Mulrane: A Risk Parity Plan Using ETFs

March 10, 2014

Managing risks is crucial, and risk parity looms large as one way to achieve it.

This article is part of a regular series of thought-leadership pieces from some of the more influential ETF strategists in the money management industry. Today's article features Ted Mulrane, vice president and director of quantitative research for Boston Advisors LLC.

The financial crisis led investors to take a closer look at asset allocation techniques that emphasize the diversification of risk.

A number of approaches to portfolio construction that use "risk budgeting" have been proposed. The process of risk budgeting involves identifying how each asset in a portfolio contributes to the volatility of the total portfolio, and allocating these assets in a way to achieve a desired risk profile.

The goal is a portfolio that mitigates exposure to—in former Secretary of Defense Donald Rumsfeld's parlance—the "known unknowns" that are reflected in the volatility of and correlation between individual assets. It's important to note that allocation-based approaches to controlling risk do not explicitly address tail risk—the "unknown unknowns," that are best hedged against using options.

Risk budgeting approaches differ from the traditional Markowitz framework of mean-variance optimization by downplaying, or completely ignoring, return forecasts and focusing on the more stable risk characteristics of individual assets.

Risk parity is a particular risk budgeting approach where each asset in the portfolio contributes an equal amount of risk. One intuitive formulation defines risk contribution for asset "i" as: the weight of asset i in the portfolio multiplied by the volatility of asset I multiplied by the correlation between asset i and the portfolio.

Thus, assets that exhibit low volatility and low correlation to other assets receive more weight, and vice versa. To determine the asset weights, one needs to solve a nonlinear optimization problem. Here we use an iterative procedure where weights of the asset classes are varied until reaching an optimal solution that minimizes the sum of pairwise differences of risk contributions. (Please refer to the technical note at the end for more detail.)

To illustrate these ideas, we start by introducing a capital parity portfolio to illuminate historical risk levels associated with certain asset classes. Then, we present two methods for constructing a risk-parity portfolio using ETFs—unleveraged and leveraged. Lastly, we share our insights into risk parity and how we prefer to construct these portfolios at Boston Advisors.

As a point of background, our sample risk-parity portfolios use a global palette of asset classes, including equity, real estate, intermediate-term U.S. Treasurys, currencies (mimicking the carry trade) and commodities.

Risk contributions and performance statistics are computed based on monthly index returns over the period April 1994 to December 2013. The portfolios use ETFs that provide exposure to each of these asset classes:

Asset Class Index ETF
US Equities S&P 500 SPY
Int'l Developed Equities MSCI ACWI EFA
Emerging Markets Equities MSCI EM VWO
Global Real Estate DJ Global REIT RWO
Agriculture GSCI Agriculture JJA
Energy GSCI Energy DBE
Precious Metals GSCI Precious Metals DBP
Currencies DB G10 Currency Future Harvest Index DBV
US Treasurys Barclays U.S. 7-10 Year Treasury Bond Index IEF, UST

The Capital Parity Portfolio

First, let's consider a portfolio holding an equal dollar weight of those ETFs. Each asset class is approximately 11 percent of the portfolio (1/9 of the total). This is an example of a 1/n allocation, where "n" is the total number of assets, or what we call a capital parity allocation.


Note from the bar chart that the contribution to total portfolio risk varies from less than 1 percent (U.S. Treasurys) to close to 20 percent (emerging market equity). The annualized average return for this portfolio, rebalanced monthly, is 7.8 percent, with a volatility of 11.3 percent.

The Risk Parity Portfolio: Unleveraged

Now, let's consider a risk-parity portfolio constructed using the same holdings:


Asset Class Ticker Weight Risk Contribution
US Equities SPY 7.9% 11.1%
Int'l Developed Equities EFA 6.4% 11.1%
Emerging Markets Equities VWO 4.5% 11.1%
Global Real Estate RWO 5.7% 11.1%
Agriculture JJA 6.7% 11.1%
Energy DBE 5.1% 11.1%
Precious Metals DBP 7.9% 11.1%
Currencies DBV 14.1% 11.1%
US Treasurys IEF, UST 41.7% 11.1%

The contribution to total risk for each of the asset classes is now equal, yet the weight allocated to each asset class varies from less than 5 percent (emerging market equity) to almost 42 percent (U.S. Treasurys).

Applying these risk-parity weights, we find that the annualized average return of 7.1 percent is less than the capital parity allocation, yet the annualized volatility of 6.9 percent is significantly lower. The result is a portfolio with an attractive risk-adjusted return.

