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At Par with Risk Parity?Samuel Kunz, CFAChief Investment OfficerPolicemen’s Annuity and Benefit FundChicago

Risk parity attempts to remove the equity dominance of a traditional beta-allocated portfolioand equalize all asset risk contributions. The problem is that expected return declines. Thesolution is to leverage part, or the whole, portfolio. The benefits of a risk parity approach—better beta diversification and more efficient portfolios—come with several trade-offs to

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consider before a risk parity approach is adopted.

onsider the following scenario. The Fed hasraised interest rates again, but inflation

remains high. Equity markets are under tremen-dous pressure, and the level and volume of the DJIAare in the red. But you are not worried because yourportfolio is well balanced. It has been designed tonavigate these types of storms. This scenario is whatall portfolio managers want—portfolios that areefficient and diversified and that provide smoothreturns with low operational risk.

I will begin by defining risk parity, and then Iwill focus on the two primary benefits of risk parity:better beta diversification with less reliance onequity and the creation of more efficient portfoliosthrough the use of leverage. Last, I will discusssome potential problems created by risk parityallocations—specifically, the use of leverage, someof risk parity’s theoretical limitations, and severalimplementation considerations.

Definition of Risk ParityTo define risk parity, I will use the example of a“traditional” portfolio allocation, which generallyconsists of 60 percent in equities and 40 percent infixed income. Although the dollar allocationbetween the two asset classes is fairly balanced, theequity contribution clearly dominates the total port-folio risk. Risk parity attempts to equalize assets interms of their risk contribution. The problem is thatin doing so, the expected return of the portfolio goesdown. The risk parity solution is to leverage part, orthe whole, portfolio.

Risk parity is ultimately about trade-offs. Onthe one hand, portfolios can be created with noleverage but lower Sharpe ratios, or on the other

hand, portfolios can be created with better risk–return attributes that require the use of leverage toachieve a reasonable rate of return.

At its core, risk is a subset of risk budgetingbecause it focuses solely on variance. Risk parityalso relaxes leverage constraints, and its goal is togenerate equity-like returns with lower volatility.Although some risk parity products combine a corerisk parity portfolio with an active alpha compo-nent, it is basically a quantitative approach used tocreate beta exposures, or alternative beta.

Although risk parity allocations can be createdregardless of the number of assets a portfolio holds,the simplified two-asset portfolio in Table 1 showsone of the trade-offs between the traditional and riskparity approaches. The expected return on Asset 1is 8.7 percent, and on Asset 2 it is 2.1 percent. Therisk of the two assets is 20.1 percent and 10 percent,respectively. Note that the numbers have beenrounded and correlations have been ignored. Theobjective is to create a portfolio that achieves an 8percent return. The traditional return-based optimi-zation tilts the portfolio heavily (90 percent) towardthe risky asset and allocates only 10 percent to themore conservative Asset 2. Risk parity, in contrast,is concerned only about balancing risk between thetwo assets. In this case, it allocates about one-thirdto risky Asset 1 and two-thirds to the more conser-vative Asset 2.

This presentation comes from the CFA Institute 2011 Asset and RiskAllocation conference held in Chicago on 5–6 April 2011 in partnershipwith the CFA Society of Chicago.

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Table 1. Effect of Risk Parity in an Optimized Portfolio of Two Assets

Item Asset 1 Asset 2 Leverage

Expected return 8.7 2.1Risk 20.1 10.0Traditional optimization 90% 10% 1.0xRisk parity 62% 125% 1.9x

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The problem, however, is that the expectedreturn of the portfolio is only 4.3 percent when usingthe risk parity approach. To bring the expected port-folio return back to the 8 percent target, the portfoliowould need to be leveraged about 1.9 times.

Risk Parity BenefitsThe earlier simplified example helps define themain benefit of risk parity—less reliance on growthin the economic cycle (i.e., equity beta) to generatethe required rate of return. Figure 1 illustrates howequity dominates portfolio risk in any given allo-cation. Similar to Table 1, the illustration showsonly two assets and ignores correlation effects.With volatilities of 20 percent for equity and 10percent for the less risky asset, the risk contributionof equity increases quickly; in fact, it increases tomore than 80 percent with an allocation of only 50percent to equity.

