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FROM A CERTAIN perspective, investing is simple. One need only decide how to split wealth between risky assets, such as shares, and safer ones, such as government bonds. The conventional answer is a static rule of thumb, like the 60/40 portfolio. Yet this approach ignores a fundamental question: what is the actual goal? Is it to die with the largest possible pile of money or to maximise one’s happiness along the way? In 1969 Robert Merton, who would later win a Nobel prize in economics, provided a powerful answer. His resulting formula for portfolio allocation is mathematically elegant and has been shown to work remarkably well in practice. That almost nobody uses it says much about the investment industry and human nature.
Imagine a dice game. You roll a fair six-sided die. If it shows a one, you lose your money. On any other number, you win more than you put in. Suppose you pay $6 to play. If you roll anything from two to six, you receive $8. On average, you would make $7—so the mathematics suggest it is a good bet. Now imagine you could play 1,000 times. Over time, luck would even out and you would almost certainly make a profit. But if you play only once, with a stake of $600 for a chance to win $800, the risk feels very different. The expected return is the same, yet one unlucky roll could wipe you out. Most people would refuse this wager. The lesson is that expected returns alone are meaningless. Risk determines whether a bet is wise.
That intuition is down to psychology. The happiness, or “utility”, that people derive from wealth diminishes with each additional dollar. A windfall of $1,000 can be life-changing for someone in poverty; to a millionaire, it is a trifle. This “diminishing marginal utility of wealth” explains why people are generally risk-averse. The pain of losing a sum is greater than the pleasure from gaining the same amount. Economists model this tendency with utility functions. The most accurate for most people displays “constant relative risk aversion”, meaning each person has a quantifiable level of risk tolerance. It is not a moral failing or an emotion, but a personal trait.
Mr Merton’s great insight was to unite this psychology with finance. His 1969 paper, “Lifetime Portfolio Selection Under Uncertainty”, demonstrated how to derive mathematically the optimal mix of risky and safe assets that maximises a person’s expected lifetime happiness. The goal is not to chase the highest returns, but to maximise utility. The result is the “Merton share”: the proportion of wealth that should be invested in risky assets. It is calculated as the expected excess return of risky assets (their return above the risk-free rate) divided by the investor’s risk-aversion coefficient multiplied by the volatility of those assets squared.
This formula is dynamic. If bond yields fall but expected stock returns hold steady, the Merton share rises, recommending more stocks. If stock markets become more turbulent, the formula suggests a shift towards bonds. It is a rational, adaptive and data-driven approach. It explains why the fixed 60/40 split is arbitrary. A young person with a stable career effectively has a large future income stream—a form of “safe” wealth—and might justifiably hold a higher share in stocks than a retiree. The model incorporates this human capital.
Theory is one thing, practice another. Victor Haghani and James White, two economists, back-tested the Merton share using 120 years of American market data. A portfolio dynamically adjusted according to the formula yielded a 10% annualised return, compared with 8.5% for a static 65/35 portfolio. Crucially, it did so with 40% less volatility. An all-stock portfolio, while sometimes delivering higher absolute returns, produced a worse risk-adjusted outcome. The mathematically optimal strategy outperformed common sense.
The formula also dictates when to rebalance, removing emotion from the process. When markets fall and expected future returns rise, it signals that investors should buy more stocks. When volatility spikes or returns compress, it suggests holding more bonds. This counters the herd behaviour of panic selling and greed-driven buying. Yet despite its elegance and empirical support, Mr Merton’s framework remains confined largely to academia. The reasons are several. The model is sensitive to its inputs: small errors in estimating expected returns or volatility can alter recommendations substantially. Many retail investors cannot easily short-sell or borrow to achieve the ideal allocation.
There is also a profound irony. Mr Merton was a co-founder of Long-Term Capital Management (LTCM), a hedge fund that spectacularly collapsed in 1998. As Mr Haghani later noted, had LTCM adhered to the risk limits implied by the Merton share, its losses would have been far smaller. Even architects of rational models can be swayed by emotion or hubris. The investment industry has little incentive to promote such a strategy. The Merton formula empowers individuals to manage their wealth cheaply using index funds and publicly available data. Wealth managers by contrast profit from complexity and the perception that their services are indispensable.
Human preferences present a final barrier. Younger investors tend to scorn modest, compounding gains in favour of asymmetric bets on “the next Apple”. Mr Merton’s method provides the prospect of stable, long-term prosperity, not billionaire-or-bust drama. It also extends to retirement spending. Rather than withdrawing a fixed sum each year, which risks depleting funds in a downturn, retirees should spend a percentage of their remaining wealth. This allows spending to rise and fall with market performance. It is uncomfortable but sustainable.
Most people, however, want the impossible: high returns without risk; predictable spending with volatile assets; and emotional comfort alongside rational optimisation. Mr Merton’s model exposes these contradictions. It redefines the purpose of investing, not as wealth maximisation but as utility maximisation. In an age of meme stocks and cryptocurrency speculation, this is a rebellion against financial noise. It demands humility and discipline, qualities in short supply. The goal is to align money with life’s real happiness curve. As a wise aphorism puts it, do not risk the necessary in the hope of winning the superfluous. ■
