Elm Wealth Research

By Victor Haghani, James White and Jerry Bell ¹
Estimated reading time: 6 min.

“Bogleheads” are DIY investors who are passionate about index investing. They gather each year to share ideas about sensible investing, and to celebrate the life and contributions of John Bogle, the founder of Vanguard and arguably the person who has done more than anyone to improve investor welfare. Victor was very pleased to attend their recent annual conference in Minneapolis, and do a Q&A session with Morningstar’s Christine Benz. There were also about a dozen authors of excellent personal finance books and blogs who gave presentations, including Christine Benz, Rick Ferri, William Bernstein, Allan Roth, Mike Piper, Jackie Cummings Koski, Karsten Jeske and Sarah-Catherine Gutierrez. Victor thoroughly enjoyed the experience, and hopes he’ll be invited back to next year’s conference in Austin!

We agree 100% with almost everything discussed over the course of the three-day conference. However, one area where we noticed our opinions diverge from the Boglehead consensus view was on asset allocation. At Elm, one of our core beliefs is that optimal asset allocation should depend on the expected return and the riskiness of the assets being invested in, and on the individual’s degree of risk aversion. Expected returns and risk change over time, and therefore, so too should one’s asset allocation.² We call our particular approach – which uses low-cost, broad coverage index ETFs to build client portfolios – Dynamic Index Investing®.

The consensus among Bogleheads – and among the vast majority of respected personal finance authors such as Charlie Ellis, Burton Malkiel, David Swensen and John Bogle – is that static asset allocation is the better approach.³ They believe that an investor should choose the percentage of their savings that they want to have in equities and then stick to that percentage through time.⁴ As John Bogle wrote in The Little Book of Common Sense Investing, “In general, investors should not engage in tactical allocation [varying the stock/bond ratio as market conditions change].” We respect these views, and know they have merit in many circumstances.

In this note, we want to explore the conditions under which the Bogleheads and like-minded investors are justified in following the static asset allocation approach – but before we dive into the details of this analysis, we want to say up front that on the broad spectrum of investment options ranging from utter folly to reasoned prudence (illustrated in the diagram below), both static and dynamic index investing are nearly on top of each other way over on the far right, sensible end of the continuum. We’re nearly as fond of Bogleheads-style static asset allocation as we are of Elm’s Dynamic Index Investing®, and in fact we do offer our clients a static index investing option if desired. So in this note, we’re really focusing a powerful magnifying glass at a very small strip of the investing spectrum.

The spectrum of investing styles for individual investors

The case for dynamic asset allocation

The theoretical case for dynamic asset allocation dates back to 1969 research by MIT economists Paul Samuelson and his student Robert Merton. One thing that came out of their research is a rule of thumb, known as the Merton share, which gives the optimal fraction of wealth (κ) that an investor should allocate to the stock market.⁵ The formula below has three inputs: the expected return of stocks over safe assets (μ), the riskiness of stocks (σ), and the investor’s individual degree of risk aversion (γ).

The Merton share
$\kappa =\frac{\mu }{\gamma {\sigma }^2}$

The fraction of wealth to invest in equities would be constant if changes in the expected risk premium were always balanced by changes of the same proportion in risk (measured as variance). Historically, the stock market’s expected risk premium and risk have tended to move in the same direction, but not in such a precise way as to keep the optimal allocation to equities constant. In fact, they sometimes move in opposite directions, and those are the times the Merton share calls for large changes in asset allocation.

Of course, any asset allocation – dynamic or static – needs estimates for the expected return and risk of major asset classes. We’ve written frequently (here, here, and here) about why we think reasonable estimates do exist and how we come up with them – and, if you don’t want to do it yourself, there are many sources online you can use. A web search for “capital market assumptions” of Vanguard, Blackrock, JP Morgan, or most other investment management firms will provide long-term expected return and risk estimates for major stock and bond markets. We’ve found that estimates from these different sources are usually clustered together, so it shouldn’t matter too much which one you choose, although you may want to average several together – or you can just use the ones we provide on our Elm Wealth website.

We have written about the Merton share and its applications in our book, The Missing Billionaires: A Guide to Better Financial Decisions. In Chapters 2 and 3, we discuss its theoretical underpinnings; in Chapter 5, we present long-term historical simulations suggesting that dynamic asset allocation, using US equities and US treasury bonds, generated a compound return 2.5% above a static asset allocation with similar risk. We believe that future excess returns will be lower. Over a long horizon, we’d suggest 1.5% as the expected pretax extra return from a dynamic approach, and around 1% on an after-tax basis, both with less risk than a static approach.

The case for static asset allocation

Now let’s make the case for static asset allocation. We’ll lay out the circumstances and beliefs about markets under which keeping your asset allocation constant is the better choice.

1) You’re a DIY investor whose cost of time is high relative to capital deployed
Changing your asset allocation in response to varying market conditions is time-consuming, and doing it tax-efficiently is doubly so. It’s certainly more challenging than keeping your asset allocation constant over time, and some DIY investors may simply not have the wherewithal to implement a dynamic approach.

If you’re a committed DIY investor, you may find the static approach more attractive if you value your time higher than your expected excess risk-adjusted return from a dynamic approach. You’ll have to put in extra hours to follow a dynamic approach, collecting and processing expected return and risk data and deciding on and executing trades. Depending on your skill level and how you value your marginal leisure time, we could see reasonably deciding in favor of static asset allocation for portfolios up to around $250,000, even if you completely agree with our views around dynamic allocation.⁶

2) If you expect the stock market risk premium and risk to stay in a narrow range
Even if the cost to you of dynamically managing your asset allocation is low, either because you have a lot of wealth or you’re willing to outsource to a low-cost manager, a static weight portfolio might be the better choice if you believe that the equity risk premium and risk are likely to fluctuate in a narrow range. While that has not been the case in the past and isn’t what we expect, it’s not a completely unsupportable view. If expected risk premium and risk are relatively stable, and if they tend to move together when they do change, then you won’t be giving up very much by opting for a static asset allocation. Furthermore, if you expect to be adding to your investment portfolio over time, you may reasonably expect that you’ll sometimes be buying equities when they’re more attractive and sometimes when they’re less attractive, and so this can have a stabilizing effect as well. Of course, it is still important to set your equity allocation in line with the average risk premium and riskiness level that you expect, and your personal level of risk-aversion.⁷

3) Your “optimal” allocation to equities is more than 100%, but you decide against leverage
A static asset allocation can make sense when your human capital is stable and large relative to your financial capital. You are likely to conclude that your optimal asset allocation is to hold a leveraged position in stocks over a broad range for the equity risk premium and risk. However, if your cost of leverage is significantly above the risk-free rate, and/or you cannot continuously rebalance your portfolio to keep this leverage constant, then you may reasonably choose to avoid leverage. In this case, you’d be right to follow a static asset allocation holding close to 100% in equities.

A few arguments in favor of static asset allocation that we don’t agree with

1) Dynamic asset allocation is market timing
We sometimes hear that dynamic asset allocation is bad because it is a form of “market timing” and market timing is bad. But what is market timing? We asked ChatGPT “what is market timing?” and here’s what we got:

Market timing is an investment strategy that involves making buying or selling decisions of financial assets, typically stocks, based on attempts to predict future market price movements… it frequently involves making short-term trading decisions based on expected near-term price fluctuations.

Defined like that, we’re not fans of market timing either – but we maintain that Dynamic Index Investing® is not market timing as defined above. It is important to recognize that this style of dynamic asset allocation – driven by changes in expected risk premia and riskiness – does not rely on any market inefficiency. It just relies on changes in the supply and demand of capital over time.

