our subjects exhibited a menu of widely documented behavioral biases such as illusion of control, anchoring, over-betting, sunk-cost bias, and gambler’s fallacy. We reviewed the syllabi of introductory finance courses and elective classes focused on trading and asset pricing at five leading business schools in the United States.[16](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-16-306) Kelly was not mentioned in any of them, either explicitly, or by way of the topic of optimal betting strategies in the presence of favorable odds. Could the absence of Kelly be the effect of Paul Samuelson’s vocal critique of Kelly in public debate with Ed Thorp and William Ziemba?[17](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-17-306) If so, it’s time to bury the hatchet and move forward. These results raise important questions. If a high fraction of quantitatively sophisticated, financially-trained individuals have so much difficulty in playing a simple game with a biased coin, what should we expect when it comes to the more complex and long-term task of investing one’s savings? Is it any surprise that people will pay for patently useless advice, as documented in studies like Powdthavee (2012)? What do the results suggest about the prospects for reducing wealth inequality, or ensuring the stability of our financial system? Our research suggests there is a significant gap in the education of young finance and economics students when it comes to the practical application of the concepts of utility and risk taking. The existence of this gap is even more surprising than the poor play of our subjects. After all, can we really blame them if they haven’t received sufficient practical training? Our research will be worth many multiples of the $5,574 winnings we paid out to our 61 subjects if it helps encourage educators to fill this void, either through direct instruction or through trial-and-error exercises like our game. --- ### Further Reading and References: - Choi, James, David Laibson, and Brigitte Madrian. *“Why does the law of one price fail? An experiment on index mutual funds,”* Review of Financial Studies 23(4): 1405-1432 (2010) - Fenton-O-Creevy, Mark, Nigel Nicholson, Emma Soane, and Paul Willman. *“Trading on Illusions: Unrealistic perceptions of control and trading performance.”* (2003) - Friedland, Keinan and Regev. *“Controlling the Uncontrollable: Effects of Stress on Illusory Perceptions of Controllability.”* (1992) - Gilovich, Thomas, A. Tversky, and R. Vallone. *“The Hot Hand in Basketball: On the Misperception of Random Sequences,”* Cognitive Psychology 3. (1985) - Green, Brett and Jeffrey Zwiebel. *“The Hot Hand Fallacy: Cognitive Mistakes or Equilibrium Adjustments? Evidence from Baseball,”* Stanford Graduate School of Business. Retrieved 2016-05-06. - Langer, Ellen J. *“The Illusion of Control,”* The Journal of Personality and Social Pyschology. (1975) - Levitt, Steven. *“Head or Tails: The Impact of a Coin Toss on Major Life Decision and Subsequent Happiness,”* NBER working paper. (2016) - Kelly, J.L. *“A new interpretation of information rate,”* Bell System Technical Journal 35, 917-926. (1956) - MacLean, Thorp and Ziemba editors. *“The Kelly Capital Growth Investment Criterion,”* World Scientific. (2010) - Miller, Joshua and Adam Sanjurjo. *“A Cold Shower for the Hot Hand Fallacy.”* (2015) - Powdthavee, Nattavudh and Yohanes E. Riyanto. *“Why Do People Pay for Useless Advice? Implications of Gamblers and Hot-Hand Fallacies in False-Expert Setting,”* Working Paper (IZA DP No. 6557) (2012) - Rotando, L.M. and E.O. Thorp. *“The Kelly criterion and the stock market,”* American Mathematical Monthly, 922-931. (1992) - Taleb, Nassim N. *“Mathematical Foundations for the Precautionary Principle,”* Working Paper. (2016) - Thorp, E.O. *“Optimal gambling systems for favorable games,”* Review of the International Statistical Institute 37, 273-293. (1969) - Thorp, E.O., 1971. *“Portfolio choice and the Kelly criterion.”* Review of the International Statistical Institute 37, 273-293. (1969) - Ziemba, W.T. *“Response to Paul A Samuelson letters and papers on the Kelly capital growth investment strategy,”* Journal of Portfolio Management, Fall, 153-167. (2015) --- 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. Subject to a maximum payout that you’ll be informed of if you get close. 3. Whether they chose to not play, or did play and went bust or hit the cap. 4. We present the Kelly criterion as a useful heuristic a subject could gainfully employ. It may not be the optimal approach for playing the game we presented for several reasons. The Kelly criterion is consistent with the bettor having log-utility of wealth, which is a more tolerant level of risk aversion than most people exhibit. 5. We define “maxing out” as players who reached at least $200 by the end, and we define “going bust” as those finishing the game with less than $2 in their account at the end. 6. A result we calculated through Monte Carlo simulation. See Section 5 for more detail. 7. In fact, one reason we suspect this experiment was not performed until now is that it is quite an expensive undertaking, even with just 60 subjects. 8. We programmed the coin to be in a flipping mode for about 4 seconds, to create some suspense on each flip, and also to limit the number of flips to about 300. 