Elm Wealth Research

Posts by:

James White

Risk and Return

George Costanza At It Again: The Leveraged ETF Episode

Apr 16, 2020, 12:00:00 AM

April 16, 2020

Risk and Return

George Costanza At It Again: The Leveraged ETF Episode

By Victor Haghani and James White ¹

Sometime in late 2018…

George: How about this stock market? Down 14% in three months. It’s killing me. Day after day and all I see are big red numbers next to every single one of my investments. Everything I buy goes straight down – I can’t take it!

Kramer: Ooooooweee, buying stocks is no good.

George: No good?

Kramer: Here’s a can’t-lose strategy for you: invest half your money in SPXL and the other half in SPXS.

George: I never heard of these stocks before – what are they?

Kramer: They’re not stocks, they’re ETFs – Exchange Traded Funds, and they’re TURRRRBO-charged! SPXL is a 3x leveraged long S&P 500 ETF and SPXS is a 3x leveraged short S&P 500 ETF. There’s no limit to how much they can go up, and you can’t lose more than you put into them. One or the other is gonna make you rich. Kaching!

George: It’s gotta be better than what I’m doing now. What could possibly go wrong?

15 Months Later…

George: KRAMER!! What’d you do to me?!!? I should never have listened to you.

Kramer: What are you talking about? What’s the problem?

George: It’s those two leveraged ETFs you told me about. The stock market is up 6% since our little chat, but SPXL and SPXS are both down big – one is down 20% and the other one is down almost 50%!

Kramer: Hmmm…doesn’t seem possible. I’ve got another idea: have you ever thought about doing the opposite of whatever you think is a good idea?

George: I tried that already, and I’d rather not talk about it.²

Leveraged ETF Returns: Not What George Was Expecting

George’s surprise at losing on both SPXL and SPXS is understandable; they sound like direct opposites of each other. Given the 3x leverage and the stock market up 6%, he probably expected SPXL to be up about 18% and SPXS to be down about 18%. Instead both under-performed the ‘expected’ result by over 30%. The ETFs were not poorly managed, and the relatively high fees (about 1%) can’t come close to explaining the performance gap. In understanding what’s going on with these ETFs, we’ll uncover an important lesson relevant to all investing, about how your choice of investment size can be more important than your choice of investment.

These highly leveraged long and short ETFs provide a perfect illustration of how overly-aggressive investment sizing can turn a good trade into a losing one. An investor who borrows money to take a leveraged position in an asset will need to keep trading the asset in order to maintain a constant level of leverage as the asset price fluctuates. For example, 3x leveraged ETFs are structured and labeled as being constantly 3x leveraged through time, on a daily basis. For a 3x long ETF, that means the ETF needs to buy every day asset prices go up, and sell when they go down. This creates a nasty surprise: if the S&P 500 starts at 2500, goes up to 3000 one day, then back to 2500, the 3x-long ETF has to buy at 3000 and then sell at 2500, locking in a loss over the two days even though the market is flat. We’ll refer to this locked-in loss that comes from trading to maintain constant leverage as ‘volatility drag.’³ Over any given day, the 3x leveraged ETF return is equal to 3x the daily return – but over multiple days, because of this daily trading, the 3x leveraged return will be lower by an amount that depends on how volatile the market has been.⁴

High leverage combined with high realized volatility has a powerfully negative impact on returns, enough to explain George’s realized return of -20% for SPXL and -50% for SPXS relative to the market return of +6%.⁵ In the chart below, we show how George’s 3x-leveraged long ETF would have done over a range of returns for the S&P 500, given the 28% realized volatility of the stock market over his holding period.⁶ For SPXL to have outperformed an unleveraged investment, the market needed to go up by more than 22% to overcome the leverage-induced volatility drag.

Market Impact of Leveraged ETFs: 1987 Portfolio Insurance Redux?

Even though George hadn’t heard about these leveraged ETFs, they’ve been around since 2006 – and they’ve grown to be more than a side-show in the marketplace. According to Lara Crigger’s research at ETF.com, leveraged ETFs had assets of close to $40 billion at the end of March 2020,⁷ and that’s just tallying up the US-listed structures that are publicly registered – there’s likely considerably more in privately-structured products and non-US vehicles.

To gauge the potential market impact of these leveraged long and short ETFs, let’s take a closer look at what trades SPXL and SPXS would have to execute after a 10% market rise:

We can see that after this 10% market rise, SPXL is now under-levered and SPXS is over-levered. To return to 3x-long and 3x-short, both ETFs need to buy more S&P 500. SPXL needs to buy $60 of the S&P 500 and SPXS needs to buy $120. If the market falls instead, the numbers are the same but the ETFs will need to sell. As you can imagine, the turnover within these levered funds can be enormous; for a 3x leveraged-long ETF assuming 1% daily moves (16% annualized), annual turnover would be 1500%, and 3000% for a 3x leveraged-short ETF.

In terms of the potential market impact of the trades these ETFs need to do each day, we estimate that the managers of these public leveraged ETFs need to buy or sell about $10 billion of equities when the stock market goes up or down by 5%, and most of that trading has to happen near the closing bell each day. Of course, many market participants are aware of these, and other similarly predictable flows coming from options-hedging and leveraged investment strategies such as Risk Parity and volatility targeting funds. In trying to profit from these anticipated flows, opportunists smooth them out and make them harder to pinpoint, but their impact doesn’t completely disappear.⁸

Sizing Your Stock Market Exposure for the Long-Term

As you know from our other research notes, we think choosing your equity allocation should be a forward-looking exercise, driven by your assessment of future return and risk, and your own circumstances and personal level of risk aversion. That said, it’s still interesting and instructive to take a look back sometimes, and we’re going to take a look at how different levels of stock market exposure – including leveraged – would have performed over the long-term.

From 1927 to the end of March 2020⁹, the annualized total return on the S&P 500 was 9.6%, which would have turned a $1mm investment into $4.5 billion today – not too shabby. Average stock market volatility was just under 19%, and T-Bills returned 3.7% p.a. If you were around in 1927 and had a crystal ball, wouldn’t you have been tempted to invest in equities on margin and really make a killing for your lucky descendants? After all, if investing 100% of your savings in equities for the long-term was sure to be great, why not invest 200% or 300% of your savings?

The table below works through this thought experiment, showing how things would have turned out for an equity investor taking on different amounts of leverage over those nearly 100 years.¹⁰ Notice that 1.5x leverage leaves you with the most money at the end, but at some point you’d have experienced a drawdown of 95%. Above 1.5x leverage, return goes down and risk goes up, driven by the volatility drag we’ve been discussing. At 4x leverage, after suffering more than a 99.99% drawdown, you’d eventually only be left with the $1 you started with (just $0.09 inflation-adjusted), and at 5x leverage you’d have been fully wiped out on October 19th, 1987. Here’s an interesting thought-experiment: what equity exposure would you have chosen standing in 1927 with the crystal ball?¹¹

Opposite George?