In contrast, stock picking or factor investing – such as overweighting exposure to small cap stocks, value stocks, etc. – are approaches which do primarily rely on market inefficiency for investors to earn extra returns above and beyond what’s needed to offset the higher costs and risks involved in such strategies. All that extra return can only come from other investors who are taking the opposite active exposures. For such investing to make sense, you need to believe that you are profiting from market inefficiencies arising from the mistakes or preferences of the investors on the other side of your concentrated bets.

2) There aren’t good risk and return estimates
We often hear people say that our Dynamic Index Investing® approach doesn’t make sense because it is not possible to estimate the expected return and riskiness of stock markets. As we explained earlier in this note, we strongly believe that it is possible to reasonably make those estimates, and that they’re readily available online from many large investment management firms and our Elm Wealth website.

Furthermore, the argument that it’s not possible to estimate return and risk does not specifically favor static asset allocation because you still need those estimates in order to arrive at the weights of your static asset allocation. Indeed, in the true absence of any estimates for expected returns and risk, how is it possible to make investment decisions at all?

3) Or, it’s best to use historical returns, and they don’t change much
We suspect that, in many cases where an investor’s estimated returns and risk are quite constant over time, what’s implicitly happening is that those estimates are primarily being anchored to very long-term historical returns. Long-term historical returns are pretty constant over time, and so an asset allocation using them as inputs will be pretty static too. However, we caution against estimating the prospective return of the stock market based on historical returns.

To see why, consider using the historical return of a 30-year treasury bond to measure its expected return. Imagine that five years ago, it was trading at a 10% yield to maturity. Over the next five years, its yield declined by half, to 5%. The historical return on this bond will look fantastic at 20% per annum – but it won’t provide any clue that the forward-looking expected return from this bond, if held to maturity, is actually only 5%, not 20%.

Broad equity markets are obviously not completely bond-like, but they’re more similar to bonds than one might think. Earnings yield provides a decent predictor of future long-term returns because corporate earnings look somewhat bond-like when viewed across an entire large economy. Accordingly, you can view the earnings you’re getting divided by the price you’re paying as a good (though imperfect) estimate for the real return you should expect. In contrast, short-term or even long-term history just doesn’t provide the forward-looking information we need.

4) Dynamic asset allocation isn’t tax efficient
Dynamic asset allocation is indeed less tax-efficient than static asset allocation, which in turn is less tax-efficient than buy-and-hold.⁸ This is not an issue for investors whose wealth is primarily in non-taxable accounts like 401ks and IRAs. For taxable accounts, the tax inefficiency of the higher volume of trading in a dynamic approach can be mitigated through tax-loss harvesting and tax-aware rebalancing.

Conclusion

Despite the intuitively appealing nature of dynamic asset allocation, for many DIY investors, static asset allocation can be a better choice. Simplicity, comfort and ease of implementation are really important features of an investment strategy, and a static asset allocation scores high in those dimensions. While we believe that dynamic asset allocation is theoretically optimal, it is important to follow an investment approach that you are sufficiently comfortable with to stick with over long periods of time and different market conditions.

While static asset allocation has fewer moving parts and might seem easier than the dynamic approach, we have observed that a static asset allocation is more difficult to stick with over time and through changing market environments. We know very few investors who have maintained their chosen static asset allocation for more than several years before they read some news that makes them uncomfortable with their level of exposure, and they move to a new “static” allocation.

For us personally, dynamic asset allocation is more stress-free because it is both intuitively appealing and theoretically sound. Importantly, it allows us to own more equities over time and worry less. Whichever approach you choose, as long as you’re like the Bogleheads Victor met in Minneapolis who build their portfolios with low-cost, broad index funds while keeping an eye on taxes and other fees, you’ll be at the very best end of the spectrum of investment choices.

Appendix: How some respected personal finance books line up on the static versus dynamic asset allocation debate

Books advocating static asset allocation	Books advocating dynamic asset allocation
The Little Book of Common Sense Investing by John Bogle	Dynamic Asset Allocation by James Picerno
Unconventional Success by David Swensen	Strategic Asset Allocation by John Campbell and Luis Viceira
The Four Pillars of Investing by William Bernstein	Continuous-Time Finance by Robert Merton
If You Can by William Bernstein	Expected Return by Antti Ilmanen
The Little Book of Safe Money by Jason Zweig	The Missing Billionaires by Victor Haghani and James White
Morningstar’s 30-Minute Money Solutions by Christine Benz
All About Asset Allocation by Rick Ferri
A Random Walk Down Wall Street by Burton Malkiel
The Elements of Investing by Charles Ellis and Burton Malkiel
Winning the Loser’s Game by Charles Ellis
Stocks for the Long Run by Jeremy Seigel
How to Think About Money by Jonathan Clements
Enrich Your Future by Larry Swedroe
Lifecycle Investing by Barry Nalebuff and Ian Ayres
Risk Less and Prosper by Rachelle Taqqu and Zvi Bodie
Personal Finance for Dummies by Eric Tyson
The Only Investment Guide You’ll Ever Need by Andrew Tobias
The Index Card by Helaine Olen and Harold Pollack
The Intelligent Investor by Benjamin Graham
Global Asset Allocation by Mr Meb Faber

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Further Reading & References

• Asness, C, Ilmanen, A., and Maloney, T. (2017) “Market Timing: Sin a Little.” Journal of Investment Management.
• Campbell, J. and Shiller, R. (1988). “Stock Prices, Earnings and Expected Dividends.” Journal of Finance.
• Faber, M. (2013). A Quantitative Approach to Tactical Asset Allocation. The Journal of Wealth Management and SSRN.
• Haghani and White. (2024). “Introducing P-CAPE: Incorporating the Dividend Payout Ratio Improves Our Favorite Estimator of Stock Market Returns.”Elm Wealth.
• Haghani and White (2022). “Man Doth Not Invest by Earnings Yield Alone: A Fresh Look at Earnings Yield and Dynamic Asset Allocation.” Elm Wealth.
• Haghani and White. (2018). “What Gamblers Can Teach the Buy and Hold Crowd.” Elm Wealth.
• Haghani and White. (2023). The Missing Billionaires: A Guide to Better Financial Decisions. Wiley.
• “Historic CAPE Ratio by country.” (2024). Barclays.

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1. This not is not an offer or solicitation to invest. Past returns are not indicative of future performance. We thank William Bernstein, Rich Dewey, Rick Ferri, Larry Hilibrand, Antti Ilmanen, Vladimir Ragulin and Jeffrey Rosenbluth for their helpful comments and suggestions. As always, we relied on and appreciate the contributions of our colleagues Jerry Bell and Steven in all aspects of researching and producing this article.
   
2. Of course, for nearly all assets, neither expected returns nor expected risk can be known precisely – but, for many core asset classes such as broad-market equities, there are reasonable metrics which are robust, well-known, and widely agreed on.
   
3. See appendix for a fuller list of select books on personal finance from both sides of the debate.
   
4. Maintaining fixed portfolio weights requires rebalancing trades, which involve buying underperforming asset classes and selling those that have done best.
   
5. Primarily assuming the stock market follows geometric Brownian motion, the safe asset is risk-free, continuous trading is possible, and the investor exhibits CRRA utility risk aversion and wishes to maximize his expected utility.
   
6. Assuming you value your time at $100 per hour after-tax, you estimate you’ll need to spend an extra two hours per month for the dynamic approach, and you expect the dynamic approach to deliver 1% extra after-tax returns.
   
7. For the average risk level, you’ll want to use your average expected variance of returns, since that is the denominator of the Merton share.
   
8. I.e. not rebalancing to maintain static weights over time.
   

By Victor Haghani, James White and Jerry Bell 
Estimated reading time: 3 min.

Announcing a new quarterly market snapshot going out to our research subscribers with long-term expected return estimates for US and global equity markets, plus some other useful bits of information which are also hard to find.

If you’d like to receive it, you can sign up here – and yes, it’s free.