9. Your opening bet, according to Kelly, would be $5 on heads. The expected gain from that flip would be $1, as there is a 60% chance of winning $5 and a 40% chance of losing *$5 = 0.6 \* 5 – 0.4 \* 5 = $1* . Your capital in the game at the moment you place that bet is $25, so the expected return on capital is 4% (*$1 / $25* ). Each successive flip of the coin will have that same 4% expected return, up until the cap is encountered, or if the subject gets down to $0.04 or less, at which point he cannot bet 20% of his account any more as we limit the subject to betting $0.01 or more on each flip. And that’s just the expected value. If a subject was very lucky, and flipped 210 heads and only 90 tails (admittedly very unlikely), then we’d have owed him about $2 billion! 10. Of course, this is not realistic, as that would be about $14 trillion trillion (*$25 \* $1.2300* ). We suspect that not even the Fed, ECB and BoJ working together could print that much money. 11. As with the St. Petersburg paradox, much of the high expected value of our game comes from unlikely but very big positive outcomes. The skew can also be seen from the fact that the median of the distribution is so much lower than the mean, which arises from the fact that if you bet 20% of your account and win, you go up to 1.2 of your wealth, and then if you bet 20% of that and lose, you now wind up at *1.2 \* 0.8 = 0.96* , or 4% less than what you had. The median outcome of 180 heads (*0.6 \* 300* ) and 120 tails would produce an outcome of only $10,504 (*$25 \* $1.2180 \* 0.8120* ), much below the $3,220,637 expected value. 12. For each flip, the expected utility is *0.6 \* ln(1.2) + 0.4 \* ln(0.8) = 0.0201* , and *exp(0.0201) = 1.02034* , which means that each flip is giving a dollar equivalent increase in utility of about 2% and so for 300 flips, we get *$25 \* $1.02034300 = $10,504* . This is also the median of the distribution, as per above footnote. If we relax the assumption regarding the player having no outside wealth, the amount he should be willing pay can be much higher than $10,000. 13. More precisely, the ratio is 0.204. 14. Perhaps more nuanced, our coin flip game generates a distribution where you make or lose a fixed amount on each flip, whereas many people believe the stock market has more of a lognormal distribution where the positive flip outcome is greater than the loss from a negative flip. That is, stocks may be characterized by outcomes of *ed* and *e-d* , whereas our coin flip has *1 + d* and *1 – d* for outcomes. 15. There are a number of assumptions in this statement, including that we display constant relative risk aversion, a common but certainly not the only representation of risk aversion among classic and modern behavioral models. 16. MIT, Columbia, Chicago, Stanford and Wharton. 17. Ziemba (2016). [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/lessons-from-betting-on-a-biased-coin-cool-heads-and-cautionary-tales) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/021-hoopla-banner-1024x487.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [What’s all the hoopla? Passive indexers are still a rare breed](https://insights.elmwealth.com/elm-wealth-research/whats-all-the-hoopla-passive-indexers-are-still-a-rare-breed) Sep 30, 2016, 12:00:00 AM September 30, 2016 Investing 101 ## What’s all the hoopla? Passive indexers are still a rare breed We’ve just passed the 40th anniversary of the first index fund (Vanguard’s, naturally) and everyone’s talking about how passive indexing is taking over the world. That may be a good or bad thing, depending on your perspective, but a more fundamental question is whether it’s actually a fair description of what’s happening? We think not. Index funds are the offspring of Modern Portfolio Theory (MPT), which tells us that the equity portfolio that provides the most attractive return-to-risk ratio is the Market Portfolio, a market cap weighted index of all equities, everywhere. The theory says we should only invest in equities through this Market Portfolio: any other portfolio choice is simply sub-optimal. The major index fund providers offer funds that give investors direct and simple access to this Market Portfolio, such as Vanguard’s aptly named Total World Stock ETF (ticker VT). If investors were truly indexing as directed by MPT, wouldn’t we expect that these index funds, designed to deliver the Market Portfolio straight up, would attract all, or at least the lion’s share, of the assets of index investors? They don’t. The chart below shows just how tiny these Market Portfolio funds are, when compared to their component building blocks. In fact, they make up well under 1% of the roughly $4tr equity index fund and ETF market. VT, the biggest of these Market Portfolio funds, barely even scrapes into the top 100 largest ETFs in the world. Why are investors doing this? We can’t know what motivates each investor, but since at Elm we are also not investing in the straight-up version of the Market Portfolio, maybe our thinking will be representative of others. In short, while we believe that MPT is a great start for building a portfolio, there are a number of assumptions in the theory that are not realistic and lead us to go beyond a market cap weighted portfolio in constructing our Baseline portfolio, such as public equity markets being incomplete, inefficient, unrepresentative and driven by more than just the single risk factor of Beta. In addition, there are tax and cost benefits in going beyond a single holding of a Market Portfolio fund. We’ve described these in more detail in the box below.