Another example is the Chicago Police pensionfund. Currently, the fund has a dollar allocation toequity of about 42 percent, but its risk contributionis more than 65 percent (equity beta is actuallyunderstated because correlations tend to spike intimes of crisis). With risk parity, portfolios are lessreliant on growth in the economic cycle to generatereturn and thus are less volatile. Because the pen-sion fund is only about 35 percent funded, pathdependency is paramount. In fact, the tension thatnegative cash flow creates between optimal andadequate allocations is probably the most importantchallenge pension funds face. Low volatility solu-tions are thus extremely valuable.

The second benefit of risk parity is its ability tocreate more efficient portfolios. In 1952, Markowitzintroduced variance as a proxy for risk and portfoliooptimization (Markowitz 1952). In other words, heasserted that risky assets can be combined in a waythat minimizes variance at each level of return andmaximizes return at any given risk level. He arguedthat rational investors should select a combinationof assets situated on the efficient frontier. In theabsence of leverage, the highest expected return ofthe portfolio is the return of the highest-returningasset class.

In 1958, Tobin argued that in the presence of arisk-free asset, risk-averse investors should holdportfolios of only two assets: the risk-free asset anda fund of risky assets (Tobin 1958). In 1964, Sharpeexamined the implications of Tobin’s two-fund sep-aration theorem to develop the capital asset pricingmodel (CAPM), suggesting that the tangency port-folio is the market portfolio that consists of all exist-ing assets weighted by market capitalization(Sharpe 1964).

I believe that risk parity is in total agreementwith Tobin’s argument but not so much withSharpe’s. Specifically, risk parity attempts to lever-age an efficient portfolio instead of increasing riskalong the efficient frontier. The portfolio it lever-ages, however, is not the tangency portfolio, whichis an important point that I will revisit later.

So, to summarize, the two main benefits of riskparity are better beta diversification through lowerequity exposures and increased efficiency throughthe use of leverage and the capital market line.

Figure 1. Risk Contribution of Equity at Various Allocation LevelsRisk Contribution of Equity (%)

100

80

60

40

20

00 10025 50 75

Allocation to Equity (%)

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At Par with Risk Parity?

Risk Parity Trade-Offs and LimitationsThe benefits of risk parity, however, also come withtrade-offs and limitations. For example, risk parityappears to reject CAPM by leveraging an allocationthat is not the tangency portfolio. Risk parity port-folios seem to fall somewhere between the capitalmarket line and a line passing through theminimum-variance portfolio, as shown in Figure 2.Unleveraged risk parity portfolios, therefore, arenot the most efficient unless all assets in the universehave identical correlations and Sharpe ratios. (Formore about this subject, see Maillard, Roncalli, andTeïletche 2010.) Under these heroic assumptions, allassets in the world would become redundant.

Risk parity proponents believe that unlever-aged portfolios are “close enough” to the efficientportfolio, but that belief suggests another trade-off.On the one hand, investors can allocate using atheory that is imperfect but fairly well defined, oron the other hand, they can use an approach that is

not very well defined but has generated attractivereturns for the past 10–15 years.

Importantly, risk parity also ignores returns,which brings up an interesting point. If it can bedefined ex ante that the risk parity portfolio willoutperform the market portfolio and thus inves-tors who disregard expected returns are better offthan those who try to predict returns, there is novalue in seeking information beyond what isembedded in historical variance and correlations.(For more thoughts about markets being informa-tionally inefficient, see Grossman and Stiglitz1980.) That assertion might be a stretch for someinvestors. Several theories that attempt to explainthe recent outperformance of risk parity portfoliosare being considered.

One of the theories is that risk parity portfoliosprovide better diversification than other portfolios,especially in different economic regimes. Althoughsome research has shown mathematical limits tothese diversification benefits, consider the experien-tial side of the claim; with a traditional allocation,

Figure 2. Position of Risk Parity Portfolio in Relation to Minimum-Variance Portfolio, Capital Market Line, and Efficient Frontier

Minimum-Variance Portfolio Capital Market Line

Efficient Frontier

Risk Parity Portfolio

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risk is dominated by economic cycles through equityexposures and fixed income and real asset alloca-tions only matter at the tails of the distribution.

