Highlights Since AQR rebranded its flagship “Risk Parity” mutual fund late last year, many clients have asked about risk parity and its potential impact on financial markets if interest rates rise. The key to a “risk-based” approach is “risk diversification” and the use of leverage. Like any investment tool, it has its advantages and limitations. “Risk parity” portfolios differ greatly, depending on the choice of assets and the portfolio construction method. There are many ways to construct a risk-based portfolio. We highlight three: fixed weights; variable weights with inverse volatility; and variable weights with optimization. Fixed-weight risk-parity portfolios are not “risk diversified” ex post. Variable-weight risk-parity portfolios constructed using inverse volatility do not guarantee equal risk allocations. “Truly risk-diversified” portfolios constructed using our proprietary optimization algorithm have consistently outperformed those constructed with inverse volatility. Our approach not only achieves better risk diversification, but can also be used as an alpha overlay strategy. Risk parity does not always outperform in the long run, but always outperforms in recessions. Rising yields alone do not necessarily hurt risk parity. The worst environment for risk parity is the combination of rising yields and the underperformance of bonds relative to both cash and stocks – because both leverage and interest-rate movements work against risk parity. Worryingly, the past three years have been like this, similar to the 1949-1969 period when risk parity would not have performed. Feature Beautiful Simulation! Ugly Reality? Ray Dalio’s Bridgewater Associates created in the 1990s “The All Weather Investment Strategy,” which is known as the foundation of the “Risk Parity” movement.1, 2 Both back-testing and real-life performance from Bridgewater show that the “All Weather” portfolio did live up to its purpose as a low-beta, long-term portfolio that weathers through different economic cycles.2 The term “Risk Parity,” however, was coined by Edward Qian in 2005, and Qian even went as far as saying that risk parity is a way to the “New Holy Grail In Investing” – i.e. “upside participation and downside protection.”3 Only after the 2008 financial crisis did risk parity gain real traction, because investors were hungry for alternative tactics after traditional asset allocation approaches all failed miserably. Invesco began offering a risk parity strategy mutual fund in June 2009, and AQR launched its risk parity mutual fund in September 2010. According to the IMF, risk parity funds had AUM of US$150 billion to $175 billion at the end of 2017,4 while Bridgewater estimated in 2016 that there were about US$400 billion AUM dedicated to risk parity strategies globally, of which about US$150 billion was managed by external managers – with Bridgewater accounting for about half of the externally managed assets.2 While most risk parity believers dedicate a portion of their assets to risk parity strategies, some investors have gone in full-heartedly. For example, in 2016, Danish pension fund ATP completed its transition to a risk-based multi-factor approach by adopting a “four-factor building-block portfolio approach” that is “…in part inspired by Bridgewater’s All Weather” yet “owes more to the thinking of investment manager AQR and the academic field of ‘financial economics’ more generally.”5 At the end of 2018, ATP’s risk allocation to the four risk factors – interest-rate factor, inflation factor, equity factor and other factors – is shown in Chart 1.6
Chart 1
On the other hand, in September 2014, the San Diego County Employees Retirement Association board decided to fire its outsourced CIO from Houston-based Salient Partners, who had favored leverage-heavy (up to five times) risk-parity investments and had been given the reins of the US$10 billion pension fund.7 In fact, the growing popularity of risk parity has been accompanied by growing criticism, especially when risk-parity funds did not do well. In December 2018, AQR re-branded its flagship risk-parity mutual fund by dropping “Risk Parity” out of its name and tweaking the strategy for more flexibility after having suffered heavy outflows.8 Even though the change in the US$344 million fund did not reflect a shift in AQR’s views on the merits of risk-parity strategies (which accounted for about US$30 billion out of AQR’s US$226 billion in assets), Cliff Asness, the co-founder of AQR, did write a long blog discussing sticking with factor investing in general. “If sticking with them were easy, the threat of them being ‘arbitraged away’ would indeed be much greater, and nobody would take the other side,” he wrote.9 Chart 2Beautiful Simulation, Ugly Reality
Beautiful Simulation, Ugly Reality
