How does Risk Parity work?

Risk Parity is a methodology to allocate capital across multiple asset classes, much like Modern Portfolio Theory (MPT), also known as mean-variance optimization. Unlike MPT, which finds the ideal mix of asset classes based on their expected returns and risks, Risk Parity allocates the portfolio by equalizing the risk contributions of each asset class, without considering their expected returns. It then uses leverage to scale the resultant allocation to the desired volatility (risk). Recent research has found that this approach can lead to a superior return for the same level of portfolio volatility. ^[1]

Two key ingredients are necessary for Risk Parity to deliver superior returns for a particular level of risk. First, the risk-adjusted return (i.e. the Sharpe Ratio) of low-risk assets (bonds) must exceed the risk-adjusted return on high-risk assets (stocks), such that leveraging a portfolio with a higher allocation to low-risk assets delivers a higher expected return than a direct investment in high-risk assets with the same level of risk. ^[2] Second, the cost of leverage (borrowing) needs to be sufficiently low, such that the expected return of the leveraged allocation net of the financing costs exceeds the return of the traditional allocation. For investors who could access leverage efficiently, Risk Parity historically has been a compelling strategy, because bonds have exhibited better risk adjusted returns than stocks for decades.

The mechanics of Risk Parity as an asset allocation methodology are best illustrated with an example. Suppose you have access to two risky asset classes, a globally diversified portfolio of stocks (“Stocks”) and a globally diversified portfolio of bonds (“Bonds”). The expected returns (as derived from the Capital Asset Pricing Model) and risks of the asset classes are reported in the table below. We’ll assume that the correlation between the stock and bond portfolios is 0.20. The table additionally reports the Sharpe ratio of each asset class, which measures the premium of its expected return over the risk free rate (assumed to be 1.75%), divided by its volatility.

	Expected Return	Volatility	Sharpe Ratio
Stocks	6.25%	17.50%	0.26
Bonds	4.00%	4.50%	0.50

Suppose an investor has a moderate tolerance for risk and is interested in investing her assets in a portfolio with an expected volatility of 11.00%, which is below the 17.5% expected volatility of a pure stock portfolio. Based on mean variance optimization, the investor’s return would be maximized by putting 60% in stocks and 40% in bonds. However, since the portfolio is tilted towards stocks and stocks are much riskier than bonds, the majority of this diversified portfolio’s risk can be attributed to the stock allocation. Specifically, if we decompose the portfolio’s overall risk into contributions from each asset class, we find that over 90% of the portfolio’s risk is due to stocks.

	Weight	Risk Contribution	Risk Share
Stocks	60%	10.36%	94.2%
Bonds	40%	0.64%	5.8%
Overall Portfolio	100%	11.00%	100%

Now let’s consider a Risk Parity portfolio constructed to have the same volatility as the MPT based 60/40 stock/bond portfolio. This portfolio can be constructed by first equalizing the risk contributions of the two asset classes and then applying leverage to achieve a target volatility of 11.0%. It turns out that to equalize the risk contributions, the portfolio would need to be allocated 20.5% to stocks and 79.5% to bonds. However, due to its high bond allocation, the overall volatility of this portfolio is only 5.5%, or half the 11% target volatility.

	Weight	Risk Contribution	Risk Share
Stocks	20.5%	2.75%	50%
Bonds	79.5%	2.75%	50%
Overall Portfolio	100%	5.50%	100%

To achieve a target volatility of 11.0%, this portfolio would need to be leveraged by a factor of 2x (11.0% / 5.5%). For the purposes of this illustration, let’s assume it would cost 3.05% per year to borrow the money.

Now let’s compare the returns on the two equivalent risk portfolios: the 60/40 stock/bond allocation, and the Risk Parity portfolio. Recall that the portfolio’s expected return is the weighted average of the underlying investments’ expected returns, multiplied by the leverage applied to the portfolio minus the cost to borrow.

The expected return on the 60/40 stock/bond allocation is 5.35% (60% * 6.25% + 40% * 4.00%). The expected return on the unleveraged Risk Parity portfolio is 4.46% (20.5% * 6.25% + 79.5% * 4.00%). After applying 2x leverage, the expected gross return rises to 8.92% (4.46% * 2), but the investor has to pay 3.05% in net financing costs, resulting in a net expected return of 5.87% (8.92% - 3.05%). Hence, the total expected return on the Risk Parity strategy is approximately 50 basis points higher than the return on the 60/40 portfolio (5.87% - 5.35%), which has exactly the same expected volatility.

This greater expected return for the same risk is the reason Risk Parity is so popular among institutions. In practice, it may be difficult for retail investors to execute a Risk Parity strategy themselves, as they may not be able to obtain leverage, and/or the cost of leverage may be sufficiently high to eliminate the entire benefit of the strategy. 

Finally, the composition of a Risk Parity strategy needs to be periodically rebalanced in response to changes in the expected volatility of the underlying asset classes. These changes shift in the composition of the portfolio which equalizes the asset class risk contributions, as well as, the quantity of leverage that has to be applied to the portfolio in order to target a fixed level of volatility. Specifically, when the volatility of the unleveraged portfolio declines, the quantity of leverage applied increases (and vice versa when the volatilities increase). 

For a more in depth look at the mechanics of the Risk Parity strategy, please see our whitepaper.

^[1] Recent papers studying risk parity strategies include: Maillard, S., et. al. (2010), “The Properties of Equal-Weighted Risk Contribution Portfolios” (accessed from: http://jpm.iijournals.com/content/36/4/60), Chaves, et al. (2012), “Efficient Algorithms for Computing Risk Parity Portfolio Weights.” (accessed from: http://joi.iijournals.com/content/21/3/150), and Asness, et al. (2012), “Leverage Aversion and Risk Parity” (accessed from: https://www.cfapubs.org/doi/pdf/10.2469/faj.v68.n1.1)

^[2] Academic research showing that low risk assets tend to have higher risk-adjusted returns dates back to Black, Jensen, and Scholes (1976). This empirical feature has now been documented across asset classes and linked to leverage constraints by Frazzini and Pedersen (2014; accessed from: https://www.sciencedirect.com/science/article/pii/S0304405X13002675)