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When we think broadly about how to invest, a good starting point is to figure out how much of our wealth we want to invest in major stock markets and how much to keep in safe investments. To make that decision thoughtfully, two major pieces of information we need are the expected return of equities and the return offered on safe assets.¹ Even those of us who plan to pick just a handful of stocks, or to invest in private or alternative investments, are well-served by starting off with a clear picture of the returns offered by broad equity markets and safe assets.

From conversations with friends and clients, we’ve become aware of how hard it is to find the information we need to make this most fundamental investing decision. Unfortunately, the essential information investors need is not printed amongst the thousands of prices, returns and other numbers published daily in the Wall Street Journal, or in any other major, broadly-available financial publication. We thought it would be interesting to see whether finance professionals had figured out how to find this information. If we found that even these investors were mostly flying blind, we could reasonably infer that most other investors would be too.

So, a few weeks ago we took the opportunity of a dinner party to poll 19 of our friends, all finance mavens, including three university professors of finance. Our fellow diners had an average of four decades of financial market experience. Spoiler alert: based on the results, we’ve decided to begin publishing this essential information at the end of each quarter.

The Survey

Our first question was to ask for the diners’ estimates of the Cyclically-Adjusted Earnings Yield (CAEY) for the broad US equity market, and the broad non-US equity market.

This question is motivated by our view that the best and most popular estimate of the long-term real return of the broad equity market is its CAEY.² This metric might be more recognizable expressed as 1/CAPE, where CAPE is the Cyclically-Adjusted Price-earnings Ratio popularized by Professors Robert Shiller and John Campbell. While there’s no universal agreement that CAEY is the best predictor of long-term real equity returns, we’re pretty sure that it is the most popular one used in practice.

At Elm Wealth, our metric of choice is P-CAEY, a variant of CAEY we’ve developed that accounts for most companies not paying out all their earnings as dividends. We’ve written a note about P-CAEY with the full background and details here.

Our dining companions were not especially well-informed about current CAEY levels, as illustrated in the two charts below. While about 40% of the respondents gave a pretty accurate reading, 60% were disturbingly wide of the mark. The standard deviation of the estimates was about 2.8%. This is roughly equal to the standard deviation you’d get from people throwing darts at a board with equal likelihood of all numbers across a range of 0% to 10%.³ In other words, it was as if people had no idea where the CAEY was other than that it was positive and less than about 10%.

Our second question was asking our diners for their estimate of the real yield on 10-year US Treasury inflation protected bonds (TIPS).

We chose the 10-year TIPS yield because it is directly comparable to the stock market return estimate provided by CAEY, which is also a real (inflation-adjusted) return. Also, TIPS are particularly relevant for long-term investors who care more about the lifetime inflation-adjusted spending their wealth can support than about the present value of their wealth. This makes long-term TIPS the safest asset they can buy. We’ve written more about this in our note here.

Our dinner companions did pretty well with this question. The average answer was 1.9%, which was pretty close to the going yield of 2.1% at dinner-time, with 70% of the respondents giving an answer in the range of 2% to 2.5%. The other 30% of the guesses were all lower than 2%, averaging 1.25%. Altogether, it seems like these finance professionals had a pretty good handle on this important piece of information.⁴

Our plans for making this information available to you

Starting in early October, we’ve been sending a quarterly email to our research subscribers with Cyclically-Adjusted Earnings Yields for broad equity markets and TIPS yields (if you’re receiving this, you’re already signed up. If you think others might enjoy, they can sign up here – and yes, it’s free). Over time, we may add other useful bits which are also hard to find. We also plan to make this information, updated daily, available on our website.

You can piece this information together from other sources, which we describe in the shaded box below. It is our hope that, before long, this information will become widely and freely accessible via the Wall Street Journal, Bloomberg and other popular media sources. It’s hard to see how investors can make sensible, informed decisions without having forward-looking estimates of stock market and safe asset returns.

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1. Metrics of risk and risk-aversion are important as well, as we discuss in our book The Missing Billionaires. In this note, we focus on the return of equities and safe assets because we believe those are inputs for which generally-accepted metrics are available using public information, but are not regularly published in major media outlets.
   
2. An alternative approach taken by some investors is to extrapolate from past stock market returns. We aren’t fans of this approach, as we don’t believe the past is generally a good predictor of the future in the domain of investments, especially when a forward-looking estimate of the expected return of the stock market is available in the form of CAEY. Another approach, embraced by most wall street stock research departments, is to make an estimate by blending a range of subjective factors, including estimates from the first two approaches above. This might be the best approach if only the experts could agree (or if an average of these estimates were published on a consistent basis). Another short-coming is that these experts tend to focus on estimating short-term stock market returns, which is extra challenging, and if followed would lead to wild swings in investor asset allocations. It would also help if the experts making these estimates were free of the conflicts that arise from them working at firms that are more profitable when their clients invest more in stocks and when the stock market goes up.
   
3. The standard deviation of a uniform distribution is (U – L)/√12, where U is the upper end of the range and L the lower end. (10% – 0%)/√12 = 2.9%.
   
4. Our dinner took place in London, and so we also asked for estimates for the yield on 10-year UK inflation-linked bonds. Our friends’ guesses were far less accurate, which reflects the fact that these yields are surprisingly difficult to find in the public domain.
   

By Victor Haghani and James White ¹

We’ve been hearing a lot of this:

In mid-2020, I got worried about inflation. I decided to protect myself against a jump in my living expenses by buying U.S. Treasury Inflation Protected Securities (TIPS). I was right to worry about inflation – prices are 21% higher today than they were four years ago, rising by over 5% per annum – but I was wrong to buy TIPS. The value of my long-term TIPS ETF is down about 0.5% in nominal terms, and down 18% adjusted for inflation.² If that’s “inflation protection,” give it to somebody else! ³

Do TIPS offer effective protection against inflation?

TIPS are designed to protect the real spending power of your wealth over a given horizon. If the frustrated investor above had bought TIPS maturing in four years, her wealth would have much more closely tracked inflation over that period.⁴ But while that’s tempting, as we’ll see below, it’s not necessarily her best course.

It’s natural that some investors think of inflation protection strictly as ensuring their portfolio value will rise during periods of unexpectedly high inflation. If that’s truly your only goal, you should buy short-dated TIPS. However, your long-term spending power is impacted not just by inflation, but also by long-term real interest rates. $1 million of wealth goes a lot further when real interest rates are at 4% than when they’re at 0%.

If your goal is to protect long-term spending power rather than the narrower goal of protecting inflation-adjusted wealth, then longer-dated TIPS (owned directly or through ETFs) make sense and are effective. However, just as “no man can serve two masters,” TIPS cannot protect inflation-adjusted wealth in the near-term while simultaneously protecting long-term spending power.

In “Back to the Future: Reviving a 19th Century Perspective on Financial Well-Being,” we discuss why we think protecting long-term spending power is the more desirable objective – and, for readers looking for a deeper dive, we discuss a number of related issues in these two notes as well:
How I Learned to Stop Worrying and Love the Bomb
A Sheep in Wolf’s Clothing

Protecting Long-term Spending Power

Let’s look at an example. You have $1 million of savings you want to convert into a 25-year string of constant inflation-adjusted annual cash flows, to “lock in” your real spending power over that time. You buy a portfolio of TIPS with amounts selected so that the interest and principal payments will generate that desired series of real cash flows. To make the math super simple, let’s assume all the bonds are available at a real yield of 0%: then the $1mm you spend on the portfolio of TIPS will provide $40,000 per year of constant inflation-adjusted income.⁶

A year later, your fears of higher inflation are realized with one-year CPI running at 5%! The Fed has hiked short-term interest rates by 4%, and all the bonds you bought are now trading at a real yield of 2%. This isn’t completely fictitious, being close to what actually did happen between April 2022 and August 2023. So now you look at your brokerage statement and see that your $1mm of starting capital plus intermediate payments has turned into just $836k, for a loss in value of 16%. You might be feeling like your inflation protection let you down – but did it?