[1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-251) ### Conclusion: most index investors are active index investors. While it’s undeniable that passive index products have witnessed great success, and investing has become more democratized as a result, we think it’s a stretch to say that passive indexing is taking over the world. Instead, investors are moving away from traditional, higher cost forms of active management and building more complex, granular and nuanced portfolios themselves using index products. At Elm, this is exactly our approach, which we call Active Index Investing®. If you’ve decided you want to put part of your savings into index funds, but feel you should be able to do better than putting it all into one global market cap weighted fund, then please take a closer look at what we do. You can read more about our approach [here](https://elmwealth.com/blog/our-asset-allocation-methodology/), or feel free to request a [callback](https://elmwealth.com/invest). --- ### Why index investors like us are not investing in Market Portfolio funds **Public equity market is incomplete.** Examples include the under-representation of large asset classes, such as real estate or emerging market equities, the fact that different regions have vastly different proportions of private relative to public companies, and, certain markets may not be freely accessible to international investors like mainland China. **Markets not perfectly efficient.** Market cap weights have a tendency to overweight over-valued markets and underweight under-valued markets. Remember the Nikkei in 1989? **More than just Beta driving returns.** Most investors believe there are other sources of risk premia such as small caps or value stocks. **Home bias.** Investing in one’s home market is more attractive than investing in foreign markets which carry currency risk, may be more costly to hold (e.g. withholding tax inefficiencies) and tend to be less relevant to one’s future consumption.[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-251) An extreme case is Warren Buffett’s recommendation for non-professional investors to hold only the S&P500 for their risk asset allocation.[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-251) Tellingly, Vanguard calls its most popular index fund that invests in only US equities the “Total Stock Market Index Fund,” which is probably not unrelated to why the US national baseball championship is called the “World Series.” **Tax benefits.** Having multiple holdings may allow a portfolio to be managed more tax-efficiently. For example, it provides more opportunities to realize short-term capital losses for US investors. **Cost savings.** These Market Portfolio funds aren’t the most cost effective. Vanguard’s VT is 14bp and iShares ACWI is 33bp. An investor would save 6 to 25 bps in fees by combining a US ETF, VTI @ 5bps, with an x-US developed market ETF, VEA @ 9bps, and an emerging market one, VWO @ 15bps. --- 1. Besides the reasons that we at Elm don’t invest in the cap weighted Market Portfolio as listed in the sidebar, there are other explanations for why index investors are doing likewise. For example, investors may make a sector by sector decision to go passive vs active. Also, many investors are susceptible to **line item bias**, or **naïve diversification**, which is the feeling that the more lines they see on their brokerage account, the more diversified they feel, even if those products are almost identical.   Studies by Professor Richard Thaler and others have found that investors like to spread their investments over many options on the menu, even when some investments are overlapping or even dominated. For example, investors will invest in two S&P500 index funds with different fees. Benartzi and Thaler, Naive Diversification Strategies in Defined Contribution Saving Plans, (2001) and separately, Fisch and Wilkinson-Ryan, UPenn, Why Do Retail Investors Make Costly Mistakes? An Experiment on Mutual Fund Choice (2014). Another reason may be investors may only go passive in certain geographies or sectors where they feel the market is completely efficient, and seek alpha in more niche areas. 2. [Kim Stockton](https://vanguardinstitutionalblog.com/author/kimberly-stockton/) of Vanguard, 2015: *“…the US equity market cap is about 49% of the global equity market, yet US investors have 71% of their assets invested domestically. The U.K. equity market is roughly 8% of the global equity market, yet U.K. investors have about 50% of their assets invested at home. And in Australia, resident investors have a 70% overweight to domestic equities relative to their 3.5% share of the market.”* 3. While it is true that S&P500 companies derive close to 50% of their sales from outside the US, limiting one’s investment to the biggest 500 US companies leaves one pretty far from the Market Portfolio, as it covers less than 50% of companies on a global basis and 80% of total US market cap. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/whats-all-the-hoopla-passive-indexers-are-still-a-rare-breed) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/020-daughter-main-1024x487.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [What I learned from my daughter (about investing)](https://insights.elmwealth.com/elm-wealth-research/what-i-learned-from-my-daughter-about-investing) Sep 5, 2016, 12:00:00 AM September 5, 2016 Investing 101 ## What I learned from my daughter (about investing) My daughter Jessica, a cognitive science major at university, caught me with a fun brain-teaser. It came up in a psychology class she was taking with Professor Phil Tetlock, author of *Expert Political Judgment: How Good Is It?