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less in fixed income (Montier 2010). ... By Timothy B. Barrett, CFA®, Donald Pierce, CFA®, James Perry, CAIA, and ... Figure 1 shows the cumulative growth of $100 invested in the S&P 500 and $100 in- ... ing uncomfortable levels of debt as a.
A reprinted article from Volume 12, Number 2, 2011

I nvestment Consulting T H E

IMCA

J O U R N A L

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O F

investment management consultants association

Dynamic Beta

Getting Paid to Manage Risks By Tim othy B. B a r re tt, CFA ® , D o n a l d Pi e rc e , C FA ® , Ja m e s P e r r y, C A I A , a n d A r u n M u ra l i d h a r, P h D

Introduction

D

ynamic beta is a program that dynamically allocates to beta assets based on formal rules. It contrasts with standard meanvariance optimization and static riskparity approaches, which are static. Dynamic beta lowers the overall risk of the fund—where risk includes volatility of returns plus drawdown1—while earning a positive return.2 A dynamic beta program implemented through an overlay and customized to each investor’s needs can help manage portfolio risk from an asset-only perspective or an assetliability perspective. The introduction of dynamic beta provides substantial improvements for traditional investment portfolios as well as portfolios with risk-parity approaches and allocations to alternatives. The dynamic beta program differs from a global macro/global tactical asset allocation program in its objectives and design. This article proposes that dynamic beta is a more-intelligent, more-informed approach to dynamically manage risk and return. It also places the dynamic beta program within the constraints of typical institutional investment portfolios by addressing governance and implementation issues. Background The 2000–2010 decade served up two major financial-market crises that

demonstrated the inadequacies of current portfolio management theory and practice. After 2000–2002, many investors went the way of the much-heralded Yale endowment, investing more in alternative investments (private equity, commodities, and hedge funds) and less in fixed income (Montier 2010). For them, it was worth relinquishing liquidity and moderating fees to earn high returns from these apparently uncorrelated investments. The Yale model, however, favored a static long-term allocation to assets with assiduous rebalancing to long-term targets derived from the optimization process, despite the fact that markets are dynamic and long-term return forecasts were probably highly suspect (Swensen 2009). However, the 2008 crisis discredited the naïve approach that called for a mix of trading strategies and illiquidity, with constant rebalancing, to achieve consistent risk-adjusted returns for institutional investors. With the 2008 crisis came talk of a “new normal,” where globally anemic growth and high debt pushed investors into balanced portfolios or risk parity. Risk parity is an attempt to equalize assets in terms of risk contribution by using leverage on the less-volatile assets.3 Increasingly clients are adopting a more risk-based allocation. The most notable major investors to have adopted a risk-

based allocation are CalPERS (Diamond 2010) and CalSTRS (Vasan 2010); some more-adventurous funds have levered up the allocations to raise the return on investment. This article demonstrates that both those approaches—static allocation and risk parity—are unsatisfactory. Both the Yale model and the riskbased approaches4 are static approaches to investing in dynamic markets and hence are likely to fail (Montier 2010; Inker 2011). The question is when and by how much, because these approaches do not consider valuation or prevailing market environment. In other words, if it’s always correct to allocate 60 percent of a portfolio to stocks, then valuation does not matter. This is where dynamic beta is different—it explicitly relies on valuation and related market factors that capture the relative attractiveness of assets in the prevailing environment. Rather than moving to the risk-based approach or allocating more to alternatives, funds would be better served by implementing a dynamic beta program that complements the strategic asset allocation (SAA). Naïve dynamic strategies that change the allocation to risky assets based purely on the funded status of the plan (termed “pension de-risking” in Mercer 2009) have been proposed and we will demonstrate how a well-designed dynamic beta program will be preferred to this strategy.