Your objective in buying this portfolio of TIPS was to create an inflation-hedged $40,000 per year of income to spend. While the present value of your portfolio is indeed lower by 16%, the cash-flow stream you created is still intact, and you’ll continue to get $40,000 per year for the next 24 years, adjusted for inflation.

This scenario is not particularly unusual, in that when inflation runs unexpectedly hot, the Fed is likely to hike short-term interest rates at a fast enough pace to eventually slow the economy and reign in inflation, which normally will lead to higher real interest rates on TIPS.

Does this make TIPS a risky investment? While the present value of the portfolio of TIPS you bought fluctuates (wildly, in this example), its long-term spending power remains constant.⁷ If you have a short horizon, buying long-term TIPS is definitely risky – but, if you think about risk with respect to your long-term spending power, long-term TIPS are relatively safe.⁸

Is it better to own TIPS via owning bonds directly or through a TIPS ETF?

The question, “Should you buy bonds or bond funds?” gets a lot of discussion in the financial press.¹⁰ We often read that it’s better to buy individual bonds rather than bond funds, as you will never suffer a loss on individual bonds as long as you hold them to maturity. We think this argument is, at best, confused.

If you want to protect against inflation or lock in a real rate of return to a specific date, then you should buy and hold individual bonds, whose maturity will naturally run down as you approach your target date. However, we think this is a relatively rare use-case. Few people, even those getting on in years, have a specific date with their name on it. Instead, many investors either have a medium-to-long and rolling horizon, or are allocating between asset classes.

In either of the latter cases where you’re trying to maintain the duration of a bond portfolio, the mechanics of holding individual bonds versus a bond ETF will be very similar. In both forms, bonds will naturally be running off, and you’ll be replacing them by buying new issues.¹¹ If the ETF is trading close to its Net Asset Value, as TIPS ETFs normally do, the returns will also be very similar between holding the ETF and a similar portfolio of individual bonds. The main difference will be that the ETF charges a management fee (0.03% in the case of SCHP), but is more convenient and likely has lower transaction costs than managing your own portfolio of individual bonds.

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1. This not is not an offer or solicitation to invest. Past returns are not indicative of future performance.
   
2. Based on the largest TIPS ETF, SCHP, and including reinvested dividends.
   
3. Or, for an expression of these sentiments in the financial press, see this FT article by Toby Nangle: “TIPSplaining a lousy inflation hedge.”
   
4. In this case, she’d still have underperformed inflation by about 4% in total, since TIPS maturing in four years were trading at a real yield of -1% in mid-2020. She also could have bought and rolled shorter-dated TIPS.
   
5. TIPS at issue come with a nice but small freebee: deflation protection. The ultimate redemption value will not be less than par, even if there has been deflation over the life of the bond.
   
6. Assume all the TIPS have 0% coupons, so they’re all trading at par with a 0% real yield. Then you’re just buying $40,000 notional of 25 bonds, with maturities from one year to 25 years from present. The portfolio costs you 25 x $40,000 = $1mm, and that will provide you with an inflation-adjusted $40,000 per year.
   
7. Some readers have asked what should they have done if they strongly believed that the yield on long-term TIPS was going to increase from -1% to +2% before long, which actually did come to pass? Are we suggesting that such an investor still buy TIPS since it is the safest way for them to protect the long-term real spending power of their wealth? No, we are not. What we are suggesting is that the investor should specify the return and risk of the various other investments he can make relative to the lowest risk asset for him, which we suggest is TIPS for long-term investors. When the investor assessed each potential investment relative to the -1% yield of long-term TIPS, he may well have decided, based on his views, that rolling T-Bills or owning equities had a sufficiently high return relative to their risk versus TIPS to warrant holding those and owning no TIPS (or even shorting TIPS). Just because TIPS are the safest asset doesn’t mean the investor needed to own them.
   
8. Some readers have asked us whether it is better to roll short-dated TIPS, as this will offer the same inflation protection as owning long-term TIPS but without the interest rate risk. We think the contrary is the case for people who are concerned with protecting the long-term spending power of their wealth; rolling short-term TIPS is the strategy with interest rate risk. If you roll one-year TIPS for 10 years and real rates drop over the period, your real spending power has gone down, and vice versa if real rates rise over the period. But if you own 10-year TIPS, you are locking in a known real quantity of spending over the period, regardless of what happens with interest rates in the meantime. In this sense, not relative to your nominal wealth but relative to your spending power, it’s the one-year TIPS which give you rates exposure, while the 10-year TIPS have none. From a “balance sheet” perspective, it’s the opposite – one-year TIPS have nearly no apparent interest rate exposure, while 10-year TIPS have plenty – but for most people, we believe the spending-power perspective is more helpful than the balance-sheet perspective, since it’s maximizing the utility of lifetime spending (and bequesting) that’s the most sensible overall financial objective function.
   
9. We wish US taxation on inflation-protected bonds was the same as it is in the UK, where only the coupon income is taxed, but not the inflation-adjustment of the principal repayment at maturity.
   
10. For example, this recent article by the WSJ’s Jason Zwieg: “What to Do With Bonds When Inflation Won’t Die.”
    
11. For ETFs which sell bonds that fall outside the index, selling and replacing with longer bonds can have a tax impact, realizing capital gains or losses, but is unlikely to have a significant impact on returns as long as the ETF portfolio remains close to the target duration.
    

It’s been a while since we last shared some thoughts on financial decision-making. The reason is that we’ve been busy finishing a book on that very topic, which should be in print by September – but we recently stumbled upon a terrific podcast interview of John Y. Campbell, a professor of finance at Harvard who has written two of our favorite books on finance and is one of the clearest communicators we know. We have learned a great deal from John over the years.

John touches on just about every important idea in investing and financial decision-making, from utility theory and risk aversion to the benefits and drawbacks of value investing. We hope you’ll listen through to the end, as we found the last few minutes particularly moving and memorable.

You can watch the video below:

You can also listen to the audio version via Spotify or Apple Podcasts, or read the full transcript on the Rational Reminder website.

By Victor Haghani and James White ¹

There’s much that’s being written about Sam Bankman-Fried (SBF) and the choices he made. We think there’s one particular aspect of his thinking and actions that has received less attention than it deserves, and perhaps explains better than anything else the arc of his narrative.²

In a range of interviews and Twitter threads (see links and excerpts below), SBF explained that he approached financial decisions with little or no aversion to risk. That’s a valid personal choice, but it’s highly unusual. In our own experience, we’ve never met anyone who made important financial decisions consistent with being anywhere in the ballpark of zero risk aversion.

To see why, it’s helpful to take a look at where risk-aversion comes from. It arises from the fact that most people derive less and less incremental satisfaction from progressive increases in wealth – or, as economists like to say: most people exhibit diminishing marginal utility of wealth. This naturally leads to risk aversion because a loss hurts more than the equivalent gain feels good. The classic Theory of Choice Under Uncertainty recommends making decisions that maximize Expected Utility, which is the probability-weighted average of all possible utility outcomes.

SBF explained on multiple occasions that his level of risk-aversion was so low that he didn’t need to think about maximizing Expected Utility, but could instead just make his decisions based on maximizing the Expected Value of his wealth directly. So what does this mean in practice? Let’s say you find an investment which has a 1% chance of a 10,000x payoff, but a 99% chance of winding up worth zero. It has a very high expected return, but it’s also very risky.³ How much of your total wealth would you want to invest in it?⁴

There’s no right or wrong answer; it’s down to your own personal preferences. However, we think most affluent people would invest somewhere between 0.1% and 1% of their wealth in this investment, based on observing other risky choices such people make and surveys we’ve conducted (e.g. here). We suspect that range sounds reasonable to you.⁵

SBF on the other hand, making his decision strictly according to his stated preferences, would choose to invest 100% of his wealth in this investment, because it maximizes the Expected Value of his wealth. In one of his interviews, he did suggest that perhaps he wouldn’t go all the way to 100%, but that he’d still invest way, way more than the typical choice of 0.1% to 1%. However, in other interviews, he didn’t back off of the implications of maximizing Expected Value – as in, for example, his conversation with the economist Tyler Cowen (March 9, 2022).

