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Risk-parity strategies attempt to derive equal percentages of risk from each asset in a portfolio. These, like all portfolios, are built on an ex ante basis wherein expected risk can deviate from realized risk. Sharpe ratio–optimal portfolios are also built on an ex ante basis. We derive a general set of conditions in which risk parity is, ex ante, also Sharpe ratio optimal. We generalize the sufficient conditions described by Kaya and Lee (2012). Based on this generalization, we construct an indicator to analyze historical episodes in which—ex post—risk parity could have been Sharpe ratio optimal. This indicator helps describe market environments wherein risk parity is more or less optimal. Although this indicator is useful for describing and explaining when risk parity is likely to be optimal, it is left for future research to predict when risk parity will likely be optimal or to expand on the prevailing market or economic conditions that make risk parity optimal.
In this article, we will use the term assets to refer to all instruments or collections of instruments (e.g., from individual securities to hypothetical collections of securities as represented by indexes) to which portfolio managers can allocate. This is because our results are general and do not depend on the level of granularity at which asset allocation decisions are made.
WHAT IT TAKES FOR RISK PARITY TO BE SHARPE RATIO OPTIMAL
Most asset allocation is focused on allocating to sources of return. The discussions typically center on increasing or decreasing the weights of specific assets, which is allocating to returns if one considers the control variables (the weights) and the mathematical expression of how the weights and expected returns of the assets translate into the expected return of the portfolio. Risk parity is a special case of a broad class of strategies that allocate to risks instead of to returns. The capital weights emerge from the control variables: the risk targets.
Risk parity is a special case of risk balancing. Risk balancing—like a balanced diet—is about choosing targets that align with a particular goal. Risk parity, on the other hand, is about getting equal sources of risk—like getting equal calories from carbohydrates, fats, and proteins. Risk balancing, and risk parity, often end up with higher allocations to lower-volatility...