What if George followed Kramer’s advice, and did the opposite of whatever he thought was a good idea so instead of buying these two leveraged ETFs, he shorted them? As we explained in our first note about George’s investing, being short is not the opposite of being long. In fact, if we assume that an investor shorting either of George’s ETFs wants to keep the value of her short equal to her capital in the trade (including unrealized losses or gains along the way), then being short the 3x leveraged long ETF looks exactly the same as being long the 3x leveraged short ETF, and vice versa.

The closest thing to achieving the opposite of the leveraged ETFs’ volatility drag would be to invest in a balanced portfolio, such as 50% equities and 50% T-bills. Maintaining the 50% / 50% weight over time would require buying equities when they go down and selling when they go up, creating a volatility ‘lift’ instead of a ‘drag’ from the portfolio rebalancing. Unfortunately, this lift is naturally limited in scale – you can create as much drag as you want by using large leverage, but you can only get the maximum lift by maintaining a position size at 50% of total capital.

Conclusion

A big problem with holding these leveraged long and short ETFs for more than one day is that most investors are likely to think they are making a decision based on a view of where the market is going: up or down. As we’ve explained though, that’s not typically what they’re getting.¹² Rather, the return on a leveraged long or short ETF held over time will incur a drag that increases dramatically with both leverage and realized volatility. As George’s experience attests, the investor can have the right call on market direction while the investment outcome is overwhelmed by the impact of high realized volatility.

The exchange between George and Kramer is fictional, but the disappointing returns on George’s two leveraged ETFs are sadly quite real. The lesson from George’s misadventure isn’t only for those thinking about investing in highly leveraged ETFs. For all investments, as position size increases, there’s a point beyond which you’ll be more likely to wind up with losses than with gains, and further still, an amount of exposure at which you’ll be almost assured of losing all your money. Much of the art of investment sizing lies in appreciating and optimizing where on the curve is right for you.

Introducing the Elm Partners All-Equity Portfolio For Non-US Investors

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

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 or set up 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 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

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 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 We measure momentum for each asset class relative to the return of the Baseline⁵ and we’ve reduced the intensity of the value signal to counter the amplification which can result from the target weight normalization process.⁶

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.

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, 1974⁷ 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. 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.

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.

Taking Stock

Mar 19, 2020, 12:00:00 AM

March 19, 2020

Risk and Return

Taking Stock

By James White and Victor Haghani ¹

The longest bull market in US stock market history is over. Uncertainty over the public health and economic impact of the coronavirus pandemic will keep markets extremely volatile, making it likely we’ll touch a wide range of price levels in the months ahead.² Amidst such uncertainty, it’s a particularly good time to take stock of long-term return prospects. In doing so, we’ll present an often-overlooked perspective on the market’s attractiveness which is both intuitive and technically sound. We hope long-term investors will find it useful in deciding how much stock market exposure they want right now, and at other levels the market may visit in the future.

One popular way of thinking about equities is that they have an ‘average’ or ‘fair’ earnings multiple to which they tend to revert, making them cheap below that multiple and expensive above it. We don’t subscribe to this view, as we discuss in our note “Market-Multiple Mean-Reversion: Red Light or Red Herring?” But we do think there are times when it makes sense to own a lot of equities, because they offer high expected returns relative to other places you can put your money, and other times when relative expected returns warrant a small equity allocation. This perspective requires two measures: 1) a forecast for the expected return of the equity market, and 2) an appropriate ‘benchmark’ investment against which to measure equities’ relative attractiveness.

Getting Real

The most widely used forward-looking indicator of the stock market’s long-term expected return is the Cyclically-Adjusted Earnings Yield (i.e. 1/CAPE).³ Importantly, it’s a forecast for what economists call the “real” return of equities, which means the return in excess of inflation. Increasing our wealth in real terms improves our well-being, increasing it in nominal terms alone does not.

Next, we need to identify the appropriate benchmark investment against which to measure equities’ relative attractiveness. Owning equities is risky, and so it’s pretty intuitive to measure the expected return on equities relative to the return offered by a risk-free asset.⁴ We probably wouldn’t want to own any of a risky investment with a 10% expected return if the risk-free rate was also 10% – why take extra risk for no extra return? The same investment with a 5% expected return and 0% risk-free rate might look great. It’s the excess return – often called the equity risk premium – we should care about when thinking about the attractiveness of equities.⁵

Our return forecast for equities is both long-term and real, and so the appropriate benchmark for the risk-free rate also needs to be long-term and real. Most suited to this role is the yield on long-term US Treasury Inflation Protected Securities (TIPS).⁶

Fifty-Year Historical Perspective on Equity Market Risk Premium

Taking the difference between the long-term expected real return of equities and the real risk-free rate gives us the Equity Risk Premium chart below. It offers our preferred perspective on the current and historical attractiveness of US and Global (US plus non-US) stock markets for long-term investors who do not hold strong near-term views. The chart ends on March 18th, 2020.

One reason you may not have seen a chart like the one above before is that the US Treasury only began issuing TIPS in 1999. To produce this chart, we had to construct a proxy series for the long-term risk-free real rate from 1970 – 1999, inferring what the long-term TIPS rate would likely have been had it existed, which can be seen in the lower panel of the chart.⁷

We see periods of generous equity risk premia (1975 – 1982), and also periods of low and even negative risk premia (1987 – 2002). An investor looking at CAPE alone might find US equities relatively unattractive right now: the current CAPE of 22.5x⁸ is higher (less attractive) than it’s been 80% of the time over the past 120 years. We think the chart above paints a very different picture, suggesting that today’s US and global stock market risk premia are attractive, in both absolute and historical terms. For example, the current global equity risk premium of about 6%⁹ is higher (more attractive) than it’s been 80% of the time since 1970, and it’s higher now than it was during the entire period from 1985 up to the financial crisis in 2008. While equity risk premia cannot tell us the future path of equity prices, especially in the short-term, they do suggest that current long-term return prospects for global equities are attractive and consistent with an above-average level of exposure.¹⁰

The History of Real Rates

Risk premia and real rates have both had a wild ride over the period shown in the chart above. One distinctive feature of this chart is that real rates are really low right now. This flies in the face of classical economic theories of interest rates that posit positive real interest rates are necessary to induce people to save for the future, rather than consuming “too much” in the present.

It’s surprisingly hard to find deep historical context, beyond living memory, to inform thinking about real rates. The reference work on the long-term, 2,000-year history of interest rates, Sydney Homer’s “A History of Interest Rates,” mentions real interest rates just once in 700 pages. This isn’t especially unusual; in the financial press it’s much more common to read about nominal rates, and investment returns are nearly always quoted in nominal terms. Market-quoted real-return instruments such as US TIPS and UK Linkers are still in early middle age, and have not really penetrated the popular consciousness yet.