Beautiful Simulation, Ugly Reality
It is easy to say “stick with it for the long run,” especially when back-tests show robust results from well-respected asset managers and researchers.10,11,12 Our own simulations also show beautiful results even for the recent period not covered by most published papers (Chart 2, top panel). In reality, however, publicly available information shows that risk parity funds have encountered some unpleasant underperformance since 2013 compared to conventional global 60/40 stock-bond portfolios (Chart 2, bottom three panels). Seven years of underperformance is a tough pill to swallow for any investor; it is little wonder we have received client requests on this subject more frequently of late. In this Special Report, we attempt not to take sides to argue for or against risk parity strategies. Instead, we focus our efforts on sorting through the jungle of confusing ways that risk-parity portfolios are defined and constructed, and highlight three typical ways used by many risk parity managers. We present simulated results using these different methods and our own proprietary optimization algorithm, aiming to answer the following questions often asked by our clients: What is risk parity? How is a risk parity portfolio constructed? What are the key differences among the various ways of constructing risk parity portfolios? Is it true that risk parity outperforms in the long run? Is it true that risk parity can outperform even if yields rise? How should asset allocators use risk-parity strategies? Risk Parity Basics There is no widely agreed-upon definition of risk parity, nor on how to construct a risk-parity portfolio. However, the “risk-based” allocation principle is the same, while differences among different managers lie largely in the process of portfolio construction, especially when the number of assets in consideration is more than two – because correlation does not matter when there are just two assets in a risk-based allocation approach. The Risk-Parity Principle: According to Bridgewater: “Risk parity is the means of adjusting the expected risks and returns of assets to make them more comparable.”13 If so, then a “better diversified portfolio” can be created by equally weighting those adjusted assets with low or no correlation with one another. This way, a portfolio with a higher Sharpe ratio can be achieved than would otherwise be possible using the conventional capital-based approach. Then, different degrees of leverage can be used to achieve desirable levels of risk and return. In terms of risk, investors need to consider not only the volatility of a portfolio, but also the risk of large portfolio drawdowns due to wrong assumptions. Since one does not know for sure in advance how each asset will perform, Bridgewater characterizes the investment regimes using growth and inflation, identifying which asset classes do well in each regime and allocating 25% weight in each of the four growth-inflation regimes.14 Despite robust back-test results from asset managers and researchers, risk parity funds have not lived up to their promise since 2013. So, one key to risk parity is to diversify across asset classes that behave differently across different economic regimes such that each asset contributes equally to portfolio risk. In general, equities do well in rising growth and falling inflation regimes, nominal bonds do well in deflationary or recessionary regimes, and commodities do well in rising inflation regimes. While Bridgewater includes corporate and EM credits and inflation-linked bonds in its universe of asset classes, not all risk-parity strategies include the exact same breadth of assets. For example, it can be argued that corporate and EM credits share more of the “equity factor,” since they have a high degree of sensitivity to rising growth as do equities, while inflation-linked bonds are a hybrid of nominal bonds and inflation. The Risk-Parity Portfolio Construction: There are many different ways to construct a risk-based diversified portfolio. The key differences are: 1) how the weights of assets are determined for the unlevered risk-parity portfolio, and 2) how leverage is determined to reach the desired return/risk profile. Based on these two key aspects, there are generally three different ways to construct a risk-parity portfolio, as shown in Table 1. The one represented by Bridgewater is more qualitative, while the other two are more quantitatively defined. Table 1Risk Parity Implementation Summary
Demystifying Risk Parity
Demystifying Risk Parity