Tyler Cowen (TC): Should a Benthamite⁶ be risk-neutral with regard to social welfare?

SBF: Yes, that I feel very strongly about.

TC: Ok, but let’s say there’s a game: 51% [chance] you double the earth out somewhere else, 49% it all disappears. And would you keep on playing that game, double or nothing?

SBF: Yeah…take the pure hypothetical… yeah.

TC: So then you keep on playing the game. What’s the chance we’re left with anything? Don’t I just St. Petersburg Paradox⁷ you into non-existence?

SBF: No, not necessarily – maybe [we’re] St. Petersburg paradox-ed [sic] into an enormously valuable existence. That’s the other option.

We’re all entitled to our own preferences, but our preferences have consequences – and there’s a lot of evidence, both philosophical and practical, that when SBF’s stated preferences encounter the real world, it results in almost surely going bust at some point, and pretty quickly for someone who knows their way around financial markets.

Such a person won’t have to search for special investment opportunities, like doing leveraged crypto arbitrage or founding a crypto exchange, to find risks that have positive expected value with low probabilities of big payoffs. For example, most would agree that the stock market has a positive expected return in excess of the risk-free rate. If out-of-the-money call options are fairly priced, repeatedly buying them would give the Expected Value maximizer ample opportunity to lose all their wealth in short order, offset by a vanishingly small chance of becoming the richest person in the world.

Below are a few examples of SBF laying out his decision-making framework.

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Interview with Jacob Goldstein on What’s Your Problem, May 24, 2022:

Jacob Goldstein: I’m Jacob Goldstein and this is What’s Your Problem… My guest today is Sam Bankman-Fried and his problem is this: how do you save the world? Before we get to the interview, I just want to take a minute here and set up this one big idea, this really useful intellectual framework that drives almost everything Sam does. It’s called Expected Value.

SBF: I try to use it a lot because I think it sort of is the default correct way in some senses to calculate something. Like, if you’re just trying to do a generic calculation I think it’s usually the right thing to use… One of the sort of takeaways that often ends up coming from really thinking hard and critically about Expected Values is that you should go for it way more than is generally understood.

JG: Go big. You should really go really big, even if you probably will fail and wind up with zero.

SBF: That’s absolutely right… if you really do care linearly about money, if you really do think that getting that marginal you know dollars worth a lot – um, you know, even once you already have a lot of money, um then, it – it should lead you to think that… And so, anytime that, like, there is some non-zero and non-negligible chance of a really really good outcome are times when you’re gonna be incentivized more than seems natural probably to choose extreme outcomes.

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Conversation with Rob Wiblin on the 80,000 Hours podcast, April 14, 2022:

SBF: Yeah. I think the way I saw it was like, let’s maximize EV: whatever is the highest net expected value thing is what we should do. As opposed to some super sublinear utility function, which is like, make sure that you continue on a moderately good path above all else, and then anything beyond that is gravy.

If you really are trying to maximize your impact, then at what point do you start hitting decreasing marginal returns? Well, in terms of doing good, there’s no such thing: more good is more good. It’s not like you did some good, so good doesn’t matter anymore…

That means that you should be pretty aggressive with what you’re doing, and really trying to hit home runs rather than just have some impact – because the upside is just absolutely enormous.

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Better is Bigger, SBF Twitter Thread. 11:19 PM · Dec 10, 2020, @SBF_FTX

SBF: …What about a wackier bet? How about you only win 10% of the time, but if you do you get paid out 10,000x your bet size?

[So, if you have $100k,] Kelly suggests you only bet $10k: you’ll almost certainly lose. And if you kept doing this much more than $10k at a time, you’d probably blow out.

…this bet is great Expected Value; you win [more precisely, your Expected Value is] 1,000x your bet size.

…In many cases I think $10k is a reasonable bet. But I, personally, would do more. I’d probably do more like $50k.

Why? Because ultimately my utility function isn’t really logarithmic. It’s closer to linear.

…Kelly tells you that when the backdrop is trillions of dollars, there’s essentially no risk aversion on the scale of thousands or millions.

Put another way: if you’re maximizing EV(log(W+$1,000,000,000,000)) and W is much less than a trillion, this is very similar to just maximizing EV(W).

Does this mean you should be willing to accept a significant chance of failing to do much good sometimes?

Yes, it does. And that’s ok. If it was the right play in EV, sometimes you win and sometimes you lose.

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It seems like SBF was essentially telling anyone who was listening that he’d either wind up with all the money in the world, which he’d then redistribute according to his Effective Altruist principles – or, much more likely, he’d die trying.

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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 Rich Dewey, Antti Ilmanen, John Karubian and Jeff Rosenbluth for their help with this article. For a deeper dive, read this excellent article by Byrne Hobart at The Diff.
   

2. This article is all about SBF applying his personal risk preferences with respect to his own money. We don’t know yet the facts of what actually happened, but nothing we discuss herein justifies any type of fraud or improper use of client or investor money.
   
3. Its standard deviation, a conventional measure of risk used for more symmetric payoff outcomes, is about ten times bigger than the expected return of the investment. Hence, its Sharpe Ratio is just 0.1 – not particularly high – although we emphasize that these conventional metrics of risk, return and quality of investment are not designed for evaluating investments such as these.
   
4. For the purpose of this thought experiment, assume that all of your wealth is financial wealth and that you are considering this as a one-time investment in isolation of other opportunities.
   
5. But if it doesn’t, just consider what it would mean to bet, say, 20% of your wealth on such an opportunity multiple times. After twenty such investments, you’d have an 82% chance of having lost 99% of your wealth, and just an 18% chance of having won at least once. We think most people wouldn’t find that distribution of outcomes very attractive.
   
6. A Benthamite Utilitarian. Sadly, there is much confusion between “utility” in the Benthamite Utilitarianism SBF has discussed a fair amount with respect to social-welfare choices, and “utility” as a tool for financial decision-making in classical economics and the Decision-Making Under Uncertainty context. These are really disparate ideas, but various issues with Benthamite Utility have (unfairly) tainted von Neumann-Morgenstern Expected Utility.
   
7. From Wikipedia: “The St. Petersburg paradox, or St. Petersburg lottery, is a paradox involving the game of flipping a coin where the expected payoff of the theoretical lottery game approaches infinity but nevertheless seems to be worth only a very small amount to the participants.”
   

By Victor Haghani and James White ¹

It’s easy to overlook the fact that, in thinking about investment risk, we are implicitly making a choice about the benchmark against which risk is measured. It’s a convention, which we often take for granted, to use our local hard currency as the risk-less benchmark – but this choice, while very convenient, can also be misleading.

Let’s take the case where what you really care about is what you can buy with your wealth over your lifetime. You’re 50 years old and you can purchase an investment in your brokerage account, with a solid government guarantee that pays one dollar each year for the next 50 years and is adjusted for inflation in the exact goods and services you want to buy. That’s a “real annuity”; right now, you can buy it for $40, but the price is always fluctuating as supply and demand drives changes in real interest rates. In fact, one year ago, the price was way up at $65 – and so, had you bought it then, your brokerage statement would now be showing a loss of about 40%.² Is this a risky investment?

