--- title: Elm Wealth Research | How Elm Works description: How Elm Works | Regular Elm Posts --- [![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: ## How Elm Works ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/EPAEP-840x420-1.jpg) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [Introducing the Elm Partners All-Equity Portfolio For Non-US Investors](https://insights.elmwealth.com/elm-wealth-research/epaep) Apr 6, 2020, 12:00:00 AM April 6, 2020 How Elm Works ## Introducing the Elm Partners All-Equity Portfolio For Non-US Investors *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-3287) Encouraged by some of our investors, we are introducing a new fund for non-US investors, the Elm Partners All Equity Portfolio (EPAEP). EPAEP will have a Baseline of 100% Global Equities, in contrast to our current Global Balanced Fund which has a Baseline of 65% Global Equities, 5% Commodities, and 30% Global Fixed Income. The Fund will be managed algorithmically with a dynamic asset allocation driven by valuation and momentum, in line with the Active Index Investing® approach we’ve applied since 2012 to our Global Balanced portfolios. EPAEP will use low cost ETFs, will charge our standard 0.12% per annum management fee and will maintain our usual focus on cost and tax efficiency. The Fund will be long-only, un-levered, and will always have a target of being fully invested in global equities. This note describes details of the asset allocation methodology, implementation and historical return simulation. Please feel free to email [info@elmwealth.com](mailto:info@elmwealth.com) or set up a [call](https://elmwealth.com/contact-us/schedule-a-call/) with us if you’d like to learn more or request a Prospectus. ### Target Investor Group The All-Equity Fund is designed for non-US investors who want Elm’s global diversification and value-and-momentum approach to equities, but who want a relatively constant amount of equity exposure or want to manage their cash and fixed-income assets on their own. In contrast, Elm’s Global Balanced Fund is designed for investors who want Elm to dynamically manage their exposure to equities versus fixed-income, with a balanced 70%/30% Baseline Asset Allocation as the starting point. This may be suitable for investors who want Elm to manage a meaningful fraction of their liquid wealth, who want to be more hands-off with their asset allocation, and who want an investment program with a risk level that varies through time as a function of the attractiveness of available investments. Investors can also invest in both the Global Balanced and All-Equity Funds to achieve a Baseline risk level in between that of the two funds. This may be suitable for investors who want the dynamic risk level of a Balanced program, but who have a tolerance for a higher level of variability and expected return. With the normal caveats about past returns not being predictive of the future, simulated historical returns for the All-Equity program over the past roughly 40 years had about 50% more variability and 20% higher real returns than did the Global Balanced strategy, as described more fully in the Historical Simulation section below. ### Background Elm’s Active Index Investing® attempts to combine the best features of active investing and index investing to deliver superior long-term risk-adjusted returns. We do not follow the market-cap-weighting regimes of MSCI or FTSE, but rather we systematically construct our own Baseline Asset Allocations which we feel are more representative, diversified and risk/return efficient. We then add a dynamic overlay to our Baseline, following the principle that allocations should be proportional to forward-looking expected real returns, and drawing on value and momentum as the two primary indicators of expected returns. Allocating proportionally to expected real return has deep roots in Samuelson and Merton’s work on Decision-Making Under Uncertainty starting in the early 1960s,[2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-3287) and commonly used applications such as the Kelly Criterion. In turn, the value and momentum perspective was popularized by Asness, Moskowitz and Pedersen in their seminal “Value and Momentum Everywhere” paper, and by our own research including “A Case Study for Using Value and Momentum at the Asset Class Level,” in the Journal of Portfolio Management, which traced this market phenomenon back to 1925.[3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-3287) We use a value-and-momentum-driven approach to asset allocation because we believe that: - Simple valuation metrics like the Cyclically-Adjusted Earnings Yield of a broad equity market are robust predictors of the market’s long-term expected real return, - Momentum is a good medium-term predictor because investors have a tendency to extrapolate future market returns from recent historical samples, which results in trends generated by “return chasing” behavior, and - Value and momentum signals often yield offsetting recommendations, which makes them more effective when used together than individually. We are attracted to broadly diversified, rules-based investing which index products tend to facilitate, and to the cost and tax efficiency of index products. One of our core principles is to focus on costs, and you can see our note [here](https://elmwealth.com/a-penny-saved-is-two-pennies-earned/) on why we think reducing costs is even more important than meets the eye to maximizing investor risk-adjusted returns. ### Methodology We start by constructing an All-Equity Baseline portfolio intended to be more representative of the Global Market Portfolio than the adjusted-market-capitalization indexes of MSCI and FTSE, with a moderate “home bias” preference for OECD non-US investors. The process is the same as applied to constructing our Global Balanced Baseline, except in the All-Equity Baseline we put a 0% weight on fixed income assets. The next step is to determine, at each portfolio rebalancing date, desired deviations from the Baseline weight of each asset bucket using a combination of a valuation metric and a momentum indicator. This is also done largely in the same way as we do for our Global Balanced program, with several modifications to fit the context of an All-Equity portfolio. Most significantly, we normalize the target weights so that they always sum to 100%, and we also impose a constraint that no bucket’s target weight can be more than twice its Baseline weight.[4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-3287) We measure momentum for each asset class relative to the return of the Baseline[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-3287) and we’ve reduced the intensity of the value signal to counter the amplification which can result from the target weight normalization process.[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-3287) The table below shows the Baseline weights and the desired targets as of March 31, 2020. You can find more detail on our Baseline construction and value and momentum overlay [here.](https://elmwealth.com/our-asset-allocation-methodology/) ### Implementation We will manage EPAEP using Elm’s proprietary Ulmus portfolio management system, and will rebalance the portfolio twice monthly. We expect portfolios to have weighted average expense ratios (excluding Elm’s 0.12% pa management fee) in the range of 0.10 to 0.12% per annum, and over time we expect ETF fees to decrease even further. The table below shows a sample of the instruments we intend to use to build the Fund’s portfolio, though many more instruments are in our database for consideration and possible use. The Fund has monthly liquidity, on the last business day of each month with at least 3 business days notice. ### Historical Simulation As usual, we stress that historical data on its own is not sufficient to establish that an investment strategy such as the one outlined in this note is a good one. We are firm believers that past returns are not indicative of future performance. However, history can lead us to conclude that a strategy is poor, and it is with that perspective that we look to the past. The chart below shows a simulated back-test from December 31, 1974[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-3287) to September 30, 2018. Our All-Equity program’s dynamic value and momentum overlay added 1.3% pa of extra return with no material increase in volatility, sampled monthly, versus the returns of a static weight All-Equity Baseline portfolio. This is in line with what we would have expected given that the value and momentum overlay applied to the Global Balanced Baseline increased returns by 2.7% a year with no material increase in volatility over roughly the same historical period, as we reported in our 2016 Journal of Portfolio Management [paper.](https://elmwealth.com/wp-content/uploads/2017/06/A-Case-Study-for-Using-Value-and-Momentum-at-the-Asset-Class-Level.pdf) This makes sense as the Global Balanced portfolio has more flexibility to vary its asset allocation compared to the All-Equity program. The variability of the difference in returns between the dynamic and static All-Equity portfolios was 1.9% pa, sampled monthly, suggesting a Sharpe Ratio for the dynamic versus static strategy of 0.7 over the full period. This is consistent with the finding that the value and momentum overlay resulted in outperformance 60% of the time to a monthly horizon. However, as we’d expect, to a longer-term horizon of five years the outperformance was more consistent, occurring in 97% of 466 rolling five-year periods evaluated at the end of each month. This is shown in the chart below. The final chart shows the simulated historical desired asset allocation of the dynamic value and momentum asset allocation. Portfolio turnover over the period averaged 60% per annum. In practice we expect lower turnover, as rebalancing would be every 40 days rather than monthly and we generally do not rebalance every bucket back to its exact desired weight. ### Back-test Assumptions and Details In order to simulate returns from 1975, we had to make a number of simplifications to the strategy owing to some data not being available over the entire history. Going forward, we would update the Baseline weights annually, but in this back-test we have kept them fixed at today’s Baseline weights. However, we do not think this has a material effect on the performance of the value and momentum dynamic overlay relative to the Baseline. Also due to limitations of the available data, the buckets we’ve used for the back-test are not a perfect match of the buckets we will divide the portfolio into going forward. For example, the back-test does not include some buckets that we intend to use in the program in the future, such as low Price/Book and small cap buckets, and on the other hand the back-test has a more granular split than we intend to use going forward, with Europe split into Europe x-UK and UK and Developed Asia split into Developed Asia x-Japan and Japan. Return figures include a 0.3% per annum reduction in the dynamic All-Equity strategy for transactions costs, fees and non-recoverable foreign withholding taxes, 0.2% for the static Baseline and 0.15% for the MSCI All Country World index to May 31, 2008, and afterwards we use the total return of the iShares ETF ACWI. We assumed rebalancing back to target each month-end rather than every 40 days. We used the same Cyclically-Adjusted Earnings Yield centering point of 6% for all regional equity markets. In most other details, we generally made choices that would make the back-test consistent with how we have implemented our Global Balanced strategies. We stress again that this historical data should not, by itself, be the basis for making an investment decision. The results suggest that an All-Equity program like we’ve conceived has been historically sensible. Still, the All-Equity program is primarily designed for investors who already like this style of investing on principle and would like Elm to provide a sophisticated and efficient implementation. ### Finally… Please be in touch with any questions or suggestions. You can request a short presentation and fund Prospectus [here.](mailto:info@elmwealth.com) --- ### Note: This is not an offering document. **Past returns not indicative of future returns.