Victor Haghani has thought long and hard about his participation in the 1998 blowup of Long-Term Capital Management (LTCM). His big mistake, he concluded, was investing 80% of his personal assets in the firm.
This loss also cratered, in econ-speak, his “utility,” which is to say it made him miserable. The take home, he writes in The Missing Billionaires, is that he didn’t size his personal stake in LTCM properly. Had he invested only half as much, he’d have been far less unhappy. Contrariwise, had his large LTCM bet succeeded, his utility would only have been slightly higher than with a half-sized bet: There’s a huge utility gap between a net worth of $0.00 and $1 billion, and a small utility gap between $1 billion and $2 billion. The book, co-written with James White, is an exploration of this epiphany.
Haghani is a world-class financial economist who sharpened his quantitative and trading skills at Salomon Brothers during the 1980s “liar’s poker” era, where he impressed legendary bond trader John Meriwether enough to make him the youngest principal in LTCM, alongside Nobelists Myron Scholes and Robert Merton. The Missing Billionaires applies these skills to guide those who want to optimize their total lifetime utility.
First and foremost, as noted above, comes the sizing of investments. In 1956, John Kelly, a Bell Labs researcher, published a treatise on how much a gambler should bet on each draw, known thereafter as the Kelly criterion, to optimize the growth rate of one’s bankroll at any given moment. In its simplest form,
optimal bet size = p – q/b
where p is probability of a win, q is the probability of a loss, and b is the payoff. For a 60% bet that pays off 3 to 1, for example, the optimal bet size = 0.6 – 0.4/2 = 40% of your pile at that point (where the numerator means that you are returned $3 for a $1 pay in, for a profit of $2). On the other hand, if there is only a 50% chance of paying off 2 to 1, then your optimal bet size = 0.5 – 0.5/1, that is, zero. Increasing the bet size beyond the Kelly criterion decreases wealth growth, and moving much beyond twice Kelly makes a negative return highly likely.
It’s difficult to apply the Kelly criterion to conventional stock/bond portfolios, but most estimates of the Kelly equity exposure center on about 160% stocks, beyond which leverage kills. In 1969, a quarter century before he joined LTCM, Robert Merton wrote a seminal paper in which he derived a series of equations that described how to optimize lifetime utility by dividing portfolios between stocks and bonds, with the calculated equity exposure, now widely known as the “Merton share.” In simplified form,
Merton share (percent stocks) = ERP/(SD2 x RRA)
where the ERP is the equity risk premium, SD is stock standard deviation, and RRA is the relative risk aversion.
RRA, then, is the other key parameter in the Haghani/White formulation. Without going into its dense math and relevant experimental data, the higher RRA is, the more afraid a person is of loss. Haghani and White reckon that the average investor has an RRA of between 2 and 3; the person who doesn’t break a sweat with 100% stock exposure has an RRA closer to 1, while someone who gets nauseous with a 10% loss likely has an RRA closer to 4. (Sam Bankman-Fried told colleagues that he’d happily take a coin flip that left the world either twice as good or destroyed; this indicates that he was “risk neutral” with an RRA of zero, to say nothing of bonkers and megalomaniacal. It’s even possible to have a negative RRA, which indicates risk-seeking behavior.)
Plug an ERP of 5%, a stock SD of 20%, and an RRA of 2 into the above Merton share equation, and we get a Merton share/equity exposure of 62.5% – within shouting distance of the traditional 60/40 portfolio. Nifty, eh?
There follows an in-depth exploration of just how investors should think and act within the framework of the Merton share, expected utility, and expected asset class behavior. The math gets pretty complicated at times, but no matter what the reader’s level of quantitative chops and financial expertise, each of the book’s 27 brief chapters supplies one or two “aha” moments.
Their utility-based framework makes Haghani and White, for example, fans of dollar cost averaging (DCA); although conventional financial wisdom observes that a lump sum strategy produces higher end wealth, DCA, by avoiding the misery of lump summing at a market high, optimizes overall utility, particularly at high levels of RRA.
Fans of John Kelly and his colleague Ed Thorp will relish the interaction of RRA and the Kelly criterion. Because of the uncertainty of the financial markets, most authorities recommend only “half Kelly” bets; Haghani and White point out that this falls directly out of plugging an RRA value of 2 into the above Merton share equation.
The Kelly/Merton utility framework provides solid spending and asset allocation advice to endowments, where optimizing utility mandates spending a lot less than the expected real portfolio return, and also to individuals, for whom TIPS and stocks maximize lifetime utility–nominal bonds and T-bills, not so much because they offer less inflation protection. In addition, life and disability insurance dramatically improve expected lifetime utility by mitigating the financially disastrous effects of breadwinner death and injury. The Kelly/Merton framework also decreases the attractiveness of options and of the buy-borrow-die strategy used by ultra-high net worth types to avoid taxes; it’s often better, the authors conclude, to sell assets than to borrow, which increases Merton share/leverage.
Their discussion of the equity premium puzzle (why stocks have had a significantly higher return than riskless T-bills) is the best I’ve seen, which they summarize as, “If a model fails when brought into contact with experimental evidence, the general procedure is to discard the model, not proclaim the real world puzzling for failing to match the chalkboard.”
Finally, the book fairly bursts with delightful brain teasers, such as why when, as occasionally occurs, a billion-dollar Powerball ticket has a positive expected return, you shouldn’t buy more than a few, since the negative utility of a large number of small losses doesn’t overcome the probability-weighted utility of becoming a billionaire. Finally, Haghani’s first-person rendition of what it was like to play liar’s poker on the Salomon Brothers trading floor is alone worth the book’s retail price.