The present value price of the real annuity fluctuates (wildly, in this example) while its long-term spending power remains constant. If you have a short horizon, it’s definitely risky – but, in terms of your personal spending that can be supported by buying the annuity and holding it, there’s no risk. Similarly, the spot prices of US inflation-protected bonds (TIPS) fluctuate a lot, but since they can be assembled into a portfolio similar to a long-term real annuity, they’re not very risky at all if you’re primarily concerned with supporting your long-term real spending.

What about the stock market? We know that stock markets fluctuate pretty significantly year-to-year, often varying from base-case returns by 20% or more. When we measure the long-term realized volatility of the stock market, we get estimates for the annualized standard deviation of returns in the 16% to 20% range for most broad markets in major currencies – but what if we thought about investing in the stock market from the perspective of our long-term real spending power, where real annuities and TIPS are essentially risk-free? How much would that change our assessment of stock market risk?

It’s hard to know the exact inflation-adjusted payments you should expect from a long-term stock market investment, but one estimate you could use is the Cyclically-Adjusted Earnings Yield, which suggests that your long-term spending which can be supported by the stock market is directly connected to average 10-year earnings.³ With this in mind, the chart below shows changes in US stock market earnings compared to price changes, decade by decade, for the past 140 years.⁴ What we see is that earnings have been about one-third as volatile as stock prices: 7% volatility for earnings and 20% for market prices. Note that this difference in perspective is quite distinct from having a short-term versus long-term investment horizon. When we compare changes in earnings versus changes in stock prices, in both cases we are looking at a relatively long ten-year horizon.

The recognition that stock prices are much more volatile than expected long-term earnings is not new. It was presented at least as early as 1980 by Robert Shiller in his seminal paper “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?”⁵ and is also at the heart of the long-debated “Equity Risk Premium Puzzle”. These days, most market scholars believe that stock market volatility arises mostly from changes in how much people value future earnings, rather than from changes in the expected future earnings themselves.⁶ Thus, if you’re focused on your long-term spending power and view a real annuity as your riskless benchmark, you will also find equities considerably less risky than their price volatility would suggest.

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PS…

We should keep in mind the very severe limitations of using US experience in predicting the future. It is just one path that history could have taken, and in the above analysis it only provides us with fourteen observations of ten-year average earnings.⁷ Taking a long-term view, we must recognize that any given stock market is always in some danger of a total wipe-out in both price and earnings, as experienced by investors in Russian and Chinese stock markets in the 20th century. The best protections against this important, existential risk are global diversification, the avoidance of leverage, and the sensible sizing of your global stock market risk against your personal benchmark.

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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. This is because long-term real interest rates in the US have risen from about -1% a year ago to +1% today.
   
3. A variety of 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 thinking about expected stock market returns and 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 (2016). They conclude:
   “Existing research indicates that the cyclically adjusted Shiller CAPE has predicted long-term [real] returns in the S&P500 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.
   

4. Using data kindly provided by Professor Robert Shiller.
   
5. For example, see Mehra and Prescott (1985) and Grossman and Shiller (1981).
   
6. See John Cochrane’s 2010 AFA Presidential address, “Discount Rates” for an excellent, broad survey of the topic.
   
7. The 95% confidence interval on the sample standard deviation measured from a sample size of 14 observations is about +/-40% of the sample standard deviation. If we believed that we were drawing from a stationary distribution (which we don’t), the 95% confidence interval on our estimates of the volatility of earnings and stock prices would be roughly 4% to 10%, and 12% to 28% respectively.
   

By James White, Mark Haghani and Victor Haghani ¹

Introduction

Scott Fawcett’s “Decade” system of golf decision-making is revolutionizing golf strategy, and we think Scott’s approach to golf has a lot of lessons for good investing too. You may have read about him in this Golf Digest piece, or heard him on Larry Bernstein’s What Happens Next show, or the Wharton Moneyball sports analytics podcast. He’s the golf guru that US Open winner Bryson DeChambeau credits with much of his success, as does 2021 rookie of the year favorite Will Zalatoris, who Scott caddied and coached to multiple amateur titles. Scott’s approach to golf is viewed as so valuable that the NCAA forbids university golf teams to invite Scott to give team seminars, because they feel it bestows an unfair advantage! Scott acknowledges he didn’t invent the approach he advocates – winning golfers have always intuitively played this way and the seminal work of Mark Broadie introduced the metrics and optimization approach on which Scott’s Decade system rests – but he was the first to systematize it and teach it in a form that golfers could use in practice. He calls his system “Decade” because it’s meant to save its users the ten years that an attentive and intelligent golfer would take to arrive organically at the same understanding.

Shot Selection Under Uncertainty

At the center of Scott’s approach are two core ideas: first, our decision-making needs to totally embrace uncertainty. We cannot make good golf decisions by focusing on the shot we want to hit, even if it’s the shot with the single most likely outcome, nor can we make a sound decision by focusing on avoiding the single worst outcome. The reality is that, even for a top pro golfer, there’s a wide range of possible outcomes for any given shot. We need to take account of all the places the ball can wind up after our shot, and their respective probabilities. In the chart below, we reproduce one of Scott’s most powerful exhibits. It’s the shot pattern of a scratch golfer (one of your authors, in fact), hitting 70 balls with a 7-iron at the target shown with a red star at a distance of 180 yards.

Shot Dispersion Pattern: Mark Hitting 70 Shots with a 7-iron, Targeting Red Star

Notice that not one of the shots finished on the target. When even a very good golfer stands over the ball, he needs to know it isn’t going to wind up where he wants it to go, not by a long shot! The standard deviation of this shot pattern is 6.2 yards left-to-right, and 3.2 yards short-to-long. Notice also the oblong pattern, indicating that a right-handed golfer tends to hit long balls to the left and short balls to the right, because the ball goes further when struck with a more closed club face. A golfer can get a shot dispersion pattern for each club, and each situation – fairway, rough or sand, wind or calm – which will provide a probability map of all the places where the ball can go.

The second pillar of the approach is using a more sophisticated way of evaluating where the ball winds up than just measuring how close it is to the hole. Scott’s system relies on research done by Columbia Professor (and very good golfer) Mark Broadie. Mark is the inventor of the “Strokes Gained” method of measuring the value of each shot, which he shared with the golf world in his book Every Shot Counts (2014). He calculated, based on millions of actual shots hit by professional golfers, the average number of shots required to get the ball in the hole from just about every conceivable position on a golf course. For example, he calculated that a ball on the green, eight feet from the hole, takes 1.50 strokes on average to get in the hole – roughly even odds of a one-putt and a two-putt. Or, from the fairway 180 yards from the hole, it takes professionals 3.08 shots to get the ball in the hole.² You’ll find a table showing these, and many more examples, in Appendix II at the end of this note.

Strokes Gained accounting provides a simple and powerful way to put a value on each possible outcome, which is much superior than using a system that is based solely on minimizing your distance from the hole after your shot. For each possible shot outcome from our current position, we just need to take the difference between the number of shots expected to finish the hole from the starting and ending position of our ball. So, if we’re 180 yards from the hole in the fairway, and we hit the ball 8 feet from the hole, we know the impact of that excellent shot was positive 0.58 strokes gained. We improved our position by 1.58 strokes, from 3.08 shots to finish the hole from 180 yards on the fairway to 1.50 shots to finish the hole when we’re on the green eight feet from the hole. It took us just one shot to improve our position by those 1.58 strokes, so this shot was worth 0.58 strokes gained.

