Research has shown that asset allocation i.e, how you allocate across stocks, bonds and other asset classes, matters more than what securities you select, in terms of determining investor’s risk adjusted returns. But here’s a half century old theory by a Nobel prize winning economist – Robert C.Merton (of Black-Scholes-Merton and Long Term Capital Management fame), that says rather than optimise asset allocation for returns, why not optimise for happiness (in effect returns and risk aversion).
The article introduces a rather intuitive concept of ‘diminishing marginal utility of wealth’ – “This is a fancy way of saying that the more money people have already, the less they enjoy getting even more. For someone who cannot afford food, $1m will be life-transforming. But a second million will raise their living standards by far less, and a third will simply make them a bit richer.
…The corollary is less obvious: that the rate at which your enjoyment of new wealth declines as you get richer and your aversion to risking large sums are two sides of the same coin.The two can be represented by a single parameter in a family of “utility functions”, which describe the pleasure derived from different amounts of wealth. Researchers have found that these “constant relative risk-aversion” (CRRA) utility functions fit most people’s attitudes to wealth fairly well. The parameter, known as “risk aversion”, can be calibrated to any individual’s level of daredevilry.”
The author then applies this concept to investing where Merton comes in:
“…Robert Merton, who later won a Nobel prize for economics, set out in a paper in 1969. His snappily titled “Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case” showed how a CRRA utility function, calibrated to any individual’s risk aversion, could be translated into a portfolio with an optimal split between high-returning but risky assets, such as stocks, and safe ones such as bonds. In Mr Merton’s procedure, “optimal” means balancing the individual’s desire for returns with their aversion to risk in such a way as to maximise their expected happiness.
…If the Merton share’s definition seems like a mouthful, consider what it implies. Should the safe asset’s yield fall, perhaps because interest rates are falling, but shares’ expected return remain the same, you should put more into the stockmarket. This makes sense: the opportunity cost of holding bonds over stocks has just risen. Conversely, if the stockmarket’s volatility is soaring, say because a banking crisis is under way, you should sell some shares to buy bonds.”
Does this work in practice?
“Victor Haghani and James White, co-authors of “The Missing Billionaires”, which seeks to popularise Mr Merton’s ideas, have crunched the numbers. They took an index of American shares as the risky asset and inflation-protected Treasury bonds as the safe one, using data from 1900 to 2022 (using a proxy for the bonds for before 1997, when they were first issued). They then compared the Merton-share portfolio with one split 65/35 between stocks and bonds.
The results are shown in chart 2. Not only would the Merton portfolio have beaten the 65/35 one, generating an annualised return of 10% compared with 8.5%. Even more remarkably, it would have outperformed the strategy of being 100% in stocks, despite involving 40% less risk.”
The article goes on to highlight the shortcomings of the model as well.
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