As a researcher, I must disclose that this simplified example applies a set of risk parity weights that were calculated over the same time frame as the performance measurement. Translation: This is an in-sample calculation that suffers from look-ahead bias.

The resulting risk-and-return statistics are not meant to be interpreted as accurate simulation results and are provided as hypothetical values to facilitate this discussion.

The Risk-Parity Portfolio: Leveraged

Since most risk parity portfolios use leverage to overcome the typically lower absolute returns, our last example is an implementation of risk parity with 1.2x leverage (arbitrary chosen for illustration). In all asset classes with the exception of U.S. Treasurys, the weights are simply scaled up from the previous example to obtain the 1.2x exposure.

For example, the weight of SPY is increased to 9.5 percent (7.9 percent x 1.2). In fixed income, we complement IEF with a leveraged ETF (UST) that seeks to return two times the daily return of the Barclays U.S. 7-10 Year Treasury Bond Index.

To achieve the overall leverage of 1.2x, the total desired exposure to U.S. Treasurys must be 50 percent. Allocating 10 percent to IEF and 20 percent to UST will get us there, as the weight allocated to UST provides double the exposure.

Ticker Leveraged Factor Unlevered Weight Desired Exposure Leveraged Weights
US Equities SPY 1 7.9% 9.5% 9.5%
Int'l Developed Equities EFA 1 6.4% 7.6% 7.6%
Emerging Markets Equities VWO 1 4.5% 5.4% 5.4%
Global Real Estate RWO 1 5.7% 6.9% 6.9%
Agriculture JJA 1 6.7% 8.1% 8.1%
Energy DBE 1 5.1% 6.1% 6.1%
Precious Metals DBP 1 7.9% 9.5% 9.5%
Currencies DBV 1 14.1% 17.0% 17.0%
US Treasurys IEF 1 41.7% 50.0% 10.0%
2x US Treasurys UST 2 20.0%
Total 100.0% 120.0% 100.0%

Keep in mind that most leveraged ETFs are designed around a daily reset frequency. To accurately mimic a true leveraged position, one desires low volatility. Out of our set of asset classes, fixed income is probably the best fit in this regard. For more on this, see "The Truth About Leveraged ETF Returns."

Consider that this leveraged portfolio leads us to a common critique of risk parity: Despite attractive risk-adjusted returns, low absolute returns often dictate leverage within the portfolio. This includes leveraging a large amount of fixed-income assets. This gives pause to many who claim we are in the ninth inning of an extended bull market for bonds.


The Dynamic Risk Parity Portfolio

An alternative approach to pursuing risk parity is to first base allocations on the proportions prescribed by risk parity and then dynamically shift the total weight of higher-risk asset classes based on market conditions.

For instance, during periods of low market stress, one could proportionally increase the weights allocated to equity and real estate, while decreasing the allocation to fixed income. The opposite holds true during periods of high market stress.

At Boston Advisors, we have created a Dynamic Risk Parity strategy that is designed this way. We use a proprietary indicator of market stress to help determine when it pays to take risk and when it doesn't. We feel that this approach retains the diversification and risk mitigation benefits of risk parity, yet is more apt to generate the higher absolute-return potential that many investors target, without the explicit use of leverage.



Portfolio construction using risk budgeting involves moving away from traditional mean-variance optimization. Risk parity is one such approach, where weights are determined by equalizing the relative risk contributions.

Over the past 20 years, risk-parity portfolios have generally exhibited higher-risk-adjusted returns, but lower absolute returns, compared with capital parity portfolios. Using leverage within risk-parity portfolios has been one approach to boost absolute returns.

However, rather than levering low-yielding fixed income in, perhaps, an era of increasing rates, we prefer to apply smart views of market stress and opportunistically adjust the levels of risk exposure to avoid the pitfalls of a static risk-parity allocation.


Technical Note: Finding the Risk Parity/Equal Risk Contribution (ERC) Portfolio

Finding the assets weights that result in equal risk contributions can be found by solving the following optimization problem via the technique of sequential quadratic programming.




Ted Mulrane, CFA, is vice president and director of quantitative research at Boston Advisors LLC, a boutique investment company. To learn more about Boston Advisors and the firm's investment capabilities, please visit or contact Chief Marketing Officer Peter Anderson at 617-348-3127 or [email protected]. Boston Advisors LLC may hold for itself, and/or its clients, shares in the securities referenced in this article. Please click here for a complete list of relevant disclosures and definitions.


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