** The value of an investment and the income from it can fall as well as rise and you may not get back the amount originally invested. --- ### Further Reading and References: - Asness, C.S., T. J. Moskowitz, and L. Pedersen. “Value and Momentum Everywhere,” Journal of Finance, Vol. 68, No. 3 (2013), pp. 929-986. - Blitz, D., and P. van Vliet. “Global Tactical Cross-Asset Allocation: Applying Value and Momentum Across Asset Classes,” The Journal of Portfolio Management, Vol. 35, No. 1 (2008), pp. 23-38. - Campbell, J., and R. Shiller. “The Dividend-Price ratio and Expectations of Future Dividends and Discount Factors.” Review of Financial Studies, 1 (1988), pp. 195-228. - Cochrane, J. “The Dog That Did Not Bark: A Defense of Return Predictability.” Review of Financial Studies, Vol. 21, No. 4 (2008), pp. 1533-1575. - De Grauwe, P., and M. Grimaldi. “Bubbling and Crashing Exchange Rates.” Working Paper, CESifo (Series No. 1045), 2003. - Dewey, R., and Haghani, V. “A Case Study for Using Value and Momentum at the Asset Class Level.” Journal of Portfolio Management, volume 42 number 3, (Spring 2016). - Fama, E.F., and K.R. French. “Business Conditions and Expected Returns on Stocks and Bonds,” Journal of Financial Economics, 33 (1989), pp. 25-49. - Fama, E.F., and K.R. French. “Dissecting Anomalies.” Journal of Finance, 63 (2008), p. 1653-1678. - Ferson, W. E., and C. Harvey. “The Variation of Economic Risk Premiums.” Journal of Political Economy, Vol. 99, No. 2 (1991), pp. 385-415. - Gnedenko, B., and I. Yelnik. “Dynamic Risk Allocation with Carry, Value and Momentum.” Working paper, ADG Capital Management LLP, 2014. - Jegadeesh, N., and S. Titman. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance, Vol. 48, No. 1 (1993), pp. 65-91. - Kahneman, D., and A. Tversky. “Judgment Under Uncertainty: Heuristics and Biases.” Science, Vol. 185, No. 4157 (1974), pp. 1124-1131. - Moskowitz, T.J., Y.H. Ooi, and L.H. Pedersen. “Time Series Momentum.” Journal of Financial Economics, Vol. 104, No. 2 (2012), pp. 228-250. - Pirrong, C. “Momentum in Futures Markets.” Working paper, University of Houston, 2005. - Soros, G. The Alchemy of Finance. New York, NY: Simon and Schuster, 1988. - Wang, P., and L. Kochard. “Using a Z-score Approach to Combine Value and Momentum in Tactical Asset Allocation.” Working paper, Georgetown University Investment Office, 2011. --- 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. See our notes [here](https://elmwealth.com/how-much-of-a-good-thing-is-best-for-you/) and [here](https://elmwealth.com/a-sharper-lens-for-sizing-up-nickels-and-steamrollers/) for a deeper discussion of this body of work. 3. A working paper version of Value and Momentum Everywhere, Asness, Moskowitz and Pedersen, was in circulation from 2009 SSRN [here](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1363476), and presented at the 2010 AFA meeting, although the paper only appeared in the Journal of Finance in 2013.. You can find a copy of our paper [here.](https://elmwealth.com/wp-content/uploads/2017/06/A-Case-Study-for-Using-Value-and-Momentum-at-the-Asset-Class-Level.pdf) 4. To normalize the target weights to 100% and impose the 2x constraint we iteratively impose the constraint and re-normalize until both the normalizing condition and the constraint are fully satisfied. 5. This is also consistent with the treatment of momentum signals in this early paper on implementing value and momentum in an asset allocation context: Blitz and Van Vliet, “[Global Tactical Cross-Asset Allocation: Applying Value and Momentum Across Asset Classes,](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1079975)” Journal of Portfolio Management (2008). 6. We set the slope of the value signal in the All-Equity program to 0.5, in contrast to 1 in our Global Balanced programs. 7. Many of the historical data series we need for this analysis begin December 31, 1974, particularly the MSCI data series for regional equity market total returns and earnings. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/epaep) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [How to Fund Your Elm Account](https://insights.elmwealth.com/elm-wealth-research/funding-your-account) Dec 19, 2019, 12:00:00 AM December 19, 2019 How Elm Works ## How to Fund Your Elm Account ### If the ultimate source of funds is currently invested in brokerage assets: - You can transfer assets to Elm through the inter-brokerage ACAT network. We’ll take care of liquidating the assets and getting funds invested on the same day, reducing timing risk. If you hold broad-market ETFs or mutual funds, it’s possible we’ll be able to use some or all of these instruments instead of liquidating them. - This will generate realized gains or losses in a taxable account. If you share an account statement with us, we can help estimate the tax impact of liquidating your assets.The ACAT transfer can take between 2 days and 2 weeks. We initiate this through Fidelity and you will receive approval paperwork to eSign. - You can liquidate assets yourself and transfer cash to your Elm Fidelity account (see below). This allows you to control the liquidation directly, but requires taking market-timing risk between when you liquidate the assets and when we re-invest them. --- ### If the ultimate source of funds is currently in cash or cash proxies: - **For Non-retirment accounts:** - If funds are currently outside Fidelity, you can wire funds into your Elm Fidelity account (same-day delivery). Wire instructions can be found on [Fidelity.com](https://www.fidelity.com/cash-management/information-needed-wire-to-fidelity-account). - If funds are currently outside Fidelity but at another brokerage, we can pull the funds into your Fidelity account through the ACAT network (1-3 days typical processing time). We initiate this through Fidelity and you will receive approval paperwork to eSign. - If funds are currently in another Fidelity account, you can instruct Fidelity to transfer the funds into your Elm Fidelity account ($200k/day limit online, no limit over the phone), or we can prepare a Journal Request form for your signature (1 day processing time). - **For Retirement accounts:** - If funds are currently outside Fidelity but at another brokerage, we can pull the assets into your Fidelity account through the ACAT network (1-3 days typical processing time). We initiate this through Fidelity and you will receive approval paperwork to eSign. - If funds are currently in another Fidelity account, you can instruct Fidelity to transfer the funds into your Elm Fidelity account ($200k/day limit online, no limit over the phone), or we can prepare a Journal Request form for your signature (1 day processing time). [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/funding-your-account) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/home-bias-v2.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [Home Biased: A Case for More Indexing](https://insights.elmwealth.com/elm-wealth-research/home-biased-more-indexing) Sep 25, 2019, 12:00:00 AM September 25, 2019 How Elm Works ## Home Biased: A Case for More Indexing *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-2930) Home Bias refers to the tendency to invest more heavily in one’s domestic equity market than global market-value proportions would suggest. When Warren Buffett advises his heirs to put 90% of their inheritance in the S&P 500 and the rest in US Treasuries, that’s an (extreme) example of the kind of Home Bias we’re talking about. At the other end of the spectrum, an investor from Switzerland investing even 10% of her wealth in Swiss stocks would be showing a high degree of Home Bias as well. Whether or not home-biased investing makes sense, the fact is that people in pretty much every country do it. Our question is: if everyone’s doing it, does it matter? Or if everyone equally over-weights their domestic market does it all pretty much wash out, with the over-weights cancelling out the under-weights? Let’s address the question with a stylized thought experiment, based loosely on Home Bias surveys. Such studies indicate that US investors invest 80% – 85% in the US market. In smaller markets, such as the UK and Canada, investors allocate about 50% of their equity investments domestically, an even larger divergence from market capitalization weights, as can be seen by comparison with the chart below.[2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-2930) We start by assuming a world with no home bias, and eleven national markets with a total value of $100: a Big market weighing in at 50% of the total, and ten Small markets representing 5% each.[3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-2930) We’ll also assume that investor wealth lines up with the size of their respective markets. --- Now we’re going to flip a switch and turn Home Bias on: Big market investors now want to be 80% invested in their domestic market, 30% above market cap weight. The ten Small markets exhibit even stronger Home Bias, wanting to be 50% invested in their home market, 45% above their 5% weight. The table below shows how the numbers play out[4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-2930): | | Big Market | **Small Markets (Combined)** | | --- | --- | --- | | Market Value: | $50 | $50 | | Big Investors’ desired allocation: | $40 | $10 | | Small Investors’ desired allocation: | $13 | $37 | | Excess Demand: | $3 | $(3) | By flipping the Home Bias switch we’ve created a supply-and-demand problem: the Big market isn’t currently big enough to take the $40 from domestic investors plus the $13 from the Small investors, as this adds up to $53 and the market-value is only $50. The Small markets in aggregate will have a corresponding shortfall in demand.[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-2930) We can see that if Big investors want to own 80% of the $50 of their market, then all that’s left for the Small investors combined is $10 of the Big market, so at most they can have a 20% allocation to the Big market. Any greater desired allocation creates excess demand for the Big market. Ultimately, this conundrum must be resolved by market values changing: specifically the Big market going up in value relative to the Small markets. All else equal it would have to go up quite a lot: 60%, from $50 to $80 if we hold the Small markets constant.[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-2930) The increase in Big market value could be accomplished either through rising prices or through new issuance. If prices rise, this would mean a reduction in the long-term expected return of the Big relative to the Small market of around 1.5% pa, a very sizable impact assuming both markets had expected returns around 4% without the Home Bias distortion. If instead there’s new issuance, such issuance would represent less attractive investment opportunities at the margin than previously outstanding equity, resulting again in lower expected returns for Big market equities.[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-2930) ### Conclusion We read so much about how indexing is causing distortions in markets, but we’ve seen here how *not* indexing can itself lead to significant distortions. If there were less home bias and more passive investing in line with global market-value proportions, US equity investors would likely enjoy lower relative valuations and higher expected returns. While we agree with Mr. Buffett’s advice to non-professional investors that indexing is the way to go, we wish he’d have encouraged his disciples to take a more worldly perspective. --- 1. This not is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. **Past returns are not indicative of future performance.**   Thank you to Vlad Ragulin, Nir Kaissar, Aneet Chachra and Jeff Rosenbluth for their helpful comments. 2. Figures vary across studies, and most are based on data which is 15-20 years old. For example, see these articles: [Home Bias in Global Bond and Equity Markets (2006 working paper)](https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp685.pdf), [Forbes 2018](https://www.forbes.com/sites/simonmoore/2018/08/05/how-most-investors-get-their-international-stock-exposure-wrong/#28f112a76aac) and this from Vanguard: [The Role of Home Bias in Global Asset Allocation Decisions (2012)](https://personal.vanguard.com/pdf/icrrhb.pdf).   Also, even the fraction of global market cap represented by the US is debated, with some analysts suggesting that 30%, the raw weight excluding free-float and investability adjustments made by FTSE and MSCI, is the more appropriate weight to use. 3. Equivalently, we could have started out with a world with 100% home bias, in which investors allocate 100% of their equity investments to their domestic equity markets. Relaxing the assumption that wealth is proportional to domestic market value will increase (decrease) the imbalance caused by Home Bias if wealth in the Big market is greater (less) than it would be under the proportional assumption. 