When there are only two assets, it is easy to show that all three methods produce exactly the same allocations for the basic risk-parity portfolio without leverage. When there are more than two assets, however, the two approaches represented by Bridgewater15 and AQR16,17 are easy to compute, but the optimization approach based on equal contribution to risk (either in the sense of marginal contribution to risk or contribution to total risk18) has high demand in computing power. Also, it is not true that risk-parity does not need return estimates. Return estimates are not needed to determine a basic risk-parity portfolio, but they are needed to determine leverage when the target is a specific return other than volatility. Does Strategic Risk Parity Outperform In The Long Run? The pioneering “All Weather” fund was launched by Bridgewater in 1996, and has been used as a “strategic asset allocation mix” that is rebalanced to keep “constant” asset weights.19 To try to understand the early thinking behind risk parity, we used Bridgewater’s method to simulate a simple two-factor constant-weight risk-parity portfolio using global stocks20 and global bonds21 in two steps: First, we used monthly return data of stocks and bonds from January 1970 to December 1995 to estimate stock volatility (Vs ) and bond volatility (Vb ). The stock and bond weights in the unlevered risk parity portfolio (RP1) are determined as follows: Wb = Vs / (Vs +Vb), and Ws = 1- Wb......................(1) Depending on the required target, leverage will be applied to RP1. The leverage ratio is simply the target volatility (or return) divided by the volatility (or return) of the unlevered risk parity portfolio. Table 2 shows the simulated results with seven different targets, which appear to support the following claims of risk-parity supporters: A risk parity portfolio is better than a 60/40 portfolio because it achieves a higher Sharpe ratio; Equities and bonds contribute equally to total portfolio risk in a risk-parity portfolio, while a 60/40 portfolio risk is dominated by equities (85% in the stated period); With the use of proper leverage, risk parity achieves higher return with the same volatility or the same return with lower volatility. The statistics in Table 2, however, are based on “in sample” data with “perfect foresight.” In reality, no portfolio manager has the luxury of going back in time to implement any portfolio. Table 2Global Stock-Bond Risk Parity Portfolios (In Sample)
Demystifying Risk Parity
Demystifying Risk Parity
So, the second step of our simulation is to test how these portfolios would have performed going forward if they were rebalanced monthly to the same weights as those in December 1995. Table 3 shows the simulated ex post results for the “out of sample” period between January 1996 and March 2019. Table 3Global Stock-Bond Risk Parity Portfolios (Out Of Sample)
Demystifying Risk Parity
Demystifying Risk Parity
Comparing Table 3 to Table 2, several observations are worth highlighting: It is not true that assets have similar Sharpe ratios over longer time frames. Bonds generated higher returns with significantly lower volatility, resulting in a Sharpe ratio of 1.05 in the 1996-2019 period, compared to 0.28 between 1970 and 1995. The Sharpe ratios of stocks in both periods were similar. It is true that RP1 (no leverage) is a better portfolio than 60/40, with a higher Sharpe ratio, even though both portfolios’ Sharpe ratios increased due to the improvement in bonds. More impressively, RP2 (with the same return as 60/40) not only generated 30 basis points of annual outperformance compared to 60/40, it achieved such outperformance with significantly lower volatility. And RP4 (with the same volatility as stocks), also sharply outperformed stocks in terms of both return and volatility. So, the simulated risk-parity portfolios constructed using data from 1970 to 1995 have done well ex post. Upon closer examination, however, two issues arise: Table 4Risk Contribution* Comparison
Demystifying Risk Parity
Demystifying Risk Parity
First, as shown in Table 4, the risk-parity portfolio constructed using information as of 1995 turned out not to be risk parity in the subsequent period – because only 12% of the portfolio risk came from bonds, compared to the intended 50%. Granted, 88% from stocks is still less concentrated than the 60/40 portfolio which had 99% risk from equities in the same period, but the ex post risk-parity performance violates the very foundation of the risk-parity principle: true risk diversification. Second, as shown in Chart 3, even though risk-parity portfolios have outperformed their reference portfolios since 1970, the outperformance has not been consistent, with long periods of under- and over-performance. The only consistent observation is that risk parity outperforms in recessions, which is not surprising given its consistently large overweight in bonds. Chart 3Does Risk Parity Outperform In The Long Run?