© 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

THE PENSION CRISIS

The idea for a dynamic beta program originated in an intelligent rebalancing program implemented in 2006 for a public pension plan—the San Bernardino County Employees Retirement Association. It corrects for the shortcomings of a static SAA approach or a naïve dynamic approach by creating a stream of positive returns that is negatively correlated to the SAA. A negative beta asset earning a positive return may seem like a violation of finance theory, but traditional finance theory only comments on the beta of static allocations to assets and hence misses this opportunity to improve returns and reduce risk through a dynamic approach (Muralidhar 2011b; Seigel 1993). Understanding the Problem Here we use defined benefit pension funds as a proxy for institutional investors, but the extension to defined contribution funds, endowments, foundations, or even sovereign wealth funds is trivial. Let’s acknowledge that most pension funds are short a stream of benefit cash flows, which can be seen as a fixed income instrument.5 This acknowledgement has led in large part to the growth of liability-driven investment (LDI) strategies, where investment banks and asset managers sell long-duration fixedincome assets to pension funds. These long-duration fixed-income assets often are in long-term bonds or sometimes a portfolio of futures or swaps for the more innovative client. It is easier to engage in an LDI strategy when a fund has more assets than liabilities (i.e., a funded status greater than 100 percent), but before 2000 many pension funds had a substantial long position in stocks. In effect, pension funds were betting that a long equity position and a short bond position would lead to better sol­vency because the return on equities was expected to dwarf the return on bonds and continually improve funded status/solvency. But pre-2000 no one considered the correlation between assets and liabilities in this equation or the possibility that the return on equities

FIGURE 1: WHY PENSION FUNDS GET INTO TROUBLE 250.00 200.00 150.00 100.00 50.00

S&P 500 Equity Index

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11 1/

10

1/

09

30-Year U.S. Treasury Futures

Source: Bloomberg

might exceed the return on assets for long periods (e.g., the post-2000 decade). Recommendations to increase the liability hedge and reduce risky asset allocations as funded status declined were not adopted until much later.6 Figure 1 shows how pension funds periodically have suffered solvency crises when the paths of bonds and stocks have diverged, e.g., during 2000–2002 and in 2008. Assume a pension plan that has a funded status of 100 percent. Figure 1 shows the cumulative growth of $100 invested in the S&P 500 and $100 invested in thirty-year Treasury futures on January 1, 1998, through August 2011. We use the S&P 500 as a proxy for the pension fund’s assets and the thirty-year futures as a proxy for its liabilities. So, when the S&P 500 returns exceed the thirty-year bond returns, the funded status of our simplified pension plan improves (as shown by the arrows pointing up); conversely, when bond returns exceed the S&P returns, the funded status of the pension fund declines (arrows pointing down). However, once the funded status falls below 100 percent and into underfunded territory, assets must grow considerably faster than liabilities grow in order to cover the liabilities. So even in periods where equities perform better

than bonds, underfunded pension funds may experience declines in funded status because of the initial funded status. Figure 1 shows that the two crises of the past decade led to substantial declines in funded status, necessitating higher contributions (anathema for the sponsor) or drastic remedial measures (reducing pensions or making dramatic changes to investment policy). Indeed, senior management has been asking many chief investment officers (CIOs) to de-risk corporate pension funds that have funded status of less than 100 percent to prevent further “large contribution” events. But sadly many of these CIOs also are being advised to either extend duration of their fixed income portfolios or implement equity put (or collar) strategies that lower risk but also reduce future fund solvency, neither of which are robust long-term solutions. U.S. Treasury assets have been the safe haven during the tech-bubble burst and its aftermath (late 1990s through 2002) and the housing and credit crisis (2008 through the present). In 20-20 hindsight, a naïve solution to portfolio underperformance would be to lever up fixed income because an overallocation to bonds in periods of crisis seems to provide protection. But to move to this approach in 2011 would

© 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

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FIGURE 2: S&P 500 AND HFRI—WHY FUNDS GOT INTO TROUBLE WITH ALTERNATIVES 250 230 210 190 170 150 130 110 90 70

31/01/2000 30/04/2000 31/07/2000 31/10/2000 31/01/2001 30/04/2001 31/07/2001 31/10/2001 31/01/2002 30/04/2002 31/07/2002 31/10/2002 31/01/2003 30/04/2003 31/07/2003 31/10/2003 31/01/2004 30/04/2004 31/07/2004 31/10/2004 31/01/2005 30/04/2005 31/07/2005 31/10/2005 31/01/2006 30/04/2006 31/07/2006 31/10/2006 31/01/2007 30/04/2007 31/07/2007 31/10/2007 31/01/2008 30/04/2008 31/07/2008 31/10/2008 31/01/2009 30/04/2009 31/07/2009 31/10/2009 31/01/2010 30/04/2010 31/07/2010 29/10/2010

50

HFRI

Index S&P

Source: Bloomberg and HFRI

FIGURE 3: DISTRIBUTION OF DAILY S&P 500 RETURNS (NOVEMBER 2001–APRIL 2011)