Haghani and White’s quantitative expertise is also the source of the book’s weaknesses. As the LTCM blowup illustrated, if the peak of your skill set centers on your math prowess, and you can perform continuous-time calculus as easily as most people can shovel their sidewalk, it’s easy to fall into the trap of believing that the secret to ever-better finance is yet more math.
Historian and author Robert Caplan observed that human history is half geography and half Shakespeare. One can apply this bon mot directly to investing; there comes a point where the financial practitioner should pay less attention to differential equations and more to investing’s Shakespeare: the frequency and nature of extreme financial events, the social psychology of booms and busts, and especially how even the most solid models can break down during them. Finance is not an electrical circuit or an airfoil; money managers can operate successfully for decades on the assumption that a metaphorical E = mc2 obtains, only to wake up one fine morning and find that that E = mc3 and that their portfolios have blown up.
This is, very roughly, what happened to LTCM.
Many readers, aware of Haghani’s LTCM involvement, will head straight for the relevant sections: What insights does the expected utility framework offer into the firm’s failure? Aside from noting that it returned 35% of its assets to its investors a year before it blew up, Haghani is largely silent on this score. The event that triggered LTCM’s blow up, the August 1998 Russian debt default, was no hundred-year flood. Not even close: A cursory glance at financial history shows the episode to have been at most a five-year rain shower, not even comparable to the Asian financial crisis of the previous year. Obviously, some of LTCM’s bets were not well-sized.
Another of the book’s over-strong assumptions is that RRA remains constant throughout life. This is nonsense on stilts. At the market peak, everyone’s a long-term investor with RRA = 1; during market panics, RRA rises dramatically. The authors seem to intuitively understand this and even quote the famous passage from Fred Schwed’s marvelous Where are the Customers’ Yachts? that encapsulates this commonplace: “There are certain things that cannot be adequately explained to a virgin either by words or pictures. Nor can any description I might offer here even approximate what it feels like to lose a real chunk of money that you used to own.”
The authors do allow that some investors panic during market downturns and imply that such poor souls should employ someone else to invest for them. A dubious proposition, that. Anyone possessed of faith in the discipline of professional money managers should read The Wall Street Journal’s coverage of how some of the University of Chicago endowment fund’s most illustrious board members blew a gasket during the 2008–2009 downturn (College Try: Chicago’s Stock Sale, August 25, 2009).
One of the Merton model’s central assumptions is the smoothing of lifetime consumption (i.e., that our patterns of spending shouldn’t change over our lives). To their credit, Haghani and White recognize that this ignores habituation and the hedonic treadmill. After all, there are few surer roads to dysutility than getting accustomed early in life to business class travel, BMWs, and a McMansion. It’s a significant oversight that they don’t apply the same degree of quantitative horsepower deployed in the rest of the book to this critical aspect of lifetime utility, covering this issue in just a single paragraph, noting simply that habituation favors taking less investment risk. One presumes that people should escalate their consumption slowly over the decades, but it would be useful to have a formal utility-based framework for doing so. For what it’s worth, this reviewer, after spending his youth not unduly discomfited by relentless Motel 6 accommodation, now experiences a Holiday Inn Express as the lap of luxury.
Finally, the authors cannot resist the siren song of valuation-based portfolio strategies that increase/decrease stock exposure with lower/higher valuation. The problem with such efforts at dynamic asset allocation, as Dimson, Marsh, and Staunton have demonstrated, is that asset class returns are nonstationary, and that rules that succeed ex post often fail ex ante, quipping that “We learn far less from valuation ratios about how to make profits in the future than about how we might have profited in the past.” (Or, to slightly paraphrase Warren Buffett, if past returns and valuations could be depended upon for alpha, then librarians would be the world’s wealthiest people.)
It’s been observed that economists get Nobel prizes for being brilliant, whereas physicists get them for being right; the average investor, in short, would do well to heed Benjamin Graham’s admonition about getting too mathy:
In 44 years of Wall Street experience and study I have never seen dependable calculations made about common stock values, or related investment policies, that went beyond simple arithmetic or the most elementary algebra. Whenever calculus is brought in, or higher algebra, you could take it as a warning signal that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment.
But enough carping. The readers of Haghani and White’s superb volume can judge for themselves the practical value of their complex models. Even if one disagrees with most of them, the book’s exposition of the expected utility framework, and especially of the Kelly/Merton paradigms, will stimulate thinking about finance, entertain, and likely repay the book’s purchase price thousands of times over, if not in dollars, then at least in total lifetime utility.
William J. Bernstein is a neurologist, co-founder of Efficient Frontier Advisors, an investment management firm, and has written several titles on finance and economic history. He has contributed to the peer-reviewed finance literature and has written for several national publications, including Money Magazine and The Wall Street Journal. He has produced several finance titles, and four volumes of history, The Birth of Plenty, A Splendid Exchange, Masters of the Word, and The Delusions of Crowds about, respectively, the economic growth inflection of the early 19th century, the history of world trade, the effects of access to technology on human relations and politics, and financial and religious mass manias. He was also the 2017 winner of the James R. Vertin Award from the CFA Institute.
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Victor Haghani has thought long and hard about his participation in the 1998 blowup of Long-Term Capital Management (LTCM). His big mistake, he concluded, was investing 80% of his personal assets in the firm.
