Risk Parity an Alternative Approach to Asset Allocation

FEATURE

Risk Parity An Alternative Approach to Asset Allocation

Alexander Pekker, PhD, CFA®, ASA, Meghan P. Elwell, JD, AIFA®, and Robert G. Smith III, CIMC®, AIF®

ollowing the financial crisis of tors, traditional RP strategies fall short respectively, but a rather high Sharpe 2008, many members of the of required return targets and leveraged ratio, 0.86. In other words, while the investment management com- RP strategies do not provide enough portfolio is unlikely to meet the expected F munity, including Sage,intensified their potential benefits to outweigh their return target of many institutional inves- scrutiny of mean-variance optimization risks. Instead we advocate a liability- tors (say, 7 percent or higher), its effi- (MVO) and modern portfolio theory based approach that incorporates risk ciency, or “bang for the buck” (i.e., return (MPT) as the bedrock of asset alloca- budgeting, a key theme of RP, as well as per unit of risk, in excess of the risk-free tion (Elwell and Pekker 2010). Among tactical asset allocation. rate), is quite strong. various alternative approaches to asset How does this sample RP portfo- What is Risk Parity? allocation, risk parity (RP) has been in the lio compare with a sample MVO port- news lately (e.g., Nauman 2012; Summers As noted above, an RP portfolio is one folio? A sample MVO portfolio with a 2012), especially as some hedge funds, where risk, defined as standard deviation return target of 7 percent is shown in such as AQR, and large plan sponsors, of returns, is distributed evenly among table 2. Unlike the sample RP portfolio, such as the San Diego County Employees all potential asset classes;1 table 1 shows the MVO portfolio is heavily allocated Retirement Association, have advocated a sample (unleveraged) RP portfolio toward equities, and it has much higher its adoption. based on sample adjusted historical cap- risk and a much lower Sharpe ratio. In The traditional MVO approach con- ital market assumptions.2 Heavily tilted addition, unlike in the sample RP port- structs a portfolio that minimizes total toward fixed income, this portfolio has folio where each asset class is allocated expected risk, defined as standard devi- modest expected return and standard 25 percent of the risk, here, U.S. equities ation of returns, subject to a desired deviation, 5 percent and 5.2 percent, make up the largest portion of the assets return target. Because equities typically have much higher expected returns TABLE 1: SAMPLE (UNLEVERAGED) RISK PARITY PORTFOLIO than other asset classes, they make up Contribution to Contribution to Weight (%) Return (%) Risk (%) the largest portion of an MVO portfolio; as a result (and because they also typi- U.S. Fixed Income 69% 55% 25% cally have higher risk than many other Global Equities 10% 15% 25% asset classes), equities also contribute U.S. Equities 12% 20% 25% the largest share of portfolio risk, often Alternatives 10% 11% 25% more than 80 percent. In contrast, RP Total 100% 100% 100% constructs a portfolio such that all asset Return 5.0% classes contribute equally to portfolio Risk 5.2% risk, with the return determined by this Sharpe Ratio 0.86 allocation. As a result, RP portfolios have a much larger allocation to fixed income TABLE 2: SAMPLE MEAN-VARIANCE OPTIMIZATION PORTFOLIO and a much lower allocation to equities Contribution to Contribution to than MVO portfolios. Not surprisingly, Weight (%) Return (%) Risk (%) then, RP portfolios generally have lower U.S. Fixed Income 28% 16% 1% risk and lower return than MVO portfo- Global Equities 10% 11% 14% lios, unless leverage is allowed. U.S. Equities 57% 69% 81% In this article, we address some of the Alternatives 5% 4% 4% key issues associated with RP strategies, Total 100% 100% 100% including efficiency, leverage, imple- Return 7.0% mentation, past performance, and the Risk 10.5% impact of rising interest rates. We con- clude that, for most institutional inves- Sharpe Ratio 0.62