15.00%

Flat Daily Return >1%

10.00% Daily Return

be equivalent to fighting past battles using static approaches—and that’s what some risk-parity approaches have done. Their allocations to bonds have risen because bonds have been less volatile than stocks (and have provided a better return), hence risk equalization across portfolio assets required greater allocation to bonds. However, a crisis in the fixed income markets (e.g., one triggered by concerns about the creditworthiness of a government in Greece, Ireland, Italy, or another highly indebted country such as Japan or the United States) could spark a sell-off in both the bond and equity markets, which may cause funds with levered portfolios to take it on the chin twice and thus suffer irreparable damage. This scenario is not a low-probability event because many developed countries are fast approaching uncomfortable levels of debt as a percentage of gross domestic product (GDP), have been subject to ratings downgrades, and have no tangible measures in place to change the trajectory of the debt-to-GDP ratio. Figure 2 shows the progress of the Hedge Fund Research Index (HFRI) Weighted Composite Index and the S&P 500 U.S. Equity Index during 2000–2002. Looking at figure 2, one can see how the 2000–2002 crisis led to many funds taking the alternative route, where assets suffered less loss. But private equity is ultimately nothing more than a levered small-cap bet (i.e., it has higher beta than the S&P 500 index) and in the long run, hedge funds proved to have more beta than anticipated—leading to a discrediting of the “Yale approach.” The decline of hedge funds in 2008 (shown in figure 2) and the decline in private equity (not shown in figure 2 because indexes do not capture the true destruction of value due to infrequent marking-to-market) highlights why many funds experienced unanticipated asset declines and solvency issues. That is why funds heavily invested in private equity (which one could proxy with the Russell 2000 U.S. Small Cap Index as a

5.00%

Positive Daily Return 53%

Best Return +11.58% 10/09/2008

0.00% –5.00% –10.00% –15.00%

Worst Return –9.03% 10/13/2008 Percentage of time in return range

Source: Broadmark Asset Management

higher beta version of the S&P 500) and hedge funds suffered in 2008, and the fact that hedge funds fell less than equities was no consolation because you still cannot pay pensions with “less losses.” The Need for a Dynamic Beta Program Static strategic portfolio allocations in dynamic markets are a prescription for trouble. Beta, the biggest contributor to risk and return, has to be managed.

John Mauldin (2011, 77) probably makes the best case for such a program going forward: The period of low volatility of GDP, industrial production, and initial unemployment claims is now over. For a period of more than twenty years, excluding the brief 2001–2002 recession, volatility of real economic data was extremely low. Going forward, higher economic volatility, combined with a secular downtrend in

© 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

Volume 12 | Number 2 | 2011

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THE PENSION CRISIS

TABLE 1: COMPARING VARIOUS PORTFOLIO RETURNS AND RISKS (JANUARY 2000−SEPTEMBER 2010)

economic growth, will create more frequent recessions. This is likely to lead to more market volatility as well. In essence, volatility in markets has increased and will continue to increase. In addition, substantial assets are under the control of hedge funds, which are less bound to benchmarks and are allowed to leverage portfolios within limits. This hedge-fund leveraging will make money move a lot faster as hedge funds take advantage of loose monetary policy or any future crisis, real or perceived. The increasing allocation of assets to these relatively unconstrained strategies will increase the speed and amplitude of market movements. In such an environment, sticking to a static asset allocation (with or without leverage) without a clearly articulated and implemented risk management strategy is more than likely a prescription for further troubles. Muralidhar (2011a) demonstrates how the entire portfolio should be managed dynamically in such an environment using an approach similar to the one provided here just for beta. Figure 3 shows daily returns of the S&P 500 Index, which had negative performance on 46 percent of the days during November 2001–April 2011.7 A static asset allocation approach with long positions would have ignored the dynamic profile of this asset market performance and effectively bet that negative performance in the portfolio, for the same percentage of time and with the same drawdown profile as the benchmark asset, would be acceptable. Adding more assets to the mix to mitigate this risk does not really solve the problem. Risk Measurement versus Risk Management Given the massive portfolio drawdowns in the two crises (some as large as 20 percent), many funds have started to focus on risk management. But in most request-for-proposals (RFPs) there seems to be a disconnect between risk mea-