* and leader of The Good Judgment Project. The problem goes like this: A fund of funds manager is telling a prospective client why he should engage him, by the following logic: 1) there are over 10,000 hedge funds out there, but only a small fraction, say 5%, are worth investing in, and 2) therefore you need an expert to sort the wheat from the chaff. Through years of experience and hard work, this manager is just such an expert and can discern the good from the bad with 90% accuracy. Taking his assertions at face value, how convinced should the potential client be by his logic? Of course, your antennae are up and you suspect the obvious answer, that the manager will create a portfolio wherein 90% of the funds are good ones, probably isn’t right. But it’s easy to see how if we think about this casually, we’d probably be taken in by this cognitive bias, known as Base Rate Neglect. What I liked about this problem is that I could imagine a real fund of funds manager actually making this argument, without realizing that in doing so, he’d be hoisting himself with his own petard.[1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-236) As you can see with a moment’s reflection, the high incidence of false positives means we should expect just under 1/3rd of the funds in the portfolio to be good funds. In case you don’t have a moment for reflection, the calculation is in the footnote below.[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-236) True, this is better than how we’d do without expert selection, but it’s probably well under the threshold that we’d require to commit our savings to this manager. And, this is a case where we assume the expert actually is an expert! Normally we see this cognitive bias in cases of medical tests or military intelligence reports, but there are certainly many fitting examples in the realm of investing, where we’re always hoping to identify that rare, neglected gem. This little brainteaser teaches us it’s a lot more challenging than we’re apt to think. --- 1. As you know, I don’t normally draw attention to the difficulties faced by traditional active managers, preferring to focus on the positive attributes of what we’re doing at Elm Partners, but I thought this little puzzle was interesting enough that our readers would want us to violate our policy at least this one time. 2. Imagine the manager inspects 1,000 hedge funds. We’d expect 50 of them to be good ones and 950 to be not so good. Our expert would correctly select 90% of the 50 good ones, or 45, but he’d also incorrectly select 10% of the 950 not good ones, for 95. So, he’d select 140 in total, of which only 45, or 32%, are good ones. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/what-i-learned-from-my-daughter-about-investing) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/019-REITs-II-banner.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [What’s up with REITs?](https://insights.elmwealth.com/elm-wealth-research/whats-up-with-reits) Jul 27, 2016, 12:00:00 AM July 27, 2016 Investing 101 ## What’s up with REITs? *By Victor Haghani* [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-218) REITs have returned 17% in 2016, outperforming the S&P500 by 9%. There are several plausible explanations for REITs’ recent strength, such as this year’s 0.75% drop in long-term interest rates. A more intriguing explanation you may have heard about involves an upcoming change in how REITs are classified in indexes. Given Elm’s focus on index investing, I thought a brief discussion of this story might be of interest. I also provide our current view of REITs, from both a value and momentum perspective. ### Real Estate gets its own sector - REITs getting their own index industry sector will more directly confront equity managers with their underweight holding of REITs - As long as REIT index funds owned by passive investors remain large, active managers in aggregate cannot eliminate their underweight position - With a 10-year inflation-adjusted dividend yield of 3.3%, we see REITs as significantly overvalued - However, REITs’ positive momentum may be a good indicator that we are likely to see further significant price appreciation, even from this point of overvaluation. ### Real Estate gets its own sector On August 31st, S&P Dow Jones Indices and MSCI will reclassify real estate companies out of the Financials Sector to a new Real Estate Sector in the Global Industry Classification Standard (GICS®).[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-218) REITs were originally put into the Financials sector about 20 years ago when REITs were too small to warrant their own sector, and Financials seemed the nearest fit. The creation of this 11th industry sector just for REITs recognizes the tremendous growth in REITs to a roughly $1 trillion market segment[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-218) and the expectation for their continued growth, as more and more real estate moves from private to public ownership.