Long-Horizon Investing, Part 1: A Ton of Feathers
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This is part one of a five-part series that develops an analytical framework for long-term, retirement-oriented investing. The author would like to thank Joe Tomlinson and Michael Finke for their helpful comments on this article series.
Which weighs more?
When I was young, a friend of mine stumped me with the following brain teaser: “Which weighs more, a ton of bricks or a ton of feathers?” The answer, of course, is that they weigh the same amount: one ton! But to the uninitiated, the question is tricky, because our perceptions about bricks and feathers lend themselves to a snap judgment that surely the bricks must be heavier.
With these childhood memories as inspiration, let’s try out a new brain teaser: “Which is worth more, a dollar of stocks or a dollar of U.S. Treasury bonds?”
I would hope the answer to this one is even more obvious: They are both worth one dollar! Yet many smart-sounding but dubious nuggets of received wisdom about stock market returns boil down to an insidious and well-hidden assumption that a dollar of stocks is worth more than a dollar of less-risky investments… especially if you plan on holding them a while.
To illustrate, suppose we modify the question slightly. I propose that we place a dollar’s worth of stocks in a lockbox marked “Do not open for 30 years.” Into an identical lockbox we place a 30-year Treasury bond worth one dollar – or really a 30-year Treasury STRIPS instrument, so that there is no reinvestment risk – and then we pose the question again: Which lockbox is worth more?
Let’s be clear about the answer up front: The lockbox is a red herring, and the contents are still each worth the same amount, even if you can’t access them for 30 years.1 But consider the implications of this fact, via the following logic:
As of this writing, the 30-year constant-maturity Treasury (CMT) interest rate stands at 4.27% per year. The interest is risk-free, meaning the bond is guaranteed to mature at a value of about $3.55 in 30 years.2 (An even more risk-free lockbox would hold a 30-year TIPS instrument, since that would hedge inflation risk as well. I’ll come back to that later in this series.)
But surely everything we know about stocks tells us that the stock lockbox (say that three times fast) is bound to be worth far more than $3.55 30 years from now, does it not? After all, since 1925, the worst 30-year total return for the S&P 500 was nearly 8.5% annualized. Even if we make a conservative estimate, doesn’t a bad stock market look like, oh, 6% per year (for a final value of $5.74)? And a good run might be 13% per year, leaving us with over $39! Right?!
Let’s think about this in reverse: Suppose we offered to the market two 30-year securities, one of which will pay out $3.55 guaranteed, and the other of which will have a final value that is uncertain but is sure to be between a minimum of $5.74 and a maximum of $39. Is there any possibility that the market would place the exact same value on both securities today? Of course not! At worst, the second security will be worth about 1.6 times the value of the first security in 30 years, and consequently it must also be worth at least 1.6 times as much today (indeed, surely more, given the extra upside), unless the market is preposterously inefficient – that is, not just bad at setting prices, but comically bad, to the point where nobody notices this glaring problem.3
Think about how market pricing works. The stock market is aware of – indeed, market participants4 set – the price, and thus the guaranteed return, of risk-free securities. The market also makes its best collective assessment of the range of possible outcomes for stocks, across all time horizons, and sets prices today accordingly. Because stocks are risky, the market should set prices such that stocks have a higher expected return than the risk-free rate over all horizons (where the word “expected” is used here in the strict statistical sense). But for those prices to be at all rational, there must also be a meaningful possibility that stocks will underperform a risk-free instrument, regardless of the time horizon. To believe otherwise makes no more sense than to believe a ton of bricks really does weigh more than a ton of feathers.
I’ve cheated a little bit. To see why, consider a different example: Into one 30-year lockbox we place a dollar’s worth of the S&P 500 Index (or Russell 3000, MSCI World, etc.) and into another we place a dollar’s worth of a single, randomly selected, small-cap stock.
The above argument still applies: $1 is still $1! But the former lockbox is almost certainly more appropriate for most investors. A broadly diversified stock index has a higher expected return, and it is also likely to outperform the risk-free rate under most future scenarios. I.e., the risk of underperformance at long horizons comes in the form of “tail risk” (more on this in Part 2). The single stock also has a high expected return – maybe even higher than the index – but that expected return is composed of a more lottery-like set of outcomes: a small chance of very sizable outperformance combined with a high probability of underperformance or even -100% return via bankruptcy.5
How about this one? Into the first lockbox we place the aforementioned 30-year Treasury. Into the second lockbox we place “cash” or a strategy that rolls short-term Treasurys. The latter is often used in models and historical analyses as the “low-risk” option. But in Part 3 of this series, I will make the case that a different form of uncompensated risk can arise in the “bond lockbox” if the duration of the bonds is significantly mismatched to the horizon. I.e., the long-term Treasury is much more appropriate for an investor with a long-term goal. It is with good reason that my “ton of feathers” for a 30-year horizon was a 30-year Treasury, not cash or T-Bills!6
Wrapping up and moving on
The aim of this series is to move beyond the simplistic example of goals that exist at a single point in the future to consider retirement, the most common purpose for long-term investing for an individual. In Parts 4 and 5, findings from those examples will be applied to real-life goals in retirement and pre-retirement, respectively. Those articles will focus on such goals as locking in a stream of (preferably inflation-adjusted) income and will consider such elements as “human capital” arising from future earnings.