Portfolio I

Portfolio II

Risk Parity

HFRI Weighted Composite

Macro

Annualized Return

2.90%

3.14%

10.45%

6.45%

7.31%

Annualized Risk

5.49%

9.81%

13.89%

9.31%

6.88%

Return/Risk

0.30

0.23

1.12

0.94

1.33

Drawdown

–36.12%

–57.76%

–29.38%

–23.45%

–7.49%

59%

58%

71%

67%

64%

–368%

–416%

–316%

–341%

–136%

Success Ratio Drawdown as % Risk

TABLE 2: COMPARING THE CORRELATION AMONG VARIOUS PORTFOLIOS (JANUARY 2000−SEPTEMBER 2010) Portfolio I Portfolio II

Portfolio I

Portfolio II

Risk Parity

HFRI Weighted Composite

Macro

100%

93%

59%

74%

18%

100%

Risk Parity HFRI Weighted Composite

68%

84%

26%

100%

61%

39%

100%

57%

Macro

surement and risk management. Risk measurement focuses on implementing systems to calculate ex-ante volatility and drawdown. Risk management focuses on adjusting portfolios to changes in the market along the lines of the dynamic beta program we propose below. Our own experience with risk measurement systems is that they produce useful reports but do not inform CIOs on how to navigate portfolios to evade bad risks. Yet we are seeing more RFPs that are heavy on measurement and less focused on management, which we believe will result in systems that are unlikely to help. Tables 1 and 2 show how a typical 60/40 portfolio performs and is correlated to a smattering of strategies— namely, 1) a hypothetical risk-parity portfolio8; 2) the HFRI Weighted Composite Index; and 3) the HFRI Macro Funds Index. For ease of analysis, we also considered two variations of the 60/40 portfolio: 1) a simple 60-percent allocation to the S&P 500 Index plus 40-percent allocation to the Barclays Aggregate Index (Portfolio I) to represent a U.S.-centric portfolio, and

100%

2) a 60-percent allocation to the MSCI All Country World Index plus 40-percent allocation to the Merrill Lynch High Yield Index to reflect a riskier, more global portfolio (Portfolio II). The period of analysis for these tables is January 2000–September 2010. Table 1 shows the annualized return of monthly observations, annualized volatility of the same monthly observations, the return/risk ratio, the drawdown of these same observations,9 the success ratio (i.e., the batting average or percentage of positive months), and drawdown as a percentage of the volatility to give an indication of the magnitude of the drawdown relative to volatility. To compare funds with different volatilities and individual risk characteristics, the returnrisk ratio, success ratio, and drawdown as a percentage of risk lend themselves to an easy comparison. The correlation matrix in table 2 shows that, with the exception of the macro, these portfolios are all highly correlated. However, looking at the returnrisk characteristics one can see the appeal of the risk-parity approach because it backtests (i.e., performs on historical

© 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

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data) very attractively versus Portfolio I and Portfolio II in terms of return-risk ratio, absolute drawdown, and drawdown as a percentage of risk. However, a 29-percent drawdown for risk parity is nothing to sneeze at; this is equivalent to a $100 portfolio declining to $71. Therefore, funds adopting a risk-parity or a risk-based allocation approach to SAA should find any strategy that can further decrease this drawdown. Case Study: Designing a Dynamic Beta Program, Version 1.0 The San Bernardino County Employees Retirement Association (SBCERA) implemented an “informed rebalancing program” in July 2006 that had many of the desirable characteristics of an optimal dynamic beta program.10 One goal at SBCERA was to improve governance of the pension portfolio through a disciplined and formal process, similar to what’s expected of external managers in managing stock and bond portfolios (Barrett 2006). This resulted in rules that used specific economic factors to value assets and decide to be overweight or underweight within explicit and formal ranges also based on the rules. For instance, if an asset was underweight and relatively undervalued (i.e., relative to other assets), the rules would recommend increasing the weight. This approach to rebalancing was recommended in Muralidhar (2007) and Muralidhar and Muralidhar (2009) and in some ways is more practical than Hodgson (2006) or Brock (2005). Sharpe (2010) writes about the flaws of traditional rebalancing and has proposed a