Does Risk Parity Outperform In The Long Run?
Does Risk Parity Outperform In The Long Run?
Also, it seems that most of the outperformance came from the period after bond yields peaked in September 1981. Risk parity did poorly during the period from 1978 to 1982, when bond yields increased sharply, while it performed slightly better than the reference portfolios between 1970 and 1978, when rates increased gradually. In reality, even strategic asset allocators do not keep weights constant for such long periods of time. How do variable-weight risk-parity strategies do in different interest-rate environments? Do Rising Yields Hurt Risk Parity? To assess how risk-parity portfolios constructed based on different weighting schemes behave in different interest-rate environments, the simulations in this section use U.S. stocks22 and government bonds23 – only because of their long history that includes both secular rising and falling rate environments. Variable weights are determined based on moving volatility with different lookback windows. Statistically, the shorter the window length and the more frequent the return measured, the more volatile the volatility estimate is. AQR uses both 1-year24,25 and 3-year26 monthly moving windows, while S&P Dow Jones Risk Parity Indexes are based on a 5-15 year period of a monthly moving window.27 The worst combination for risk parity is rising yields and the underperformance of bonds relative to both cash and stocks. Worryingly, the past three years have been like this. Our research shows that a 1-year monthly moving window is too short, even though it produces higher total returns than longer windows. Chart 4A and 4B show the simulated results of three different moving windows – 36 months, 180 months and 360 months – for two risk-parity portfolios. RP1 is leveraged to have the same volatility as a monthly rebalanced 60/40 U.S. stock-bond portfolio, and RP2 is leveraged to have the same volatility as U.S. stocks. The weights calculated using formula (1) change monthly, based on the corresponding moving window. The following observations are true concerning the choices of our lookback period: Chart 4AU.S. Risk Parity* Vs. 60/40
U.S. Risk Parity* Vs. 60/40
U.S. Risk Parity* Vs. 60/40
Chart 4BU.S. Risk Parity* Vs. Stocks
U.S. Risk Parity* Vs. Stocks
U.S. Risk Parity* Vs. Stocks
The longer the lookback period, the more stable the asset weightings and leverage ratios, and vice versa (bottom three panels in Charts 4A and 4B). This is not specific for risk parity, though. Any approach using historical mean-variance-correlation estimates share this feature. The leverage ratio spikes more often when the window length gets shorter, which may be too uncomfortable for some investors. RP2 has equity weight consistently over 60%, no matter what lookback period is used (this is also true for fixed-weight risk parity). In comparison, the less-leveraged RP1 only briefly assigns higher than 60% to equities when the lookback period is very short (panel 4 in 4A and 4B). In terms of absolute performance from March 1933 to March 2019, the shorter the window length, the better the overall full-period total return (panel 1 in 4A and 4B). However, this outperformance comes with much higher leverage ratios, which may be too high for the majority of investors (panel 5 in 4A and 4B). In terms of relative performance versus the corresponding reference portfolio, longer window options have not done well overall. Only the shorter window option produced a marginally better relative performance for the full 86-year period (panel 2 in 4A and 4B). However, there are three stages of relative performance: a secular underperformance period from 1950 to 1970, a secular outperformance window from 2000 to July 2016, and a cyclical under- / over-performance period from 1970 to 1999. For the 36-month window, which has a longer history dating back to 1933, it also has a long period of outperformance from 1933 to 1949, as shown in Chart 5. Chart 5Does A Rising Bond Yield Hurt Risk Parity?
Does A Rising Bond Yield Hurt Risk Parity?
Does A Rising Bond Yield Hurt Risk Parity?
Risk parity has a heavy weighting in bonds. It is natural to think that underperformance occurs only when rates rise, and vice versa. As shown in Table 5, however, this is true only for three periods. Risk-parity portfolios outperformed from March 1933 to July 1941, and from January 2000 to July 2016 when rates dropped (Table 5 rows 1 and 6). They underperformed from January 1950 to December 1969 when yields rose (row 3). Table 5What Drives Risk Parity Performance?
