Portfolio Investment Optimization through the application of Risk Parity

Diversification by Risk

The goal of an asset manager is to construct a portfolio capable of achieving the highest possible expected return, given a volatility target.

According to CAPM, to maximize the Sharpe Ratio, which is a ratio that quantifies the risk-adjusted return of an investment portfolio, an investor should hold the market portfolio, levered according to investor’s risk preference.

At the end of 90s, Ray Dalio and his portfolio management team at Bridgewater Associates introduced a new approach to asset allocation: a risk parity approach. (Fabozzi, F. A., Simonian, J., & Fabozzi, F. J, 2021).

This kind of approach was enucleated theoretically firstly by Edward Quian of Panagora Asset Management in 2005 (Qian, E., 2011).

A risk parity method is based on the premise that a common 60/40 portfolio of stocks and bonds or the market portfolio, are not properly diversified when we evaluate the marginal contributions of each asset class to overall portfolio risk.

Indeed, the volatility originating from the stocks is much higher than the bonds. Consequently, fluctuations in the stock market contribute to nearly all the volatility observed in both the market portfolio and the 60/40 portfolio. 

As a matter of fact, these two portfolios are not diversified in terms of actual risk, even though they are in terms of the total amount of money invested in the various asset classes. In fact, historically, in a 60/40 portfolio, about 90% of volatility is due to its equity exposure.

Given this, we can easily understand the concept behind a risk parity approach: diversify by risk, not by dollars. 

In order to pursue this goal we have to overweigh low-risk assets and underweigh high-risk assets. This approach could lead to a situation, where, even if the return per unit of risk of the risk parity portfolio is higher, the portfolio isn’t able to address a sufficient return for the investor due to too low risk. We will see later that we could solve this problem leveraging the risk-balanced portfolio achieving both the desired expected return and a true risk diversification. However, we have to consider also the risks and practical concerns related to the introduction of leverage.

Diversification benefits of Risk Parity

The Risk Parity Portfolio provides diversification benefits because it allows investors to achieve higher returns with the same amount of risk. Three important elements to consider in this regard are the return correlations of portfolios with stocks and bonds, portfolio exposure, and loss contribution.

The first concept is pretty straightforward: when compared to a 60/40 Portfolio, risk parity portfolios exhibit equal correlations with both stocks and bonds, while the latter usually demonstrates extremely high correlation with stocks and extremely low correlation with bonds. This disparity in return correlations enables risk parity portfolios to be more diversified, as they are not solely reliant on stock returns.

The second element pertains to the beta of underlying assets. The concept here is that stocks are riskier and therefore much more volatile than bonds in terms of standard deviation. Consequently, a diversified portfolio should have a lower beta to stocks and a higher beta to bonds. This is better achieved by a Risk Parity Portfolio compared to a 60/40 Portfolio, where betas may only appear to be more balanced.

Finally, the last element to consider is the loss contribution from underlying assets to the expected losses of the entire portfolio. It can be demonstrated that in a Risk Parity Portfolio, stocks contribute only half of the losses, whereas for a 60/40 Portfolio, loss contribution equals risk contribution (thus exceeding 50%). This concept is crucial for investors, as they are concerned with downside risk. Therefore, if they want to protect their positions against significant losses, risk parity portfolios are to be preferred.

From the research paper "Indexing Risk Parity Strategies" (Berlinda Liu et al., 2020), which analyses the period from January 2000 through June 2020, we obtain a practical example of the diversification benefits achievable through a Risk Parity Portfolio. The authors begin by examining historical performance and cross-correlations among major asset classes, followed by a comparison of risk/return characteristics among multi-asset portfolios. They then construct a rudimentary three-asset risk parity portfolio, including equities, bonds, and commodities, to illustrate the strategy's benefits compared to other weighting schemes. The conclusion of the research is that equities are actually negatively correlated with investment-grade bonds; therefore, adding the latter to an equities portfolio can reduce portfolio volatility and potentially increase returns per unit of risk.

Table 1 - Asset Classes correlation

Source: Indexing Risk Parity Strategies - Berlinda Liu, Philip Brzenk, and Tianyin Cheng (2020) 

Levered and Unlevered Risk Parity Portfolio

An unlevered risk parity portfolio does not employ borrowing or the use of derivatives to increase exposure, but rather it focuses on achieving an equal allocation of risk from each asset within the portfolio through asset allocation without more leverage. However, this approach leaves the owner with a portfolio that is very heavily weighted towards lower-risk assets (e.g. bonds, as they have a lower volatility in comparison to equities).

A core belief of risk parity is that diversification can lead to enhanced portfolio efficiency. The idea is that by holding a variety of investments, the poor performance of any one investment potentially can be offset by the better performance of another, leading to more consistent overall returns.

On the other hand, a levered risk parity portfolio employs leverage to amplify the returns of the portfolio. By borrowing funds or using derivatives, a levered portfolio increases the exposure of all assets by the same magnitude, ensuring the risk parity balance but amplifying the return profile. By applying leverage, it ensures the returns of the safer asset classes are more in line with those of riskier assets.

Leveraging assets can be enticing where low-risk assets offer low nominal returns, as this process enhances the yield of these assets. On the other hand, it introduces the complexity of managing the leverage ratio and the additional risk associated with borrowing.

Deciding between levered and unlevered risk parity approaches completement depends on the investor’s risk tolerance. While leveraging can offer higher potential returns, it comes with increased risk of loss, especially in turbulent market conditions. On the other hand, unlevered strategies potentially offer lower returns, but are more stable and may be more suitable for risk-averse investors.