4. The Big market investors want to put $40 into their home market, leaving $1 to invest in each of the ten Small markets. The Small market investors want to put $2.50 into each of their home markets, and allocate their other $2.50 of investments according to market cap weights – so $1.32 (50/95) into the Big market for a total of $13, and the rest, $1.18, split equally among the other nine Small markets. 5. More generally, with one Big market making up 50% of the total market, and many small ones comprising the other 50%, the Home Bias deviation from market weight in the Small markets needs to be two times the deviation in the Big market to balance out. Any Small market Home Bias less than that results in excess demand for the Big market (and vice versa). The formula for the balancing amount of Small market Home Bias as a function of Big market Home Bias and the Market Weights of the Big and Small markets is: *HBSmall = 1 – (1 – HBBig)(1-MWSmall)/MWBig* where *HB* is Home Bias, and *MW* is Market Weight. 6. This result depends on the choice of starting point and assumptions regarding domestic wealth. One way we can get this result is by making the simplifying-but-imprecise assumption that domestic wealth moves in line with the value of the home market.   Alternatively, we can arrive at this result with the assumption that investors initially exhibit 100% home bias, and that market weights are $50 for the Big market and $5 for the Small markets, and then investors change to wanting to have 80% in the domestic market for the Big investors and 50% in the Small market for the Small investors. To arrive at balance, holding the value of the Small markets constant, the Big market needs to jump to a value of $80. If we allow both the Big and Small market values to change, there are an infinite set of moves of Big and Small markets that would accomplish the balancing, such as Big up 20% and Small down 25%. 7. Another flavor of this resolution is for equity long-short funds to short the Big market and go long the Small markets, but again, this presumably would require an inducement in terms of a positive expected return spread between the Big and Small equity markets. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/home-biased-more-indexing) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/tax-cake-840x420.jpg) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [Tax Efficiency and Dynamic Asset Allocation: Can We Have Our Cake and Eat It Too?](https://insights.elmwealth.com/elm-wealth-research/tax-efficiency-and-dynamic-asset-allocation-can-we-have-our-cake-and-eat-it-too) Sep 4, 2018, 12:00:00 AM September 4, 2018 How Elm Works ## Tax Efficiency and Dynamic Asset Allocation: Can We Have Our Cake and Eat It Too? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-2199) We are frequently asked about the tax efficiency of our dynamic value-and-momentum investment approach. The concern is often that with estimated turnover of 50% – 100% per year, returns might be less tax-efficient than a simple static, buy-and-hold type of approach, which is generally recognized as the gold-standard of tax-efficient investing.[2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-2199) As we’ll explain below, we believe our dynamic approach is expected to be, and has been, as tax-efficient as a static one. In this note, we will: - describe the historical tax-efficiency of our approach, as experienced by an actual investor for the past six years. In the Appendix, we show simulated results for the past 11 years, and… - explain why we expect to continue to deliver tax-efficiency in US taxable portfolios, particularly through the inherently favorable tax characteristics of momentum-induced rebalancing and from the account-by-account, tax-aware portfolio-rebalancing tools we’ve developed in-house. ### Tax-Efficiency of an Elm Investor (2012-2017) While tax performance in a particular instance will strongly depend on the specific path of the market and the investor’s entry and exit point(s),[3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-2199) the actual experience of one of our early investors may be a useful illustration of the degree of tax-efficiency we can deliver.[4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-2199) The example below is from an investor in our Delaware Fund. While our Fund is different in a number of material ways from an SMA account, we chose this example as it allows us to share a history twice as long as what we have for SMAs.[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-2199) We have also run longer-term comparative simulations based on investment start dates from 2007 to the present, with results consistent with the example we show here – see the Appendix for details. As always, we emphasize that even ten years of historical experience, in and of itself, cannot tell us much about what to expect in the future.[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-2199) In the table below, we compare the income and its tax character from our chosen investor versus a simulated fixed-weight portfolio with the same Baseline weights as Elm’s strategy,[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-2199) and rebalanced back to those weights each month. | | Actual Investment in Elm Fund | Static Fixed Weight Asset Allocation | Tax Rate: Approximate Allocation | | --- | --- | --- | --- | | Start Value: Jun. 1, 2012 | $10,000,000 | $10,000,000 | | | End Value: Dec. 31, 2017 | $15,540,340 | $15,095,500 | | | Increase in Investment | $5,540,340 | $5,095,500 | | | Unrealized Capital Gains | $3,644,880 | $3,164,590 | 15% | | Total Realized Capital Gains | $298,700 | $291,924 | | | Short-term Capital Gains (Losses) | ($459,360) | $45,243 | 41% | | Long-term Capital Gains | $758,060 | $246,681 | 24% | | Qualified Dividends | $867,580 | $848,738 | 24% | | Int Inc & non-Qualified Dividends | $610,850 | $629,692 | 41% | | Tax-exempt Income | $118,330 | $160,556 | 0% | | Blended Tax Rate on Investment | **17.1%** | **18.8%** | | | Past returns and tax characteristics may not be indicative of future returns and tax character. Note: summarized k-1 data: e.g. foreign tax credits and misc deductions are not shown separately. | | | | The right-most column displays the assumed Federal tax rate applied to each type of income. Notice that we use 15% for unrealized capital gains, 9% lower than the 24% for realized long-term capital gains, in recognition of the benefits of deferring capital gains tax.[8](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-8-2199) If we applied an 18% rate to unrealized gains for the dynamic strategy and 15% for the static strategy, to reflect the higher expected turnover of the dynamic strategy in the future, this would increase the blended tax rate of the dynamic strategy by 1.9%, putting it roughly in line with the static approach. Bottom line: not only did our chosen investor do over 4% better than a simulated static weight investor on a pre-tax total return basis (with about 10% lower risk),[9](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-9-2199) but, over a reasonable range of assumptions, he experienced an effective blended tax rate that was attractive in absolute terms, and also was roughly equal to, or possibly even lower than, that of a static weight investor.[10](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-10-2199) ### Elements of a Tax-Aware Approach Over this period, if our Fund had rebalanced exactly back to our desired asset allocation each month, turnover would have averaged about 80% per year, while the static, fixed weight approach would have experienced turnover of just 14% per year. However, in practice, both turnover rates would be lower as neither strategy would be rebalanced exactly back to target each month. Despite the higher turnover of Elm’s strategy, there are several subtle but significant effects that together yield high expected (and so far, realized) tax-efficiency for our dynamic approach. First, the momentum overlay is what generates most of the additional turnover compared to a static approach. Its nature is to generate frequent but small short-term capital losses punctuated by less frequent but large long-term capital gains. Second, our portfolio turnover generally takes the form of buying and selling a small ‘top’ slice of the portfolio, which typically has relatively low built-up gains or losses. Beneath this ‘top’ slice, there will tend to be a more static base layer of the portfolio that can hold a buildup of unrealized long-term capital gains. Keeping track of specific tax lots also contributes to greater tax efficiency. Finally, a substantial fraction of total income is generally in the form of tax-preferred Qualified Dividends and tax-exempt municipal bond income, a benefit enjoyed by both the dynamic and static-weight strategies.[11](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-11-2199) In addition to the features described above, which relate to Elm’s core asset-allocation strategy, we apply additional tax-aware portfolio management techniques at the execution level. Our rebalancing algorithm recommends the transactions that will achieve the best trade-off between minimizing realized gains, minimizing transaction costs, maximizing realized losses, and staying close to our asset-allocation targets.[12](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-12-2199) Because many of the dozen or so markets we invest in are related, and several different instruments are generally available per market, we can often achieve a much better tax result for our investors than if we naively re-balanced each market exactly to target without thinking about taxes. Our taxable investors also benefit from periodic tax-loss harvesting, and our system automatically works to prevent tax-adverse wash sales between groups of linked accounts. ### Conclusion We hope this admittedly-limited treatment of this important topic sheds some light on our ability to deliver tax efficient returns through a systematic, dynamic and tax-aware asset allocation approach. We put a lot of focus on tax-efficiency, just as we do on efficiency in fees, as both are risk-free improvements to investor returns worth more than the same amount of expected but uncertain extra return we could try to earn by taking more risk. To paraphrase Ben Franklin: *“A risk-free penny saved is worth two expected but risky pennies earned.” [13](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-13-2199)* --- ### Appendix: Simulated Experience for Global Balanced Taxable SMA over a Full Cycle (2007-2017) The chart below provides a summary of the tax efficiency of our dynamic Global Balanced asset allocation strategy for the 11 full years to the end of 2017, in both absolute terms and relative to a static-weight Baseline strategy. This analysis provides a picture over an entire economic and financial market cycle, including the recession and bear market of 2008-2009. In the bottom section of the chart, the lines show the tax benefit (or cost) of realized capital losses net of realized capital gains. Realized short-term and long-term capital losses (and gains) are valued at tax rates of 41% and 24% respectively. The simulation of our dynamic asset allocation approach was calculated by running our current tax-aware rebalancing algorithm over the historical period 2007-2017, but it does not include the further potential benefit of doing tax-aware “harvest” transactions at times other than on our 40-day rebalancing cycle. For the static-weight portfolio, the simulation assumes that we rebalance the portfolio back to the Baseline weights every 40 days in a tax-aware manner, also without any extra “harvest” transactions. The chart shows that not only did Elm’s dynamic asset allocation approach provide a significantly higher pre-tax total return over the period, 110.5% versus 72.2%, but also until the end of 2015 it achieved this with greater tax efficiency too. By the end of the 11-year period, the total tax benefit delivered by our dynamic strategy falls just slightly below the net tax benefit enjoyed by the static-weight strategy, which is partly a result of the higher return of the dynamic versus static strategy during the period. The salient feature of the cumulative tax benefit of our dynamic strategy occurs in the period of late 2008 and early 2009 during the bottom of the market when our rebalancing strategy realized substantial short-term and long-term capital losses, which resulted in a long-lasting cumulative tax benefit of about 2%, or roughly 0.2% per annum amortized over the full 11-year period. In sum, and keeping in mind the usual caveats about the past not necessarily being indicative of the future, this historical backtest does not contradict the proposition that Elm’s dynamic asset allocation strategy can deliver tax-efficiency comparable to that of a static, buy-and-hold style approach. