When everyday investors have to make personal finance decisions, rules of thumb can be easy and comforting. For instance, to decide what percentage of your portfolio should be devoted to stocks, simply subtract your age from 120. In other words, a 40-year-old should invest 80% of their retirement savings in stocks.
But rules of thumb don’t take investors’ personal circumstances into account, says James Choi, a professor of finance at Yale SOM. Factors such as an investor’s existing savings or expected income trajectory can make a big difference to their optimal asset allocation.
At the other extreme, economists have developed sophisticated ways to consider these nuances and produce personalized recommendations. But their methods are far too difficult for an average investor to reproduce. They’re “intellectually fantastic,” but there’s “nothing practical that I could take away,” Choi says.
To bridge that gap, Choi and his colleagues took a middle road they call “practical finance”: They translated research-backed economic findings into a spreadsheet-based tool that an average person could fill out. The spreadsheet’s answers are approximations of optimal solutions, but they’re close enough that people won’t be much worse off than if they’d used the original academic method, the team found.
And the tool often produces results that are very different from those given by rules of thumb or target-date funds (which set portfolio allocations based on the person’s expected retirement year). For instance, it sometimes recommends a much heavier allocation to stocks. For many people, “you probably should be holding more stocks than you are,” Choi says.
The origins of the research date back to pioneering work in the early 1970s by Nobel Prize-winning economist Robert Merton. He developed the idea that if your future wages are risk-free—that is, you can count on a particular salary trajectory for the rest of your life—those future earnings act like a giant bond that regularly pays you interest.
For young people with meager savings, their biggest economic asset is this future income, also known as their human capital. “Instead of just the $10,000 I have in my bank account, I actually have the $10,000 plus this enormous bond that’s paying me every pay cycle,” Choi says.
Many people don’t think of their wealth this way; in their minds, only their savings or their home count as assets. “People too narrowly frame their investment problem,” Choi says. “They don’t take into account that they have this huge stock of human capital.”
The logical conclusion of Merton’s work is that, since so much of a young person’s wealth is tied up in a bond-like asset, they can take much more risk when investing their savings—that is, by investing it in stocks. Let’s say that they expect to earn $2 million from their jobs over their lifetime. If they invest $10,000 of savings into stocks, Choi says, “even if I lose it all, I still have $2 million of human capital.”
Of course, people’s income isn’t risk-free; there’s always a chance of a layoff or other career detours. So in a 2005 study, another team of economists wrote computer code to solve for an investor’s optimal asset allocation in a way that accounted for potential income setbacks. Their methods also factored in nuances such as the person’s risk aversion and how much they had already saved.
But that study reported answers for only a small number of case studies. Choi, Yale PhD student Pengcheng Liu, and Canyao Liu, a Yale PhD who is now at Hudson River Trading, decided to solve the asset allocation problem for more than 5,000 combinations of different parameter values. Then they created formulas that would allow people to quickly get an approximation of the right answer.
For example, one scenario considered a 45-year-old college graduate who had saved 1.5 times their annual income. The team’s formula recommended that the person invest 100% of their savings in stocks, even if they were pessimistic about expected stock market returns and the investor was fairly averse to risk.
This figure is higher than the allocation suggested by the “120 minus your age” rule (which would be 75% in stocks) or even fairly aggressive target-date funds. For instance, Fidelity’s target-date fund for people retiring in about 20 years currently allocates 90% to stocks; Vanguard’s and Schwab’s allocate 82% and 83%, respectively.
A key factor in the formula’s determination is the amount of savings, which rules of thumb and target-date funds don’t take into account. In the example above, the investor’s savings are still small relative to their bond-like future income, so the formula suggests they invest the money very aggressively. However, if the exact same 45-year-old had saved 2.4 times their income, the formula would suggest only 75% stocks. More of that person’s assets are tied up in savings relative to future earnings, so some money is shifted to bonds to keep their overall allocation the same.
Another factor that can dramatically change the results is the investor’s risk aversion score, which captures how much unhappiness losing money would cause versus how much additional happiness more money would bring. (When using the team’s spreadsheet tool, people can determine their score by answering a question about a thought experiment involving a gamble versus a sure amount of money.) The higher an investor’s risk aversion, the less the formula will recommend that they allocate to stocks. For instance, in the example above, the 45-year-old who had saved more than twice their income had a risk aversion score of 7 on a scale of 1 to 10. A score of, say, 10 or 4 would tilt the recommended 75% stock allocation downward or upward.
Choi notes that his team’s method doesn’t account for another aspect of investor psychology: the likelihood of panicking during market crashes. A nervous investor who’s likely to feel stressed and sell shares at a loss during market downturns wouldn’t be served well by holding 100% in stocks. “If you can’t sleep at night, is it really worth it to you to do exactly the optimal thing?” Choi says.
The team also estimated how well their method performed compared to the optimized answers, focusing on the example of a 22-year-old starting out with no savings other than the salary they had just earned. They found that, averaged across all the parameter values they consider, the loss of “welfare,” or overall well-being, that would result from using their approximate answers rather than the exactly optimal solution was 0.06%. It’s “a trivial amount,” Choi says, which suggests that “our approximation is pretty good.”
When they ran the same comparison for various other methods of determining stock allocation, some guidelines didn’t perform too badly. For example, one older rule of thumb is to invest “your age in bonds” or “100 minus your age in stocks.” Following this guideline would decrease welfare by 2% on average. And holding a steady 60% in stocks reduced it by 3.8%. “They’re not terrible,” he says.
Holding no stocks at all was far worse; that allocation led to a 7.9% average decrease in welfare. “If you’re never investing in stocks for your whole life—and a lot of people are in that boat—that’s pretty bad for you,” he says.
Another caveat is that the tool doesn’t account for housing. For many people, their biggest asset besides their human capital is their home, but “housing is extremely challenging to model,” he says. So the formula assumes that the subject is a life-long renter.
Still, the spreadsheet tool offers a perspective that may be useful for investors to weigh alongside other approaches. “It’s taking a canonical model from the academic research literature” and bringing it into the real world, Choi says. “There is now a solution available that customizes itself to your particular circumstances and preferences.”
“The Yale School of Management is the graduate business school of Yale University, a private research university in New Haven, Connecticut.”
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