The chart below shows the expected strokes to finish a hole for shots landing in various positions on and around the iconic green of the 18th hole at Pebble Beach.³ The green slopes down back to front, and left to right – so, if the ball winds up in the sand trap on the pin-side of the green, the expected number of shots to finish is 2.85, as it would be so difficult to get the ball to stop close enough to the hole to putt it in on the next shot. If the ball lands on the beach or in the ocean to the left, we count that as a 4.0, because a penalty of one stroke is assessed and the golfer will still be in a position from which he’ll need about 3 more shots to get the ball in the hole.⁴

18th Green, Pebble Beach.
Numbers in Green Represent Expected Number of Shots to Finish the Hole From Each Position

Now that we have a way of assigning a value to each possible shot outcome, we can calculate the value of shooting for any target, taking full account of the fact that there’s going to be quite a bit of dispersion in our shot outcome. We should choose the target that will leave us with the lowest expected number of strokes to finish the hole, which is equivalent to saying we should choose the target that gives us the highest expected strokes gained. The three illustrations below compare the expected outcomes for three possible targets that a golfer could select from 180 yards in the fairway.

Target = Pin.
Expected Shots to Finish Hole = 2.01.
Assumes Mark’s Shot Dispersion from Roughly 180 Yards Away in the Fairway

Target = Center of Green.
Expected Shots = 2.03.
Assumes Mark’s Shot Dispersion from Roughly 180 Yards Away in the Fairway

Target = Scott Fawcett Suggested Target.
Expected Shots to Finish Hole = 1.92.
Assumes Mark’s Shot Dispersion from Roughly 180 Yards Away in the Fairway

Choosing the pin as the target would result in the shot pattern represented in the first panel above. Notice that there are lots of balls that finish close to the hole, but that two balls would be on the beach or the ocean, and eleven balls would be in the sand trap left of the green – a tough spot to be in. Averaging over the 70 shot outcomes of Mark’s shots gives us 2.01 expected shots to finish the hole, using the pin as a target. While this is the target which would minimize the expected final distance of the ball from the hole, most seasoned golfers would recognize that it isn’t the optimal target. In the second panel above, we show the shot pattern if the golfer aimed at the dead center of the green, a target which has conventionally been considered the ‘smart’ and conservative shot. Here, the expected shots to finish the hole is 2.03, which is a little bit worse than aiming for the flag. Finally, we show the expected outcome choosing the target that Scott Fawcett’s system would recommend, which is a few yards to the right of and below the pin. Here we get 1.92 expected shots to finish the hole, a pickup of 0.09 expected strokes versus aiming at the flag.

An improvement of 0.09 shots may seem like a small amount of improvement from good decision-making – but picking up 0.09 strokes per shot on, say, 20 interesting shot situations per round can add 7 shots in a four-round tournament (0.09 x 20 x 4 = 7.2 shots), and can make the difference between a Top Ten finish versus middle of the pack.⁵

Of course, most golfers don’t carry strokes-gained tables, shot dispersion patterns, and computers around with them for making detailed expected-strokes-gained calculations for each possible shot target. This is where Fawcett’s Decade system comes in, providing decision-making heuristics players can follow in real-time on the course.

Scott the Financial Advisor

Scott’s insistence on taking uncertainty into account in making good decisions applies equally to golf and investing. We cannot reach good decisions by focusing on the base-case return of an investment. Instead, we need to weigh up all possible investment outcomes, the cost or benefit of each one to us, and the probability of each. And, just as we need the “Strokes Gained” accounting system to evaluate each possible shot outcome, we need to evaluate different monetary investment outcomes by the change they bring to our welfare – or Utility, as it’s called in economic theory.

Just as Scott tells us not to make golf decisions based on minimizing the expected distance from the hole after each shot, or alternatively, maximizing the number of birdies per round, so too in investing it’s important to choose the appropriate objective to maximize. In investing, making decisions that maximize the expected amount of money we’ll have can lead to poor, often nonsensical decisions. For example, maximizing expected wealth tells us to always take as much risk as we possibly can – using as much leverage as we can get – in any investment with a positive expected return. This is the policy which results in the highest expected wealth, but also results in a near-certain chance of going bankrupt sooner or later! The better objective is to make decisions that maximize our Expected Utility, which takes into account the fact that increasing amounts of wealth lead to smaller and smaller increases in our welfare.

In both golf and investing, we need to take account of the inherent, uncontrollable dispersion of outcomes, figure out what each outcome is worth to us, either to our golf score or to our personal welfare, and then find the decision which gives us the best expected overall outcome. Just as saving a mere 0.09 strokes on about one in four shots can add up to a very significant improvement over the course of a full golf tournament, in investing it’s also the case that small gains can add up to a big difference in outcomes. For example, a reduction of 0.75% in annual investment management fees over 40 years of saving and investing can result in 20% more savings to spend in retirement.

You might ask, “what if all golfers adopt Scott’s Decade system?” Naturally, it won’t provide the relative advantage it offers when few golfers are using it, but it will still represent the optimal approach to posting low scores. Investing, in contrast to a golf tournament, is not a zero-sum game, and so all investors can “win” from the application of good decision-making in investing. However, many of the cognitive biases that afflict golfers – the illusion of control, extrapolation bias, recency bias, overconfidence bias, and fallacy of the hot hand – also stand in the way of better investment decision-making. Scott has succeeded in giving us a system that makes golf a lot simpler, but he rightly warns us that embracing uncertainty and sticking with the program isn’t easy!

Relax and Enjoy the Ride

There’s a lot more to Scott’s system than what we’ve described here, and the deeper we dig the more of his wisdom and insights we find applicable to investing. Here are a few of Scott’s pearls of wisdom. We’ll let you decide whether they’re equally useful as applied to your investing:

• Eliminate the bogeys and birdies will take care of themselves.
• Don’t abandon your strategy just because you’ve had a run of bad outcomes.
• Keep things simple. Find the shot shape that’s natural for you, and stick with it. Hitting a good golf shot is already difficult enough without trying to put a different spin, trajectory and shape onto each shot.
• Almost never worry about how your opponents are doing. Make decisions that will lead to your best expected strokes gained outcome on each shot. It’s too confusing and complex and you don’t have enough information to strategically modify your play against your opponents.
• “The single most important thing I teach my students is expectation management.”

Players using Scott’s Decade system for reaching golf decisions report a feeling of calm and liberation from knowing they’re following a sound process and recognizing that they cannot control the individual shot outcomes. Accepting that their golf shots are more like the pattern of pellets from a shotgun, rather than a bullet from a rifle, gives them a totally different outlook and experience from a round of golf. It becomes all about making good decisions, and accepting that there’s just going to be a lot of luck – good and bad – in each round. But they know that, if they keep making good decisions, they’ll make the most of whatever technical skill they have in the long-run and be able to accept the ups and downs along the way with greater equanimity.

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Appendix I: Does It Make Sense to Give Up Expected Shots to Add Variability?

As Scott says, “The bottom-line of game theory in golf is that it is exhausting to constantly try to run iterations of finishing positions AND find situations where you can increase your scoring variance WITHOUT destroying your overall expected score.” It may seem like a good idea to accept a worse expected score in exchange for greater score variability, since money payoffs in golf tournaments are a convex function of finishing place. However, we agree with Scott that it’s unlikely to be the right thing to do in most cases. For example, a casual look at the payouts for the 2021 US Open at Torrey Pines suggests that if it cost 0.5 expected shots to generate two shots of extra variability per round, it generally would not pay to go for higher variability.

Bear in mind that the normal variability in a round of golf for a tour player is 2 to 3 strokes per round – holding course, condition and golfer form constant – so intentionally adding two shots of variability would be a pretty big deviation from optimal play. A fuller analysis would also bring risk-aversion – via the player’s Utility function – into the analysis, which will further push against the idea of accepting a worse expected score for higher variability. We agree with Scott’s advice to keep it simple in golf, and we think it applies to investing too: “…saving your energy and just sticking to the system is the optimal play for almost everyone.”

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Appendix II: Average Number of Shots a PGA Tour Player Takes to Hole Out from Various Lies and Distances from the Hole

For example, starting from the tee 400 yards from the hole, PGA Tour pros average 3.99 strokes to hole out. Starting on the green eight feet from the hole, the PGA Tour average strokes to hole out is 1.50. A recovery is an obstructed shot to the hole, e.g., a shot from behind a tree that forces a pitch back to the fairway. Reproduced with permission from Mark Broadie from his book Every Shot Counts (2014).

