"A mean-variance benchmark for intertemporal portfolio theory." Journal of Finance 69:1-49 (Feburary 2014) DOI: 10.1111/jofi.12099 (ungated version here.)
After all these years, it is still a thrill when an article gets published, and this being a bit of a personal day on the blog (see last post), I can't resist sharing it.
This paper started when John Campbell presented "Who should buy long-term bonds?" (with Luis Viceira, American Economic Review) in the late 1990s at the Booth (then, GSB) finance workshop. John pointed out that long term bonds are the riskless asset for long-term investors, so we should build portfolio theory around indexed perpetuities, not one-month T bills.
I thought, "that's so obvious!" and, simultaneously, kicking myself, "why didn't I think of that?," a sign of a great paper. (I was also inspired by Jessica Wachter's "Risk Aversion and the Allocation to Long Term Bonds" which came out in the Journal of Economic Theory 2003.)
But if indexed perpetuities are the "riskfree asset," then surely the claim to the aggregate dividend or consumption stream is the "risky asset," and everyone lies on some sort of line between the two. We should be able to describe portfolio theory -- even in an intertemporal, dynamic, incomplete-market environment -- with standard mean-variance pictures. Why I'll just write this down and I'll have a great paper in a week. 15 years later, here it is. Well, thanks for the inspiration, John!
You may wonder why the Journal of Finance allowed me page after page of prose before getting to the point, and how this seems to massively contradict my own advice to get to the facts. Is the JF lax with old-timers like me? No, actually. I sent them a sparse draft which just set out the theorems. The editor and referees' main complaint was that I need to explain why this is important. They asked for it, though possibly not in the volume they got!
In the end, though, I think this paper functions better as essay than as math. It's a "benchmark" because it really is a "parable." Quadratic utility is a terrible approximation for long horizon investing, and you can't rely on normal distributions either. So, thank you Journal of Finance (Cam Harvey editor and anonymous referees) for letting me sneak in a rather good (I think) essay on portfolio theory in the guise of a paper!
I hope the article inspires someone to figure out how to make a payoff-centered portfolio theory practically useful too. (Ph. D. students, before you try to apply it, read my endless appendix "long run mean-variance analysis in a diffusion environment," detailing all my failed attempts.)