By Victor Haghani and James White¹
ESTIMATED READING TIME: 4 min.

Regular readers know we’ve been evangelizing a unified approach to lifetime investing and spending for a long time. We devoted a whole section of The Missing Billionaires to it, and wrote about it most recently in Riding the Wheel of Fortune, where we explain how we put this framework to work helping individuals and families with their biggest financial decisions. The core idea: find the spending and investing policy that maximizes the lifetime utility you get from your consumption.

So we were delighted – if a little jealous – to see a WSJ article about James Choi’s recent work, in which he and his co-authors took a full-featured academic lifetime model² and boiled it down into a simple spreadsheet that a wide range of investors can use without expert help. Choi is a professor at Yale, and his co-authors were his students there, and we’d love to see this work make the “Yale Model” synonymous with sensible personal financial decision-making, rather than concentrated bets on high-fee, illiquid alternative investments popularized by the Yale endowment’s longtime investment approach.

The foundation of both Choi et al.’s approach and our thinking at Elm is the “Merton share” – a rule of thumb for how much to put in stocks, based on their risk and expected excess return, and your personal degree of risk-aversion.³ The WSJ’s base case assumed a 3% annual equity premium over Treasuries with 18.5% annual volatility. They pose a question to calibrate risk-aversion, similar to what we described in our 2018 note “Measuring the Fabric of Felicity”. Most investors we’ve worked with land on a risk-aversion coefficient between 2 and 3.⁴

The other key input is your estimate of future earned income and expected retirement income, adjusted for inflation. Choi et al. discount wage income at an average real rate of 4% to 5%⁵ – above the 2% risk-free rate, because wages are risky (though assumed uncorrelated with stocks) – and discount social security income at closer to the safe rate.⁶ They also account for expected longevity. At Elm, we take a very similar approach.

The punchline: Choi et al.’s model often calls for a higher allocation to stocks than conventional wisdom suggests, especially for investors who are at the start or end of their working years. The chart below shows their recommended equity allocation (at two levels of stock market risk premium) compared to the “100 minus your age” rule⁷ and Vanguard-style target date funds.⁸ Our own framework at Elm lines up closely with Choi’s.

For young investors, who typically have lots of human capital relative to their financial capital, Choi et al.‘s model will almost always recommend 100% equities.⁹ The intuition is straightforward: your risk-adjusted future income stream acts like a bond. Blend that “income bond” with your financial portfolio and you’re much less exposed to stocks than you think. This income stream also means your true total wealth exceeds your financial wealth – the difference is your “human capital.” As you age and your human capital shrinks, your optimal equity allocation naturally falls – not because you’ve gotten more cautious, but because that implicit bond is running off.¹⁰

Note that the optimal allocation to stocks rises when the equity market offers a higher expected return relative to safe assets, which makes both intuitive and theoretical sense. If you believe as we do that equity risk premia and market riskiness vary over time, and can be estimated with useful accuracy, your asset allocation should respond to changing market conditions, rather than remaining static as implied by rules of thumb like ‘age minus 100’ and conventional target-date funds.

Our Elm Lifetime Investing and Spending Analysis (ELISA) is pretty similar to the full model underlying Choi et al., so agreement is expected when inputs line up.¹¹ Where ELISA goes further is in directly accounting for taxes, subsistence spending, time preference, bequest motives, and individualized income volatility and equity correlation – all of which get simplified out in the Choi et al. model.

Connecting the Dots

Lifetime models have two big outputs: how much risk to take, and how much to spend. Professor Choi has tackled the investing side; we wouldn’t be surprised to see him go after spending next. In a recent Rational Reminder podcast, he mentioned wanting to develop a simple spending rule to improve on the conventional “4% rule” – which basically says: take 4% of your wealth at retirement, spend that amount each year adjusted for inflation, and cross your fingers.

One of our most rewarding missions at Elm has been making the best academic work on decision-making under uncertainty accessible to practitioners and individual investors. Professor Choi is clearly on the same mission, and we couldn’t be more pleased to see his work getting such broad attention.

1. This is not an offer or solicitation to invest, nor are we tax experts and nothing herein should be construed as tax advice. Past returns are not indicative of future performance.
   Thank you to Joe Pinsker, Peter Santilli, James Choi, Canyao Liu, and Pengcheng Liu.
   
2. Cocco, J., Gomes, F., and Maenhout, P., (CGM), “Consumption and Portfolio Choice over the Life Cycle,” (2005).
   
3. This rule of thumb is exact given major assumptions of: normal IID returns, continuous rebalancing, no subsistence spending, CRRA utility, no earned income.
   
4. An investor with a coefficient of risk-aversion of 2.5 would be indifferent to a 50/50 gamble where his wealth either increased by 40% or decreased by 20%.
   
5. Relative to the mortality-adjusted values.
   
6. What they actually do under the hood is find a set of age-dependent discount rates which best align the Merton share using capitalized income with the full CGM model under a wide range of input scenarios. This tends to result in an average real discount rate in the 4-5% range.
   
7. Your allocation to stocks should be 100 – your age, e.g. if you are 30 years old, then you should have 70% in stocks.
   
8. We assume 18.5% volatility, 2.5 CRRA risk aversion, $100k of starting financial wealth at 25, then $200k/year of real post-tax income until retirement at 70, followed by $80k of real post-tax retirement income. We assume no subsistence and a wealth trajectory consistent with the optimal spending policy.
   
9. Really greater than 100%, but a no-leverage constraint caps it at 100%.
   
10. In the presence of social security, it won’t ever go all the way to zero.
    
11. For very young investors both models agree at 100%, and as labor income approaches 0 (or all income is certain, e.g. social security) both models in the absence of a subsistence spending level converge to the Merton Share. The path connecting these points won’t be identical between ELISA and Choi et al., but pretty close.