On Risk Parity

I was recently asked by a large asset management firm for my opinion on risk parity as a form of portfolio construction. This is what I wrote for them and I thought I’d share it (since there was no mention of an NDA) to spark a bit of debate on a concept I think needs more attention.

Risk Parity (RP), a method of creating portfolios based on allocating a volatility budget equally across asset classes, has gained popularity in recent years. RP differs from Modern Portfolio Theory (MPT) in that it does not involve the optimization of weights given expected returns and covariances. Almost[1] all portfolios constructed using RP are inefficient[2] according to the MPT framework. But MPT suffers from enough pitfalls[3] to leave a large gap for alternatives, such as RP, to get a foothold. RP is gaining traction mostly because its empirical record beats those of mean-variance (MV) portfolios and strategies such as a 60/40 equity bond split[4]. In RP portfolios, weights are more evenly shared across asset classes, and such portfolios do comparatively well in times of stress. But RP suffers from its own shortcomings and lacks adequate theoretical underpinnings. I will argue that because it does not consider expected returns or correlation, uses a poor proxy for true risk and is not optimized according to sources of risk, RP is not a robust form of portfolio construction.

If asset classes represented distinct sources of risk and were priced so as to compensate the investor for taking these risks, constructing a portfolio according to risk budgets would have appeal. But asset classes do not perfectly coincide with sources of risk and equally weighting asset classes according to realized volatility – which the simplest form of RP advocates – is arbitrary. Not all sources of volatility offer a risk-premium, let alone on an equal basis. For example, shorting equities generates volatility in a portfolio, but this is not a source of risk-premium. Constructing portfolios according to an Arbitrage Pricing Theory (APT) framework is more satisfactory from this point of view.

Moreover, realized volatility is not an accurate measure of the risk an investor should expect to face[5]. This is one of the same issues that MV comes up against – in the absence of stationarity, sample variance may be a poor estimator of true variance. For certain asset classes, such as credit, the distribution is quite likely not symmetric; this further reduces the merit of relying heavily on the second moment.

The simplest RP methodology ignores the off-diagonal entries of covariance matrices. Portfolios exist as a means of diversifying idiosyncratic risks; the extent of diversification is determined by correlation coefficients. Low or negative correlation is desirable, so long as it is accompanied by a positive risk premium. RP considers the volatilities of asset classes, but does not optimize with regard to how they interact. This suggests that the diversification benefits of RP would be greater, were the weights to be optimized.

In spite of these theoretical arguments, some studies, such as Hurst, Johnson and Ooi (2010) and  Asness, Frazzini and Pedersen (2011) point to periods of relative out-performance of RP as evidence of its strength. While outperforming an arbitrary, though computationally straightforward, strategy such as 60/40 may be laudable, it has been shown that low beta assets – which RP overweights – systematically outperform high beta assets[6] – which MV and 60/40 have in abundance – on a risk-adjusted basis (i.e. Sharpe Ratio). By inadvertently gaining from a flaw in a competing approach – namely that beta does not work in practice the way it does in theory – RP is flattered. In this case, any portfolios that have a relatively low allocation to high beta assets should outperform, but RP cannot claim to produce the best of these necessarily.

RP leaves open a number of questions that MPT provides answers to, such as what asset classes are in the investable universe and how much leverage is best. That the latter’s answers are wrong or not useful does not commend the silence of the former. If asset-classes could be replaced with distinct sources of risk, and if weights were calculated conditional on the risk premiums on offer, the RP approach might have a stronger footing; but, in its current guise, it will not stand the test of time.

[1] If a set of asset classes have equal Sharpe Ratios and the same correlation coefficients, equally weighting according to volatility would be optimal under MV; Maillard, Roncalli and Teiletche (2010) provide a proof of this.

[2] An RP portfolio, even with leverage, will never sit above the capital allocation line and is therefore no better than holding the market portfolio and using leverage to satisfy tangency with a given set of indifference curves.

[3] MV efficient portfolios are not knowable ex ante and estimates rarely work (see Fama and French 2004). Issues surrounding the market portfolio highlighted by Roll (1977), non-stationary and asymmetrical distributions at the securities level, instability of frontier portfolios, and high sensitivity of outputs to noise in inputs are sufficient to render the empirical success of the MV framework and, by extension, the CAPM quite low.

[5] Various writings and quotes  from James Montier and Warren Buffett provide arguments supporting this.

[6] See Frazzini and Pedersen (2013) and Black, Jensen, Scholes (1972) for more details. One explanation comes from Asness, Frazzini and Pedersen (2011) who suggest that MV fails, in part, due to leverage aversion, whereby investors are reluctant or unable to invest more than 100% in the market portfolio and instead opt to invest in higher beta assets. This increases the price and lowers the expected return of these securities, thereby giving low-beta securities disproportionately better returns. 


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