Demystifying Risk Parity
Demystifying Risk Parity
What is puzzling is how risk parity performed in the following three periods: From August 1941 to December 1949, when rates rose slightly yet risk parity outperformed significantly (row 2); From January 1970 to September 1981, when interest rates rose even more than the previous period from 1949 to 1969, but risk parity did not underperform significantly (row 4); From October 1981 to December 1999, when yields dropped more than 900 basis points, yet risk parity did not outperform at all (row 5). Other than interest rates, what are the other forces driving risk parity performance? A closer examination of Table 5 reveals that the direction of interest-rate movements alone does not fully explain the performance of risk parity relative to its reference portfolio. It is the reason why rates rise or fall, combined with how assets react to those reasons, that determine how risk parity performs. This makes sense because risk parity not only overweights bonds in general, but uses leverage. The worst combination for risk parity is when interest rates rise such that bonds underperform both cash and stocks, as in the period from January 1950 to December 1969 (Table 5 row 3) – because leverage and interest-rate movements both worked against risk parity. This may not sound very encouraging for risk parity going forward, because the current period from July 2016 to March 2019, albeit very short in length, has so far shared similar characteristics to the period from 1949 to 1969 in terms of annualized excess return of stocks and bonds as well as relative performance between stocks and bonds. Table 5 also shows that during the hyper-inflationary period from 1970 to 1981, both stocks and bonds underperformed cash, which also underperformed inflation. Even though risk-parity portfolios performed in line with their reference portfolios, this period was actually the worst for investors because real returns were negative for all three assets. The key to risk parity is to diversify across asset classes that behave differently across different economic regimes such that each asset contributes equally to portfolio risk. So how does diversification across asset classes and geographic regions impact risk parity performance? How To Achieve True Risk Diversification? Commodities outperformed inflation during the hyper-inflationary period from 1970 to 1981. Intuitively, adding commodities to the asset mix would have been beneficial for that period. How about other periods? To assess the impact, we add commodities28 to our two-factor U.S. risk parity and two-factor global risk-parity portfolios to simulate three-factor risk-parity portfolios with two different lookback periods (36 months and 180 months) and three different volatility targets (10%, 12% and 15%). The weight of each asset for the unlevered risk parity portfolio is calculated using the inverse of the volatility (V) of each asset: Wi = (1/Vi) / ((1/Vs +1/Vb +1/Vc)...................(2) Where i stands for s (stocks), b (bonds) and c (commodities). The volatility of the unlevered risk-parity portfolio (URP) in each window period is then calculated as Vurp and the leverage ratio is calculated as Vtarget / Vurp. Chart 6A and 6B compare how the addition of commodities to the asset universe changes the performance of risk parity. For a longer history of performance, we show the simulations with the 36-month moving window. Chart 6ACommodity Impact On U.S. Risk Parity
Commodity Impact On U.S. Risk Parity
Commodity Impact On U.S. Risk Parity
Chart 6BCommodity Impact On Global Risk Parity
Commodity Impact On Global Risk Parity
Commodity Impact On Global Risk Parity
Overall the addition of commodities has performed in line with the two-asset risk parity portfolios. However, the three-factor risk parity portfolio did significantly outperform the two-factor portfolio before 1990. After more than a decade of ups and downs, relative performance made a strong rebound during the GFC, only to give up all the gains in the next seven years (Charts 6A and 6B, panel 1), coinciding with a sharp change in commodities-stocks correlations (panel 5). A “truly risk-diversified” portfolio constructed using our proprietary optimization algorithm outperforms consistently a risk-parity portfolio based on inverse of volatility. Chart 7Risk Contributions