All in all, both types of risk parity portfolios aim to exploit the benefits of diversification by equalising risk contributions from various asset classes.

Comparison between a Levered Risk Parity Portfolio, a 60/40 Portfolio and the Mean-Variance Portfolio

An empirical investigation, represented in Figure 3, examines the performance of these portfolios in terms of their Sharpe Ratios, which measure the risk-adjusted returns. The graph delineates the Sharpe Ratios for three distinct portfolios: a Value-Weighted Portfolio, a 60/40 Portfolio, and a Risk Parity Portfolio, over three different time frames: 1926–2010, 1973–2010, and 1973–2010 including commodities and credit.

 Figure 1 - The Risk Parity, Market, and 60/40 Portfolios: Sharpe Ratios

Source: Leverage Aversion and Risk Parity - Clifford S. Asness, Andrea Frazzini, and Lasse H. Pedersen

Analysis of the Chart

In the first segment, spanning from 1926 to 2010, which incorporates data for stocks and bonds, the Risk Parity portfolio outperforms the traditional portfolios, exhibiting a higher Sharpe Ratio. This implies that the RP strategy offered better risk-adjusted returns over this extensive period, highlighting the benefits of risk diversification.

From 1973 to 2010, with stocks and bonds as the components, the RP again demonstrates a higher Sharpe Ratio compared to the 60/40 strategy, reinforcing the argument for RP's efficiency. Notably, this timeframe excludes the volatile periods of the Great Depression and World War II, suggesting the RP's robustness even in relatively stable times.

Finally, the third segment, including commodities and credit from 1973 to 2010, showcases the adaptability and performance consistency of the RP approach. By incorporating commodities and credit, the RP portfolio incorporates a broader spectrum of asset classes and still maintains a higher Sharpe Ratio, underscoring its efficacy in diversifying risk and optimising returns. (Asness, C. S., Frazzini, A., & Pedersen, L. H, 2012)

Mean-Variance Portfolio and Leverage Aversion

The Mean-Variance (MV) Portfolio, derived from Modern Portfolio Theory (MPT), seeks the most efficient risk-return trade-off. It aims to achieve the highest possible level of return for a given amount of portfolio risk, as reflected in the efficient frontier. The MV approach often results in portfolios that are heavily weighted towards equities, given their higher expected returns.

However, the RP portfolio introduces leverage to balance the lower risk-adjusted returns of safer asset classes like bonds. Leverage aversion, a reluctance or inability to employ financial leverage, may inhibit some investors from pursuing the high returns of an equity-dominated portfolio. In such contexts, the RP strategy becomes particularly appealing as it allows for risk parity without disproportionate exposure to any single asset class.

Empirical Evidence and Practical Implications

Figure 2 - Efficient Frontier, 1926–2010

Source: Leverage Aversion and Risk Parity - Clifford S. Asness, Andrea Frazzini, and Lasse H. Pedersen

The empirical evidence presented in figure 2. suggests that leveraging in a RP strategy can be a powerful tool in the arsenal of portfolio management, enabling investors to consume the high risk-adjusted returns of safer assets. The outperformance of the RP portfolio across various samples and periods indicates that it is not merely a result of historical anomalies or data mining, but rather a robust strategic approach that stands up to the empirical scrutiny across different asset classes and market conditions.

In conclusion, the analysis of Sharpe Ratios over different periods and the comparison between RP, 60/40, and MV portfolios suggest that the RP strategy can significantly enhance portfolio efficiency. It offers a compelling alternative for investors who are averse to leverage or seek a more stable and consistent risk-adjusted performance. The empirical evidence, as displayed in Figure 2, supports the theoretical underpinnings of the RP approach and its practical viability for long-term investment strategies. (Asness, C. S., Frazzini, A., & Pedersen, L. H, 2012)

References 

Asness, C. S., Frazzini, A., & Pedersen, L. H. (2012). Leverage aversion and risk parity. Financial Analysts Journal, 68(1), 47-59. Available at: https://www.tandfonline.com/doi/abs/10.2469/faj.v68.n1.1 [Accessed 13 Apr. 2024]

Fabozzi, F. A., Simonian, J., & Fabozzi, F. J. (2021). Risk parity: The democratization of risk in asset allocation. The Journal of Portfolio Management, 47(5), 41-50. Available at: https://www.pm-research.com/content/iijpormgmt/47/5/41.abstract [Accessed 13 Apr. 2024]

Qian, E. (2011). Risk parity and diversification. Journal of Investing, 20(1), 119. Available at: https://www.panagora.com/assets/secure/JOI_Spring_2011_Panagora2.pdf [Accessed 13 Apr. 2024]

Liu, B., Brzenk P., and Cheng T. (2020). Indexing Risk Parity Strategies. S&P Dow Jones Indices. Available at: https://www.spglobal.com/spdji/en/documents/research/research-indexing-risk-parity-strategies.pdf [Accessed 13 Apr. 2024]

Aqr.com. (2014). Risk Parity: Why We Lever. [online] Available at: https://www.aqr.com/Insights/Perspectives/Risk-Parity-Why-We-Fight-Lever [Accessed 13 Apr. 2024].

Benham, F., Obregon, R. and Kaya Yontar, T. (n.d.). Risk Parity Risk Parity Quarter 2 • 2019 7. [online] Available at: https://caia.org/sites/default/files/risk_parity_0.pdf [Accessed 13 Apr. 2024].

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