However, a 2019 paper by Yale economic-historian Paul Schmelzing, “Eight Centuries of Global Real Interest Rates,” has shed valuable light on the history of real rates. Here we reproduce a chart from the paper showing the core findings:

A few takeaways from this chart:

Periods of negative real interest rates, such as much of the developed world is currently experiencing, are relatively common and can be protracted. While negative nominal interest rates historically have been difficult to impose on investors who have the option of keeping cash “under the mattress” rather than in a bank, negative real rates don’t run up against any such hard barrier.
There does not appear to be an average or “natural” level of real interest rates around which actual rates fluctuate.
There appears to be a downward trend in the level of real rates, estimated at 2bp / year. However, we caution that this trend-line does not have strong predictive power.

Technical Sidebar

We see nothing in the historical data which makes us disagree with the market’s current expectation of near-zero real rates – but what should an investor (we’ll call her Tipper) do who doesn’t share that view, believing instead that risk-free real rates will rise and TIPS prices will fall? A full treatment of this question merits its own note, but for a sense of how one might approach it consider a simplified world with three available investments: TIPS, the stock market and T-Bills, with TIPS being the minimum-risk asset for Tipper, an investor with a long-term horizon.¹¹ Tipper has her equity return forecast, expressed relative to TIPS as we’ve been discussing, and because she thinks TIPS prices will fall, she’s also forecasting a high return for T-Bills relative to TIPS. She now needs to decide the optimal combination of equities and T-Bills to hold, based upon their expected excess return relative to TIPS, their risk and their correlation to each other. If we assume that they are uncorrelated, as suggested by both data and a desire for simplicity, then we can determine the optimal allocation to each of the trades separately, driven by their own expected return and risk relative to TIPS and Tipper’s personal level of risk aversion.¹² In this case, Tipper’s desired equity exposure is still driven solely by their expected return relative to TIPS. Her real rate view makes her want to hold more T-Bills, not less equities, and if her desired equities plus T-Bills exposure is greater than 100% she’ll need to have a negative (short) allocation to TIPS to bring the sum of the allocation weights to 100%. If however she can’t or won’t short TIPS (and we too are generally opposed to shorting any asset), then she wouldn’t be able to hold all the equities and T-Bills she wants and would optimally reduce both her desired equity and T-bill exposures instead.

Conclusion

For an investor who accepts as fair the market real rate offered by TIPS, should the absolute level of real rates impact the equity allocation decision? All else equal, our answer is no. Lower risk-free rates imply lower absolute expected returns for risk-free and risky assets. This is an unfortunate fact for any investor, but in deciding how much to invest in equities, investors should want to scale risky investments proportionally to the risk premium, not the absolute expected real return. Of course, ‘all else equal’ is just the starting point for a fuller assessment. For example, lower real rates means more of the value in equities comes from longer-dated cash-flows, which may increase the long-term riskiness of equities and impact how much an investor should want to own for a given level of expected excess return. And of course, investors taking a long-term view of equity market attractiveness will still want to make adjustments for identifiable near-term impacts to earnings streams, such as those arising from the current coronavirus pandemic.

We hope the framework presented in this note gives you a fresh perspective for evaluating the attractiveness of the broad stock market to a long-term horizon. Indeed, if we accept that today’s low real rates represent a fair expectation of the future, P/E ratios which seem otherwise elevated may join low and negative interest rates as part of the ‘new normal’ investing landscape.

How to Fund Your Elm 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.
- 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

Risk and Return

Mind the Gap: Inequality and Diversification

Dec 11, 2019, 12:00:00 AM

December 11, 2019

Risk and Return

Mind the Gap: Inequality and Diversification

By Victor Haghani, Jeffrey Rosenbluth and James White ¹

Introduction

Understanding the origins of wealth inequality is critical in the debate over what, if anything, to do about it. In this note, we propose a simple model which is still rich enough to reproduce observed patterns of wealth inequality. We call it the Concentrated Asset Betting (CAB) model. A key element of CAB is a phenomenon known in the gambling world as “over-betting the edge.” Our approach was inspired by Bruce Boghosian’s Scientific American article “Is Inequality Inevitable?” which provides an introduction to a straightforward model of wealth inequality called the “Yard Sale Model” (YSM).

In a Yard Sale model, it is assumed that people enter into repeated exchanges with each other. In each exchange one party is chosen at random to be the “winner” and one the “loser.” The absolute size of the exchange is determined by the assets of the less wealthy party. As the number of exchanges increases, the model converges to one person having all the money in the economy. To match observed levels of wealth inequality in different countries at different times, the YSM is then extended to include wealth redistribution and a couple of other enhancements.

Model Description

The model we propose is based on the observation that a high fraction of investors have experienced sub-par growth in their savings, after allowing for consumption and philanthropy, relative to the tremendous long-term growth in the public stock market. Victor presented some anecdotal evidence of this in his TEDx talk, “Where Are All the Billionaires and Why Should We Care?” Some of the reasons put forward to explain the shortfall in investor returns include investment fees, commissions and taxes. Our model suggests there may be something even larger and more insidious at work – pervasive and systematically poor money management. Here, money management means the task of sizing and diversifying the risks of a portfolio of investments.

Numerous academic studies have documented the tendency of investors to hold significantly undiversified portfolios, especially in the pre-Vanguard era up to the early 1990s. With commissions of $70 or more per trade, investors had an incentive to minimize the number of individual stocks they held.² A study by Vanguard observed that from the 1950s through the 1980s investors’ equity exposure came almost entirely through directly-held stocks, and the median investor held only two stocks.³

The most basic version of our model begins with a population of households all with the same initial wealth. Each household starts off fully-invested in one stock.⁴ If their wealth increases, they increase the number of stocks they own, thereby increasing their diversification. We add one stock to their portfolio each time their wealth doubles. Each portfolio is split equally among however many stocks they own, rebalancing monthly.

Every stock has an annual expected return of 6%, which roughly matches the US stock market’s annual price appreciation over the past hundred years.⁵ We assume a 19% standard deviation of monthly returns, consistent with Hendrik Bessembinder’s large-scale study “Do Stocks Outperform Treasury Bills?” For simplicity, we assume the stocks are uncorrelated with each other.⁶

In our simulation, we flip a coin for each stock every month. If heads, the stock in question gains 19.5%. If tails, it loses 18.5%. This gives us the desired 19% standard deviation, with monthly expected return of 0.5% (6% annualized) for each individual stock.⁷ The chart below shows the ending wealth distribution after running this simulation for 100 years on 1000 families. Like the YSM, our model predicts a high level of wealth inequality. Unlike the YSM, our model features a growing economy.

