If the wealthiest families from the past 100 years had spent a reasonable portion of their wealth, invested in the stock market, and passed their wealth down to their children, there would be tens of thousands of billionaires with inherited fortunes today - but there are none that fit that description on any rich list anywhere in the world. This is the core puzzle of The Missing Billionaires, and the authors make the case that this isn't the result of poor investment selections, but moreso poor investment sizing. This book introduced me to plenty of new ideas around portfolio theory, but is it going to change my investment behaviour? Probably not.
There's a Persian proverb Victor's father was fond of, which seems improbable at first, but the truth of which has become a main motivation for this book: “It's more difficult to hold on to wealth than it is to make it.”
Victor's mom played the game just for fun and when asked why she bet on tails on a few occasions, she said, “I knew I shouldn't, but I just couldn't help myself. It just felt like tails was due to come up.” In the behavioral economics literature, this is referred to as the “gambler's fallacy” or the “illusion of control bias.”
It is widely believed that both Apple's iTunes and Spotify have made their algorithm for “shuffling” songs from a playlist somewhat nonrandom because in early versions when it was truly randomly generated, they got so many complaints from users that the play order just didn't seem random to them.
Over the last 50 years, US equities had an excess annual return over T‐Bills of about 7.5%, and returns had about 18% annual variability. We can summarize the overall quality of returns over that period by looking at the ratio of excess returns to variability, which is about 0.4. A 70/30 biased coin has a similar ratio, so in broad strokes we can view the last half‐century of equity returns as being similar to 50 flips of a 70/30 coin. It was a very good 50 years for US equities!
Is it any surprise that people will pay for patently useless advice, as documented in studies like the aptly titled “Why Do People Pay for Useless Advice?” (link)
With fractional betting strategies like we're considering, winning and losing (or losing and winning) a pair of bets doesn't leave us back where we started—we're down slightly, and this “drag” gets bigger quickly as the bet size increases.
Two effects are at work over a series of bets: There's a “lift” from winning more bets than we're losing. There's a “drag” from having lots of win/lose and lose/win pairs. As bet size increases, both lift and drag increase, but the drag increases faster. This [...] explains why even for a great series of bets with a positive edge, betting too big can still most likely be a losing strategy. We'll refer to this drag arising from the variability of outcomes as, not surprisingly, “volatility drag.”
In the previous chapter, we arrived at a very useful rule of thumb for investment sizing decisions, the Merton share.
The most popular metric for estimating the expected return of a broad stock market is known as Shiller's cyclically adjusted price‐to‐earnings ratio (CAPE).a When the CAPE ratio is high, investors are paying a high price for a normalized stream of earnings, and the prospective return of the stock market is low. This finding makes logical and intuitive sense and is borne out in historical data over a long horizon. However, we caution that this relationship holds only for broad stock markets, not for individual stocks or sectors. We can say something still more specific and powerful: 1/CAPE is a pretty good, though imperfect, predictor of the inflation‐adjusted (i.e., real) return of the stock market over a long horizon. The measure 1/CAPE is known as the cyclically adjusted earnings yield (we'll often shorten to “earnings yield”) because it's calculated as earnings divided by price. If you invest in the stock market when the earnings yield is 6%, your best expectation is that you'll earn a long‐term return (after inflation) of 6%.
[...] and a nearly 50% higher excess return‐to‐risk ratio, commonly referred to as the Sharpe ratio. (link). In calculating the Sharpe ratio, we are adding ½ σ2 to the geometric realized return to convert to an arithmetic return to use in the numerator of the ratio.
When we look back to assess whether dynamic asset allocation has served us well, we must be careful to view outcomes not solely based on return, but also to take account of how much risk we took along the way.
In Jack Schwager's series of Market Wizard books, he finishes each interview with the question: “What advice would you give someone aspiring to be a successful trader?” More than three‐quarters of his subjects answered with the dictum: “Cut your losses early; let your profits run.”
[...] following a dynamic asset allocation using the Merton share doesn't rely on market inefficiency. Market expected returns naturally change over time as the supply and demand for capital changes, even in highly efficient markets, nor is it necessarily inefficient for long‐term returns to be somewhat predictable.
Investing in the stock market has usually been a good thing, but to a varying degree relative to safe assets. It is useful to have a logical, simple framework, such as the Merton share, to decide how much to own as conditions change rather than the more seat‐of‐the‐pants, subjective approach that is evoked by market timing. When the stock market offers lower expected excess returns, all else equal, it's both good theory and good sense to own less of it. We think there's a fundamental flaw in the prevailing conventional advice given to individuals, in which the investor decides how much risk to take based solely on whether they have a “high” or “low” risk tolerance, without factoring in how much they're being “paid” to take that risk. It would be like deciding to bet the same amount on a biased coin regardless of whether it's 70/30 in your favor or fair at 50/50.
In the Merton share formula, the best amount of the risky asset to own is a function of its expected excess return relative to the safe asset.