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Further Reading and References

• Broadie, Mark. Every Shot Counts: Using the Revolutionary Strokes Gained Approach to Improve Your Golf Performance and Strategy. Avery. 2014.
• Broadie, Mark, “Assessing Golfer Performance on the PGA TOUR,” Interfaces, Vol. 42, No. 2, 146-65. 2012.
• Rapaport, Daniel. “Has This Data Nerd Created a Golf Cheat Code?” Golf Digest. 2021.
• Scott Fawcett’s Decade Elite online program.

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1. Victor is the founder and CIO of Elm Partners and James is Elm’s CEO. Mark is pursuing a Masters degree in Data Science and is a captain of the golf team at the University of Pennsylvania.
    

   The authors thank golf strategy experts Mark Broadie and Scott Fawcett for their foundational work that made this note possible, and for their helpeful comments on this note. Thanks also to Larry Bernstein, Jonathan Garrick, Larry Hilibrand, Peter Hirsch and Cade Massey for reading a draft of this note and sharing their comments, and thanks to our Elm colleague Steven Schneider for doing such an artistic job with the exhibits. Of course, any errors rest with the authors. This note is not an offer or solicitation to invest.
   

2. Strokes Gained data for college golfers is also available, but most people use the numbers for the PGA tour players.
   
3. The pin position is from the first round of the 2019 US Open.
   
4. We’ve made a conservative approximation here in that the golfer might be able to hit a shot from the beach if he finds his ball in a good location, or depending on where his ball goes out of play, he may be in a position where his expected strokes to finish the hole could be somewhat below 3.
   
5. Also, seven shots made the difference between winning the 2021 US Open vs tying for 15^th place.
   

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.

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1. This not is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. Past returns are not indicative of future performance.
   
2. Earnings growth measured in earnings per index unit.
   
3. Earnings-Yield is calculated as 1/PE. PE data from Vanguard.com for VTI and VXUS ETFs.
   
4. Based on a view that Cyclically-Adjusted Earnings Yield is a good indicator of long-term expected real returns.
   

By Victor Haghani and James White ¹

Most of us associate the maxim “A penny saved is a penny earned” with Benjamin Franklin, but what he actually said is far more insightful: “A penny saved is two pence clear”. By the time he penned this, in “Hints for Those That Would be Rich” of the 1737 Poor Richard’s Almanac, Franklin was an experienced businessman who understood the nature of risk and uncertainty. Although he didn’t elaborate on this pithy bit of advice, we think that he was trying to convey an idea much more profound than the simple identity expressed in the misquote. We believe he was getting at the notion that one risk-free penny saved is worth two pennies of expected but uncertain business income.

Ben Franklin was a man well ahead of his time: it wasn’t until about 230 years later that Paul Samuelson and Robert Merton arrived at the same conclusion using the tools of mathematical finance.² Starting with the standard set of assumptions³ of a risk-averse investor and a single risky asset, they showed that if the investment in the risky asset is “perfectly” sized, the investor should be equally happy with a riskless investment delivering half the expected excess return of the investment in the risky asset.⁴ We could also say that under these circumstances, the investment’s “risk-adjusted return” is equal to half its expected excess return.

When Fees Saved are Worth More than Uncertain Extra Expected Return

One intriguing implication of this idea is that 1% more in investment management fees requires more than 1% in extra expected return, if getting the extra expected return increases the risk the investor is bearing. Just how much extra expected return an investor needs in order to offset the certain cost of higher fees depends on how much extra risk the manager has to take. For example, say an investor is considering moving from an index fund into an actively managed fund that charges 1% more in fees. Also assume that the index fund has a risk of 16%, but the active fund has a higher risk of 19% because it’s trying to generate higher returns by holding a more concentrated portfolio of stocks. In this case, the active fund needs to have a pre-fee expected return about 2% higher than the index fund to make the investor indifferent between the index fund and the active fund, a modern-day illustration of Franklin’s maxim.⁵

Conclusion

Philadelphia’s most famous resident tirelessly promoted the virtues of efficiency and rational thought which contributed so much to America’s economic success. It’s inspiring to realize that some of his ideas wound up being proven correct using mathematical techniques developed over 200 years later. Ben Franklin was a successful entrepreneur and his insight about the relative value of risky versus risk-free sources of return was developed in that light, but we see that it still has high practical value today for investors and business owners alike.

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Appendix: A Slightly Deeper Dive

If we start with a risky portfolio which follows a geometric random walk,⁶ and then graph the relationship between Expected Excess Return, Risk-Adjusted Return, and the Price of Risk, it looks like this:

As the fraction of wealth invested in the risky portfolio increases, Expected Excess Return goes up in a straight line, while Risk-Adjusted Return goes up, peaks, then goes back down as risk starts to dominate. The optimal holding is the holding which maximizes Risk-Adjusted Return, or an allocation of 50% of wealth in this example.

Now we can also see that at the 50% point, Risk-Adjusted Return looks like it’s about half of the Expected Excess Return. In fact, it’s exactly half. In the theory of financial decision-making under uncertainty pioneered by Samuelson, Merton et al., there’s a result that within a standard set of assumptions the optimal Risk-Adjusted Return will always equal half of the Expected Excess Return at that optimal wealth allocation.⁷

So, to get one cent worth of Risk-Adjusted Return, the investor – regardless of their level of risk-aversion – would need two cents of Expected Excess Return if their wealth is optimally allocated. Risk-adjusted Return can be thought of as the risk-free return equivalent to the Expected Excess Return,⁸ so at the optimal allocation point we have a 2:1 ratio between the “risky” Expected Excess Return and the equivalent risk-free return.

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1. Victor is the Founder and CIO of Elm Partners, and James is Elm’s CEO. Past returns are not indicative of future performance. This not is not an offer or solicitation to invest.
    

   Thank you to Larry Hilibrand, Vlad Ragulin and Jeff Rosenbluth for their helpful comments.
   

2. Samuelson and Merton weren’t the only ones or the first who arrived at this conclusion, but theirs is perhaps the most general formulation. See Robert C. Merton, “Lifetime Portfolio Selection under Uncertainty: the Continuous-Time Case,” The Review of Economics and Statistics (51), 1969, here.
   
3. The standard set of assumptions are that the portfolio consists of a single risky asset following Geometric Brownian Motion, the portfolio is continuously re-balanced, interest rates are constant, and the investor’s risk-aversion is consistent with iso-elastic utility (Constant Relative Risk-Aversion).
   
4. Where “perfectly” sized means sized to deliver optimal expected utility or optimal risk-adjusted return, and “equally happy” means to derive equal expected utility or equal risk-adjusted return.
   
5. In general, the relationship between fees and extra expected return needed to make the investor equally well-off will vary, as it is a function of how much extra risk the higher fee investment needs to take on to deliver the extra expected return. The lower the extra risk, the smaller the ratio will be (and if the higher fee investment has a lower risk, it can have a lower expected excess return).
    

   Also, the example assumes that the investor will move his holding to a new optimal asset allocation reflecting the new risk and return characteristics of the actively managed investment. The ratio between $1 of risk-free marginal return and the equivalent risky expected excess return may not be exactly 2:1 as in our stylized example, but it is generally valid that we should give extra weight to a source of risk-free return- the penny saved- compared to a risky source of extra expected return- the two pennies earned.
   

6. And the investor has a standard form of risk-aversion (CRRA), and re-balances the portfolio continuously.
   
7. For a more detailed mathematical treatment, see Appendix C of our note here.
   
8. Because an investment with a 1% risk-free return will also have a 1% Risk-Adjusted Return.