Interpreting Model Results

All families have identical prospects starting out, yet high levels of wealth inequality naturally arise anyway. What’s at work here? First, with portfolios concentrated in just a few individual stocks, chance creates a lot of inequality in wealth outcomes.⁸ Second, good luck, measured by the number of heads flipped, translates into increasingly large incremental gains in wealth. That means wealth as a function of luck is highly convex in the long-term, as good or bad luck compounds multiplicatively rather than additively. This can be seen in the dramatic curvature of wealth plotted against number of heads flipped over 100 years in the chart below.

The third force leading to extreme inequality causes many families to wind up with near zero wealth despite investing in stocks that are all expected to rise 6% a year, as can be seen in the chart above. Over the 1,200 months of the 100-year simulation, the expected number of heads is 600, half of the total flips. Yet, the chart shows that if a household experienced 600 heads, they’d wind up with close to 0 wealth. In fact, they need to get 642 heads just to break even.⁹ This results from “over-betting the edge,” defined as taking so much risk that you lose money in the central case of flipping an equal amount heads and tails. If a single stock portfolio gains 19.5% one month and then loses 18.5% the next month, the total return over the two months is not the +1% you’d get from two months of +0.5% expected return per month. Rather, it is -2.6% as illustrated in the diagram below.¹⁰

In addition to being able to generate different levels of inequality to a given horizon, we can also influence the degree of wealth mobility in our system by choosing how quickly we allow families to diversify their portfolios by adding more stocks with increases in a household’s wealth. Through this mechanism, the winners get more diversification, lessening their over-betting and increasing the chance of keeping and growing their winnings.

An important parameter in the basic form of our model is the number of stocks initially held. The chart below shows how greater initial diversification, and thus less over-betting, dramatically lessens wealth inequality. For each distribution of wealth curve, we calculate the Gini coefficient, a popular summary metric of inequality.¹¹ Holding 100% of wealth in an 8-stock portfolio represents the acceptable amount of risk for a gambler who bases her risk-taking on the Kelly Criterion, a commonly-used metric which gamblers generally agree sets an upper bound on how much risk to take for a given opportunity.¹² Even though an investor with an 8-stock portfolio in our framework can no longer be accused of over-betting, she could still improve the quality of her portfolio dramatically with more diversification. If we had investors start off with portfolios of 1,000 stock holdings, we’d get very little wealth inequality, which is what we’d expect if most families held the market portfolio through an index fund.

The chart below displays the actual distribution of wealth in the US in 2000,¹³ which is a good fit with our model using a 9-stock initial portfolio for each investor.

Conclusions and Future Research

While we recognize that there are many causes of wealth inequality, the CAB Model provides a simple and empirically-supported explanation for how the level of wealth inequality seen today came about. Some of the assumptions we’ve made may seem extreme by today’s standards, such as using a 19% monthly standard deviation of stock returns, but the CAB results are robust to more moderate assumptions. Indeed, if the US investing scene for most of the 20^th century resembles developing markets today, then a recent paper by Campbell et al, “Do the Rich Get Richer in the Stock Market? Evidence from India (2018),” provides direct support for the CAB explanation of wealth inequality resulting from pervasive under-diversification.¹⁴

We hope this short note will spur further research focused on understanding the properties of this model of wealth inequality, and on refinements to make the model more realistic while still retaining its parsimonious structure. In particular, we hope to explore its ability to match observed levels of wealth mobility, the impact of a wealth-redistribution tax, and how to incorporate non-participation and underinvestment in risky assets as another important cause of long-term wealth inequality.

The CAB model provides an alternative to that proposed by Thomas Piketty in “Capital in the 21^st Century” (2014), which assumes that equity returns are high and constant, so once a household gets rich enough to have significant investable wealth, they’re going to get richer and richer.¹⁵ Unlike Piketty’s Capital model, CAB tells us where the “missing billionaires” may have gone, incorporates pervasive sub-optimal risk sizing, and predicts the frequently observed downward mobility of the undiversified wealthy. It also points the way to a more level potential distribution of wealth in the future, due to the growth over the past 20 years of index funds and other diversified mutual funds.¹⁶

Unlike the Piketty and the Yard Sale models, the CAB paradigm does not see extreme wealth inequality as an inevitable and convergent feature of “pure” capitalism absent specific offsetting policies such as wealth redistribution. Rather, it shines a bright and hopeful light on one possible path to less wealth inequality in the future, which is for investors to think more carefully about diversification and investment-sizing, thus improving their chances of participating in the long-term expected wealth creation opportunities offered by public markets.

Negative Interest Rates and the Perpetuity Paradox

Nov 19, 2019, 12:00:00 AM

November 19, 2019

Risk and Return

Negative Interest Rates and the Perpetuity Paradox

By Victor Haghani and James White ¹

“We are actively competing with nations who openly cut interest rates so that now many are actually getting paid when they pay off their loan, known as negative interest. Who ever heard of such a thing? Give me some of that. GIVE ME SOME OF THAT MONEY. I WANT SOME OF THAT MONEY.”
– President Donald Trump, Economic Club of New York, November 12, 2019

If President Trump had his way, the US would be sporting significantly negative rates right now. While there is wide-ranging disagreement on the long-term impact of negative interest rates ² – good, bad or neutral – there is growing acceptance that negative interest rates are the ‘new normal’ with 30% of the world’s government bonds trading at sub-zero yields, as illustrated in the table below.

Negative Rates and Ultra-Long-Term Bonds

For Wall Street’s bond-pricing models, negative interest rates mostly have been no big deal; the same code usually works just fine when yields are negative instead of positive.³ But there is at least one exception, a bond type that cannot abide a negative yield: the Consol bond.⁴ Even though governments don’t issue them anymore, they’re one of the simplest and oldest of all bonds. Also known as Perpetuities, these bonds provide the holder with a fixed interest payment each year in perpetuity. They were issued and re-issued by governments such as the UK, France and the US, and were often the market’s largest and most actively-traded issues. The UK retired their last Consol bonds in 2015, and today there are virtually no government-issued perpetual bonds outstanding. However, there are plenty of other perpetual or near-perpetual cash flow streams investors can buy, and recently issued sovereign bonds with maturities of 50 to 100 years may feel like near-perpetual offerings to many investors.

The basic formula for the price of a perpetual is simple:

p = c y

where symbols represent price, coupon and yield, for y > 0 .

Two noteworthy aspects of the formula: 1) for any positive coupon and positive finite price, the perpetuity cannot have a negative yield, and 2) price approaches infinity as the yield of the perpetuity approaches zero.

The chart below illustrates the relationship between the price and yield of a perpetuity and annuities with different maturities. Notice how extremely convex these curves become at very low interest rates. This kind of convexity is generally an attractive characteristic for buyers of such investments, and a terrifying one for short-sellers.

