"Risk Parity" investing (vs. MPT)

There’s an entertaining fistfight going on in letters to FAJ. It began with… “In the May/June Editor’s Corner, Rodney Sullivan takes on a noble goal. His thrust is warning investors to be suspicious of free lunches and to beware of trying to close shortfalls by increasing leverage.” Among the replies we find Cliff Asness discussing “risk parity” investing (Sep/Oct): “Without naming it, Mr. Sullivan is critiquing something that has become known as “risk parity” investing. Strategic asset allocation is usually thought of in terms of the dollars placed in each asset class. Because equities represent a large amount of the world’s dollars and are more volatile than bonds, typical institutional portfolios are dominated by equity exposure. Risk parity advocates strive for diversification by risk (hence the name!) rather than dollars. This approach generally results in a lower expected return portfolio (although a higher risk-adjusted expected return).” Laurence Siegel also chimes in (Sep/Oct)… “Echoing Sullivan (2010a) and Waring and Whitney (2009), Goldsticker (2010) helpfully added that the riskless asset relevant to most investors is not cash but rather the liability-defeasing asset or portfolio, and that 100 percent of the fund needs to be held in this portfolioall the way up the efficient frontier (rather than reducing the holdings weight of this portfolio to make room for equities). Thus, leverage is needed if one is also going to hold equities and other non-liability-defeasing assets.” These are just excerpts; full letters available in the journal. I pointed out this discussion because it (I think) challenges some of the tenets of MPT as usually taught.

What tenets of MPT do you think risk parity challenges? It still incorporates diversification and is quite clear that a risk-parity portfolio will have lower expected returns than an MVO portfolio (but also higher risk-adjusted expected returns). In general, I don’t really like the idea of risk parity since it implies that every asset has the same contribution to overall risk. Why should EM and US stocks have the same contribution to risk? I like the idea of a benchmark that has the contribution of each asset to portfolio risk equal to their market cap weight. More intuitive anyway.

I’m doing some work on a system that is effectively using (for position sizing) a risk parity model. One of the big issues is that the least volatile asset tends to take up the largest portion of the portfolio. If you have identified a source of alpha, I’m thinking that it makes sense to allocate tactical overweights and underweights based on risk parity, but that you’d want your strategic allocation to include long term correlation figures. Anyway, it’s an interesting discussion.

bchadwick, In my experience risk parity (or allocations based on the contributions to portfolio risk) makes more sense with strategic allocation rather than the tactical allocations. The main reason is that the formulas used for calculating the contribution to portfolio risk do not always produce short positions that would make sense. If you are using a simple strategic allocation+tactical allocation=portfolio weight formula, then the tactical allocation can be expected to have several negative weights. I’m not aware of a risk parity calculation that can handle these well (might exist, but I don’t know). There’s no reason why your strategic allocation couldn’t be done on the basis of risk parity and with long-term correlation figures. For instance, you could use the past ten years covariance matrix as an input to the risk parity strategic allocation and then the past 1-2yrs covariance matrix for your tactical allocation. Similarly, if you decide to obtain a tactical allocation using risk parity (or some other simpler technique), you can still back out the expected returns with reverse optimization and blend that with the implied returns from your strategic allocation using Black-Litterman and optimize the posterior returns with MVO. (For reference, when I do risk parity, I set the component value at risk, w*(sigma*w)/(w’*sigma*w), to 1/n at each element. I imagine it is also possible to do this with the breakdown for conditional value at risk, but I haven’t tried it before. You can also replace the 1/n with some vector of market-cap weights and also incorporate expected returns into the above formula.)

That’s an interesting discussion; thanks.

Good point… I’m using a simplified risk parity model which is basically equal variance weighting. There are naturally a lot of unrealistic assumptions that go into that version, and we often think of it as “equal risk weighting,” but of course we didn’t include the correlations for now, and true equal risk weighting would include the correlation components. We plan to deal with the correlation aspect in future iterations through a variety of means… shrinkage with MVP, and other methods similar to what you had mentioned. We’re just trying to get the other aspects of our process running smoothly before we add that component. So good points you bring up.

Not sure how you set up the equal variance weighting, but if the way you check that you got the correct weights is by multiplying the weights by the variances than you’ll get the wrong weights. It should be the weights squared. If you’ve done this, than you’ll get the same answer as I would have with my formula (assuming all the correlations are 0, which is basically what you’ve done).

DarienHacker Wrote: > “Without naming it, Mr. Sullivan is critiquing > something that has become known as “risk parity” > investing. Strategic asset allocation is usually > thought of in terms of the dollars placed in each > asset class. Because equities represent a large > amount of the world’s dollars and are more > volatile than bonds, typical institutional > portfolios are dominated by equity exposure. Risk > parity advocates strive for diversification by > risk (hence the name!) rather than dollars. This > approach generally results in a lower expected > return portfolio (although a higher risk-adjusted > expected return).” I guess the underlying assumption is that the dollar-weighted index represents the well diversified portfolio that would be hard to outperform. Dollar weights represent implied expected returns. Equal-risk portfolio would give a different set of implied returns. Either way the fundamental idea is to eliminate reliance on historical forecasts of expected returns. > “Echoing Sullivan (2010a) and Waring and Whitney > (2009), Goldsticker (2010) helpfully added that > the riskless asset relevant to most investors is > not cash but rather the liability-defeasing asset > or portfolio, and that 100 percent of the fund > needs to be held in this portfolioall the way up > the efficient frontier (rather than reducing the > holdings weight of this portfolio to make room for > equities). Thus, leverage is needed if one is also > going to hold equities and other > non-liability-defeasing assets.” How is this different from ALM?