[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-218) REITs become the 11th sector of the S&P500 on August 31st, 2016 ### Impact on Active Equity Managers So why might this index change be responsible for REITs’ recent market outperformance? The explanation starts with the observation that many active equity stock pickers manage their risk by keeping their portfolios within certain tolerances as measured against the GICS industry sectors. For example, they might want to keep their exposure to each industry within a 25% tolerance. With this new change in sector classification, their position in REITs will be explicit for the first time, and the manager might be compelled to buy or sell REITs to bring his portfolio into compliance with its risk limits. The next question is whether active managers, as a group, are under- or overweight REITs relative to their industry weight? According to [research](http://www.bloomberg.com/gadfly/articles/2016-05-09/reits-are-coming-of-age-for-investors) by Morningstar and Bloomberg, actively-managed mutual funds are more than 50% underweight REITs, as shown in the chart below.[5](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-5-218) There are a number of explanations for why these managers under-weight REITs as part of the Financial sector allocations. They may view REITs as being too sensitive to interest rates, too dissimilar to financials, overvalued (see further below for our view on REIT valuation), or just plain boring (aka low beta). In any case, once real estate becomes its own sector, these managers are likely to try to match the real estate weighting in their portfolio more closely to the index sector weight of 3%. How big an effect might this be? Let’s say these active managers decide to reduce their underweight position from 50% to 25%. They would need to buy more than $100 billion of REITs, more than enough to give the sector a very noticeable lift.[6](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-6-218) Actively-managed mutual funds are underweight more than 50% in REITs Source: Bloomberg, Morningstar. Note: Benchmarks based on Russell indices; Funds include open end; Data pulled May 6, 2016. ### Trapped, with no way out? We may not need the Morningstar research to infer that active managers are underweight REITs. Why? Because the REIT sector is one of the most indexed of all individual market segments, making REITs more indexed than other S&P sectors relative to their sizes. REIT index funds own about $100 billion in REITs, or 15% of those in the S&P500. Vanguard’s REIT index fund alone owns about $60 billion of REITs. If we view the market as made up of passive investors who own index funds and active investors who own individual equities, then unless REIT index funds shrink (and recently they’ve been growing), in aggregate, active managers are trapped in an underweight position of approximately $100 billion REITs.[7](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-7-218) A recent academic paper titled “Curse of the Benchmarks” focuses on exactly this phenomenon. It argues that when active managers are measured against market cap weighted indexes, and a sector they are underweight outperforms the rest of the market, the dollar value of their underweight position increases and they are forced to buy that sector. This in turn increases their losses and exacerbates their predicament, leading to more forced buying. We have also written on this topic in our paper on [return chasing](https://elmwealth.com/blog/return-chasing-can-be-hazardous-to-your-wealth/), and drawn a link with how this can result in short-term momentum in stock prices, followed by longer-term reversion to fair value. If anything, this problem is actually more likely to get worse in the near term. Having their own industry sector may further increase the size of REIT index funds. StateStreet, for example, recently created a new sector fund just for real estate, XLRE, which will start off at about $3 billion.[8](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-8-218) The index changes we are discussing were announced in March 2015, so it is possible that much of the price impact has already taken place. However, Morningstar used data as of only a couple of months ago, and since that date REITs have not outperformed the S&P500. This suggests that this story has not yet played out in full. Stay tuned; given the size of positions involved, in the near or medium term, we may be in for some hair-raising appreciation of REITs, and more pain for active equity managers as a whole. ### REITs from a Value and Momentum Perspective Currently, we are slightly underweight versus our Baseline allocation, because we see REITs as significantly overvalued, but with positive momentum that partly reduces our desired underweight. As REITs are required to pay out most of their free cash flow each year, our valuation of REITs focuses on dividends, rather than reported earnings, and we do not factor interest rates into the analysis.[9](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-9-218) We feel that a 4 – 5% real return for the risk of owning real estate through REITs is fair, and a little lower than what we feel is fair for the broad equity market. Our evaluation of a fair return is not based on a historical average return, but rather what we think is fair compensation for bearing the risk of holding those assets, given what we guess is the risk aversion of many high net worth investors. Translating this fair return of 4-5% into a dividend yield leads us to a round number of 6%, as we assume that about 20% of the stated dividend is a return of capital[10](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-10-218), leaving investors with a real return of 4.8% (80% of 6%), assuming that rental income grows with inflation.