To avoid having to deal directly with infinity – clearly a price that no-one would be willing or able to pay – we’ll consider a 1,000-year annuity paying $1 per year, rather than a Perpetuity. If we know interest rates are fixed for the next 1,000 years, we can easily calculate and see the annuity’s price on the chart above, but what’s a reasonable fair price given some uncertainty in interest rates? Let’s approximate this value by imagining 1,000 different interest-rate scenarios. Let’s say that, in 999 scenarios, interest rates will equal 2%. But in just one scenario, we’ll assume rates will instead average -1%, in the spirit of the ‘new-normal’ for interest rates and the possibility that interest rates can be negative for sustained periods of time in the future. The Expected Value of the annuity is the probability-weighted average of the Values of the annuity that result from those scenarios, producing a result which is pretty remarkable:

99.9% probability of 2% rates; annuity value of $50

0.1% probability of -1% rates; annuity value of $2,316,257 (!)

Expected Value of the annuity is $2,366, which is a yield of -0.15%.⁵

A Potential Perpetuity Paradox

What we’re calling the Perpetuity Paradox is the conundrum facing a person who simultaneously believes that there’s a small chance negative interest rates can persist for long periods of time, but would not pay a price anywhere close to the $2,366 Expected Value of the annuity for more than a de minimis amount. We are not claiming that most people hold these beliefs…but if you do (and we don’t think it’s unreasonable to do so) then you’ve got a paradox on your hands.

One solution to this potential paradox is suggested by the resolution to the St. Petersburg Paradox, proposed by Daniel Bernoulli in 1738. The St. Petersburg Paradox involves a game that no one would pay much to play, despite the game having an infinite Expected Value. The common thread in both the Perpetuity Paradox and the St. Petersburg Paradox is that what someone will be willing to pay is, in the absence of riskless arbitrage, often determined by their Expected Utility and not the Expected Dollar Value of the gamble.⁶

In working with Expected Utility, we’re going to assume a level of risk aversion typical of 30 of our investors we surveyed a year ago. We find that even at a price of just $51 for the annuity a typical investor would optimally invest only 1/2000th (0.05%) of her wealth, even though the price represents a 98% discount to Expected Value.⁷ Much closer to the Expected Value of $2,366, a price of $2,100 merits an optimal investment of only 1/10,000th (0.01%) of wealth. Thus, we can see the Expected Utility line of reasoning presents one resolution to the ‘paradox’: even though the small possibility of negative rates makes the ‘gamble’ on the annuity highly valuable, an ordinary investor wouldn’t bet more than a tiny fraction of wealth on it. Sadly, the UK government can forget about issuing one 1-Pound-per-year inflation-indexed Perpetuity to pay off the entire national debt!

Conclusion

We can’t say how long the new-normal of negative interest rates will continue – but given the negative long-term nominal and real rates we see in a number of major economies, it seems difficult to dismiss negative rates as just a fleeting phenomenon. That means it’s worth seriously thinking through the issues involved in valuing and investing in long-lived cash-flow streams, whether arising from government bonds, real estate or equities, near and below the zero interest rate frontier.

Regardless of your position on negative interest rates, we hope this note has illustrated two important and intriguing considerations that impact many important investment decisions under uncertainty:

Convexity matters: The Expected Value of long-term cash flows is highly convex, especially in the region of low discount rates. It’s noteworthy, in this case, how only a tiny assumed probability of negative rates has such an enormous impact on Expected Value.
Utility matters more: Supply and demand is what sets prices, and in the absence of arbitrage, Expected Utility trumps Expected Value in assessing how much demand investors will have for an investment.

Appendix: Using a Probabilistic Interest Rate Model to Put a Value on a Near-Perpetuity

It’s hard to describe how far-out the idea of negative interest rates has been to economists and market participants throughout history. What would Sidney Homer, co-author of the 4,000 year survey “A History of Interest Rates” and Salomon Brother’s first director of Bond Research, have made of UK investors’ locking in a 65% loss in the purchasing power of their savings by buying 50-year inflation-linked bond at a yield of -2.03%? ⁸ Influential economists and philosophers through the ages, including Marshall, Fisher, von Mises, Hicks, Hayek, Knight, Keynes and Friedman, all wrote books and articles proposing differing theories of interest rates. One common thread was that none of them envisioned negative interest rates as a realistic phenomenon they needed to explain.

It wasn’t until the late 1970s that economists started to directly embed uncertainty and randomness into interest rate models, thereby taking account of the convexity of discounted cash flows so central to the Perpetuity Paradox we’re discussing. Since then, many stochastic interest rate models have been proposed, including those by Vasicek (1977), Cox-Ingersoll-Ross (1985), Heath-Jarrow-Morton (1989), Black-Derman-Toy (1990) and White-Hull (1990, 2006). For the case at hand, simplicity and familiarity persuaded us to use a model similar to one that we used at Salomon Brothers, called the 2+ model, in the days when banks were allowed to invest their own capital in proprietary trading.⁹

We’ll use this model to generate 1,000 possible paths for future interest rates, which in turn produce bond prices and corresponding yields. We’ll parameterize the model so that the expected bond prices are roughly consistent with the pricing of German bonds with maturities of 1, 5, 10 and 30 years, taken from Table 1.

Below is a description of the model. An important feature is that it allows the short-term interest rate to go as negative as h:

dx = ƛ dt + 𝞂₁ dw₁
dy = -ɣ y dt + 𝞂₂ dw₂
dz = -k (z – x – y)dt
r = e^z – h

The chart below shows the value of a $1 a year 1,000-year annuity for each of 1,000 paths we generated with this model, arranged from smallest to largest value, and plotted on a log scale since some of the values are so large.

You can see how the Expected Value of the annuity is heavily influenced by a small number of very large expected dollar values, just as we suggested in our two-scenario analysis in the body of the note. This is the distribution of values of the 1,000-year annuity which are consistent with the current market pricing for German government bonds, taking into account the uncertainty around future interest rates and the possibility that interest rates stay negative for prolonged periods, consistent with the new-normal perspective.

As noted above, we are using a no arbitrage model of interest rates for this analysis. This means that in theory, if the 1,000 year annuity were trading at a price below the model price, an arbitrageur could buy it and hedge it with other bonds and make a riskless profit equal to the difference between the market and model price of the annuity. There are significant limitations involved in doing this in practice for such a long horizon asset, including transactions costs and frictions in holding the required highly leveraged long and short positions of the hedge portfolio, the necessity of the particular interest rate model chosen to have a form and parameterization which accurately describes how interest rates evolve in the future and the extremely long horizon involved in forcing convergence to the model.

