When I was asked to review Introduction to Risk Parity and Budgeting by Thierry Roncalli, I accepted with pleasure. Thierry Roncalli, head of Research at Lyxor and Research Associate at EDHEC Business School, combines both mathematical rigour and practical applicability in all of his research. The title of his book is well chosen as it reveals his key message. Risk parity is a special case of risk budgeting, where all percentage contributions to risk are equally weighted. At the same time the title is a polite understatement. First, it offers a concise treatment of risk-based portfolio construction in general, not only risk parity. Second, it goes well beyond what I would call an introduction.
Part I of the book provides a concise treatment of portfolio theoretic concepts that relate to risk parity investing. Chapter 1 offers a quick introduction into mean-variance optimization. This could be boring, but this chapter is not. It offers a nice detour into less well known but important topics, such as return synchronization, regularization techniques, covariance denoising, shrinkage, penalized regression and resampling. Chapter 2 expands from mean-variance optimization (optimally allocating risk to where marginal return equates marginal risk) to risk budgeting (judgmentally allocating risk where the investor wants to take risk) to risk parity (equally allocating risk), which is equivalent to moving from a general solution to the special case of a special case. Roncalli is aware of the loss of efficiency but hopes for an increase in robustness, i.e. an increase in diversification. He admits this to be difficult to prove as diversification turns out to be an elusive concept that knows many conflicting positions. In particular, I enjoyed the section on duplication invariance properties: risk parity offers no safeguard against adding mean-variance spanned assets to a portfolio.Footnote1 Cleary this is not intuitive and presents a mayor disadvantage relative to a mean-variance optimizer.
Part II builds on the theoretical insights of Part I and contains a selection of case studies that represent the many applications of risk-based investing currently discussed among practitioners.
Chapter 3 starts with a comparison of risk-based investment methodologies with fundamentally indexed and market-weighted portfolios applied to the EuroStoxx 50 universe. Roncalli adds the equally weighted and the most diversified portfolio (portfolio that maximizes a somewhat arbitrarily chosen diversification index) as further contenders. As some of these methods act on risk information alone, Roncalli includes several covariance estimators in his backtests. While risk parity indexation seems to outperform a capitalization-weighted index (in the sense that risk parity offers higher risk-adjusted returns), it remains unclear whether risk-based portfolio construction is a better way to construct portfolios or just a clumsy way to extract risk-based anomalies for long only investors. In any case the careful reader can infer from this chapter, that we cannot make a statement about diversification (from looking at concentration measures) without a simultaneous reference to an equilibrium model. We simply need to know which risks are rewarded and which risks are diversifiable. An equally weighted portfolio might look diversified, but in reality it creates exposure to small stocks.
Chapter 4 applies the central theme of Chapter 3 (capitalization vs. risk-based weightings) to government bonds. Despite the somewhat populist claim that capitalization-weighted bond indices are inefficient as they give more weight to bad creditors (yet over the last 10 years many active management houses struggle to keep up with capitalization-weighted indices), Roncalli finds no clear evidence that risk parity offers a better alternative in bond portfolios. In any case the chapter provides a good introduction into the differences of bond and equity indexing and the current discussion between old school index providers and some new school academics.
Chapter 5 investigates risk parity for alternative investments. It starts by describing standard hedge fund practices that always used risk parity when weighting strategies/positions. For a hedge fund, this is natural, as risks of individual strategies are scaled to a common constant, selected to offer little correlation and expected to display similar risk/return ratios. Risk parity is also used often in hedge fund allocation. Roncalli offers an interesting case study budgeting expected shortfall for 10 hedge fund subindices (Credit Suisse) using the Cornish/Fisher approximation.
Chapter 6 applies risk parity across asset classes. This is at current the most widespread use for risk parity in investment portfolios. The author starts gently with a simple (two asset) equity bond portfolio and with an insightful review of leverage aversion. Leverage averse investors buy volatile assets because they dislike (or cannot use) leverage. This leaves low-volatility stocks cheap (high future returns) and high-volatility stocks expensive (low future returns). This is important as leverage aversion establishes a somewhat credible alternative to consumption-based asset pricing (as one of the theoretical underpinnings of risk parity). Roncalli then continues quickly with more advanced topics like factor risk parity or risk parity with liability constraints. The chapter ends with a brief discussion on active risk parity (establishing risk parity for the naive anchor portfolio in the absence of strong convictions, e.g. in a Black/Litterman setting).
The book benefits from a clear notation. Graphs and tables are well chosen and help the reader to better follow the storyline. One of the best features of the book is the set of well thought out exercises that allow readers to understand the technical aspects of this interesting monograph. In my view, the book is best read in conjunction with a copy of Pfaff (2012), Financial Risk Modelling And Portfolio Optimization With R, Wiley. The latter gives the reader instantaneous access to several R libraries to easily implement the core concepts on a Saturday afternoon.
The core strength of this book is its practicality. At the same time, it is its biggest weakness. While Roncalli is well aware that risk parity is a heuristic (no foundation in decision theory) that is largely dependent on the chosen universe (forecast free?) and the low-risk anomaly (low-risk assets have equal or higher Sharpe ratios than high-risk assets), which does not feature prominently in his book. Neither does the focus on total risk (rather than non-diversifiable risk) as a driver of cross-sectional differences in expected returns seem to concern him. Given the wealth of criticism that can be brought against risk parity and its relatives, the section on potential cons is remarkably small with little reference to more critical empirical work. I also would wish to read more about the impact of volatility scaling (cross-sectional, time series, cross lead/lag effects) on risk parity performance, and more on the conditions under which risk parity beats mean-variance optimization. After all mean-variance portfolios will learn that low-volatility assets offered larger (historical) Sharpe ratios. I would also encourage the author to expand his treatment of scenario generation/optimization. Scenario-based risk measures (like conditional value at risk) are designed to deal with multivariate non-normality, which should create growing interest given the current asymmetric risk in government bonds.
In summary this is a wonderful manual on risk-based investing for those already convinced this is the right way to invest. It is a positive description of available tools and a confirmation for those already vested in the concept, but offers limited normative help.
Bernd SchererManaged Futures Hedge Fund in Vienna and Visiting
Professor, WU Vienna
© 2014, Bernd Scherer
Notes
1 A mean-variance spanned asset is an asset that offers no excess return over a linear combination of already-existing assets in a portfolio.