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Robert Merton and the Effect of Time on Portfolio Choice
From "Buttonwood," The Economist
When it comes to investing, it is easy to forget about the clock. Or, as some call it, the investment time horizon – the total length of time that an investor expects to hold a security or a portfolio. Robert Merton (insert), the “resident scientist” of the London office of Dimensional Fund Advisors, has had a lifetime fascination with the scientific application of this theory, including how, and when, it should be applied.
Merton bought his first stock aged ten and completed a risk-arbitrage trade (on a takeover by Singer, a maker of sewing-machines) aged 11. He rebuilt his first car aged 15. In 1997 he became a Nobel Laureate – Economics at age 53, a career high. A year later, a career low: ltcm, the hedge fund he co-founded, imploded. These markers of the passing years matter. For Mr. Merton’s specialism is the mathematics of time applied to finance.
Merton bought his first stock aged ten and completed a risk-arbitrage trade (on a takeover by Singer, a maker of sewing-machines) aged 11. He rebuilt his first car aged 15. In 1997 he became a Nobel Laureate – Economics at age 53, a career high. A year later, a career low: ltcm, the hedge fund he co-founded, imploded. These markers of the passing years matter. For Mr. Merton’s specialism is the mathematics of time applied to finance.
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His first paper about time applied to finance was published almost exactly 50 years ago. Its title – “Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case” – is forbidding. The ten pages of equations that follow are daunting. But for Mr. Merton, the equations are tools, allowing him and subsequent researchers to clarify an important question: when does time horizon matter in investing and when does it not?
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To start to understand the paper’s importance, go back to the birth of modern portfolio theory. Over half a century ago, finance theory had been mostly a collection of stories and rules of thumb. Some was useful (“sell down to the sleeping point”), and little was rigorous. A new generation of scholars in the 1950s changed this. They assumed that investors seek the highest returns for a given amount of risk, emphasizing that risk is an inherent part of higher reward. The issue for portfolio choice is how much of this risk to bear, assuming that an investor will take on more risk only if he or she is expecting more reward (and able to handle the stress related to that additional risk).
In this new, formalized set-up, investors decide how to divide their financial wealth based on an assumed time (or life) span that functions as a one-period model. But real-life investing is a movie, not a snapshot. Time is a factor, on top of risk appetite. Mr. Merton wanted to go further and discover how investors, faced with an uncertain future, should decide at each moment on their mix of risky and safe assets. The folk wisdom of the time said that young people should hold a riskier portfolio than older ones, because the passing of time makes stocks less risky. That turned out to be wrong—or, at least, it was not quite right.
In two papers published in August 1969, Mr. Merton and his mentor, Paul Samuelson, showed that time horizon should make no difference to portfolio choice. But the result holds only if risk appetite is unchanging and stock prices are unpredictable. Alter these assumptions, as future researchers would, and the results change. Mr. Merton’s use of continuous-time mathematics created a valuable template that finance theorists were able to apply to related problems. An example of this is the Black-Scholes Merton (BSM) model, perhaps the world’s most well-known options pricing model that is regarded as one of the best ways of determining fair prices of options. This earned Merton a Nobel prize in Economics in 1997, along with Myron Scholes.
In this new, formalized set-up, investors decide how to divide their financial wealth based on an assumed time (or life) span that functions as a one-period model. But real-life investing is a movie, not a snapshot. Time is a factor, on top of risk appetite. Mr. Merton wanted to go further and discover how investors, faced with an uncertain future, should decide at each moment on their mix of risky and safe assets. The folk wisdom of the time said that young people should hold a riskier portfolio than older ones, because the passing of time makes stocks less risky. That turned out to be wrong—or, at least, it was not quite right.
In two papers published in August 1969, Mr. Merton and his mentor, Paul Samuelson, showed that time horizon should make no difference to portfolio choice. But the result holds only if risk appetite is unchanging and stock prices are unpredictable. Alter these assumptions, as future researchers would, and the results change. Mr. Merton’s use of continuous-time mathematics created a valuable template that finance theorists were able to apply to related problems. An example of this is the Black-Scholes Merton (BSM) model, perhaps the world’s most well-known options pricing model that is regarded as one of the best ways of determining fair prices of options. This earned Merton a Nobel prize in Economics in 1997, along with Myron Scholes.
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A lot of finance theory that came later would tease out the circumstances in which time horizon really does matter. The reckoning changes, for instance, when wealth is looked at in the round to include non-tradable human capital—knowledge, skills and abilities. Sitting in a London office, Mr. Merton gives an illustrative example. |
Mr. Merton wanted to go further and discover how investors, faced with an uncertain future, should decide at each moment on their mix of risky and safe assets: When does time horizon matter in investing and when does it not?
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Say, a young person’s human capital, which determines his future earnings, is 90% of his lifetime wealth, with the balance in stocks. And say that for an almost-retired person the proportions are reversed. If the stock market crashes by 40%, the young person has lost only 4% of his wealth. But the nearly retired person has lost 36%, which is much more serious. For older people, having all their financial wealth in stocks is not a sensible risk to take, says Mr. Merton. Human capital is low-risk. If you have lots of it, you can take more financial risk.
The best lifetime strategy is a complex problem to solve, even for brainy people such as Mr. Merton. Needs drive innovation, says Mr Merton. “That is why I’m an optimist.”
The original article was originally published by The Economist.
The best lifetime strategy is a complex problem to solve, even for brainy people such as Mr. Merton. Needs drive innovation, says Mr Merton. “That is why I’m an optimist.”
The original article was originally published by The Economist.