Alternative interest rate models will produce charts that can look substantially different than the one above. For example, models that assume interest rates will mean-revert to a fixed and pre-known positive level will not produce paths that put such high values on the annuity, but then we’d suggest that such models are not really in the spirit of the new-normal for interest rates. As discussed above, we believe that Expected Utility analysis is the best tool for figuring out what an individual would be willing to pay for this distribution of outcomes, and thereby resolves the apparent paradox of perpetuity pricing in a future that may experience negative interest rates for sustained periods.

Update:

Bloomberg author Brandon Kochkodin wrote a great piece in response to our post on negative interest rates, which you can read by clicking the link below:

How Negative Rates Can Send Bond Prices Soaring

Victor also took a moment to talk about negative rates on BloombergTV, watch the full interview below:

There’s No Place Like Home: The Case For and Against Extreme Home Bias in Equity Investing

Oct 30, 2019, 12:00:00 AM

October 30, 2019

Featured Insights

There’s No Place Like Home: The Case For and Against Extreme Home Bias in Equity Investing

By Victor Haghani and James White ¹

If you’re a US investor, international equity exposure has never been so readily available at such a low cost. Nonetheless, surveys indicate US investors typically allocate 80 – 85% of their equity holdings to US equities, much higher than their proportion of global market value. We recently wrote about how this kind of “Home Bias” can impact expected returns. Here we turn to evaluating 10 arguments often heard in support of high levels of Home Bias.²

1. US equities have outperformed non-US equities by 170% over the past 10 years

Ironically, we really couldn’t make the point for international diversification any better than this. Ten years ago, few would have or did put forward this magnitude of US outperformance as a likely scenario, but it happened.³ Over long periods of time, individual equity markets can significantly outperform or underperform in ways which are very difficult to predict, though easy to explain ex-post with the benefit of hindsight. Ten years sure feels like a long time, and it’s tempting to conclude that it’s long enough to draw some conclusions about what the next ten years will hold, but if ever there was a place to say it, it’s here: past performance is not indicative of future returns.

Sources: Bloomberg, MSCI, FTSE. Emerging Market equities included from December 1989.

2. Over the past 10 years, an internationally diversified portfolio wasn’t anywhere near optimal

The theory of diversification is not that a diversified portfolio is likely to ever look optimal in hindsight, but rather that it has superior risk/return characteristics looking forward given an uncertain future. A concrete example may be helpful:

Over the last 10 years, the portfolio that had the highest realized return-to-risk ratio (i.e. Sharpe Ratio), was a portfolio that had about 20 stocks in it, chosen from all members of the S&P 500.⁴ The reason everyone doesn’t now own just those 20 stocks is that many investors have an accurate sense that it will be a different small group of stocks doing the best over the next 10 years. And indeed, the best risk-adjusted “hindsight” portfolio from 1999-2009 is completely different than one from 2009-2019. The idea behind diversifying to own 500 stocks is not that 500 stocks will beat every combination of 20 stocks over any given period. Instead, the problem is we don’t know which will be the best 20 stocks looking forward, and without this knowledge, the diversified portfolio looks better than choosing a more concentrated portfolio. But, if you know the big winners with hindsight, they’ll always look a lot better than owning the diversified portfolio.

So too with international diversification. Over any given period, there’s very likely to be one or two markets which significantly outperform the globally diversified portfolio, and in recent years amongst major markets, that outperformer has mostly been the US. That doesn’t reflect a flawed theory of diversification, just a recognition that – in both theory and practice – the benefits of diversification are to be seen through the windshield looking at the road ahead rather than in the rear-view mirror.

3. Investors favor the familiar

This is completely understandable, but it’s a cognitive bias that can potentially come at a high cost. For most people still in their earning years, their human capital is often their largest asset, and domestic markets are much more highly-correlated with that human capital than are foreign markets. All other things equal, we’d be better off owning things less correlated with our primary asset, the very opposite of this bias.

US investors may be especially unaware of this subtle cost of concentration because the history of US equity markets has been so benign in our investing lifetimes. However, US investors in the 1930s or 1970s, Japanese investors in the 1980s, or Russian investors in the early 1900s and late 1990s all received a first-hand lesson in the value of international diversification.

4. International equities don’t offer much diversification, because whenever US equities experience a large correction, international equities usually go down as much or more

Over short horizons of days, weeks, and months, large moves are indeed typically shared by nearly all public equity markets. This is also true of equities within the same market, yet we intuitively understand that despite this, owning a portfolio of 500 stocks spread out over all sectors of the economy provides meaningfully more diversification than owning just a handful of stocks. While individual equities may often be highly correlated during large moves over short time periods, such as during the 2008 financial crisis, most investors have longer horizons over which these correlations tend to dissipate. This is true of the correlation between US and international equity markets as well, as we see in the chart below:

Sources: Bloomberg, MSCI, FTSE. Emerging Market equities included from December 1989.

A number of studies support the view that international diversification works over the long term as differences in underlying economic, demographic, political, social and regulatory fundamentals between countries and regions make themselves felt in equity market returns. For example, see International Diversification Works (Eventually) by Asness, Israelov and Liew (2010): “Over longer horizons, underlying economic growth matters more than short-lived panics with respect to returns, and international diversification does an excellent job of protecting investors.” Increased globalization has likely led to higher correlations among regional equity markets, but it’s far from clear whether this globalizing trend will continue or start to reverse.

There’s also an important point to make about the limits of the historical record: even a long past fails to plumb the depths of possible futures. Many events are possible which have never happened before and don’t show up in any data series. Diversification offers an effective first line of defense against low-likelihood but large-impact scenarios.

5. US companies earn a meaningful fraction of revenue internationally, thus investors get international diversification just from US equities

US equities do have substantial international earnings. However, all US companies share exposure to a long list of significant US-specific risks — economic, political, financial, regulatory, tax, labor, etc. These are important risks, and non-US stocks can provide diversification from them in a way that US stocks with significant international earnings streams cannot.

According to Morningstar, 35% of the revenue of US public market companies came from outside the US in 2018. While this may seem to provide broad exposure to international economic activity, it offers less diversification than it seems. US companies’ international revenues come from big companies in a concentrated set of industries. For example, in 2018, 60% of the revenues of the information technology sector came from non-US markets while the utilities, real estate and financials sectors received just over 10% of their revenues from overseas.⁵ And there are many segments of the non-US economy which US companies hardly touch at all, particularly in less open economies in the developing world.

6. Non-US equities are riskier than US equities

International equity market returns measured in dollars have been more volatile than US market returns. For example, since 1990, the volatility of US equity returns was 14.5% compared to 17% for non-US equities.⁶ However, this by itself is not an argument against diversification. The three main inputs into the “portfolio optimization” problem are volatility, return, and correlation – and all three matter. There is still a significant benefit from a large non-US allocation if non-US equities are more volatile than US equities, but also offer a higher expected return and diversification benefits through imperfect correlation. The “extra” volatility of non-US equities is known and should already be incorporated into market prices and thus into expected returns.