Risk parity takes another approach. First, itidentifies a set of economic regimes, or states of theworld, and then selects a set of risk contributionsthat equally addresses these different states of theworld by allocating equally to these risk factors.From a beta allocation perspective, this nonquanti-tative argument is intuitively attractive and is oneof the best lines of defense for risk parity portfolios.

Unfortunately, it is not without problems. First,the approach is quite subjective. Second, correla-tions between the assets as well as correlationsbetween the assets and the different states of theworld need to be estimated. These correlations mustalso be assumed to be stable over time. More impor-tantly, some risk parity products assign equal prob-abilities to the states of the world, which has notbeen the case historically.

A second theory that some risk parity propo-nents are putting forward to justify recent returns isleverage aversion. Most investors are restricted bychoice or by regulation in how they can apply lever-age to their portfolios. As a result, in an attempt toearn the desired rate of return, they must increaseallocation to the riskier assets (i.e., equities) in theirportfolios. Thus, the theory posits that risk parityportfolios are able to capture a leverage aversionpremium embedded in low-risk assets. The lever-age aversion theory, however, is also burdened bya limitation related to market efficiency. If a lever-age aversion premium does exist, then increased

allocations to risk parity would arbitrage away thisadvantage over time.

Focusing on risk more than in the past is anexcellent goal for investors. But putting no valuewhatsoever on forecasting returns would free uptime for most investors, and the savings could beused to address some of the other problems thatcome with risk parity—one of them being leverage.As I pointed out earlier, risk parity increases alloca-tions to lower-volatility assets to gain diversifica-tion benefits, which lowers the expected return ofthe portfolio. To regain a competitive return, lever-age must be applied to the portfolio, primarily onthe low-volatility asset classes.

There are, of course, mathematical limits to thebenefits of leverage (see Ruban and Melas 2010). Forexample, the level of correlations between assets ina portfolio obviously matters a great deal. Butequally important is consistency in correlationsover time. Certainly, 2008 and 2009 were a harshreminder that correlations fluctuate over time, evenbetween bonds and equity.

Figure 3 illustrates these two points—correlations between portfolio assets and the consis-tency of the correlations over time—using a 36-month rolling correlation between equity, repre-sented by the S&P 500 Index, and bonds, representedby the Barclays U.S. Aggregate Index. Panel A showshow volatile the correlations have been over the pastthree decades, reaching a high of 60 percent, or 0.6,in the early 1990s and a low of –40 percent, or –0.4,about 10 years ago. Panel B shows the relative vola-tility of equity and bonds, which also has fluctuateda great deal over the past three decades.

Figure 3. Volatility of the 36-Month Rolling Correlation of Equity and Bonds, 1978–2008

Note: Equity is represented by the S&P 500, and bonds are represented by the Barclays U.S. Aggregate Index.

A. Volatility of Correlation

1

0

–178 0888 98

B. Relative Volatility of Equity and Bonds

6

3

078 0888 98

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At Par with Risk Parity?

Location also makes a difference. In Figure 4, Iused long-term data to compare the level of effi-ciency between equities and bonds in differentcountries. As before, I ignored correlations. It isclear that the level of efficiency is not constant fromcountry to country. Some countries, such as Swit-zerland (CH), have higher efficiency in bonds, andsome countries, such as Australia (AUS), havehigher efficiency in equity. Because various coun-tries have different efficiencies in assets and thusdifferent Sharpe ratios, earning a certain returnrequires different amounts of leverage. For exam-ple, using historical data, investors in Swedenwould only need to leverage their portfolios 1.4times to earn an 8 percent return but investors inItaly need closer to 4.0 times.

The benefits of leverage also fluctuate with bor-rowing rates, especially in fixed income. Lower bor-rowing costs mean that leverage has a lot morevalue, and changes in interest rates cause shifts in theminimum-variance portfolio, the capital market line,and most likely, the efficient frontier. Leverage alsoincreases uncertainty, and higher levels of uncer-tainty make probabilistic calculations suspicious.

This issue is particularly relevant to backtesting andis extremely problematic when the forecaster is fac-ing unknown probability distributions. Such risks askurtosis, skewness, liquidity, counterparty, and con-tagion, among others, are all magnified.