The “rule” is that the more we have, the more sated we feel. Economists lovingly call this “diminishing marginal utility of consumption,” which just means that each incremental item brings us somewhat less happiness than the one before it. It's such a simple idea, but it's central to essentially everything in this book.
Satisficing is an approach to decision‐making that involves searching through available alternatives until an acceptability threshold is met.
Why use crude approximation when you can apply a comprehensive framework that can give you results equivalent to having meaningfully more wealth, without needing to save more or take more risk? The only cost to this almost‐free lunch is the time and mental energy needed to understand, embrace, and use this framework, which has been freely available in the public domain since Merton and Samuelson put it there in 1969.
In modern times, annuities are typically offered by insurance companies, and they provide the purchaser a fixed monthly payout for as long as he or she lives. It lets individuals or couples virtually eliminate the risk of outliving their savings by allowing them to pool their longevity risk with others.
Just as we see images that are far from us in less detail, so too do we imagine the future in less detail when it's remote. This is why we habitually agree to do unpleasant things that are far in the future that we wouldn't agree to do tomorrow.
Human capital refers to the lifetime earnings of individuals from their labor, usually thought of after‐tax and in excess of basic, subsistence living expenses.
The economist Moshe Milevsky wrote a book, Are You a Stock or a Bond?, that focused precisely on this question. The more your earnings rely on the economy being strong—think high‐level executives in banks or industrial companies—the more your human capital is like a stock. In contrast, the more your job is insulated from economic fluctuations—think doctors or tenured professors—the more your human capital is like a bond.
For example, over the past 50 years, the geometric annualized return of the US stock market was 10.3%, while the average annual arithmetic return was 12.0%. The difference between the two is the volatility drag we've previously discussed, which is a function of the variability of returns.
No matter how efficient or inefficient markets may be, the returns earned by investors as a group must fall short of the market returns by precisely the amount of the aggregate costs they incur. It is the central fact of investing.
In practice it is not that difficult to construct stories that make a wide range of investment strategies sound plausible, especially when explained by a charismatic manager. When combined with a positive track record, it is easy to understand why so many investors choose to have their savings actively managed, despite higher fees, less diversification, and often much higher tax costs than from more diversified asset class investing.
The central idea behind factor investing is that the best way to explain individual expected stock returns is with multiple systematic drivers, called factors.
In a seminal 1992 paper, Fama and French proposed the three‐factor model, which became the foundational tool in the multi‐factor framework. They argued that the CAPM, based on a single “total market” factor, can be significantly improved by adding two additional factors:
They found that exposure to both the value and size factors had historically earned a positive risk premium and that their three‐factor model did a much better job than the single‐factor CAPM of explaining individual stock returns.
Perhaps the mother of all investing sins is “return chasing,” making investment decisions based on an extrapolation of recent past performance. This tendency seems to be a deeply ingrained behavioral foible, as documented in a wide range of academic studies.
In classical portfolio theory with well‐behaved asset prices and the kind of utility preferences we've been assuming, we can use what's known as Tobin's separation theorem—a result that helped popularize index investing—to simplify the problem of choosing an optimal portfolio by separating the task into two easier‐to‐handle pieces: Find the portfolio of risky assets with the highest Sharpe ratio (ratio of excess return to risk). Find the optimal amount of that risky portfolio to own, based on your attitude toward risk, and keep the rest in the safe asset (or borrow if the optimum amount is greater than 100%). The theorem implies that for any two investors with CRRA utility, their optimal mix of risky assets will be the same—they'll simply hold differing amounts of whatever risky portfolio has the highest Sharpe ratio.
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%–20% range for most broad markets in major currencies over long horizons.
Our approach to saving is all wrong: We need to think about monthly income, not net worth. —Robert C. Merton, Harvard Business Review (2014)
The hardest thing in the world to understand is the income tax. —Albert Einstein
In the idealized world of Finance 101, with only a risk‐free and a risky asset to choose from, no taxation, no transactions costs, and asset prices that follow random walks, your optimal allocation to the risky asset is a function of just three variables: the risky asset's excess expected return, its risk, and your level of risk‐aversion.
We might define an efficient market as one in which price is within a factor of 2 of value, i.e., the price is more than half of value and less than twice value… . By this definition, I think almost all markets are efficient almost all of the time… . —Fischer Black, 1986 presidential address to the American Finance Association titled “Noise”
[...[ adopting the lifetime perspective suggests we should be measuring our wealth as was customary in bygone times, as the real annual spending it can support, rather than the value of our net assets today.
Don't sweat the small stuff—you can safely leave those decisions to your gut and intuition. But for the big decisions, we hope you'll slow down your thinking, and reach for the Expected Utility toolkit to answer the particular flavor of the “how much” question you're facing. In the long run, the expected improvement in your financial welfare can be very substantial.
Consider reducing exposure to investments that are correlated with your human capital, such as equity of the company where you work.
I'm James—an engineer based in New Zealand—and I have a crippling addiction to new ideas. If you're an enabler, send me a book recommendation through one of the channels below.