But first, for analytical simplicity, Part 3 will investigate the base example of a single, $N (real or nominal) goal at a given time horizon. I will make the case that historical research results would be expected to show the increasing appropriateness of stocks versus cash or (relatively short-term) bonds as the horizon increases, merely due to the riskiness of duration-mismatched bonds, without necessarily requiring mean reversion or other risk reduction in stocks. I will (qualitatively) propose an MPT-analogous theory in which the efficient frontier of two risky portfolios – stocks and bonds – will vary with time horizon, such that stocks comprise an increasingly high percentage of the efficient risky portfolio as the horizon increases. But the risk-free rate (for U.S. investors) would be the horizon-matched Treasury/TIPS rate, and the optimal combination of the risky stock/bond portfolio and this risk-free security would vary at all horizons based on risk tolerance and risk capacity.7
But that concept and all that will be built upon it would be pointless if we knew in advance that stocks are a sure winner in the long run. That’s why Part 2 will tackle this possibility, explaining further why it is so improbable that a ton of bricks weighs more than a ton of feathers, in theory and in practice.
In his role as chief investment officer for Round Table Investment Strategies, Nathan Dutzmann is responsible for applying financial science and investment research to the process of constructing portfolios tailored to our clients’ individual needs and goals. Nathan was previously an investment strategist with Dimensional Fund Advisors and a partner and chief investment officer with Aspen Partners. He holds an MBA from Harvard Business School and a master’s degree in international political economy and a bachelor’s degree in mathematical and computer sciences from the Colorado School of Mines.
1 For anyone who is unconvinced of this, please be advised that an arbitrageur (a fancy name for an investment professional who profits from market inefficiencies) will gladly sell you a lockbox with a dollar of stocks in exchange for a lockbox with a dollar of bonds plus whatever you believe the difference in value to be. The arbitrageur will then post the bond lockbox as collateral for an offsetting 30-year swap position that precisely cancels out the 30-year obligation… and will pocket the extra money from you free and clear.
2 The formula here involves converting to an annual percentage yield of (1 + 4.27%/2)^2 - 1 = 4.32%, due to the semiannual compounding assumption built into CMT rates.
3 This argument holds true no matter the price path in the meantime, due to the “Law of One Price” (to be discussed in Part 2 of this series). The basic intuition is that a seller with a shorter horizon can always find a buyer with a longer horizon. I.e., it doesn’t work to claim that near-term risk-aversion creates a guaranteed long-term return premium. In fact, there is already a security that is risky in the short-term and risk-free in the long-term: The risk-free asset! (I.e., a long-term Treasury bond.) Much more on this to come in Part 3.
4 And the Fed, sure. But (A) the market’s mere awareness of the risk-free rate is sufficient to make this argument and (B) the longer the duration, the less apparent influence the Fed has on interest rates anyway.
5 For more details, see the research paper, “Do Stocks Outperform Treasury Bills” by Hendrick Bessembinder at the W.P. Carey School of Business: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2900447
6 Prof. Michael Finke from the American College of Financial Services pointed me toward Harvard economics professor John Campbell’s research, which prefigured several ideas in this series, including this one. For example, see Campbell’s article, “Strategic Asset Allocation: Portfolio Choice for Long-Term Investors” from December 2000, or Campbell’s and Luis Viceira’s book of the same title from April 2001, published by Oxford University Press but available as an e-book from Duke University.
7 Risk tolerance refers to an investor’s ability to stomach the ups and downs of the market and willingness to accept the possibility of lower income and wealth in exchange for the probability of higher income/wealth. Risk capacity refers to the amount of risk an investor is theoretically able to take, e.g., before the potential downsides threaten non-negotiable goals. I generally view risk capacity as the more fundamental consideration, arising as it does from concrete realities of goals-based analysis. When client risk tolerance indicates far less risk exposure than their risk capacity would allow for, I may try to convince them to take on more risk by illustrating the safety already built into their plan. (It’s important to understand a client’s limits, though.) But when client risk tolerance indicates far more risk exposure than their risk capacity would allow for, I will attempt to talk them out of putting their non-negotiable goals on the line unnecessarily.
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