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Practical Considerations and constitute 81 percent of the risk. depends on a key assumption, namely Thus, the sample MVO portfolio, while that funds can be consistently borrowed The first consideration in implementing achieving the desired return target, is at a relatively stable low rate. If this RP is the same one that befalls MVO: more risky and less efficient than the assumption is violated to a high enough its reliance on asset risk and correla- sample RP portfolio. degree, RP is no longer as appealing. tions estimates, either ex post or ex ante, As noted above, despite its high Indeed, in reality the cost of leverage which may or may not be at all indica- Sharpe ratio, the sample RP portfolio is varies. Market volatility, the amount bor- tive of the future. Each provider of not very attractive to most institutional rowed, the low quality of the underlying a RP strategy will use different methods investors—its expected return is just collateral, and rising overall levels to determine these parameters too low. However, by introducing lever- of interest rates are all factors that are (e.g., indexes corresponding to asset age, RP can be adjusted to reach the likely to increase borrowing costs. In par- classes, observation-period length, required return target, making it more ticular, the impact of market volatility on observation frequency, potential incor- competitive with an MVO portfolio. leveraged RP portfolios cannot be under- poration of correlations, forward-look- estimated. In times of extreme market ing adjustments, etc.), leading to some Leverage and Its Risks stress (such as the financial crisis of nontrivial variations in asset allocations To bring the sample RP portfolio to a 2008), the cost of borrowing rises sharply between RP strategies. Indeed, it’s gen- return target of 7 percent while main- while liquidity generally plummets. In erally well-known that small variations taining the same equal risk decomposi- such an environment, asset returns fall in risk assumptions, including correlation among asset classes, leverage must far below borrowing costs, and the fund tions, probably the most elusive MPT be employed. Assuming that the cost of may have to sell assets (if it can, given assumption to estimate, can lead to borrowing is fixed at 1 percent (or 0.5 the illiquidity of the markets) at inoppor- large variations in optimal asset alloca- percent above cash), the required lever- tune prices to meet margin and collateral tion (e.g., Elwell and Pekker 2010). This age is 49 percent (1.49 × 5.2% – 0.49 × requirements. This lose-lose proposition, unfortunate and inescapable variation in 1.0% = 7.0%). As table 3 shows, relative while seemingly remote, is an important parameters is at the root of all asset to the sample unleveraged RP portfolio, risk to keep in mind whenever borrowing allocations based on MPT. the Sharpe ratio is slightly lower, 0.83 vs. is involved, especially at such a high level The second consideration in imple- 0.86, but it is still much higher than that (almost half of the assets). menting RP is rebalancing. Typically RP of the sample MVO portfolio; in addi- Leverage often comes with other portfolios are rebalanced monthly or tion, the volatility of the sample lever- risks and costs as well. For example, quarterly based on risk parameters aged RP portfolio, 7.8 percent, is much while government bonds can be lev- computed over rolling time periods lower than that of the MVO portfolio. eraged through bond futures (which (e.g., rolling three-year periods). Thus Clearly, with its return equal to are traded on an exchange and con- RP rebalancing is typically more fre- that of the MVO portfolio and a lower sequently have virtually no counter- quent and involves greater dollar risk and greater efficiency (i.e., higher party risk and little basis risk), leverag- amounts than traditional strategies, Sharpe ratio) than the sample MVO ing other asset classes potentially would leading to higher transaction costs. portfolio, the sample leveraged RP port- require some kind of swap, introducing Occasionally, rebalancing may be folio becomes more appealing to insti- counterparty risk, basis risk, and addi- impossible due to lack of liquidity asso- tutional investors. All this analysis tional implementation costs. ciated with some alternative assets (e.g., hedge funds with lock-up peri- TABLE 3: SAMPLE LEVERAGED RISK PARITY PORTFOLIO ods or illiquid real estate), thus unravel- Contribution to Contribution to ing (at least in part) the whole premise Weight (%) Return (%) Risk (%) of RP. Moreover, if RP involves multiple U.S. Fixed Income 102% 4.1% 25% asset managers (e.g., specialists by asset Global Equities 15% 1.1% 25% class), the coordination of leverage and U.S. Equities 18% 1.5% 25% rebalancing across asset classes may be Alternatives 15% 0.8% 25% particularly cumbersome. Leverage –49% –0.5% 0% Finally, in today’s low-interest-rate Total 100% 7.0% 100% environment, RP requires extra scrutiny because of its high allocation to fixed Return 7.0% income and, in the case of leveraged Risk 7.8% RP, borrowing costs, both of which are Sharpe Ratio 0.83 closely tied to interest rates. This consid-

eration once again reveals the key draw- FIGURE 1: RANGE OF 1-YEAR RETURNS FOR UNLEVERAGED RP, LEVERAGED back of using MPT to construct asset RP, AND MVO PORTFOLIOS, ASSUMING INTEREST RATES RISE BY 1 PERCENT allocations: It is based on long-term 25% risk/return assumptions, not on current market conditions, economic outlook, or expectations for interest-rate shifts (and their impacts on asset returns). 15% RP in a Low-Interest-Rate Environment