Finally, low volatility is not the same as low risk.Looking at risk exclusively through the lens of vol-atility lacks dimension. For example, demographicchanges or secular shifts are not captured by vola-tility. I doubt that 10 years ago many investors werevery worried about the possible default or down-grade of developed European countries’ sovereigndebt. Historical correlations and volatilities do notcapture this type of unlikely, but possible, event. Ofcourse, these types of problems will also hurt atraditionally allocated portfolio. The difficulty isthat when a portfolio uses leverage, the unexpectedbecomes more relevant and makes other types ofrisk management techniques more important. Inother words, risk parity does not get rid of the tail.It just switches from one type of tail, equity risk, toanother, the unknown.

Products and ImplementationsThere are several key differences in products andimplementation among risk parity providers.These differences include leverage, risk exposures,asset classes or vehicles, and beta-only versus betaplus alpha.

Leverage. A product can have differentamounts of leverage—minimum, average, andmaximum levels. Leverage can also be imple-mented in various ways. For instance, it can beachieved through borrowing and leveraging theentire portfolio or through levering up only spe-cific assets by using derivative instruments.

Risk Exposures. The types of risk exposureincluded in risk parity portfolios vary. Althoughmost managers focus on equity, interest rate, andinflation betas, other managers include credit riskand other factors in their allocations.

Asset Classes. The asset classes and invest-ment vehicles used to express a manager’s viewsalso vary. Considerable differences exist amongportfolios (for example, OTC swaps versus a listedfuture or exchange-traded funds versus individualstocks).

Beta-Only vs. Beta Plus Alpha. Some prod-ucts are quantitative beta-only, others combine betaand qualitative alpha, and yet others are solelyalpha strategies (qualitative and/or quantitative).

Figure 4. Efficiency Level of Equities and Bonds for Various Countries

Note: AUS is Australia, CH is Switzerland, and BE is Belgium.

Source: Elroy Dimson, Paul Marsh, and Mike Staunton, Triumphof the Optimists: 101 Years of Global Investment Returns (Princeton,NJ: Princeton University Press, 2002).

Sharpe Ratio, Equity

AUS

U.S.

CH

BE

Sharpe Ratio, Bonds

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Liquidity and Fees. All of these product dif-ferences affect the level of fees and the level ofliquidity. Liquidity is usually a little bit lower andfees are a little bit higher than those of more tradi-tional beta exposures.

Volatility Estimates. Another important andinteresting difference is how volatility is estimatedas a key input to risk parity allocation. Some man-agers use a more backward-looking historical viewto build portfolios, whereas others have a moreforward-looking approach and try to forecast futurevolatilities.

Benchmark and Attribution. A major deci-sion is the benchmark that will be used to measurethe performance of the risk parity product becauseit greatly affects performance attribution and riskmanagement. Although I am not convinced it is theright benchmark to use, the traditional 60/40equity/bond split is commonly used. Other optionsinclude the policy portfolio, cash, and even T-bills.My preference is to use the policy portfolio as an“opportunity cost” index. But remember that inmost cases, a levered product is being comparedwith an unlevered benchmark, which will probablyrequire some testing and adjustments.

Tolerance for Tracking. A high tolerance fortracking is needed because risk parity portfolios canand will underperform under certain market condi-tions. They will also, of course, outperform in othermarket conditions, but that scenario is usually lessof a problem. Risk parity investors thus must keepa long-term view, which can be a challenge with

intermediate-term performance evaluation cycles,as well as changes in trustees, consultants, andinvestment staff.

ConclusionRisk parity has profound implications because itconcerns such important issues as volatility or, inother words, risk management, dynamic beta allo-cations, and market efficiency. Yet, it still appears asa work in progress. The decision to implement riskparity depends on an investor’s beliefs about theseissues, as well as his or her own needs and resources.For all of its benefits, its trade-offs can be consider-able. Specifically, investors need to assess their abil-ity to implement adequate risk management andperformance attribution practices, which are a seri-ous challenge with alternative investments. Thechoice of risk parity solutions is also based on inves-tors’ need for efficiency, which can be found bycomparing the Sharpe ratio of their portfolios withthat of risk parity products.