Risk Contributions
Risk Contributions
It is worth noting that diversification across asset classes and geographies is not exclusive to risk parity. It is a well-accepted practice in the asset management industry. Panel 4 in both 6A and 6B show that a 50/40/10 stock-bond-commodity portfolio also outperforms or underperforms a 60/40 equity-bond portfolio in line with the movement of relative asset performance. Risk parity, however, amplifies the upside by using leverage and slightly limits downside risk by allocating risk in a more diversified fashion (Chart 7). Chart 7 shows that a conventional portfolio, despite a 50% weight in equities, is dominated by equity risk, while the risk-parity portfolio has much less concentrated risk allocations. However, the three assets in the risk-parity portfolio do not have an equal share of risk contribution. Why? Because we constructed the risk-parity portfolio using the inverse of volatility according to formula (2). It assigns a higher weight to a lower volatility asset, but does not guarantee equal allocation of risk. How will a more precisely equal risk allocation improve risk-parity performance? We ran another simulation using the same three global assets and a 180-month moving window. However, asset weights were optimized using a proprietary optimization procedure such that each asset contributed equally to total portfolio risk. Chart 8, shows that the optimized risk-parity portfolios have outperformed those constructed by using formula (2), i.e. inverse volatility. Impressively, the outperformances are consistent through time in terms of both returns and Sharpe Ratios (panels 1 and 2). The optimized risk contributions are equally distributed (panel 4) as intended. By contrast, when the weights were constructed using inverse volatility, each asset's contribution to total risk varied considerably (panel 3). This makes sense because the optimization procedure takes into consideration not only volatility but also correlations between assets. Correlation between stocks and bonds, and correlation between stocks and commodities, have both gone through significant changes over time, especially since 2006 when the directions reversed. (Chart 9, panel 5). Consequently, on an unlevered basis, ex ante volatility of the optimized portfolio has turned lower since 2006, resulting in a higher Sharpe ratio (Chart 9, panels 3 and 4). Chart 8True Risk Diversification Works Better
True Risk Diversification Works Better
True Risk Diversification Works Better
Chart 9Why Does True Risk Diversification Work Better?
Why Does True Risk Diversification Work Better?
Why Does True Risk Diversification Work Better?
Even though the returns of the two unlevered portfolios are similar, the optimized portfolio’s lower volatility permits a higher leverage ratio at any given target portfolio volatility, which in turn drives much better returns of the leveraged portfolios (panels 1 and 2). The bottom line is that a “truly risk-diversified” portfolio constructed using our proprietary optimization algorithm does produce better results than a risk-parity portfolio constructed using less risk-diversified approaches, such as the inverse of volatility. It does require more computing power, but this will become much less an issue with technological advancement. Our finding can also be used as a pure alpha overlay strategy. The implementation, though, is out of the scope of this report. Conclusions The key features of a “risk-based” approach is “risk diversification” and the use of leverage. The risk parity approach is one of many investment tools. Like any other investment tool, it has its advantages and limitations. Because of choices in the universe of assets and also portfolio construction methods, not all “risk parity” portfolios are equal. Investors should apply rigorous due diligence before choosing a risk-parity manager. Based on our simulations, we find: Risk parity outperforms in recessions due to its large allocation to bonds. The direction of interest-rate movements alone does not fully determine how risk parity performs. The worst environment for risk parity is the combination of rising