new approach called “adaptive asset allocation” (Sharpe 2010; Flood 2010).11 A dynamic beta program is the next step in the evolution of asset allocation. It allows for a formal quantitative process to determine which risks are being best compensated on a relative basis. Everyone knows to “buy low and sell high,” but few have reliable indicators of what is low enough or high enough. A dynamic beta program can provide indications of high-enough and lowenough as well as the pause required to wait for the next opportunity. The program design presented to the SBCERA board included the following: 1. The rules developed to tilt the portfolio beta would be based on peer-reviewed journal articles to provide a clear basis for decision making,12 resulting in rules that have a decidedly economic or valuation bias. 2. The goal of the program would be to use informed rebalancing to achieve a positive excess return relative to letting the portfolio drift or adopting a range rebalancing approach. 3. The tilts would be limited to assets in the strategic asset allocation and the sum of the tilts would be zero (i.e., an overweight in one asset will be offset with an underweight in another). (This applied to U.S. stocks, international stocks, and U.S. bonds initially; other strategies later were developed for currency, large-capitalization versus small-capitalization stocks, value versus growth stocks, and credit versus core bonds.)

TABLE 3: DYNAMIC BETA EXCESS RETURNS AND RISKS (JANUARY 2000−SEPTEMBER 2010) Dynamic Beta Annualized Return

0.60%

Annualized Risk

0.98%

Return/Risk

.61%

Drawdown

–1.27%

Success Ratio

50%

Drawdown as % Risk

4.

5.

6.

7.

8.

–129%

The tilts in any asset class would be limited to the ranges permitted by the board. The tilts would be adjusted just once a month—initially through cash reallocations that are part of the usual monthly process of managing pension funds, then later through derivatives. The informed rebalancing program would have a turnover similar to that of the 3-percent range rebalancing program. Because this approach appears to lower the drawdown of the fund more than other strategies, the rebalancing ranges were increased from 3 percent to 5 percent for each asset class. In response to concerns about data mining, the investment consultant requested an out-of-sample test on results from 1962–1982. This test also provided information about a period when markets were significantly different from the past two decades.

TABLE 4: COMPARING THE CORRELATION AMONG VARIOUS PORTFOLIOS (JANUARY 2000−SEPTEMBER 2010) Portfolio I Portfolio I

100%

Portfolio II Risk Parity HFRI Weighted Composite Macro

Portfolio II

Risk Parity

HFRI Wtd Composite

Macro

Dynamic Beta

93%

59%

74%

18%

–29%

100%

68%

84%

26%

–15%

100%

61%

39%

–20%

100%

57%

–29%

100%

Dynamic Beta

–15% 100%

© 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

Volume 12 | Number 2 | 2011

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THE PENSION CRISIS

Interestingly, the San Diego County Employees Retirement Association (SDCERA) staff made a similar recommendation to its board in 2006 for the effective management of beta— a program they called Beta Engine. At the time, this recommendation went against the grain of most rebalancing recommendations, which focused on lowering tracking error and argued for tighter ranges. Recall that policy implementation at the time implied that any deviation from the strategic target detracted from achieving the board’s risk

and return expectations (Swensen 2009); consequently, the number of overlay managers in the industry to effect policy implementation increased (which ironically is a building block of a more dynamic approach because these overlay managers can be used to implement the dynamic beta programs). Implicit in achieving the SBCERA goal of reducing the drawdown was the result that the rules make money, and they make money when the target SAA portfolio is suffering. Statistically speaking, the rules lead to a positive excess re-

FIGURE 4: EXAMINING THE NEGATIVE CORRELATION OF DYNAMIC BETA TO REFERENCE PORTFOLIOS 6-MONTH ROLLING 0.8

0.6

0.4

0.2

–0.2

04/07/2000 20/09/2000 07/12/2000 23/02/2001 14/05/2001 31/07/2001 17/10/2001 03/01/2002 22/03/2002 10/06/2002 27/08/2002 13/11/2002 30/01/2003 18/04/2003 07/07/2003 23/09/2003 10/12/2003 26/02/2004 14/05/2004 02/08/2004 19/10/2004 05/01/2005 24/03/2005 10/06/2005 29/08/2005 15/11/2005 01/02/2006 20/04/2006 07/07/2006 25/09/2006 12/12/2006 28/02/2007 17/05/2007 03/08/2007 22/10/2007 08/01/2008 26/03/2008 12/06/2008 29/08/2008 17/11/2008 03/02/2009 22/04/2009 09/07/2009 25/09/2009 14/12/2009 02/03/2010 19/05/2010 05/08/2010

0

–0.4

–0.6

–0.8

–1.0

–1.2 6-Month Rolling Correlation of Portfolio I vs. Dynamic Beta 6-Month Rolling Correlation of Portfolio II vs. Dynamic Beta