Ultimately, investors cannot have it all. There ismore to risk than volatility, and volatility parity isnot risk parity. Thinking about risk is a necessarystep in the right direction because path dependencymatters a great deal. But higher efficiency throughextreme diversification also creates the need forleverage, and with leverage comes uncertainty. Effi-ciency makes a portfolio sharper, but portfolioreturns pay the bills, and with leverage, the devil isstill in the left tail.

This article qualifies for 0.5 CE credits.

REFERENCES

Grossman, Sanford J., and Joseph E. Stiglitz. 1980. “On the Impos-sibility of Informationally Efficient Markets.” American EconomicReview, vol. 70, no. 3 (June):393–408.Maillard, Sébastien, Thierry Roncalli, and Jérôme Teïletche. 2010.“On the Properties of Equally-Weighted Risk Contributions Port-folios.” Journal of Portfolio Management, vol. 36, no. 4 (Sum-mer):60–70. Markowitz, Harry. 1952. “Portfolio Selection.” Journal of Finance,vol. 7, no. 1 (March):77–91.

Marks, Howard. 2011. The Most Important Thing: UncommonSense for the Thoughtful Investor. New York City: ColumbiaUniversity Press.Ruban, Oleg A., and Dimitris Melas. 2010. “The Perils of Parity.”MSCI Barra Research Paper No. 2010-19 (May).Sharpe, William F. 1964. “Capital Asset Prices: A Theory ofMarket Equilibrium under Conditions of Risk.” Journal of Finance,vol. 19, no. 3 (September):425–442. Tobin, James. 1958. “Liquidity Preference as Behavior TowardsRisk.” Review of Economic Studies, vol. 25, no. 2 (February):65–86.

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Q&A: Kunz

Question and Answer SessionSamuel Kunz, CFA

Question: How is the leverage obtained in most risk parity programs?

Kunz: The most common approach is to leverage specific assets through the use of futures, which lowers counterparty risk. And for those who manage liquid-ity well, this approach also lowers borrowing risk.

Question: What other risks do you see in risk parity portfolios?

Kunz: With leverage comes contagion risk. Counterparty risk and cash management risk are also present in risk parity portfolios.

Question: If volatility parity is not risk parity, then how do you achieve risk parity?

Kunz: Volatility, from a statisti-cal point of view, lacks dimension. From an operational point of view, there is certainly more to risk than just volatility. I give examples of risk as demographic change and such long-term secu-lar shifts as changing technologies as well as natural disasters. Risk is not just a number. Volatility is a narrower view of the world than is the concept of risk.

Howard Marks (2011) starts one of the three chapters he

devoted to risk in his last book with a quote from Elroy Dimson that astutely captures this idea: “Risk means more things can hap-pen than will happen.” Investors face a myriad of risks, including counterparty, model, concentra-tion, headline, pricing, and of course, leverage.

In other words, reducing anintricate concept into a singlenumber might indeed create afalse sense of confidence and thuscreate the risk of missing the bigpicture.

Question: So, risk parity is not risk parity?

Kunz: Correct, risk parity is vol-atility parity. Risk parity is a good step in the right direction, but I do not think it is a finished product. When I was evaluating risk parity, I thought about a product that would use semivariance as the input for risk because we all know that the good side of volatility is performance.

Volatility was good, for exam-ple, in 1998 when the equity mar-ket was going up. But volatilityalso has a bad side, so maybe theanswer is a product that focusesexclusively on the negative side ofthe volatility.

Question: How important is rebalancing in a risk parity program?

Kunz: Rebalancing is extremely important. Because the relative volatilities of the assets included in a risk parity portfolio fluctuate over time, allocations need to be adjusted almost continuously. The use of leverage means that rebalancing needs to occur not only at the asset level (relative exposures), but also at the overall portfolio level because most of these strategies target specific vol-atility levels.

Again, some managers rely on historical data to adjust the weightings, and others use a more forward-looking approach in an attempt to forecast volatilities. Interestingly, one might think about risk parity almost as a con-vex strategy.

Because spikes in volatilitygenerally occur during down-turns, positions in assets with thelargest volatility expansions aretypically reduced the most intimes of stress (and vice versa). Ina risk parity strategy, investorsbuy when prices rise and sellwhen they fall, which tends togenerate a unique and interestingpattern of results as long as thereis a trend.

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