Managing Risk Exposures Using the Risk Budgeting Approach

Abstract

The ongoing economic crisis has profoundly changed the industry of asset management by putting risk management at the heart of most investment processes. This new risk-based investment style does not rely on return forecasts and is therefore assumed to be more robust. 2011 was marked by several great successes in transforming the practice of asset management with several large institutional investors moving their portfolios to minimum variance, ERC or risk parity strategies. These portfolio constructions are special cases of a more general class of allocation models, known as the risk budgeting approach. In a risk budgeting portfolio, the risk contribution from each component is equal to the budget of risk defined by the portfolio manager. Unfortunately, even if risk budgeting techniques are widely used by market practitioners, there are few results about the behavior of such portfolios in the academic literature. In this paper, we derive the theoretical properties of the risk budgeting portfolio and show that its volatility is located between those of the minimum variance and weight budgeting portfolios. We also discuss the existence, uniqueness and optimality of such a portfolio. In the second part of the paper, we propose several applications of risk budgeting techniques for risk-based allocation, like risk parity funds and strategic asset allocation, and equity and bond alternative indexations.

Risk parity portfolios with risk factors

“…This approach has been largely studied by Bruder and Roncalli (2012), who present, for instance, an example of the risk budgeting policy of a pension fund. Another example of such approach is the SAA policy adopted by Danish pension fund ATP.…”

“…Approaches such as equally-weighted, minimum variance, most diversified portfolio, equallyweighted risk contributions, risk budgeting or diversified risk parity strategies have become attractive to academic and practitioners alike (see e.g. Meucci, 2007;Choueifaty and Coignard, 2008;Meucci, 2009;Maillard et al, 2010;Bruder and Roncalli, 2012; for they provide elegant and systematic methodologies to tackle the construction of diversified portfolios.…”

“…Meucci (2009)'s work on diversification across principal component factors provided a clue to resolving this unfortunate problem by focusing on underlying risk factors. In this paper, we build on this idea and combine it with the risk-budgeting approach of Bruder and Roncalli (2012) to develop a risk-budgeting methodology focused on risk factors. When used with the objective of maximizing risk diversification, our approach is tantamount to diversifying across the 'true' sources of risk and often leads to a solution with equally-weighted risk factor contributions.…”

Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Tactical and Strategic Asset Allocation

“…The constraint b i > 0 implies that we cannot set some risk budgets to zero. This restriction is necessary in order to ensure that the RB portfolio is unique (Bruder and Roncalli, 2012). When using a standard deviation-based risk measure, we have to impose a second restriction:…”

How to Design Target-Date Funds?

“…In the case where the interest rate is nul and the contribution function is linear, we obtain the approximated formula given in Appendix A.4. In Figure 5, we have reported the glide path computed by Monte Carlo and by approximation 11 . We notice that the approximated formula gives a good result 12 .…”