Financial markets are a volatile blend of cold numbers and hot tempers. Despite the oceans of academic ink spilled on how to invest rationally few people seem inclined to follow the script. Rather they chase tips from TikTok or hunches from finance bros, armed with more confidence than calculus. Yet tucked inside a now half-century-old paper is a formula that, in theory, could guide investors through boom and bust alike—if only they could bear to use it.
In 1969 Robert Merton, a young economist with a taste for stochastic calculus and stiff assumptions, laid out a method for allocating savings over a lifetime. His “Merton share” calculated the precise proportion of your wealth to invest in risky assets (such as stocks) versus safe ones (like government bonds), based on three ingredients: your aversion to risk, your expectations about returns and the volatility of risky assets. The outcome was a clear, mathematically rigorous strategy. For anyone seeking to balance risk and reward, it was—quite literally—the optimal answer.
The Merton portfolio, applied with historical hindsight, is persuasive. Victor Haghani and James White, former finance professionals turned evangelists of rational investing, recently ran the numbers. From 1900 to 2022, a Merton-optimised portfolio of American shares and inflation-protected Treasury bonds would have delivered a 10% annual return—beating not only the traditional 65/35 stock-bond blend (8.5%) but even a 100% equities strategy, all while taking on 40% less risk. For a framework built from first principles, this is no mean feat. Yet few retail investors, and not many professionals either, follow its prescriptions.
One problem is practical: the Merton share relies on estimates of volatility and expected returns—slippery concepts at the best of times. Small errors can yield wildly different allocations. Add in the difficulty of quantifying your own “human capital” (expected lifetime earnings) and the model’s neatness begins to fray. For a twentysomething with decades of earnings ahead, the formula might recommend leveraging their modest savings to buy shares on margin. Few are able or willing to do so—and rightly fear the consequences of being wrong.
Another obstacle is psychological. Investors are not utility-maximising automatons. They are flesh and fear. In Merton’s framework risk is defined as volatility. But in real life it is defined as the sickening sensation of watching your life savings halve on a red October morning. A model that says to buy more when prices fall sounds good—until prices do, and you don’t.
There is the conflict of interest, too. As Mr White notes financial advisers have little incentive to push Merton’s ideas. The model calls for a one-time calculation and the purchase of a few boring index funds. There are no alpha-chasing thrills, no churn to justify high fees. A wealth manager who recommended it might struggle to pay for their own yacht, let alone yours.
Worse still, the framework confronts investors with some uncomfortable truths. Consider retirement. Merton’s logic implies retirees should spend a fixed percentage of their wealth each year, not a fixed dollar amount. This makes intuitive sense: if markets tumble you tighten your belt; if they soar you loosen it. But few people relish the idea that their standard of living should fluctuate with the S&P 500. They want certainty, not contingency. Merton gives the latter.
This gap between theoretical elegance and human behaviour reflects a deeper divide. Economists model people as if they made decisions based on expected utility—a concept rooted in diminishing marginal returns to wealth. But many investors act as if wealth were a lottery not a ladder. They favour strategies with long odds and big payoffs, even when the maths says otherwise. This “billionaire or bust” mindset may be irrational but it is intoxicating.
Indeed one of the most remarkable features of the Merton framework is that it tells you not only how to invest, but how much you should value wealth at all. The curvature of your “utility function”—a graph of how much satisfaction each extra dollar gives you—shapes every financial decision. Those who fear losses more than they prize gains should tread cautiously. Those who see money as a tool, not a scorecard, should diversify and rebalance. It is not your returns that determine your happiness, but how you feel about them.
For all its abstraction, then, the Merton share is deeply grounded in real economic principles. It incorporates the central insight of investing: that risk and reward are two sides of the same coin, and cannot be separated by willpower alone. It explains why a single roll of a high-stakes dice is terrifying, but 10,000 rolls are a sure thing. And it reminds investors there is no free lunch—only better packed ones.
In an age of robo-advisers and meme stocks, Merton’s ideas deserve a second look. They are not a panacea. But they provide a consistent, coherent way to think about the trade-offs that investing inevitably demands. And unlike most financial advice, they are not trying to sell you something.
In an age of robo-advisers and meme stocks, Merton’s ideas deserve a second look. They are not a panacea. But they provide a consistent, coherent way to think about the trade-offs that investing inevitably demands. And unlike most financial advice, they are not trying to sell you something.
If Merton had one flaw it was assuming too much rationality. His framework rests on the idea that people care more about outcomes than stories. Reality suggests otherwise. Still, his model may be the most rational rebellion against irrational investing yet devised: a rejection of hype in favour of reason, of instinct in favour of insight. Whether the world is ready to follow is another matter. As any seasoned investor knows, being right too early is the same as being wrong. ■