Source: Bloomberg and HFRI

TABLE 5: SUMMARY STATISTICS PRIOR TO ALLOCATION TO DYNAMIC BETA (JANUARY 2000–SEPTEMBER 2010)

Annualized Return Annualized Risk

Portfolio I

Portfolio II

Risk Parity

HFRI Weighted Composite

Macro

Dynamic Beta

2.90%

3.14%

10.45%

6.45%

7.31%

0.60%

9.81%

13.89%

9.31%

6.88%

5.49%

0.98%

Return/Risk

0.30

0.23

1.12

0.94

1.33

0.61

Drawdown

–36.12%

–57.76%

–29.38%

–23.45%

–7.49%

–1.27%

Success Ratio Drawdown as % Risk

59%

58%

71%

67%

64%

50%

–368%

–416%

–316%

–341%

–136%

–129%

turn that is negatively correlated to the target portfolio. Previously such negative correlation was limited to static put option strategies, where the negative correlation was ensured by the choice of instrument, but where one had to pay for insurance that the put provided. But by finding rules that create positive excess with negative correlation to the reference portfolio in effect pays you to manage risk. For simplicity, we will refer to this as dynamic beta. To avoid data mining in demonstrating the results, we use the results of the model developed in 2005 and implemented in 2006. The model was found to be robust over different economic cycles, including the outof-sample 1962–1982 period. Table 3 shows the excess-return and risk statistics obtained.13 Note that these are excess returns and different from the returns in table 1, which would be core returns; these excess returns are returns generated from deviating from a given static SAA. Table 4 is similar to table 2 and shows returns for the informed rebalancing in the dynamic beta column as well as the correlations between investment approaches. Because the intelligent rebalancing program generates positive excess return during 2000–2010 (table 3) and is negatively correlated to the reference portfolios (table 4, right-hand column), we know that such a program can be designed with these unique characteristics. Figure 4 shows that the negative correlation is dynamic: When beta does poorly (e.g., 2000–2002, 2008), the correlation is negative and dominantly so; when beta does well, the correlation is less negative. In a perfect world, the correlation would be zero to positive when beta is rising and negative when beta is falling, but this is not feasible. Application So, what would happen to portfolios with an allocation to a dynamic beta program? Would these portfolios achieve lower drawdowns?

© 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

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A dynamic beta program can be run using futures and implementation platforms used to equitize cash or rebalance to neutral daily. Because the sum of all tilts is zero, applying such a program doesn’t increase leverage, it just tilts portfolio beta at the margin. As a result, because most pension funds are good credit risks, the required margin is a fraction of the target risk. For example, using the dynamic beta program implemented by SBCERA, cash required to run a program at a 1-percent target risk on the

entire assets of the portfolio would equal about 0.2 percent of the total assets. Let’s assume that a fund allocates 99 percent of its assets to any of the reference portfolios and keeps 1 percent as cash margin for a dynamic beta program. Recall that Portfolio I and II were simple 60/40 mixes of equity and bond indexes; one purely domestic (Portfolio I) and the other more global (Portfolio II). Each of these new portfolios is referenced by adding “A” to the title so Portfolio IA is equal to 99 percent invested in Portfolio I and

TABLE 6: SUMMARY STATISTICS ASSUMING 1% ALLOCATION TO DYNAMIC BETA (JANUARY 2000−SEPTEMBER 2010) Portfolio IA

Portfolio IIA

Risk Parity A

HFRI Wtd Composite A

Macro A

Annualized Return

3.47%

3.71%

10.95%

6.98%

7.84%

Annualized Risk

9.16%

13.21%

8.87%

6.31%

5.34%

Return/Risk

0.38

0.28

1.23

1.11

1.47

Drawdown

–31.68%

–53.10%

–26.83%

–19.13%

–7.10%

60%

59%

71%

66%

66%

–346%

–402%

–303%

–303%

–133%

Success Ratio Drawdown as % Risk

TABLE 7: HOW DYNAMIC BETA AFFECTS PORTFOLIO I’S DISTRIBUTION OF RETURNS Dynamic Beta Positive

Dynamic Beta Negative

Portfolio I Positive

22.5%

36.4%

Portfolio I Negative

27.9%

13.2%

TABLE 8: HOW DYNAMIC BETA AFFECTS RISK PARITY’S DISTRIBUTION OF RETURNS Dynamic Beta Positive