[11](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-11-218) So how are REITs valued today? They paid a dividend of approximately 3.9% last year. However we like to look beyond just the past year of dividends. The inflation- adjusted dividend yield over the past 10 years is 3.3%. Comparing this 3.3% dividend yield to our fair dividend yield of 6% means that we see REITs as extremely overvalued. REITs would need to fall by 45% in order to deliver a 6% dividend yield, all else equal. Based on valuation alone, we would reduce our Baseline allocation to REITs by 60%. And how do REITs look from a momentum perspective? At Elm, we compute our simple measure of momentum by comparing the current value of an asset to its average over the past 12 months, taking into account inflation and a risk premium. Currently, REITs are firmly in positive momentum territory at +15%, which, by itself, would cause us to overweight REITs by one third relative to its Baseline allocation. However, when combined with our view on their overvaluation, we currently have a roughly one quarter underweight allocation to REITs.[12](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-12-218) Our positioning in REITs is consistent with the view that in the near term, REITs are likely to continue to deliver healthy returns as active managers try to reduce their underweight exposure, while in the long term, REITs will be repriced lower to provide a fair expected long term return, as the demand from passive and active REIT investors is eventually met through the persistent growth in the sector through REITs continuing to acquire privately held real estate. --- ### Further Reading and References: - Bloomberg: [REITs Coming of Age](http://www.bloomberg.com/gadfly/articles/2016-05-09/reits-are-coming-of-age-for-investors) - MarketWatch: [New Real Estate Sector Gives REITs a Home](https://www.marketwatch.com/story/stock-markets-new-real-estate-sector-gives-reits-a-home-2016-05-11) - MarketWatch: [Onetime Event Will Give a Boost to REITs](https://www.marketwatch.com/story/this-one-time-event-will-give-a-boost-to-reits-2016-04-27) - Research Affiliates: [REIT Valuation Methodology](https://www.researchaffiliates.com/Production%20content%20library/AA-Real-Estate-Investment-Trusts-Methodology.pdf) - The Nest: [Tax Treatment of REIT Payouts](http://budgeting.thenest.com/tax-treatment-reit-payouts-22852.html) - Vayanos and Woolley, [“Curse of the Benchmarks”](http://www.lse.ac.uk/fmg/assets/documents/paul-woolley-centre/articles-of-general-interest/DP747CurseoftheBenchmarks.pdf) (March 2016) - WSJ: [When the S&P500 Breaks out REITs](http://www.wsj.com/articles/when-the-s-p-500-breaks-out-reits-you-may-get-a-tax-bill-1467990564?tesla=y) --- 1. Victor is the Founder and CIO of Elm Partners. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest.   Thanks to my colleague Samantha McBride, who did much of the research behind this note, and to my friends Larry Hilibrand, Aneet Chachra, Arjun Krishnamachar, Rich Dewey and Bruce Lafranchi for their useful comments and suggestions. Of course, all errors are my own. 2. GICS is the leading classification system for stock exchange-listed equities worldwide and since its creation, until this change, has divided companies into 10 industry sectors. 3. REITs in the S&P500 have a market cap of about $600 billion. 4. See our [note on REITs](https://elmwealth.com/if-you-want-to-own-property-reits-provide-a-huge-head-start-vs-direct-investment/) published on our blog in April. 5. It is likely that stock pickers who run mandates for large institutions or operate inside hedge funds have been underweight too, but I have not been able to find any research on that question. 6. Assuming the market is 70% active and the total market cap of US equities is $25 trillion, we get *70% \* $25 trillion \* 25% \* 3% = $131 billion.* 7. This also assumes that REIT index funds and ETFs are held mostly by passive investors and not active stock picking managers. 8. XLRE is going to be spun out of StateStreet’s XLF Financial sector fund on September 21st in a mostly non-taxable return-of-capital transaction. 9. I’m often asked the question of why we don’t factor interest rates into this analysis. After all, with interest rates so low, doesn’t that make REITs more attractive? True, REITs may indeed look like good value versus owning 30 year US Treasury bonds, but what we’re trying to decide in our investing is what we think of REITs in and of themselves, not relative to bonds. If we overweight REITs because they are cheap relative to fixed income, but then fail to short fixed income as a hedge (and we do not take any short positions at Elm) then we stand to lose if REITs go down regardless of interest rate changes. We lose even if REITs decline less than the fixed income assets against which we viewed them as cheap. Often, the simplest approach is the best. 10. Historically, about 30% of REIT dividends have been classified for tax purposes as return of capital and capital gain. However, we believe that some of this category actually represents a pass-through of excess depreciation, and so should be thought of as income. Hence, we assume that 20%, not 30%, of the dividend is return of capital. 11. Looking at the historical record, it is difficult to conclude that REIT nominal dividends have kept up with inflation, let alone per capita income growth. Dividends have been quite volatile, making it difficult to discern a trend over the 20 year period of 1996 to 2016. It is likely that nominal dividend growth was tempered by the growth of the REIT sector through acquisitions, where new property purchases were generally at lower yields than existing holdings. 12. *Allocation relative to Baseline = 100% – 60% (value) + 33% (momentum) = 73%* , which is 27% underweight. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/whats-up-with-reits) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/016-REITs-banner-1024x487.png) [Investing 101](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) ### [If You Want to Own Property, REITs Provide a Huge Head Start vs Direct Investment](https://insights.elmwealth.com/elm-wealth-research/if-you-want-to-own-property-reits-provide-a-huge-head-start-vs-direct-investment) Apr 20, 2016, 12:00:00 AM April 20, 2016 Investing 101 ## If You Want to Own Property, REITs Provide a Huge Head Start vs Direct Investment *By Victor Haghani* [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-1-495) If you’ve decided you want to allocate some of your savings to real estate, you may want to compare the merits of publicly listed REITs, like Vanguard’s (VNQ), versus investing in buildings directly, through private investment partnerships.[2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-2-495) At Elm Partners, we use REIT ETFs, particularly Vanguard’s VNQ and VNQI, for US and non-US property exposure in our globally diversified portfolios. The many individual benefits of REITs add up to a surprisingly big head start over private investment vehicles. While discerning private investors should be able to identify individual properties with higher returns than the average REIT-owned property, they need to generate returns about 4% higher just to catch up with the efficiencies of REITs. As detailed in the table below, this 4% comes from four main sources: higher costs, higher taxes, less diversification and lower liquidity of private investments. This 4% hurdle translates into an 8% hurdle for return on equity when the property investment is 50% leveraged with debt.[3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-3-495) A major worry of REIT investors is that it’s impractical to analyse all the individual holdings, resulting in the risk of buying real estate at a substantial premium to fair value (NAV). Unfortunately, US REITs are not required to give an estimate of their NAV and so we have to rely on several specialist research companies to make those estimates. As you can see in the chart below, over the past 25 years REITs have averaged a 4% premium to NAV, within a wide range of a 45% discount in 2009 to a 35% premium in 1997. Given the enormity of the task of valuing thousands of properties without specific, inside details about each property, we shouldn’t expect these third party NAV estimates to be very accurate. Indeed, it appears that the divergences may be exaggerated by the NAV estimates lagging public market price moves. Making a simple adjustment for this lag reduces the volatility of the divergence from NAV by about 40%, and brings the average to a 1% premium, as shown by the black bars. I didn’t list this as a cost or benefit of REITs vs private holdings, because, depending on timing, this could reduce or enhance returns. To flesh out a plausible negative scenario, let’s assume an investor bought REITs at a 10% premium and sold them 15 years later a 10% discount. That would cut the REIT head start of 4% a year down by only about 15%, in terms of the required return on the underlying unleveraged property investment. The return reduction could turn out to be even less than that, because when REITs trade at a premium to NAV, it is possible for them to add to their property portfolios by issuing shares to private sellers, and thus the premium to NAV can come down without harming returns. I’d be remiss if I didn’t list any benefits of holding property directly. Some argue that illiquidity can be a blessing in disguise, forcing investors to hold for the long term. Ignorance of daily price fluctuations may make the private investing experience more blissful too. Indeed, it may be that many large fortunes have arisen from people feeling “locked” in to the companies they built or the properties they bought. Property investors also derive comfort and psychic value from the tangibility of their property investments, and the ability to touch and see their investments may make their investments feel less risky than more abstract and indirect holdings through REIT ETFs. Finally, while REITs may be the dominant structure for delivering passive real estate exposure, private capital may remain the preferred structure for certain activities such as development and aggregation, even if ultimately for sale to REITs. The benefits of REITs are already well known. Investors have been enthusiastically voting for REITs with their investment dollars, bringing the value of REITs close to $1 trillion. REITs currently own about 1/8 of commercial real estate in the US, up from less than 1% in 1990.[4](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-4-495) REITs are on track to own over 50% of all US commercial real estate by 2040 even if these trends slow down by half. I hope this note has been helpful in cataloguing and attempting to quantify the relative merits of REIT vs private ownership, summing up to a 4% hurdle that privately owned properties need to exceed relative to REITs. In a future note, I’ll address the more fundamental question of the long-term expected return of real estate given today’s valuation levels. ### Table: Comparison of REIT vs private real estate investing | 0.7% | **Avoiding transactions costs**. Typically, when buying a building, an investor will incur about 5% as brokerage, legal, transfer tax and other fees, and loan arrangement fees of 2%, which together equate to about 0.6% pa over the 15 year investment horizon we assume throughout this analysis.