One way to evaluate investment strat- 5% egies is through market simulation and stress testing, i.e., shocks to the status quo. A simple way to model interest rates is to apply a parallel 1-percent -5% upward shift to the Treasury yield curve and to model equity returns sto- chastically (based on the capital market assumptions used in portfolio –15% Unleveraged RP Leveraged RP MVO construction). 5–25th 25–50th 50–75th 75–95th Assuming a 1-percent parallel shift in the Treasury yield curve, expected equity and alternatives returns over a rising interest rates (indicating a strong constructed a (leveraged) RP portfo- one-year period of 5.5–8.5 percent, and economic recovery), then MVO, or for lio and an MVO portfolio and reviewed no rebalancing during the year, RP and that matter any equity-heavy asset allo- the portfolios’ performances over the leveraged RP pale in comparison with cation, is likely to outperform both lev- same 20-year period (Allen 2010). In MVO: Their mean returns are near eraged and unleveraged RP by as much other words, the authors assumed per- 0 percent, while the MVO mean return as 8–14 percent at the 75th–95th per- fect foresight in terms of capital market is almost 5 percent. Yet, the range of centile. This approach, while somewhat assumptions, thus removing estimation returns—depending on the volatility of simplistic, illustrates the importance of error as a possible reason for one port- the non-fixed-income-sensitive asset market simulations in evaluating asset folio outperforming another. classes—is much narrower, as figure 1 allocation risk in the context of investor By construction, both portfolios shows. Thus, on a risk-adjusted basis, risk tolerance. achieved the 8.25-percent annualized unleveraged RP does not perform as return over the 20-year period ending Historical Performance poorly as might be expected in a rising September 30, 2009, yet on a cumulative rate environment. Various consulting firms, hedge funds, basis RP underperformed MVO until the Moreover, if we expect poor equity and academics have conducted studies financial crisis of 2008. That is, an inves- returns to accompany rising interest on past performance of RP strategies, tor had to wait 18 years for RP to out- rates (indicating a severe market melt- and the results are mixed (e.g., Allen perform MVO. In reality, of course, it is down), unleveraged RP is the clear win- 2010; Peters 2010; Asness et al. 2012; unlikely than a RP investor would have ner, outperforming leveraged RP and Anderson et al. 2012). Perhaps the main been willing to wait that long, especially MVO by 0–5 percent at the 75th–95th revelation is that performance depends because MVO outperformed RP in every percentile. (As for leveraged RP, due to strongly on the assumptions and meth- five-year period through June 30, 2001. the negative fixed income returns and odology (risk and correlation parame- On the other hand, in all subsequent increased cost of borrowing, it under- ters, borrowing costs, rebalancing, etc.), five-year periods, RP outperformed. performs unleveraged RP, assuming time period considered, and economic These results are not surprising if we submedian equity returns.) Of course, environments studied. recall the economic environments of the in reality, any strategy with a 69-percent A comprehensive and illustrative 1990s (strong stock market returns) and allocation to core fixed income is likely study was conducted by Callan 2000s (volatile stock market returns and to perform similarly to unleveraged RP. Associates (Allen 2010). Based on actual strong bond market returns). On the other hand, if we expect historical data for the 20-year period As for the 8.25-percent return tar- strong equity returns to accompany ending September 30, 2009, the authors get, MVO handily outperformed that