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest. 2. And far more tax efficient than most hedge fund and other alternative investments, as discussed [here.](https://elmwealth.com/us-tax-reform-leaves-even-less-pie-investors-alternatives/) 3. Half of our SMA investors who have been with us for more than six months have added to their SMA portfolios at least once. Additions tend to improve tax efficiency of returns. 4. There are many other limitations to the usefulness of our example, such as the short period of time covered, the relatively benign market environment over that period, and the recognition that tax rates and law will change over time in ways that are impossible to predict. 5. See [here](https://elmwealth.com/how-to-invest-with-elm-fidelity-smas-vs-fund/) for some of the salient differences between an investment in our Fund compared to an investment in an SMA managed by us at Fidelity. 6. Please see our note [“What’s Past is Not Prologue”](https://elmwealth.com/whats-past-is-not-prologue/) for more on the limits of historical data in investing. 7. You can find our latest Baseline weights in the second table in our latest investor report [here.](https://elmwealth.com/wp-content/uploads/2017/12/Dec-2017-Monthly-Performance-Report-for-Elm-Partners-Portfolio-LLC-1.pdf) 8. This is roughly in-line with an expectation of deferring capital gains for about 20 years with an equity nominal return of about 7%. 9. The annualized standard deviation of monthly pre-tax returns of the Elm Fund was 6.0% compared to 6.9% for the static Baseline portfolio over period. 10. Some of the difference in blended tax rate comes from the short-term capital losses that were generated, which we assume investors can make use of to offset short-term capital gains elsewhere in their investment portfolio. Even without that benefit, our dynamic approach still achieved a slightly lower blended tax rate than the naive static weight approach.   We also note that the static approach could have achieved a lower blended tax rate if we had applied some of the same tax aware portfolio management strategies, but our purpose here was to illustrate the potential benefits of all that we can bring to bear in delivering tax efficient returns versus. a “vanilla” static-weight investment approach. 11. Our Delaware fund structure also benefits, in a rising market, from new investors coming in to the fund, allowing us to buy new higher basis tax lots, and investors redeeming and taking capital gains allocations with them. 12. With short-term gains weighted significantly more heavily than long-term gains. We discuss how tax considerations impact portfolio rebalancing in more detail in this note [here.](https://elmwealth.com/how-much-should-the-tax-tail-wag-the-asset-allocation-dog-a-rule-of-thumb-for-weighing-capital-gains-taxes-in-portfolio-rebalancing-decisions/) 13. See [here](https://elmwealth.com/a-penny-saved-is-two-pennies-earned/) for more on Ben’s maxim, and [here](https://elmwealth.com/us-tax-reform-leaves-even-less-pie-investors-alternatives/) for a more general discussion of tax efficiency in long-term equity investing versus alternative investments. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/tax-efficiency-and-dynamic-asset-allocation-can-we-have-our-cake-and-eat-it-too) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/most-important-840x420.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [The Most Important Number Not Printed in the WSJ](https://insights.elmwealth.com/elm-wealth-research/the-most-important-number-not-printed-in-the-wsj) Aug 30, 2018, 12:00:00 AM August 30, 2018 How Elm Works ## The Most Important Number Not Printed in the WSJ *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-2191) We are often asked for our estimate of the long-term return of the equity market. Our framework currently indicates 5.3% above inflation for global equities, which we know strikes many investors as high. This is understandable, given that the most available and frequently cited valuation ratio – the S&P500’s CAPE[2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-2191) – currently stands at about 30, which is higher than it’s been 96% of the time since 1900 and far above its average level of about 17.[3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-2191) How do we arrive at our estimate of 5.3% real return? First, we need a simple and fundamentally sound predictor for each major regional equity market. One such measure is the Cyclically Adjusted Earnings Yield, i.e. 1 / CAPE, as suggested 30 years ago in a seminal paper by Shiller and Campbell.[4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-2191) While there isn’t enough historical data to statistically derive a high level of confidence in this predictor, such evidence as there is combined with its fundamental economic rationale supports its use as a reasonable indicator.[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-2191) By way of anecdotal context, the Cyclically Adjusted Earnings Yield in 1968 was 4.6% for US equities, and the actual real return over that period has been 5.8% – not spot on, but not too bad either given all that’s happened over those 50 years.[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-2191) Next, we need a good decomposition of the global equity market. The table below presents current data: | Region | CAPE | Earnings Yield (1/CAPE) | Market Cap. Weights | | --- | --- | --- | --- | | US | 28.4 | 3.5% | 37% | | x-US Developed | 18.5 | 5.4% | 31% | | Emerging Markets | 13.9 | 7.2% | 32% | | Global Earnings Yield | | 5.3% | | | **Source:** World Federation of Exchanges, Bloomberg, MSCI.[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-2191) | | | | As you can see, non-US equities offer a much higher earnings yield than US equities. This has a major impact on our return estimate given non-US equities represent almost 2/3rds of the global equity market on the basis of pure market capitalization. There is good evidence that investors, and particularly US investors, tend to significantly over-weigh the US in their thinking about global equities. Even though the US represents less than 25% of global GDP and less than 5% of global population, many investors think of the US equity market as a proxy for the global market, which just isn’t the case. The big index providers, MSCI and FTSE, are also partly to blame for this biased perception, as they assign a weight of over 50% to US equities as a result of adjustments they make for free-float and investability factors. They do this so that their indexes can be investable on a massive scale with minimal distortions, but at the cost of rendering their indexes less representative of the global market. Fortunately, investors who are not constrained to track MSCI or FTSE indexes can achieve a truer and more balanced representation of the global equity market, particularly on a forward-looking basis, by using un-adjusted market cap weights as presented in our table – so long as not everyone tries doing this at the same time.[8](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-8-2191) Another reason that our estimate may strike some investors as high is that we do not make an adjustment for the reversion of CAPE to its historical mean level. In a recent Bloomberg [note](https://elmwealth.com/market-multiple-mean-reversion-red-light-red-herring/), we explained why deviations from the mean for CAPE don’t actually tell us much about expected market returns above and beyond what the absolute level of CAPE already tells us. Hence, including mean-reversion does not improve CAPE as an indicator of long-term return.[9](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-9-2191) We don’t include market momentum in our estimate, as we are focused on long-term returns and the effects of momentum average out to zero over long time horizons. We also stopped short of making an adjustment for taxes, as this will vary according to personal circumstances.[10](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-10-2191) As a general matter, equity investing is among the most tax-efficient forms of long-term investing, given the ability to defer capital gains and the preferential treatment of dividends in many tax regimes. The simple framework we’ve described in this note is not meant to have near-term predictive power. Instead, we hope it provides a useful starting point for thinking about the long-term return of equities, which is one of the most critical inputs into lifetime decisions about how to invest, save, and spend. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest. 2. Cyclically Adjusted Price to Earnings ratio, which is the current equity index price divided by the past 10 years of inflation adjusted earnings. CAPE was first suggested by Graham and Dodd (1934), but popularized by Professor Robert Shiller. 3. Using Robert Shiller’s [reference data.](http://www.econ.yale.edu/~shiller/data.htm) 4. Campbell and Shiller, [“Stock Prices, Earnings and Expected Dividends”.](http://www.nber.org/papers/w2511.pdf) 5. We have presented our views on this several times in the past, such as in this Elm video from three years ago: [The Most Important Number You Won’t Find in the Wall Street Journal](https://elmwealth.com/video-the-most-important-number-you-wont-find-in-the-wall-street-journal/) (2015).There is a plethora of literature on this subject, presenting sometimes opposing perspectives, and we recognize that it is more the topic of a book than a one page note. A variety of simple structural corporate-growth models can produce the result that real equity returns will be centered around the earnings yield.   One basic condition under which real returns will equal the earnings yield would be if company earnings can grow with inflation with all earnings paid out currently to shareholders. While these models are all caricatures of the real world in a variety of ways, they nonetheless provide a solid starting point for making sense of long-term historical data. For a more up-to-date evaluation of CAPE as a predictor of real equity returns, particularly assessed in non-US equity markets, see [Keimling and Huber](https://www.starcapital.de/fileadmin/user_upload/files/publikationen/Research_2016-01_Predicting_Stock_Market_Returns_Shiller_CAPE_Keimling.pdf) (2016). They conclude: *“Existing research indicates that the cyclically adjusted Shiller CAPE has predicted long-term returns in the S&P 500 since 1881 fairly reliably for periods of more than 10 years. Furthermore, the results of this paper indicate that this was also the case for 16 other international equity markets in the period from 1979 to 2015.”* 6. Again Robert Shiller’s [reference data.](http://www.econ.yale.edu/~shiller/data.htm) 7. CAPE figures are based on an average of MSCI and Bloomberg historical earnings numbers for major regional markets. For non-US markets, historical earnings are converted to US dollars at historical exchange rates and the current index price is converted to US dollars at the current exchange rate. 8. See our [note](https://elmwealth.com/our-asset-allocation-methodology/) here for a fuller discussion of how we arrive at our regional equity market weights in our Baseline portfolio, which are in between the unadjusted market cap weights from the table and the MSCI and FTSE adjusted weights. 9. The main points in our note were that much of the apparent mean-reversion in CAPE is explained by cyclically adjusted earnings catching up with stock prices, rather than the other way around, and the fact that a random walk will give the illusion of mean reversion when looking backwards, but in reality we won’t know the mean of the distribution in advance. 10. For the sake of clarity, in this note we’ve put to the side a further consideration in thinking about equity returns, which is the “convexity” effect, stemming from equities having the attractive characteristic of unbounded upside and bounded downside.   Our return estimate is a central estimate of the long-term return, but if the actual long-term compound return turns out to be 2% better than the estimate, that results in a much larger gain than the loss for a return 2% lower than our estimate. This convexity effect can have a material impact on asset allocation decisions, depending on the magnitude of return variability. See our paper on this topic [here.](https://elmwealth.com/what-our-market-return-forecasts-really-mean-equity-convexity-and-investment-sizing/) [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/the-most-important-number-not-printed-in-the-wsj) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/hhhhhhhhhhhh-840x420.