Merton's Classic Solution and the Merton Share

In this episode, we welcome back James Choi, Professor of Finance at the Yale School of Management, to unpack one of the most important—and misunderstood—questions in personal finance: How much of your portfolio should be in stocks? Drawing on his new paper, Practical Finance: An Approximate Solution to Lifecycle Portfolio Choice, James walks us through the classic portfolio choice problem first solved by Robert C. Merton, later extended by Francisco Gomes and co-authors, and now made dramatically more usable through a spreadsheet-based approximation. We explore how risk aversion, wealth, labor income risk, and expected returns shape optimal asset allocation, why simple rules like "100 minus your age" aren't terrible but still costly, and how James and his co-authors managed to approximate a complex dynamic optimization model with an error of less than 0.1% in lifetime welfare.

Key Points From This Episode: (0:04) Introduction and why this episode delivers on "mathy roots."

(1:10) James Choi's new paper: Making lifecycle portfolio choice solvable in a spreadsheet.

(5:15) The portfolio choice problem: How much should you allocate to stocks versus risk-free assets?

(6:09) The classic Merton (1969, 1971) solution and the "Merton share."

(8:00) The equity premium formula: Expected excess return ÷ (risk aversion × variance).

(11:20) Extending the model to risky labor income (Cocco, Gomes, and Maenhout).

(14:27) Why labor income behaves bond-like—even when it's risky.

(16:33) How wealth, risk aversion, and labor income characteristics affect optimal equity allocation.

(20:52) Transitory vs. permanent labor income risk—and why permanent risk matters more.

(23:04) Solving thousands of parameter sets to approximate optimal lifecycle allocations.

(27:09) How close is the approximation? ~3–4 percentage points on average, with

(29:56) Comparing to rules of thumb: 100 minus age and 60/40.

(32:08) Why 0% equities is often far worse than 100% equities.

(33:33) What the optimal allocation typically looks like over the life cycle.

(38:55) Walking through the publicly available Google Sheet to calculate your allocation.

(44:39) Estimating your risk aversion using a coin-flip thought experiment.

(46:08) Forecasting future labor income and using wage imputation.

(48:05) Why housing is excluded—and why it's so hard to model.

(50:35) How often you should update your assumptions (hint: not often).

(53:06) Leverage, constant leverage ETFs, and why young investors might rationally use them.

(58:55) Discussing lifecycle advice from Scott Cederburg and co-authors.

(1:07:40) What practical finance problem James wants to tackle next (hint: the 4% rule and retirement spending).

Links From Today's Episode: Meet with PWL Capital: https://calendly.com/d/3vm-t2j-h3p

Rational Reminder on iTunes — https://itunes.apple.com/ca/podcast/the-rational-reminder-podcast/id1426530582. Rational Reminder on Instagram — https://www.instagram.com/rationalreminder/

Rational Reminder on YouTube — https://www.youtube.com/channel/ Benjamin Felix — https://pwlcapital.com/our-team/

Benjamin on X — https://x.com/benjaminwfelix

Benjamin on LinkedIn — https://www.linkedin.com/in/benjaminwfelix/

Cameron Passmore — https://pwlcapital.com/our-team/

Cameron on X — https://x.com/CameronPassmore

Editing and post-production work for this episode was provided by The Podcast Consultant (https://thepodcastconsultant.com)