Risk parity portfolio construction

Category: Asia, Global
By Lionel Martellini, Vincent Milhau, and Andrea Tarelli*

Intuitively appealing and empirically attractive, but not without flaws

Risk parity has become an increasingly popular approach for building well-diversified portfolios within and across asset classes. In a nutshell, the goal of the methodology is to ensure that the contribution to the overall risk of the portfolio will be identical for all constituent assets, which stands in contrast to an equally-weighted strategy that would also recommend an equal contribution but instead simply be expressed in terms of dollar budgets as opposed to risk budgets (see Roncalli (2013) for a formal introduction to risk parity and a detailed discussion of its applications).

While intuitively appealing and empirically attractive, this approach suffers from two major shortcomings. On the one hand, typical risk parity portfolio strategies used in an asset allocation context inevitably involve a substantial overweighting of bonds with respect to equities, which might be a problem in a low bond yield environment, with mean-reversion implying that a drop in long-term bond prices might be more likely than a further increase in bond prices. On the other hand, standard approaches to risk parity are based on portfolio volatility as a risk measure, implying that upside risk is penalised as much as downside risk, in obvious contradiction with investors’ preferences.

Traditional approach

The traditional approach to constructing risk parity portfolios uses rolling-window estimates for volatilities, which raises a number of concerns that we attempt to analyse in recent research1 at EDHEC-Risk Institute conducted with the support of Lyxor Asset Management as part of the “Asset Allocation Solutions” research chair. The first concern is of a statistical nature: these volatility estimates depend on a particular series of observed returns, which exposes the investor to sample risk. The second concern is that the true values for the risk parameters are not stationary: rolling-window estimates reflect past true volatility levels, but do not necessarily correspond to the conditional volatility of future returns. While this second concern can in principle be alleviated by replacing rolling-window volatility by a GARCH volatility estimate, our results suggest that the two risk parity strategies have overall similar properties.

In our research, we introduce an alternative bond volatility estimate, which relies on the model-free approximation of a bond return as the product of (the negative of) duration times the change in yield-to-redemption. This volatility measure offers the advantage of being instantaneously observable.

The third and last concern raised by the use of historical volatility in standard risk parity strategies is related to the choice of volatility as a risk measure. As mentioned earlier, volatility does not disentangle downside risk from upside risk. This is a particularly serious concern in the current low yield environment, with interest rates that have been decreasing since the early 1980s, to reach historically low levels after the 2008 financial crisis. While such low levels of interest rates signal an increase in downside risk, historical volatility of bonds has not increased in parallel.

In this context, we analyse ”conditional risk parity” strategies, i.e. strategies that are more responsive to changes in market conditions in general, and yield levels in particular. In response to the first two major problems identified with historical volatility, namely sample dependency and backward-looking bias, we introduce in our research an alternative bond volatility measure, which we refer to as “duration-based volatility” (in short, DUR volatility). This measure is suggested by the model-free approximation of the return on a bond portfolio as the product of the negative of duration times the yield change. Our empirical analysis confirms that the DUR volatility measure has followed an increasing trend due to the decreasing trend in bond yield levels. To reinforce this effect and address the third concern with standard risk parity strategies, one may replace volatility by a downside risk measure, such as semi-volatility or Value-at-Risk (VaR).

As a result, we propose to use the Cornish-Fisher VaR, which incorporates information on stock and bond return skewness and kurtosis. Among the conditional risk parity strategies that we test, we find that the one that equalises the contributions to this non-Gaussian VaR is the strategy that implies the lowest bond allocation in a low yield environment, and also that it is the one for which the bond allocation is the most likely to decrease after a decrease in interest rates.

In spite of these advantages, conditional risk parity strategies have their own challenges. In particular, these strategies are more demanding than unconditional risk parity in terms of parameter estimation. The strategy based on non-Gaussian VaR requires co-skewness and co-kurtosis parameter inputs, which are well known to dramatically increase the number of parameters as the investment universe grows. This concern, however, should be of limited importance if these strategies are employed in an asset allocation context, with a limited number of asset classes. More problematic is the estimation of expected returns, in view of the notorious lack of robustness of statistical estimates of these quantities (see Merton (1980)).

In our research, we have proposed a relatively rough way to address this issue, by shrinking forecasted returns towards a prior, but the literature has provided numerous methods to improve expected return estimates. It would be interesting, and practically relevant, to assess the sensitivity of conditional risk parity portfolios to estimation errors in expected returns, and to study the benefits of explicitly taking into account parameter uncertainty, even if our analysis suggests that the impact of errors in expected return estimates are much less pronounced compared to the case with standard mean-variance portfolio optimisation.

The research from which this article was drawn was supported by Lyxor Asset Management as part of the “Asset Allocation Solutions” research chair at EDHEC-Risk Institute.


  • Maillard, S., T. Roncalli, and J. Teïletche. 2010. The Properties of Equally Weighted Risk Contribution Portfolios. Journal of Portfolio Management 36 (4): 60–70.
  • Martellini, L., V. Milhau and A. Tarelli, April 2014, Towards Conditional Risk Parity — Improving Risk Budgeting Techniques in Changing Economic Environments, EDHEC-Risk Publication supported by Lyxor Asset Management
  • Merton, R. 1980. On Estimating the Expected Return on the Market: An Exploratory Investigation. Journal of Financial Economics 8 (4): 323–361.
  • Roncalli, T. 2013. Introduction to Risk Parity and Budgeting. Chapman and Hall, CRC. Financial Mathematics Series.

* Lionel Martellini is professor of finance at EDHEC Business School and scientific director at EDHEC-Risk Institute; Vincent Milhau is deputy scientific director and Andrea Tarelli is senior research engineer, both at EDHEC-Risk Institute

1 Martellini, L., V. Milhau and A. Tarelli, April 2014, Towards Conditional Risk Parity - Improving Risk Budgeting Techniques in Changing Economic Environments, EDHEC-Risk Publication supported by Lyxor Asset Management.