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [HHHHHHHHHHHH: Is there a message in there?](https://insights.elmwealth.com/elm-wealth-research/12-heads-row) Nov 20, 2017, 12:00:00 AM November 20, 2017 How Elm Works ## HHHHHHHHHHHH: Is there a message in there? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-1663) The 12-month winning streak of the stock market through the end of October reminded me of a Friday afternoon on the Salomon trading floor in early January 1987.[2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-1663) The markets had closed, the day’s trades were confirmed and we were sitting around discussing weekend plans. In walked six and a half feet of the most enthusiastic and well-liked of all the Salomon MDs, a man who believed nothing was impossible.[3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-1663) *“How about that stock market! Up every day this year so far – six days in a row! I think it’s going to be up every day this year. What odds would you guys give me on $1,000 that I’m right?”* We perked up. There were another 245 trading days left in the year, and even if we assigned an 80% chance to the market being up each day, the probability that it would be up the next 245 in a row was about a trillion trillion to one.[4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-1663) We agreed to syndicate the risk among five of us, and we offered him odds at 5,000:1, but only on $50. He scoffed and walked away dissatisfied – no bet.[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-1663) Then, as if to show us that anything remotely possible might just happen, we watched the Dow go up every day for the next seven days, an 11% rally altogether, until the streak finally ended on the 14th day.[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-1663) Bloomberg just published a short note we wrote ([here](https://www.bloomberg.com/view/articles/2017-11-14/this-stock-rally-really-is-improbable)) that takes a more in-depth look at stock market streaks. We reviewed 150 years of US stock market history and found that there have been six streaks of 12 months or longer. While it’s very *likely* we would witness one streak of 12 or more winning months in a row, it is highly *unlikely* to see six or more such streaks if the stock market followed a random walk, with each month’s return independent of prior returns. What history suggests is that, in the short to medium term, the stock market exhibits momentum, or trending, which likely goes hand-in-hand with longer term mean reversion.[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-1663) As you know, at Elm we believe it makes sense to take account of valuation and momentum in the asset allocation decision. While the past is not necessarily indicative of the future, our review of stock market streaks does not contradict our view of market behavior. --- 1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. **Past returns are not indicative of future performance.** This not is not an offer or solicitation to invest. 2. My memory of these events is a bit fuzzy, but the main aspects of the story are accurate. 3. For those readers who were at SB at the time: OG. 4. And it took a good few seconds for our HP12C to do that calculation. 5. We didn’t think about it in these terms at the time, but it turns out that this was a positive expected utility bet for us, even assuming the chance of us losing was 0.01%, rather than 2.0e-24. 6. Even more unlikely than the stock market’s 13-day winning streak at the start of 1987 was the Monday later that same year, on October 19th, when the stock market fell by over 20% in one day. 7. You may be wondering what happened after each of the five market winning streaks of 12 months or more ended. The average total return following each of those five streaks, starting one month after the streak ended, was about 15%. It was positive in four out of five of those cases. While five data points do not produce a result of statistical significance, this result is not inconsistent with the hypothesis that the stock market displayed positive momentum or trending in the past. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/12-heads-row) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/041-red-herring-banner.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [Market Multiple Mean-Reversion: Red Light or Red Herring?](https://insights.elmwealth.com/elm-wealth-research/market-multiple-mean-reversion-red-light-red-herring) Oct 2, 2017, 12:00:00 AM October 2, 2017 How Elm Works ## Market Multiple Mean-Reversion: Red Light or Red Herring? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-1379) This post was first published on [Bloomberg Prophets.](https://www.bloomberg.com/opinion/articles/2017-10-02/what-if-high-stock-values-revert-to-normal-levels) There may be many reasons to worry about the current record price levels of U.S. equities, but agonizing over the fallout from valuations reverting back to their historical averages should not in itself be high on the list. In fact, deviations from the mean for one popular valuation measure – the cyclically adjusted price-to-earnings ratio – don’t actually tell us much about expected market returns. What makes this particularly important now is that the CAPE stands at 30. The CAPE was equal to higher than it is today in only 59 of the 1,640 months going back to 1881, or less than 3.6 percent of the time. [2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-1379) On average it takes about five years for the CAPE to move halfway back to its 16.8 historical average, based on a simple regression analysis. Investors are understandably concerned that if it’s correct to expect the market to revert to a CAPE of about 24 over the next five years, then equities should drop about 22 percent, assuming earnings stay constant. No wonder so many are waiting for a stock market correction before putting more of their savings to work. *Data courtesy of Yale professor Robert Shiller.* [3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-1379) Although there is statistical evidence that the CAPE is indeed mean-reverting, this process isn’t as strong as it can appear from the chart above. There’s a well-known result referred to as “reversion-to-the-mean bias,” which is that even random events, which by definition have no mean-reversion, often appear to be doing so for a while, sometimes quite a while, if the observer wrongly assumes that the recent level is the true mean. That’s essentially what we’ve done by looking at the CAPE history relative to the mean calculated from today’s vantage point. Elroy Dimson, a London Business School professor and renowned stock market historian, sees this as a big effect: “Much of the evidence for mean reversion is based on optical illusions based on hindsight.” Also, a significant amount of the CAPE’s mean reversion is realized by earnings catching up with stock prices, rather than the other way around. For example, assuming the S&P 500 and earnings stay roughly where they are, the CAPE will drop from around 30 to about 25 in three years as the depressed earnings of the 2007-2009 period drop out of the 10-year lookback window for the CAPE.[4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-1379) Most importantly, the outright level of CAPE, or more precisely, the cyclically adjusted earnings yield, known as 1/CAPE, is itself a pretty good predictor of future real equity returns.[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-1379) This makes it hard for another metric based on CAPE, such as its deviation from its mean, to add much information. The cyclically adjusted earnings yield when used by itself in a linear model explains about 25 percent of the variation in realized 10-year equity returns. Adding CAPE’s deviation from its mean as a second factor fails to explain any meaningful additional variation, indicating it has little extra predictive power.[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-1379) Today’s CAPE is telling us that we should expect equities to give us a real return in the long-term of 1/30, or about 3.33 percentage points, above inflation. This is a lot less attractive than the real return of 6.4 percent delivered by the U.S. stock market since 1881, though it’s somewhat more attractive compared with today’s long-term real rate offered by U.S. Treasuries of just under 1 percent. As CAPE changes over time, the expected return of equities will also vary. Investors should be dynamic in their asset allocation, sizing exposure roughly in proportion to expected return.[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-1379) All else equal, investors should want to own less equities given today’s expected return than if CAPE was at 20 and the expected return was 5 percent (1/20). However, most investors would want to own no equities – or even run a short position – if they believed they’d be taking a 22 percent hit caused by CAPE reverting halfway back to its average over the next five years.[8](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-8-1379) History and common sense tell us that paying a higher earnings multiple for equities lowers the return one should expect to earn. History, however, is not telling us that a mean reversion of the CAPE is likely to deliver either a hit, or a windfall, to equity returns. Of course, history is not necessarily indicative of the future, and investors may have other reasons to expect equities to perform worse or better than predicted by 1/CAPE, especially in the short term. A historically driven fear of mean reversion should not be one of them. --- 1. Victor is the founder and CEO of Elm Partners, a HNW Robo-investment manager. James works with Elm Partners in addition to pursuing his own research and investment interests. 2. Of course, much has changed since 1881, when the U.S. flag had only 38 stars. 3. Data can be found [here](http://www.econ.yale.edu/~shiller/data.htm). CAPE was popularized in Campbell and Shiller’s “Stock Prices, Earnings and Expected Dividends,” found [here](http://scholar.harvard.edu/files/campbell/files/campbellshiller_jf1988.pdf). The idea goes even further back, to Graham and Dodd’s famous work “Security Analysis” (1934). 4. We find that on average, for every 10 percent the CAPE has been above or below its historical average, 10-year real average earnings increase (or decrease) by about 2 percent relative to their long-term average growth rate, which accounts for about 20 percent of the superficial mean-reversion we see in the CAPE data. 5. That 1/CAPE is a good predictor of the real return of the equity market is consistent with a story that corporate earnings would grow with inflation if they were paid out in full each year. You won’t be surprised to learn that professors Shiller and Campbell were among the first to write about this too in their 1988 paper. There are other equally powerful predictors, similar in spirit to 1/CAPE, such as ones that use dividend yields and real dividend growth parameters to predict equity returns. 6. We’re describing very simple linear models here, but there’s no evidence that more complex models produce different results, and Ockham’s Razor would counsel us to err on the side of simplicity. We’ve also made a choice to focus on a relatively long realized return horizon, namely 10 years. When looking at shorter horizons, 1/CAPE explains much less of the variation in return, and CAPE’s deviation from the mean similarly adds very little. 7. Most frameworks for asset allocation, such as the Merton Rule, suggest investment should be proportional to excess expected return. 8. Some people feel the expected return should be thought of as a bit higher than that, taking into account of the positive convexity of equities – that is, that equities can go up a lot but cannot go down more than 100 percent. More in this note [here.](https://elmwealth.com/what-our-market-return-forecasts-really-mean-equity-convexity-and-investment-sizing/) [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/market-multiple-mean-reversion-red-light-red-herring) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/038-tax-tail-banner.