7. US investors spend their savings in dollars, and so they should only invest in dollars to avoid the currency risk associated with non-US equities

It’s a useful simplification to split investment assets into two buckets: minimum-risk assets (risk-free assets, in theory) and risky assets. An investor’s base level of expected future spending in retirement should ideally be supported by minimum-risk assets. To the extent that spending is going to be in one’s home currency, then the minimum-risk assets must also be in that currency.⁷ For a risky asset though, the main things that matter for how it fits in a portfolio are its expected return, volatility, and correlation with other investments. For a given level of volatility, return and correlation, it doesn’t matter that some of that volatility comes from currency risk rather than some other source. Hence, US investors should not shun foreign equities just because they are not denominated in dollars, as long as their expected return is sufficient given their contribution to overall portfolio risk.⁸ Additionally, although it may be difficult for US investors to imagine, there are circumstances when being diversified away from one’s domestic currency can be beneficial.

8. The US is the greatest place on Earth to invest

We agree that the US has been a terrific environment for business and this is likely to continue, but sadly this is no secret and so should already be reflected in the pricing of US equities. If anything, there’s little room for this common view to be strengthened over time, and significant room for it to be weakened.

9. Investing in non-US equities is difficult and expensive

This certainly used to be the case, but not so much anymore. The expense ratio of Vanguard’s non-US equity index fund (VXUS) stands at 0.09% down from a 0.45% initial average expense ratio for their European, Asian and Emerging Market equity index funds, launched in 1990, 1990 and 1994 respectively. While Vanguard’s US equity index funds with an expense ratio of 0.03% are cheaper than their non-US equity index funds, the gap is quite narrow at just 0.06%. There is still a tax wedge between US and non-US dividends as a smaller fraction of non-US dividends have the preferred “qualified” status, which, for high marginal rate US taxpayers, gives them a roughly 20% lower tax rate than non-qualified dividends. We estimate that the total of expense and tax differences adds up to about a 0.15% extra cost for holding non-US equities. In a simple mean-variance framework, this changes their optimal portfolio weight by about 5%, providing justification for a bit of Home Bias.⁹

10. US equities are about 55% of the MSCI global equity index, so isn’t owning 80-85% of US equities a pretty minor deviation?

The major index providers, MSCI and FTSE, include significant “investability” and free-float adjustment factors in their market weights. These adjustments make sense in the context of creating an index which can accommodate the benchmarking of trillions of dollars of investment, but they do have the effect of exaggerating US market weights. The raw, unadjusted global market value weight of US equities is closer to 35%, and it is expected to decline in the future as the developing world catches up with the US, so an 80-85% US allocation represents a dramatic departure from global market-value weights today, and in the foreseeable future.

The chart below illustrates the expected gain possible from different levels of international diversification from a US investor’s perspective. It assumes 40% in US equities is the optimal weight, based on unadjusted global market value weighting¹⁰ while also taking account of the extra expense and tax costs of owning non-US equities. Moving from 100% in US equities to 85% captures only about 40% of the benefit of optimal diversification. Moving further to 55% in US equities captures more than 90% of the total diversification gain available. Notice that the closer we get to the optimal point, the gain curve becomes flatter and there’s less available gain from each 1% change in allocation.

Conclusion

You’ve probably gathered that we don’t find much merit in most of the arguments supporting a high degree of Home Bias in global equity investing. However, as seen in the chart above, there’s a relatively broad range of choices around the optimal allocation which are reasonable and which involve little sacrifice in portfolio quality. Indeed, Elm’s offerings use a Baseline US equity exposure of about 50%, significantly higher than the 35% raw market-value weight while still delivering the vast majority of expected diversification benefits. Some of this adjustment from 35% to 50% comes from the small extra cost associated with holding non-US equities, as described in [9] above. Most of it, though, comes from taking into account investor preferences, happily in a way which isn’t significantly sub-optimal.

This note reflects how we think about determining our “Baseline” allocation to US and non-US equities. This Baseline serves as the starting point for our dynamic asset allocation approach. Depending on the level of current expected returns for each asset bucket, we vary allocations away from the Baseline.¹¹

Some of the above arguments for US Home Bias have been famously made by Warren Buffett, who has received a lot of attention for taking a strong “no-place-like-home” position. Indeed, he’s instructed his heirs to avoid non-US equities completely by taking all their equity exposure through a low-cost S&P 500 index fund. Perhaps he’ll reconsider his advice after reading this note.

A Few Quick Responses to Michael Burry’s Index-bubble Remarks

Oct 4, 2019, 12:00:00 AM

October 4, 2019

Investing 101

A Few Quick Responses to Michael Burry’s Index-bubble Remarks

Burry: “This is very much like the bubble in synthetic asset-backed CDOs before the GFC in that price-setting in that market was not done by fundamental security-level analysis, but by massive capital flows based on Nobel-approved models of risk that proved to be untrue.”

Is there any market in the which the ‘normal’ state is for the marginal buyer to be a value-focused fundamental securities analyst? Even long before ETF and index funds, we’re pretty sure that’s not how most markets ever functioned
Credit ratings agencies made a business decision to rate large swaths of the sub-prime and alt-A CDO market AAA, then used a useful model to justify that decision. We know of no models approved by Nobel prize-winners supporting the idea that home-prices can’t go down, or that mortgage defaults should be uncorrelated in all states of the world
Money being allocated to broad equity ETFs (or active managers, or equities generally) isn’t largely being driven by false belief in any particular model (faulty or otherwise) nor an idea that there’s no risk in equities, it’s being largely driven by cash real rates at 0 and investors making a knowing decision to take more risk vs holding cash

Burry: “And now passive investing has removed price discovery from the equity markets. The simple theses and the models that get people into sectors, factors, indexes, or ETFs and mutual funds mimicking those strategies – these do not require the security-level analysis that is required for true price discovery.”

Active managers are still more than 50% of equity funds
Private-equity funds are larger than ever and can take under-valued public firms private
HF long-short funds are larger and more active then ever and can make market-neutral bets of almost unlimited size
If there was truly not enough price discovery, you’d expect large mis-pricings that sophisticated investors could capitalize on: so long-short funds should be having a field day, and private equity funds should find an incredible target-rich environment of great companies under-valued by the public markets. But neither seems to be happening
If passive vehicles were really distorting markets, you’d expect significant discrepancies between public and private valuations, and if there’s a public-markets bubble you’d expect the public market valuation to be much higher. But in fact, many companies are choosing to stay private because they’re getting higher private-market valuations, in an environment where in theory all the private investors are sophisticated securities-analyst types. By way of example, Wework’s latest private valuation was $47B, while now they’re talking about an IPO at more like $10B because the public markets are so much more skeptical of Wework’s fundamentals than the private markets have been

Burry: “In the Russell 2000 Index, for instance, the vast majority of stocks are lower volume, lower value-traded stocks. Today I counted 1,049 stocks that traded less than $5 million in value during the day. That is over half, and almost half of those – 456 stocks – traded less than $1 million during the day. Yet through indexation and passive investing, hundreds of billions are linked to stocks like this.”

