Thursday, February 6, 2014

A mean-variance benchmark

"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.

Two stories.

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.)


  1. How are bonds "riskfree" given the possibility of unanticipated inflation?

  2. TIPS. Riskfree except for the possibility of US government default. As close as we get, at the abstract level of this paper.

    1. 1. The Bureau of Labor Statistics (operated by the federal government) can't change it's definition of inflation? See 1994 Boskin Commission, 1983 substitution of owner's equivalent rent, chained CPI, etc.

      2. The U. S. government can't run a surplus or swap fixed interest securities for inflation adjusted securities whenever it feels the need to?

    2. John,

      Also, see:

      "What happens to TIPS if deflation occurs?"

      "The principal is adjusted downward, and your interest payments are less than they would be if inflation occurred or if the Consumer Price Index remained the same. You have this safeguard: at maturity, if the adjusted principal is less than the security's original principal, you are paid the original principal."

      Still think TIPs are "risk free"?

  3. its funny to have this conditional probability those days especially in Europe and not only! but if the meaning of Rf is lost than what about the risk premiums undert that state probabilities?

  4. Great! A paper I can talk about in my Indiana U. Kelley School undergrad general regulation class. Last class I asked them a question I always ask: Since perpetuities are easier to price and don't have to be rolled over, why don't companies use them? I got a couple of good replies I hadn't heard before:
    1. Inflation would drive the value inexorably down to where a $1,000/year bond wouldn't be valuable enough to buy a candy bar (my phrasing). Indexing would take care of that, of course.
    2. Wouldn't it be confusing to know how to value the asset in the bankruptcy that would inevitably occur, since there's no principle to use? (and we could add to that the problem of what kind of instant redemption to require if the bond covenant is violated).

    1. Eric,

      The reason that perpetuities are not used has more to do with solvency risk (liabilities greater than assets) than bankruptcy risk (expenditures greater than income).

      Most long term corporate bonds are used to fund long life capital investments (factories, office buildings, etc.). Those fixed assets have a depreciable lifetime. The problem with perpetuities is a duration mismatch between asset and liability. No bank is going to lend for 500 years against a building that will maybe last 100 years.

    2. As said not all assets have the same lifespan also not for all assets the expected and the required payback period is the same. Gordon Shapiro made this mathematical simplification for "non real" assets for binding agreements among people for lifetime promises like the "mmarriage". This lifetime promise cannot be made on real assets like machinery etc. Unless it's your laptop (even this will be obsolete by processor). By the way can the posts sent by an email whenever updated?


    "U.S. Representative Patrick McHenry, a North Carolina Republican, asked if Yellen agreed with the European Union's top bank regulator who recently said there is no such thing as a risk-free asset, even if it's sovereign debt. The EU, McHenry said, seems to be going in a different direction on sovereign debt than the U.S., where the Volcker Rule allows banks to continue to prop-trade U.S. Treasuries, as if they were risk-free."

  6. The underlying intuition of Campbell's work should be referred to more often in academic work. Empirically, an interesting portion of changes in term structures of interest rates in recent decades is ascribable to the relative growth of institutional investor pools with longer-maturity 'natural' holding periods and this is often integrated into 'great conundrum' research among market practitioners. A lot of term premium/risk premium theory needs to be turned around to reflect this.


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