Rudin and Marr: A Reformulation of RP Methods of Portfolio Construction

Rudin and Marr: A Reformulation of RP Methods of Portfolio Construction

A recent article by Alexander Rudin and William M. Marr, in The Journal of Alternative Investments, seeks to change the terms of discussion of the risk parity method of portfolio construction in a way that might remove some of the counter-intuitive consequences that can dog the approach.

The paper, “Investor Views, Drawdown-Based Risk Parity, and Hedge Fund Portfolio Construction” is also a valuable roadmap to recent scholarly and participant debates on the still-controversial but widely accepted RP approach.


Risk parity is a portfolio management approach that starts by ignoring (or, to be kinder, starts by abstracting from) any information about assets available to the investors other than that inherent in the historical volatilities (the conventional proxy for risk) of those assets and in the correlations among those risks. Thus, in a portfolio consisting only of asset classes X and Y, with uncorrelated risks: if asset class X represents a larger risk to the portfolio than does Y, then X will be sold and Y purchased until parity is achieved.

This means that RP relies far less upon equity than certain other “traditional” approaches do.  It is more conservative in its choice of assets, but it is more aggressive on the matter of leverage, than those other approaches.

Mark Rzepczynski, a founding partner of AMPHI Research and Trading, has called this idea “one of the most important advancement in portfolio construction over the last decade.”

The Big Benefit

The application of this method is straightforward so long as the risks of the different assets in the portfolio do remain uncorrelated.  But of course they often are correlated, so it can get complicated. The housing crisis and its financial aftermath should have taught us all that the prices of a house in Connecticut is likely to rise and fall at much the same time as the price of a house in Vermont,  for example, and may not be entirely independent even of prices in Arizona.

Still, the difficulties of the application can be overcome, and the big benefit of risk portfolio will, like the Dude,  abide. The big benefit is precisely the fact that RP ignores return or expected return, variables about which mistakes are easy to make, and as a consequence RP de-emphasizes equity. This lets it get the investors the same rate of return a CAPM efficient portfolio would get them while decoupling the investors’ fortunes from the booms and busts of the business cycle.

Another arguable benefit? If you believe that many market participants are leverage averse for psychological or institutional reasons or some combination of the two, then you may infer that there is money to be made by the embrace of leverage, that is, that low-risk assets have a liquidity aversion premium built into them.

Rudin and Marr, in their study, cite a 2012 article on this point in the Financial Analysts’ Journal. In that article, Clifford Asness, Andrea Frazzini, and Lasse Pederson, all of AQR Capital Management, outlined this “theory of leverage aversion” at some length, and called it a “realistic theory that holds up consistently in out-of-sample tests across and within different asset classes and countries.”

Rudin and Marr

But what Rudin and Marr add to this discussion is the idea that “risk parity” can be understood not simply as historical volatility but as expected drawdown (EDD). They look to the idea of a maximum drawdown as elucidated by mathematicians working on the application of probability theory to Brownian motion.

To the extent that focus turns to EDD, it allows discussion of some of the matters ignored, or abstracted-from, in the initial stages of creating the TP model. Investor views on valuations are allowed back in, insofar as they contribute to a discussion of what those drawdowns will be in various circumstances. Thus, RP is enhanced.




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