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [How Much Should the Tax Tail Wag the Asset Allocation Dog?](https://insights.elmwealth.com/elm-wealth-research/how-much-should-the-tax-tail-wag-the-asset-allocation-dog-a-rule-of-thumb-for-weighing-capital-gains-taxes-in-portfolio-rebalancing-decisions) Sep 12, 2017, 12:00:00 AM September 12, 2017 How Elm Works ## How Much Should the Tax Tail Wag the Asset Allocation Dog? *By Victor Haghani and James White* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-1138) For investors who feel the expected return of equities isn’t as attractive today as it was 5 to 10 years ago when PEs were lower, it’s natural to be thinking about reducing exposure to the market. For taxable investors, reducing your allocation will also mean paying capital gains tax.[2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-1138) As we’ve done in past notes on coin flipping and optimal trade-sizing, we’ll use a few basic assumptions about individual risk aversion to suggest a simple, intuitive rule-of-thumb for weighing up the trade-off between saving on tax versus achieving your target equity allocation. Our general finding is that if you’ve already held your equities long enough to qualify for long-term capital gains treatment, then the virtues of rebalancing to your target allocation far outweigh the efficiency from deferring a tax payment. In this case, it’s optimal to rebalance your portfolio most of the way to your target – and simply rebalancing all the way to target is almost as good. *However*, if waiting to rebalance will deliver the relatively large benefit of converting short-term gains to long-term gains, or you expect a significant cut in capital gains tax rates in the next few years, then you will probably be willing to keep an allocation to equities well above the optimal level you’d desire if you were investing from scratch. Let’s illustrate the question with an example. Say 6 years ago you had a view that the long-term pre-tax excess return of US equities over cash was 5%,[3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-1138) and based on that you invested 50% of your taxable savings in US stocks, and the other 50% you kept in cash. Since that time, your equities have doubled in value, excluding dividends, and they’d have grown to represent 67% of your portfolio.[4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-1138) But you now find equities less attractive to own than you did back then, as higher current PEs suggest lower future returns. Let’s say you think equities’ expected excess return is now down from 5% to 3%, and if you were investing your portfolio from scratch you’d want to have an allocation to equities of just 30%. If you reduced your exposure down to 30% from 67%, you’d have to make a hefty capital gains tax payment of roughly $12.50 per $100 of equities you own, or 4.6% of the value of your portfolio, assuming a long-term capital gains rate of 25%.[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-1138) …So what to do? You’d think this is a pretty basic question that would have some well-distilled answers. Well, we asked Google “how to decide whether to realize a capital gain” and we found a lot of answers – more than 15 million in fact. But we didn’t see any in the top 100 that went beyond “it depends” and “consult your tax advisor.”[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-1138) We are most definitely not qualified tax advisors, and this is not tax advice, but let’s see if we can come up with a more useful analysis than “it depends.” First, we need to quantify how much tax you’d save by not selling your appreciated equities today. We’ll start off by assuming the long-term tax rate is constant at 25% for your remaining investment horizon – later we’ll discuss results with modified assumptions. In this case, your tax savings arises entirely from deferring the realization of the capital gain – in doing so, you are in effect getting the use of the funds you’d have paid in taxes to invest in your portfolio. If the expected return on your portfolio of equities and T-bills is 1.9% – the blend of 30% in equities with a nominal expected return of 4% and 70% in T-Bills earning 1% – then for every $100 of equities you don’t sell, you get to earn 1.9% on the $12.5 of tax you’re not paying right now. This equates to a benefit of 0.24% per annum.[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-1138) Great. We’re halfway there. Now we just have to figure out what it costs us to hold more equities than our original target of 30%. Here’s where we have to draw on a bit of our past discussions about optimal trade-sizing (you can find a brief refresher, illustrated with ketchup and fries, [here](https://elmfunds.wpengine.com/2016/12/how-much-of-a-good-thing-is-best-for-you/)). Recall that, if you were investing the portfolio from scratch, we assumed that you want to have 30% of your savings in equities based on your view that equities had an expected excess return of 3%. A basic model of personal risk-taking, known as the Merton Rule,[8](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-8-1138) says that your optimal holding of a risky asset should increase in direct proportion to its expected return. That’s as simple a financial formula as you’ll find, and it seems pretty reasonable too. It’s simply saying that if you want to have 30% of your savings in equities when you expect equities to deliver a 3% excess return, then, all else equal, if you feel that the expected return of equities is 4%, you should want to have 40% in equities; more generally, for every extra 1% of return, you’d want to have an extra 10% allocated to equities. We now put the two halves of the analysis together to get our answer. Every extra dollar of appreciated equities you don’t sell has an extra return of 0.24% a year. If you want to hold an extra 10% of equities for every 1% of extra expected return, then it follows that for an extra 0.24% of return, you’d optimally like to own an extra 2.4% of equities. So, your tax-adjusted optimal allocation to equities is 32.4%, very close to your optimal allocation ignoring taxes of 30%.[9](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-9-1138) This suggests you should move about 95% of the way to your 30% target allocation from your current allocation of 67%.[10](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-10-1138) Working through this example suggests this very simple rule-of-thumb: Extra equities to own above your optimal allocation ignoring taxes = B \* Q r , where:   *B = annual tax benefit on appreciated equities not sold   Q = how much equities you’d want to own ignoring taxes   r = your expected excess return on equities* The bigger the unrealized gain, the higher the tax rate, the higher the return on equities or T-bills or the less risk-averse you are, the further you should be willing to diverge from your optimal allocation ignoring taxes. In our example, the benefit from holding a 32% allocation versus 30% is relatively modest, but the benefit in rebalancing down from 67% to 30-32% is high. At 67% allocation, the portfolio earns a risk-adjusted rate of -0.1%, suggesting you’d be better off owning nothing than maintaining your allocation at that level. Let’s put this rule-of-thumb to work on a few other salient examples representing commonly encountered tax situations. All cases keep to our Base Case assumptions regarding expected excess return for equities, level of personal risk aversion and amount of capital gain:[11](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-11-1138) | Description | Current Tax Rate | Long-term Tax Rate | Horizon (Years) | Extra Allocation vs. Optimal from “Scratch” Allocation | | --- | --- | --- | --- | --- | | Base Case: deferring long-term cap gains | 25% | 25% | 1 | 2% | | Hold to death for basis step-up, or donate | 25% | 0% | 30 | 8% | | Move from high-tax to low-tax state (e.g. NY to WY) | 31.5% | 25% | 5 | 12% | | Big Long-Term CG tax cut | 25% | 15% | 5 | 16% | | Hold on for Short-term CG to turn into Long-term CG | 44.6% | 25% | 0.5 | 37% | | Tax rate increase that exactly offsets value of deferring | 25% | 25.35% | 1 | 0% | ### What if I Expect Higher Tax Rates in the Future? The last entry in the above table shows how much tax rates would need to rise over the next year to exactly balance the value of deferral: just 0.35% with the assumptions we’ve used. In practice, the problem is more complex than this, as, for one thing, you would want to consider the analysis to multiple horizons. If the expected increase in tax rates outweighs the value of deferral to the relevant horizon, then this simplified analysis suggests you should realize capital gains entirely, pay the resulting capital gains tax and then reinvest in equities to your desired allocation from scratch. ### Conclusions Our simple rule-of-thumb suggests that in most scenarios involving a realization of long-term capital gains, when you do not expect a reduction in capital gains rates in the next few years and you’re pretty far from where you’d like to be, your optimal move is fairly close, but not all the way, to your desired allocation ignoring taxes completely. However, when it comes to bearing extra risk in order for a short-term capital gain to convert into a long-term capital gain, you should be willing to take quite a lot of extra risk to enjoy the benefit of that lower tax rate. At Elm Partners, in rebalancing portfolios for both our Fund and SMA clients we are willing to tolerate quite high deviations from target allocations to avoid short-term capital gains, but we are much less tolerant for avoiding long-term gains. Thus, our approach to tax-efficient investing is broadly consistent with the rule-of-thumb we have presented here. ### Caveat Emptor! The purpose of this note was to provide a simple rule-of-thumb to help illustrate some, but not all, of the factors investors should consider in trying to take account of tax effects in their investment decisions. The tax code is much more complex than the simple representation we have used in our examples. For example, we did not give any treatment to the fact that there is an asymmetry in capital gains taxation, in that we pay tax on gains, but we may get very limited refunds from the government on capital losses. Or more succinctly, as some unfortunate soul once said, “Man cannot live on capital loss carry-forwards alone.” We likewise did not treat whether investors form their target allocation views based on pre-tax or post-tax returns, or whether investors view portfolio risk inclusive or exclusive of tax liabilities. Also, state taxation varies from state to state and adds another layer of complexity. And adding insult to injury, tax policy changes over time in hard-to-predict ways. In the words of Albert Einstein, *“The hardest thing in the world to understand is the income tax.”* --- ### Further Reading and References: - Balcer, Y., and Judd, K., 1987, “Effects of Capital Gains Taxation on Life-Cycle Investment and Portfolio Management,” *Journal of Finance*, 42, 743-761. - Dammon, R., C. Spatt, and H. Zhang, 2001a, “Optimal Consumption and Investment with Capital Gains Taxes,” *Review of Financial Studies,* 14, 583-616 - Dybvig, P., and Koo, H. K., 1996, “Investment with Taxes,” Unpublished working paper, Washington University in St. Louis. - Merton, R., 1971, “Optimum Consumption and Portfolio Rules in a Continuous-Time Model,” *Journal of Economic Theory,* 3, 373-413. - Odean, T., 1998, “Are Investors Reluctant to Realize Their Losses?,” *Journal of Finance,* 53, 1775-1798. --- 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.   A big thank you to Larry Hilibrand, Ayman Hindy and WK, as well as our colleagues at Elm – Jeff, Arjun, Bruce, Gregg and Tara – for your help with this note. 2. Assuming the investments are not held in tax-advantaged retirement accounts. Also, we’re assuming the investor is not able to achieve total portfolio level asset allocation changes either through making exaggerated changes in non-taxable retirement accounts or through adding to investment accounts with further savings from earnings each year. Both of these can be tax efficient ways of moving one’s asset allocation without incurring capital gains taxes. 3. To be precise, that 5% is the expected arithmetic return in excess of T-bills, a standard proxy for cash. Also, for the purposes of this example, we’re assuming that the T-bill rate = 1%. We are using US equities for this example for simplicity, but as you know, at Elm Partners we believe in global diversification. 