A Primer on Risk-Parity

Risk Parity - Cover Foto

The concept of risk parity is not well-known among market participants. However, its resiliency to different market environment makes it a very interesting capital allocation strategy. It was first theorized in the sixties by Ray Dalio – founder of Bridgewater Associates – when he tried to find an answer to the following question: “What kind of investment portfolio would you hold that would perform well across all environments, be it a devaluation or something completely different?” Subsequently, three decades later in 1996, the first fund adopting this particular strategy was introduced. Today “All Weather” Bridgewater’s flagship fund has the stunning amount of $60.7 billion of AuM.

The typical conservative portfolio which is kept by most of retail and also by institutional investors is the 60:40 portfolio: 60% of the capital is invested into bonds and the remaining 40% into stocks. The overall volatility of the portfolio however is mainly related to the equity part as you can see from the following graph. Actual data confirm this: the linear correlation coefficient between SPY and the portfolio is 0.97061577, while between AGG and the portfolio is as low as 0.00981784.

  Risk Parity - Figura 1

Chart 1: SPY, AGG and Portfolio 60/40 Performance (source of chart data: Bloomberg)

Here we try to explain the underlying concepts of the strategy and we build a risk parity portfolio made of two assets.

We select two assets that are representative of equity and bond market in US. For the equity part we take SPY, which corresponds generally to the price and yield performance of the S&P 500® Index; for the bond part we consider AGG, iShares Core U.S. Aggregate Bond ETF which tracks an index of US investment-grade bonds. Both of them have low expense ratios and are very liquid, thus we can afford to keep them for a long period and we do not have to pay too much in spread cost when we rebalance our position. We plan to rebalance our position once a month so that the weights of the assets reflect new measures of volatility.

The basic idea behind a risk parity portfolio is that each asset contributes in the same way to the portfolio’s overall volatility. In this case, given that we have only two asset, 50% of the portfolio risk comes from equity, the remaining 50% from bonds. We base our model on the mathematical solution provided by Maillard and Roncalli, who find the optimal weight distribution as the solution of a minimization problem. Here we extract only the relevant part, not all passages are stated. For a more analytical approach check their paper “On the properties of equally-weighted risk contributions portfolios” (Maillard, Roncalli 2009).


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