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Endnotes target in all five-year periods through Finally, we recognize that for the vast 2002, struggled a bit through 2007, out- majority of investors, assets are invested 1 Naively, RP ignores correlations between performed through mid-2008, and then to meet some liability over some time asset classes; however, in this article, we underperformed. RP, on the other hand, horizon (e.g., benefit payments for pen- account for the covariance terms (by stating struggled to reach the 8.25-percent sion plans, claims for insurance com- that contribution to risk is the weight times return target in all five-year periods panies, grants for foundations, etc.). As the marginal contribution to risk). through 1997, outperformed it slightly a result, we advocate a liability-focused 2 Risk/return assumptions are as follows: U.S. through mid-2008, and then underper- approach to asset allocation and risk fixed income: 4.0 percent, 3.7 percent; global formed. Thus, viewed in isolation (and management. Combining liability- equities: 7.5 percent, 17.1 percent; domes- not compared with MVO), RP achieved focused investing with our economic tic equities: 8.5 percent, 15.1 percent; alter- the return target frequently and with outlook, market simulations, and port- natives: 5.5 percent, 21.7 percent; cash: 0.5 modest volatility. No grand slams, but folio research, we design multi-asset percent, 0.6 percent. no huge strike-outs either. strategies that combine traditional fixed References The studies ultimately show that nei- income and tactical asset allocation ther RP nor MVO are successful all the to help our clients achieve long-term Allen, G. C. 2010. The Risk Parity Approach time (i.e., on a rolling-period basis) and investment goals. In today’s low-yielding to Asset Allocation. Callan Investment that the economic environment really environment, deep economic analysis, Research Institute (February). http://www. matters. Indeed, a consideration of the judicious rebalancing, and efficient cash- callan.com/research/download/?file=papers/ economic environment as well as timely flow management are the hallmarks of free/368.pdf. adjustments should be as much a part sound investment management. Anderson, R. M., S. W. Bianchi, and L. R. of portfolio construction as any MPT- Goldberg. 2012. Will My Risk Parity Strategy based parameters. Alexander Pekker, PhD, CFA®, ASA, Outperform? Financial Analysts Journal 68, is vice president–quantitative no. 6 (November/December): 75–93. Conclusion analysis and research with Sage Asness, C. S., A. Frazzini, and L. H. Pedersen. Due to its low expected returns, asset Advisor Services, Ltd. Co. in 2012. Leverage Aversion and Risk Parity. allocation based completely on unlev- Austin, TX. He earned a BS in Financial Analysts Journal 68, no. 1 eraged RP generally is not attractive to mathematics and an MS in computer (January/February): 47–59. institutional investors, while leveraged science from Stanford University, Elwell, M., and A. Pekker. 2010. Rethinking RP may be more attractive because it is, an AM in mathematics from Modern Portfolio Theory: New Lessons at least theoretically, more efficient and Harvard University, and a PhD in about Old Standards. Investments & Wealth less volatile than traditional MVO. On mathematics from The University Monitor 24, no. 2 (March/April): 12–16. the other hand, leveraged RP involves of Texas. Contact him at Nauman, B. 2012. OCIOs Commingle to Expand leverage and all its risks (such as liquid- [email protected]. Opps in Alts. FundFire.com (August 17). ity risks), costs (such as high transaction http://www.fundfire.com/c/398101/44911/ costs), and implementation challenges Meghan P. Elwell, JD, AIFA®, is vice OCIOs_Commingle_to_Expand_Opps_in_ (such as rebalancing across multiple president–quantitative analysis and Alts. managers). Even assuming away all research with Sage Advisor Services, Peters, E. 2010. Counter-Point to Risk Parity these issues, the historical record does Ltd. Co. in Austin, TX. She earned Critiques. FQ Perspectives 7, no. 7 (June). not suggest that RP is far superior to a BA in mathematical economic http://www.firstquadrant.com/down- other asset allocation strategies. analysis from Rice University and a loads/2010_06_Counter-Point_to_Risk_ Yet not all is lost with RP: Its focus on JD with honors from The University Parity_Critiques.pdf. risk budgeting (rather than return tar- of Texas School of Law. Contact her Summers, M. 2012. Institutional Investors geting) certainly enlightens asset alloca- at [email protected]. See Opportunity in Risk Parity. FundFire. tion decision-making. Taking it a step com (September 13). http://www.fundfire. further, we believe that it’s important to Robert G. Smith III, CIMC®, AIF®, is com/c/408821/46091/Instl_Investors_See_ view risk in its traditional definition as president, chief investment officer, Opportunity_in_Risk_Parity. the standard deviation of returns as well and principal with Sage Advisory To take the CE quiz online, as across its many other dimensions, Services, Ltd. Co. in Austin, TX. He visit www.IMCA.org. including cash-flow risk, liquidity risk, earned an MBA in finance from the regulatory risk, implementation risk, etc. New York University Stern School of Indeed, each of these risks is important Business. Contact him at and should be budgeted accordingly. [email protected].