4. Assuming you spent your investment income. Also, more significantly, we’re ignoring the fact that you have a tax liability (think of it as negative cash) of $12.5 (25% of 50% of $100 of appreciated equities), which, if you think of it as negative cash, you may wish to subtract from your $50 of cash, leaving you with $41.7 of cash. Your allocation to equities taking this tax liability into account is actually 71%, higher than the more conventionally calculated allocation of 67% we’re using here. 5. Federal + Obamacare tax + a gross-up for the phase-out of itemized deductions, but assuming you live in a state with no capital gains tax like Wyoming, Florida or Texas. See [“How High are Capital Gains Tax Rates in Your State?”](https://taxfoundation.org/how-high-are-capital-gains-tax-rates-your-state/). As per the previous footnote, we are not taking the embedded capital gains tax liability into account in doing this calculation of how much you have invested in equities. You’d need to sell even more equities to get to 30% in equities taking the capital gains tax liability into account. 6. We did find several thorough treatments of this question in the academic literature, which we listed in the reference section below. For an example of the more typical treatment of this question, see this recent NY Times article [here](https://www.nytimes.com/2017/08/25/business/market-portfolio-drift.html). Perhaps an explanation for why this problem hasn’t gotten the attention it deserves is because we so often delegate to active managers who don’t have an incentive to defer the realization of gains. However, long-term investing in broad index funds, as typified by the type of investing we do at Elm Partners, will force us to confront the question posed in this note more frequently. 7. While we have considered plausible arguments that would lead us to value deferral at either the equity expected return or the risk-free rate, it should be noted that your choice of rate will not alter the general conclusion that the value of deferral is not significant enough to move you far from your optimal allocation ignoring taxes, unless your basis is very low. This is the case wherein you defer the capital gains indefinitely and your post-tax portfolio return converges to the pre-tax return, as shown by this formula:   *After tax rate of return = ((1 – τ) \* (1 + r)T + τ)(1 / T)– 1* where *r* is the pre-tax return on your portfolio, *τ* is the tax rate and *T* is your horizon. You can also see this by realizing that in the very, very long-term, if you never sold your equities, the initial basis would converge to a tiny fraction relative to the value of your holding. So, at that point, you’d be earning the pre-tax return on your entire tax liability which would result in an after-tax return equal to the pre-tax return. 8. Merton rule: for a portfolio with cash earning rate *r* and a risky investment with expected return *µ* and volatility *σ* , the optimal fraction of wealth to invest in the risky asset is *(µ – r) / (γ σ2)* , where *γ* reflects the investor’s idiosyncratic level of risk-aversion. For an investor who has an optimal holding of equities of 30% for a 3% expected excess return, and assuming equity market annual volatility of 18%, we get a coefficient of risk aversion of 3, signifying the investor is three times as risk averse as a Kelly bettor. 9. This is a rule-of-thumb, so we’ve left out the effect of your blended rate at the adjusted allocation being different than the blended rate at the optimal allocation ignoring taxes. This is a relatively small effect, and seems worth putting to the side for a rule-of-thumb. 10. If, even after the 100% equity rally, the investor still felt that the expected excess return of the stock market was unchanged at 5%, then 50% would remain her optimal allocation ignoring taxes, and the optimal rebalancing factoring in taxes would be to reduce the allocation to equities from 67% to 54%. 11. Calculations for tax benefit in each case are as follows, where *g* is the gain, *r* is the blended return on portfolio at desired allocation ignoring taxes, *T* is the horizon in years, *τ0* is the tax rate at start, and *τT* is the tax rate at horizon:   • Base Case: *g\* τ0 \* r*   • Hold-until-you-die: *Base Case + g \* τ0 / (1 – τ0) / T*   • Tax cut or move to lower tax jurisdiction: *g\* τo\* r + g \* (τ0 – τT) / (1 – τ0) / T*   • Converting ST to LT: *g \* τT\* r + g \* (τ0 – τT) / (1 – τT) / T* In case of Converting ST to LT, the maximum deviation is the starting allocation minus desired allocation. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/how-much-should-the-tax-tail-wag-the-asset-allocation-dog-a-rule-of-thumb-for-weighing-capital-gains-taxes-in-portfolio-rebalancing-decisions) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/too-much-840x420.jpg) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [How much of a good thing is best for you?](https://insights.elmwealth.com/elm-wealth-research/how-much-of-a-good-thing-is-best-for-you) Dec 9, 2016, 12:00:00 AM December 9, 2016 How Elm Works ## How much of a good thing is best for you? *By Victor Haghani and Andrew Morton* [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-1-343) ### A thought experiment: You can invest your wealth in only two assets: a risk-free one and a market portfolio of all public equities. Your investment choices, however, are limited to: A) put 100% in the risk-free asset, or B) 10% in the risk-free asset and 90% in equities. You cannot mix A) and B) – you must choose one or the other. What is the lowest return (above the risk-free rate) you would need to expect from equities for you to choose B? [2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-2-343) Do you have your number in mind? Great. Now imagine you’re still in this two asset world and you wake up one day and find that the expected return of equities is, in fact, exactly equal to your answer above. But now you’re no longer limited to just options A and B; you’re completely free to invest however much you like in equities, from 0% to 100% or more. How would you invest now? We’ve asked about a dozen friends this question, all financial professionals. If you’re like them, you’ve likely read the question twice, trying to understand exactly what we’re getting at. You may feel like you just answered that question, and isn’t 90% the answer? Well, no, we don’t think it is. Please read on as we try to explain why we think 45% is about the right answer, and how we can use the perspective of this problem to answer some other interesting questions.[3](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-3-343) You can get an immediate intuition for the problem and its solution by replacing our first question with: how much ketchup on your fries would be so much that you’d be indifferent between no ketchup and that much ketchup? [4](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-4-343) And then replace our follow-up question with: how much ketchup is your optimal amount? Our first question was calibrating your risk aversion via indifference points, and the follow-up question involved choosing an optimal point *anywhere* in between. The halfway point is a pretty good estimate, and exact in some investing models. ### Putting a price on risk: The properties of risk aversion are central to this problem, so let’s analyze the simplest type of risk, a 50/50 coin flip. A side payment is needed to make a typical, risk-averse person indifferent to risking a fraction *f* of his wealth on such a flip. How should this required side payment vary with *f* ? There is a very good reason to suggest that it should be proportional to *f2* , meaning we should demand four times the side payment for twice the risk. To see this, compare a single flip risking *√2%* of your wealth with two consecutive flips each risking 1%. In both cases the mean and variance of total wealth change are the same (0 and 2).[5](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-5-343) It seems reasonable that the total side payment should be the same too, which is only the case if the side payment is proportional to *f2* . Thus the problem of side payments for coin flips boils down to choosing the specific multiple of *f2* as your indifference point. Although it’s a matter of individual preference, we suggest a reasonable range for this multiple is 1 to 2.[6](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-6-343) Let’s use 1, meaning you are indifferent to an offer of 1% compensation to take on a ±10% of wealth flip, or 4% to take on a ±20% flip and so on. You would accept coin flip offers with higher side payments than this, and decline those with lower. To connect the coin example to the stock market, let’s simplistically model investing 90% of savings in the stock market for one year as risking 18% of wealth on the flip of a coin, meaning over a year we’ll either lose 18% or gain 18%.[7](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-7-343) The rule suggests that we’d require a side payment of 3.2% (i.e. 0.182) of our wealth, or 3.6% on the 90% we have invested in equities, to be indifferent.[8](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-8-343) You can see that in answering the question about what expected return you would need to be indifferent between putting 90% of your savings into equities or 0% in equities, you were calibrating your function of risk aversion. Let’s now turn to the question of how much you should invest given the freedom to choose any trade size you like. Consider what happens as you increase your investment from 0. Your expected gain goes up proportionally, but your risk – and hence, the required reward for bearing it – goes up with the square of the investment. Adding these two effects gives the diagram below, illustrating why the optimal point is halfway between the indifference points of 0% and 90%.[9](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-9-343) So, someone who is indifferent to investing 90% in equities if they had a 3.6% expected return would optimally invest 45% of his or her wealth in equities at that expected return. In general, optimal size is half the indifference point size. ### What kind of questions can we answer with this simple framework? - *What expected return on equities would you need for your optimal allocation to be 75%?* Recall that the required minimum return you said would make you indifferent to being 90% invested in equities, *R90%* , is also the expected return for which 45% is your optimal allocation. Optimal allocation varies in proportion to expected return, and so for it to be 75%, the expected return needs to be 75%/45% higher than your *R90%* . For our prototypical investor who has *R90%* of 3.6%, the expected return of equities at which a 75% allocation would be optimal is 6%.[10](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-10-343) - *What is the effect of over-investing?* As can be seen from the diagram, if you invest double your optimal allocation, you’ve thrown away all the benefit of the investment, and things get worse at an increasing rate from there. This means we should err on the side of taking less risk in the face of uncertainty about the probabilities of future returns. - *At the other extreme, what about small investments? For example: a $100 coin flip for an investor whose net worth is $100,000?* The *f2* rule of thumb suggests being indifferent at a side payment of about (0.0012) x $100,000 = 10 cents! That seems crazy. But if that investor has 45% in the stock market and the rest in the riskless asset, over about one hour his or her wealth will fluctuate by about $100 (with stock volatility of 20%). Using the same 3.6% excess return of equities as earlier, the expected gain in that hour is about 19 cents. So if optimally invested wealth is producing 19 cents for $100 of risk, he or she is roughly indifferent to a side payment of half that. The framework therefore suggests (if needed!) accepting smaller rewards for small risks than might at first seem intuitive. - *Should a passive investor in the stock market have a static allocation to equities?* Investment advisers typically subject their clients to a risk evaluation to determine an appropriate allocation to equities, often taking the form of the kind of indifference questions we posed. If you believe that the expected return and/or risk of the equity market change over time, then your optimal allocation to equities should also change.[11](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-11-343) - *Does horizon matter?* To the extent investments are like coin flips, following a random walk, with the risk we care about (variance) and the compensation we’re being offered to accept that risk both growing proportionately with time, then, whether we choose a month, a year or a decade as the horizon for our investment won’t affect our choice of the optimal amount we should invest in it. Whether we’re flipping a biased coin once or 300 times, the amount we put at risk as a fraction of wealth should be the same. - *How much is it worth to be able to invest in equities?