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The Risk Parity Tower of Babel

Update, Nov. 7 2012: Evidently the interviewer was Bob Litterman, renowned in several areas of quantitative finance, especially for the Black-Litterman model.

The first several times I heard of or read about risk parity I was puzzled. The media, it seemed, had distilled descriptions of risk parity into some variation on “a leveraged bond portfolio” or “portfolio in which the bonds are leveraged until they have the same volatility as equities.” The first time I grasped what risk parity really is was when I read Chris Levell’s piece for NEPC.

It was clear that risk parity was something broader than as described by the media: it was simply a portfolio in which the assets’ contributions to variance were equal. Notice the lack of any mention of the words “bonds” or “leverage” in that definition.

Somehow the attention the investment media pays to risk parity focuses on examples of multi-asset class portfolios that use leverage. In Qian’s earliest writing on risk parity, he described one possible implementation as simply an alternative to a bond portfolio, one with better diversification than a bond-only portfolio.

Bottom line: you can find examples of risk parity portfolios with no bonds and with no leverage, and yet when people talk about risk parity they almost always refer to them as leveraged bond portfolios. The Risk Parity Tower of Babel (RPTB) endures.

RPTB Comes to Chicago
I was glad to see that Eugene Fama had agreed to appear at the CFA Institute annual meeting in Chicago this past spring. Fama is always interesting, opinionated, and he does not speak in public often enough. Former students know he is often quite funny, sometimes hilarious. At times taking a class from him seemed like taking a class from Don Rickles.

In class Fama spent considerable time discussing empirical papers. Whenever he wanted to fast-forward the discussion he would just ask, “OK, what’s the punch line?”

Fama delivers the punch line
Listen to this interview of Fama at this year’s CFA conference in Chicago.

Even if you’re not a CFA Institute member you may listen to the session in iTunes, and I encourage you to do so.

While it is interesting throughout, the session becomes comical at the 41st minute. Here is my attempt at a transcription:

41:07-41:37
Interviewer: “What do you think of the risk parity asset allocation strategy?”

Fama: “Never heard of it.”

Fama: “What is it…”

Interviewer: “OK…” (laughter) “uh…”

Fama: “…in my terms?”

Interviewer: “I think it’s the idea that you, uh, find a bunch of different asset classes…”

Fama: “mm-hmm”

Interviewer: “…and then use leverage to get them all to the same volatility. Equal risk across different asset classes…”

Fama: “OK.”

Interviewer: “and, uh, Bridgewater has done this very successfully for a long time.”

Fama: “OK. Stupid!”

(Loud laughter)

Interviewer: “OK.”

Fama: “If you think about your portfolio problem, you never start with a proposition like that. What you’re thinking about if you’re a mean-variance investor is, how do I form these things to minimize variance? That would not tell you to lever them up all in the same way.”

Chicago Booth comedy
One of Fama’s best known students is Cliff Asness, co-founder of AQR and one of the world’s best known hedge fund managers. Asness is also one of the most vocal proponents of risk parity. I assume Fama and Asness are on pretty good terms since in 2004 Asness endowed $1 million to Chicago Booth for classroom in Fama’s name. Fama asking “what it it?” shows that when he and Asness communicate, they’re not talking shop!

Reconciling “stupid” with non-stupid practitioners
Fama is correct: A mean-variance investor would never leverage bonds as the interviewer described.

At the same time, Cliff Asness is not stupid, and neither is risk parity. Nor are Ray Dalio, Wai Lee, Bob Prince, or Ed Qian, to name a few of its better known practitioners.

I will attempt to explain why risk parity is not stupid, and reconcile the explanation with Fama’s take. It’s really quite simple:

Risk Parity investors are not mean-variance investors!

As Fama elaborated on his answer he qualified his interpretation as that of a mean-variance investor. But a risk parity investor is not a classic mean-variance investor!

The difference between a mean-variance investor and a risk parity investor
A mean-variance investor’s objective is to maximize return relative to risk, consistent with his utility for return versus risk. A risk parity investor’s objective is to maximize a specific type of diversification, that being contribution to portfolio variance. By ignoring expected return in his objective function, an risk parity investor is implicitly skeptical or agnostic about modeling expected returns. No “mean” -> no “mean-variance”.

The interviewer’s description was due to the Risk Parity Tower of Babel. I would have preferred the interviewer to have said “risk parity is an allocation method in which the assets’ contributions to portfolio variance are equal. By the way, Cliff Asness is one of its loudest evangelists.”

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