He seems to be arguing that investors in aggregate should hold a lot less of these small/less liquid stocks than they do, but doesn’t that seem to cut against the idea that these smaller, less liquid stocks are significantly under-valued because of passive investing?

Burry: “Potentially making it worse will be the impossibility of unwinding the derivatives and naked buy/sell strategies used to help so many of these funds pseudo-match flows and prices each and every day. This fundamental concept is the same one that resulted in the market meltdowns in 2008.”

We have no idea what this means

Burry: “The bubble in passive investing through ETFs and index funds as well as the trend to very large size among asset managers has orphaned smaller value-type securities globally,”

We’d think the proliferation of value and small-cap funds would make investing in smaller value-type securities easier and more widespread than it ever has been, far from orphaning them. Micro-cap names may be getting excluded, but it’s not like micro-caps were easy or common to invest in prior to passive investing either

James White

How Elm Works

Home Biased: A Case for 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

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

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 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 out⁴:

	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 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 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

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.

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.
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), Forbes 2018 and this from Vanguard: The Role of Home Bias in Global Asset Allocation Decisions (2012).

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.
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.
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.
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:
HB_Small = 1 – (1 – HB_Big)(1-MW_Small)/MW_Big

where HB is Home Bias, and MW is Market Weight.
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%.
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

Investing 101

Do US Industry-Sector Weights Explain the Higher Valuation of US vs non-US Equities?

Aug 20, 2019, 12:00:00 AM

August 20, 2019

Investing 101

Do US Industry-Sector Weights Explain the Higher Valuation of US vs non-US Equities?

By Victor Haghani and James White ¹

Global equity market Investors are acutely aware of the tremendous outperformance of US equities versus non-US equities over the past ten years, as illustrated in the chart below.

About 2/3 of this 135% cumulative outperformance is accounted for by higher earnings per share growth of US versus non-US equities.² The remaining 1/3 is attributable to the relative change in earnings multiples, leaving the one-year trailing Earnings Yield of US equities at 4.9%, 2% lower than the 6.9% for non-US equities.³ The difference in the 10-year cyclically-adjusted Earnings Yield is even wider, at roughly 3%.

In a recent conversation we had with Seeking Alpha founder David Jackson, he posed a good question: to what extent could the difference in Earnings Yield between US and non-US equities be explained by US market-cap indices being more heavily weighted towards technology companies with high growth potential, while non-US markets lean towards lower-growth natural resource and financial companies? And if sector differences do explain much of the differential Earnings Yield, might we conclude that non-US equities may not in fact offer substantially higher long-term expected returns? ⁴

The table below addresses this question. Indeed, the US stock market has a 10.9% heavier weight than the non-US stock market in Information Technology companies, trading at a PE of 23.4x, counter-balanced by a roughly 11% lower weight in Basic Materials and Financial Services, trading at a significantly lower PE of about 15x. However, the differences in weights and PEs aren’t enough to explain much of the total difference in Earnings Yields between the broad US and non-US markets. We arrive at this conclusion by applying US industry-sector Earnings Yields to both US and non-US sector weights, and finding the difference in sector weights only accounts for 0.3% of the 2% difference in Earnings Yields between the broad US and non-US equity markets, as shown in bold in the table below.

Of course, it’s possible that a deeper dive into the growth prospects of each US and non-US sector might explain more of the difference in Earnings Yields. But, given that sector-makeup differences don’t seem to materially drive total-market Earnings Yield differences, perhaps it’s more likely that the higher valuation of the US equity market is a consequence of factors such as the much faster pace of US stock buybacks as well as the well-documented powerful home-bias of US investors. Long-suffering investors in non-US equities may well be in for still more suffering, but at least they should be comforted that the higher Earnings Yield of non-US equities is not a mirage that disappears when looked at through the lens of industry-sector weights.

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.
Earnings growth measured in earnings per index unit.
Earnings-Yield is calculated as 1/PE. PE data from Vanguard.com for VTI and VXUS ETFs.
Based on a view that Cyclically-Adjusted Earnings Yield is a good indicator of long-term expected real returns.

James White

James White

George Costanza At It Again: The Leveraged ETF Episode

Sometime in late 2018…

15 Months Later…

Leveraged ETF Returns: Not What George Was Expecting

Market Impact of Leveraged ETFs: 1987 Portfolio Insurance Redux?

Sizing Your Stock Market Exposure for the Long-Term

Opposite George?

Conclusion

Further Reading and References:

Introducing the Elm Partners All-Equity Portfolio For Non-US Investors

Target Investor Group

Background

Methodology

Implementation

Historical Simulation

Back-test Assumptions and Details

Finally…

Note:

Further Reading and References:

Taking Stock

Getting Real

Fifty-Year Historical Perspective on Equity Market Risk Premium

The History of Real Rates

Technical Sidebar

Conclusion

Further Reading and References

How to Fund Your Elm Account

If the ultimate source of funds is currently invested in brokerage assets:

If the ultimate source of funds is currently in cash or cash proxies:

Mind the Gap: Inequality and Diversification

Introduction

Model Description

Interpreting Model Results

Conclusions and Future Research

Further Reading and References

Negative Interest Rates and the Perpetuity Paradox

Negative Rates and Ultra-Long-Term Bonds

A Potential Perpetuity Paradox

Conclusion

Appendix: Using a Probabilistic Interest Rate Model to Put a Value on a Near-Perpetuity

Update:

Further Reading and References

There’s No Place Like Home: The Case For and Against Extreme Home Bias in Equity Investing

1. US equities have outperformed non-US equities by 170% over the past 10 years

2. Over the past 10 years, an internationally diversified portfolio wasn’t anywhere near optimal

3. Investors favor the familiar

4. International equities don’t offer much diversification, because whenever US equities experience a large correction, international equities usually go down as much or more

5. US companies earn a meaningful fraction of revenue internationally, thus investors get international diversification just from US equities

6. Non-US equities are riskier than US equities

7. US investors spend their savings in dollars, and so they should only invest in dollars to avoid the currency risk associated with non-US equities

8. The US is the greatest place on Earth to invest

9. Investing in non-US equities is difficult and expensive

10. US equities are about 55% of the MSCI global equity index, so isn’t owning 80-85% of US equities a pretty minor deviation?

Conclusion

Further Reading and References

A Few Quick Responses to Michael Burry’s Index-bubble Remarks

Home Biased: A Case for More Indexing

Conclusion

Do US Industry-Sector Weights Explain the Higher Valuation of US vs non-US Equities?