* We don’t need to believe that we can beat the market for us to put a positive value on the opportunity to invest in equities. Recall that we’re choosing an allocation to equities that maximizes the *surplus* of what we’re expecting to be paid over what we need to get paid to accept that risk. That surplus is equal to half of the risk premium multiplied by our optimal allocation. So, for example, if we see equities priced to deliver a 5% expected return, and our optimal allocation is 60%, then our surplus is *1⁄2 \* 60% \* 5% = 1.5% pa* . This tidy sum should make us feel pretty good, even grateful, about the existence of the equity market and our ability to freely choose how much of it we’d like. We’re being invited to play a game with favorable odds, like betting on the flip of a coin that has a 60% heads bias, or playing in a poker game where the other players have more money than skill.[12](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-12-343) - *What is “Kelly” betting, and how does it relate?* The Kelly criterion, named after the scientist at Bell Labs credited with formulating it in 1956, tells us how to bet to maximize the expected growth rate of our wealth. Implicit in the Kelly criterion is a level of risk aversion that is half of what we’ve been using in these examples. So a Kelly investor in the stock market would need only 1.8% excess return to be indifferent to holding 90% of wealth in the market versus nothing – equivalently, he or she would only need to expect 3.6% to optimally be 90% invested in equities.[13](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/1#easy-footnote-bottom-13-343) This is a much more aggressive posture than most investors we’ve met seem comfortable with. ### Conclusion: We hope this discussion has given you some simple but versatile tools for thinking about a broad range of investment-related questions. Seeing the risk-taking decision more like tuning the dial on a radio, rather than flipping an on-off switch, enables us to get the most out of any game where the odds are in our favor, including investing in the stock market. The trick is to tune your portfolio to the point where the cost of risk, which is increasing quadratically, is just about to grow faster than the expected return you’re being paid to take that risk, which is increasing linearly. We hope you’ve found some “utility” in this brief summary, and that we haven’t taken too many liberties in attempting to distill what are some of the most valuable insights in finance from the last 400 years, from Daniel Bernoulli to Bob Merton, and many brilliant minds in between. --- ### Further Reading and References: - Arrow, Kenneth J. *“Alternative Approaches to the Theory of Choice in Risk-Taking Situations,”* Econometrica, Oct 1951. - Bernoulli, Daniel. *“Exposition of a New Theory on the Measurement of Risk,”* (1738). Translated in Econometrica, (1954). - Haghani, Victor and Richard Dewey. *“Rational Decision-Making under Uncertainty: Observed Betting Patterns on a Biased Coin,”* [SSRN](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2856963), 2016. - Merton, Robert C. *“Continuous-Time Finance.”* 1990. - Norstad, John. *“An Introduction to Utility Theory,”* Norstad.org, 1999. You can also see our pieces [here](https://elmwealth.com/video-the-most-important-number-you-wont-find-in-the-wall-street-journal/), [here](https://elmwealth.com/revisiting-the-expected-return-of-the-stock-market/) and [here](https://elmwealth.com/video-how-risky-is-your-stock-market/) on estimating the long-term expected return of the stock market and its risk. --- 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. We will always use “the expected return of equities” to mean the expected return above the risk-free rate. 3. If you answered 45%, you can pat yourself on the back and get back to teaching your finance students. 4. Sorry, but we’re assuming you’re North American and do like ketchup on your fries. 5. To be precise, if the second flip is for stakes of 1% of the new wealth, the variance of wealth change is 2.0001%. 6. A multiple of 1 corresponds to that of an investor with power utility function with relative risk aversion parameter *n = 2* . The power utility function is given by: *u(w) = (w1 – n – 1)/(1 – n)* for *n ≠ 1* , *u(w) = ln(w)* for *n = 1* . With *n = 2* , we won’t accept a fair coin flip where we lose half of our wealth, no matter how big the upside if we win. 7. Investing in the stock market isn’t the same as flipping a coin with known probability of outcomes. There is uncertainty in addition to risk concerning the distribution of outcomes. The setup of the problem in this note leaves out many real world practicalities, such as the value of one’s human capital, the correlation of future consumption with the market, and the existence of other assets, to name just a few. We also have modeled the stock market as normally, rather than log-normally, distributed to the one year horizon. 8. By the same logic, the risk of the stock market is *18% / 0.9 = 20%* . 9. The net value for any allocation, *k* , to equities is: *kα f2 – k(α f)2* , where *α* is the proportion committed to the risky investment, and *k* is the coefficient of risk aversion. The objective is maximized with respect to *α* when *α = 1⁄2* . 10. Let’s use the notation *(P,f)* for earning a side payment of fraction *P* of wealth in exchange for risking fraction *f* on a fair coin flip. What is the optimal fraction of wealth, *k* , of this risk we should choose, assuming we are indifferent to flips of *(f2,f)* ? To be indifferent, we need to choose *k* such that *(kf2 = kP* , or *k = P / f2* . The optimal choice is half of that, so  k = 12 P / f2 You can see that the optimal allocation, *k* , moves in proportion to expected return, *P* , and in inverse proportion to the square of risk, *f* . So, if stock market risk dropped by 10% (say from 20% to 18% in our example), then your optimal allocation to equities would go up by  1(1 – 10%)2~24% 11. Except if the changes in the return and risk of the market are such as to keep the ratio of return to variance constant. 12. We could also view this 1.5% a year as the risk-free payment we’d need to receive to forego being able to invest in the equity market, and only be able to invest in the risk-free asset. We’ve asked a version of this question to about 30 of our friends. We’re still conducting this survey, so stay tuned for the results in a future note. 13. As above, assuming 20% annual stock market volatility. The Kelly criterion in continuous time gives an optimal fraction to invest,  f = Rσ2 where *σ* is the annual risk of the stock market. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/how-much-of-a-good-thing-is-best-for-you) ![](https://insights.elmwealth.com/hubfs/Imported_Blog_Media/018-how-to-invest-banner.png) [How Elm Works](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) ### [How to invest with Elm – Fidelity SMAs vs Fund](https://insights.elmwealth.com/elm-wealth-research/how-to-invest-with-elm-fidelity-smas-vs-fund) Jun 29, 2016, 12:00:00 AM June 29, 2016 How Elm Works ## How to invest with Elm – Fidelity SMAs vs Fund We offer US taxable investors a choice: a separately managed account at Fidelity, or a Delaware private Fund. (for US IRA investments, we only offer SMAs at Fidelity). The following are some of the main differences between these two ways you can invest with us. Please see the [SMA Investment Management Agreement](https://elmwealth.com/signup/IMA) for full details or [contact us](https://elmwealth.com/contact-us) to receive the fund prospectus. Please consult your tax advisor and investment advisor, as the below is not being given as advice, and each investor’s circumstances will vary. ### Some benefits of investing in the Fund over the SMA: - The fund is slightly more cost efficient, owing to its larger size compared to the average SMA account, which for example allows access to institutional share classes of some index funds in which the fund invests. If you are considering making an investment of over $2mm there would not be much difference. - If the fund continues to grow, as we hope, inflows allow us to rebalance the portfolio more cost and tax efficiently by buying what we need to increase and allowing dilution to reduce what we want to decrease, rather than having to sell and thereby pay transactions costs and realize capital gains. - The fund uses Vanguard as its custodian and broker and pays zero commissions on all trades. On the other hand, trades in an SMA at Fidelity are subject to commissions on ETF and mutual fund trades. Those commissions don’t add up to many basis points on an SMA if the SMA is $1mm or more, but for a $300k SMA the commissions add in the region of 2-3bp in a typical year of cost. Although we take commissions into account in our management of the each SMA, they can be more or less than that each year. - The Fund has a slightly more granular and diversified Baseline asset allocation, with 21 buckets as compared to 15 buckets for the SMA program. The main differences in asset buckets are that SMA program does not have separate buckets for commodities and non-US real estate companies, and Europe x-UK and the UK are combined, as are Japan and Developed Asia x-Japan. - The fund has an administrator and produces audited financials each year, while the Separately Managed Accounts do not. The fund produces a tax statement in the more summarized form of a k-1 rather than the 1099 and list of trades that come from Fidelity for the managed account. - If you are a US citizen resident in the UK for tax purposes, the Fund may be more tax efficient if you don’t redeem until after you are no longer UK tax resident. ### Some benefits of investing in one of our SMAs over our Fund: - The main attraction of the SMA, besides the reduced minimum and being available to investors who are not Qualified Purchasers, is that the account is in your name and you can take over the account at any point in time by instructing Fidelity to remove Elm Partners as manager of the account, which provides in effect daily liquidity, as compared to the monthly liquidity of our fund. - With an SMA, if you want Elm to stop managing your account, your holdings are not liquidated, and so, if you have unrealized capital gains in your investments in your SMA, removing Elm does not realize those gains. If you are an investor in our Fund and you request a redemption, that will be a taxable event, and if you have gains, they will become realized as we pay redemption proceeds to you in cash. - The SMA offers even greater transparency than the fund in that you get to see a confirm of each transaction we do in your account the day we do it (for some this could be a negative, but then you could suppress confirm reporting). - The SMA benefits from $500k of SIPC insurance. - The fund allows investors to subscribe and redeem at NAV each month, and the transactions costs, which are quite small given the type of holdings in the fund, are borne by all investors who remain in the fund, whereas in the SMA you are only subject to the transactions costs that pertain to your own subscriptions and redemptions. This is a hard effect to quantify and we think it’s a pretty small effect, especially as the Fund heavily uses index funds which themselves allow investment and redemption at NAV without a transactions cost. - If you are a US citizen resident in the UK for tax purposes, the SMA may be more tax efficient if you plan on redeeming part of your investment while you are UK tax resident and your investment has increased in value. --- ### Disclaimer: Fidelity Investments is an independent company, unaffiliated with Elm Partners. Fidelity Investments is a service provider to Elm Partners. There is no form of legal partnership, agency affiliation, or similar relationship between your financial advisor and Fidelity Investments, nor is such a relationship created or implied by the information herein. Fidelity Investments has not been involved with the preparation of the content supplied by Elm Partners and does not guarantee, or assume any responsibility for, its content. Fidelity Investments is a registered trademark of FMR LLC. Fidelity Clearing & Custody Solutions® provides clearing, custody, and other brokerage services through National Financial Services LLC or Fidelity Brokerage Services LLC, Members NYSE, SIPC. \[eReview number 830247.2.0\]. [James White](https://insights.elmwealth.com/elm-wealth-research/author/james-white) [Read More](https://insights.elmwealth.com/elm-wealth-research/how-to-invest-with-elm-fidelity-smas-vs-fund) [1](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works) [2](https://insights.elmwealth.com/elm-wealth-research/tag/how-elm-works/page/2)