yields and the underperformance of bonds relative to both cash and stocks – because both leverage and interest-rate movements work against risk parity. Worryingly, the past three years have been like this, similar to the 1949-1969 period when risk parity would not have performed. Fixed-weight risk-parity portfolios are not truly risk diversified ex post. An inverse volatility approach generates less concentrated risk allocation, but not necessarily equal risk contribution. Risk-parity portfolios constructed with shorter lookback periods outperform those with longer lookback periods if historical volatility estimates are used. Risk-parity portfolios constructed using our proprietary optimization algorithm that truly allocates risks equally to all assets, consistently outperform those constructed using approximation, such as inverse volatility. This finding not only proves that “true risk diversification” works, it can also be used as an alpha overlay strategy for asset allocators. Xiaoli Tang, Associate Vice President xiaoliT@bcaresearch.com Footnotes 1 Bridgewater Associates, “The All Weather Story” 2 Bridgewater Associates, “Our Thoughts about Risk Parity and All Weather,” Daily Observations, September 16, 2016. 3 Edward E. Qian, “Risk Parity Fundamentals,” CRC Press, 2016. 4 Sergei Antoshin, Fabio Cortes, Will Kerry and Thomas Piontek, “Volatilities Strike Back,” IMF Blog, dated May 3, 2018. 5 Rachel Fixsen, ”ATP: Rebalancing the risk diet,” IPE Magazine, July/August 2016. 6 “Annual Announcement of Financial Statements 2018,” ATP Group. 7 Jeff Macdonald, “Pension board to consider firing CIO,” The San Diego Union-Tribune, September 18, 2014. 8 Miles Weiss, “AQR Strips ‘Risk Parity’ Name From Mutual Fund After Redemptions,” Bloomberg, December 7, 2018. 9 Cliff Asness, “Liquid Alt Ragnarök?” AQR Alternative Investing, September 7, 2018. 10 Bridgewater Associates, “Our Thoughts about Risk Parity and All Weather,” Daily Observations, September 16, 2016. 11 Edward E. Qian, “Risk Parity Fundamentals,” CRC Press, 2016. 12 Clifford S. Asness, Andrea Frazzini, and Lasse H. Pedersen, “Leverage Aversion and Risk Parity,” Financial Analyst Journal, Jan/Feb 2012. 13 Bridgewater Associates, “Our Thoughts about Risk Parity and All Weather,” Daily Observations, September 16, 2016. 14 Bridgewater Associates, “The All Weather Story” 15 Bridgewater Associates, “The All Weather Story” 16 Clifford S. Asness, Andrea Frazzini, and Lasse H. Pedersen, “Leverage Aversion and Risk Parity,” Financial Analyst Journal, Jan/Feb 2012. 17 Brian Hurst, Bryan Johnson, Yao Hua Ooi, “Understanding Risk Parity,” AQR, Fall 2010. 18 Edward E. Qian, “Risk Parity Fundamentals,” CRC Press, 2016. 19 Bridgewater Associates, “Our Thoughts about Risk Parity and All Weather,” Daily Observations, September 16, 2016. 20 MSCI All Country World Total Return Index in U.S. dollars, unhedged, from December 1987 to now. For back history, we used the MSCI World from December 1969. Prior to December 1969 we used the S&P 500. 21 Bloomberg Barclays (BB) Global Aggregate hedged total return in U.S. dollar from January 1990 to the present. For back history, we used the BB Global Treasury hedged total return in U.S. dollar from January 198, the BB U.S. aggregate total return from January 1976, and the BB U.S. Treasury total return from December 1972. Prior to December 1972 we used our own calculations based on U.S. 10-year government bond yield. 22 MSCI U.S. Total Return Index from December 1969 to the present. Back history was the S&P 500 Total Return Index. 23 Bloomberg Barclays (BB) U.S. Treasury Total Return Index from December 1972. Back history was calculated based on U.S. 10-year government bond yield. 24 Brian Hurst, Bryan Johnson, Yao Hua Ooi, “Understanding Risk Parity,” AQR, Fall 2010. 25 Brian Hurst, Michael, Yao Hua Ooi, “Can Risk Parity Outperform If Yields Rise?,” AQR, July 2013. 26 Clifford S. Asness, Andrea Frazzini, and Lasse H. Pedersen, “Leverage Aversion and Risk Parity,” Financial Analyst Journal, Jan/Feb 2012. 27 https://eu.spindices.com/indices/strategy/sp-risk-parity-index-12-target-volatility-tr 28 GSCI Commodities Total Return Index from December 1969, before which the total return index of the Bloomberg Commodities Index was used.