[5](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-5-495) When investing in a REIT, these costs have already been paid. | | --- | --- | | 0.5% | REITs typically have **lower borrowing costs.** I assume REITs can borrow about 1% more cheaply from banks than private borrowers on individual properties. | | 0.9% | REITs generally benefit from **lower management costs** due to economies of scale, and lack of carried interest. This calculation assumes REITs have 0.5% lower management fees and no 15% carried interest. The cost savings can be much higher in the case of small properties managed by the investor, if the investor were to accurately bill himself for the value of his time. | | 0.6% | **Tax savings** will vary depending on the characteristics of the investor and the site of the property. One benefit of ownership through a REIT is that income that is passed out as dividends are not subject to state (or city) tax, in most states. For high tax sites, like NY or CA, this can amount to a tax saving of 10% of income, assuming that the ultimate investor is in a low or no tax state. REITs allow for longer term holding than private investments, as the manager usually has an incentive to realize gains to be paid his incentive fee. A further potential saving is that private ownership structures usually throw off miscellaneous itemized deductions which many high rate US taxpayers cannot deduct.[6](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-6-495) For non-US investors, the tax savings of REITs over direct investments might be 0.8% greater. [7](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-7-495) | | 1.0% | Substantial **diversification** is provided by REIT ETFs, such as (IYR), (VNQ), (SCHH) and (RWR), which hold over 100 individual equity REITs. These REITs in turn provide ownership in thousands of properties in different locations and of different types, many of them large properties in prime locations that would be hard for most investors to access through private ownership. I estimate this effect perhaps over-simplistically by assuming a private portfolio will be 25% riskier than a diversified REIT ETF, and so the investor would need to get 25% more return for bearing that risk. | | 0.5% | **Liquidity**: REITs are liquid. Private property takes time to transact, and the decisions to buy or sell may depend on the desires and personal circumstances of the manager of the property or other investors in the private deal. REITs are easily marginable, which allows investors to efficiently raise temporary liquidity. Listed options markets that have developed around REITs give investors even greater flexibility. An overview of the academic literature on pricing illiquidity by A Damodaran of NYU suggests a number much higher than 0.5%, but I am sympathetic to the notion that liquidity is valuable but over-priced by the market.[8](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2#easy-footnote-bottom-8-495) | | **4.2%** | **Total Head Start of REITs vs Private Ownership** | --- 1. Victor is the Founder and CIO of Elm Partners. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest.   Thanks to Chip Parkhurst, who did much of the research for this note as a summer intern at Elm Partners, my friend Larry Hilibrand for invaluable help from start to finish, and my colleagues at Elm Partners. 2. In this note, I am using the term REIT to refer to publicly traded equity Real Estate Investment Trusts in the US. There are other types of REITs and also there is a large and growing non-US REIT market. 3. REITs are one of the most indexed of all market segments, with Vanguard, Blackrock and StateStreet owning about 30% of the large REITs, twice the ownership level in other large US equities, mostly for their index broad market and REIT index offerings. StateStreet recently created a new sector fund just for real estate, XLRE. Expense ratios for REIT ETFs range from 0.07% for Schwab’s (SCHH) to 0.43% for iShares (IYR). 4. Size of US commercial real estate market according to this [study](https://www.sandiego.edu/business/documents/sizeofthemarketdraftApril26.pdf) was $10T in 2009, which I assume has grown to $12T today. Size of REIT market cap and leverage ratio from [REIT.com](http://www.reit.com/data-research/data/industry-snapshot). REIT market ownership from 1991 based on the rate of growth of market cap of REITs being 22% and the NAREIT REIT price index growing at 4.7% pa over the period. 5. Further assumptions are 5% initial property yield, growing 2% a year, and leverage of 50% at a rate of 4%. 6. For this calculation, I assumed 5% lower tax rates and that 33% of management expenses are non-deductible for the private investor. 7. Investing through a REIT ETF such as IDUP LN can eliminate capital gains tax, reduce the income tax rate by over half to 15% and eliminate the drag of non-deductible miscellaneous itemized deductions. This should not be taken as tax advice. 8. [“The Cost of Illiquidity”](http://people.stern.nyu.edu/adamodar/pdfiles/country/illiquidity.pdf) (see page 27 in particular). [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/if-you-want-to-own-property-reits-provide-a-huge-head-start-vs-direct-investment) [1](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101) [2](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/2) [3](https://insights.elmwealth.com/elm-wealth-research/tag/investing-101/page/3)