Dynamic Beta Negative

Risk Parity Positive

39.5%

40.3%

Risk Parity Negative

10.9%

9.3%

1 percent invested in dynamic beta. This is an extreme analysis because we are assuming collateralization that exceeds what is required by a substantial amount, but since we penalize all portfolio options equally, it does not matter in the relative analysis. Now let’s examine the portfolio risk characteristics: volatility, drawdown, and the ratio of drawdown to volatility of the original portfolios (table 5) to the new portfolios, which include an allocation to a dynamic beta program (table 6). Table 6 shows that delevering the overall portfolio by placing 1 percent in the dynamic beta program results in higher returns, lower volatility of returns, lower drawdowns, and better ratios of success and drawdown to volatility. The biggest improvements are to the HFRI Weighted Composite (which should be an alert to all investors in funds of hedge funds) and the traditional U.S. 60/40 portfolio, but even the impact on the risk-parity portfolio is nontrivial. How Dynamic Beta Leads To Enhanced Risk Management The simple dynamic beta program alters outcomes by managing the tails. Traditional tail risk hedges involve buying expensive out-of-the-money options. But tail risk management can be achieved less expensively through the dynamic beta program. For example, table 7 shows Portfolio I has negative performance in 41.1 percent of the months (i.e., the sum

TABLE 9: CORRELATION OF SPECIFIC HEDGE FUND STYLES TO DYNAMIC BETA AND 60/40 PORTFOLIOS (JANUARY 2000−SEPTEMBER 2010)

Annualized Return Annualized Risk Return/Risk Correlation to Dynamic Beta Correlation to Portfolio I (60/40)  beneficial correlation

HFRI EH: Short Bias Index

HFRI Equity Hedge (Total) Index

HFRI Event– Driven (Total) Index

HFRI Macro (Total) Index

HFRI Relative Value (Total) Index

HFRI RV: Fixed Income– Convertible Arbitrage Index

Dynamic Beta

Portfolio I (60/40)

HFRI ED: Merger Arbitrage Index

0.61%

3.30%

6.13%

4.46%

5.81%

8.01%

7.47%

7.47%

7.47%

6.10%

0.97%

9.78%

3.53%

19.07%

9.18%

6.94%

5.50%

4.64%

8.71%

5.01%

0.63

0.34

1.74

0.23

0.63

1.15

1.36

1.61

0.86

1.22

–0.60

–0.41

0.58

–0.55

–0.48

–0.19

–0.41

–0.37

–0.46

0.59

–0.68

0.76

0.72

0.18

0.59

0.50

0.60

–0.60

HFRI RV: MultiStrategy Index

 non-diversifying correlation

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Volume 12 | Number 2 | 2011

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of the last line in the table, but also one minus the success ratio from table 2). In approximately 75 percent of those negative months (27.9% divided by the sum of 27.9% and 13.2%), dynamic beta had positive performance, indicating that the dynamic beta program was providing a positive contribution when the portfolio was underperforming. This means that losses were mitigated 75 percent of time the original portfolio performance was negative. The answer to the question of whether negative performance of the original portfolio could have been overcome by the positive dynamic beta performance is a function of the amount of risk allocated to the dynamic beta program; tables 5 and 6 show that allocating just 1 percent to dynamic beta led to a mild improvement in the success ratio. Conversely, the dynamic beta program created negative returns when Portfolio I was positive (table 7, upper right), but this happened only

62 percent of the time that Portfolio I was positive (36.4% divided by 58.9%). Thus a dynamic beta program helps improve daily mean returns and their distribution. Table 8 shows a similar comparison of returns for the risk-parity approach. The risk-parity portfolio was the most-robust base portfolio, yet dynamic beta provides insurance when risk parity underperforms; this can also be seen by comparing the risk parity columns in tables 5 and 6. Application to Alternatives: Hedge Funds, Funds-of-Hedge Funds, and Private Equity In our analysis, we were surprised to find that many hedge funds and funds of hedge funds correlated strongly to the portfolios of pension funds and endowments. Table 9 shows correlations of the dynamic beta program and the typical 60/40 portfolio over January 2000–September 2010. Note that the 60/40 portfolios are positively correlated with just about every hedge fund style in the HFRI database (e.g.,

distressed, macro, equity hedged, fixed income, relative value) and negatively correlated with only short-biased. The dynamic beta program negatively correlated with every style except equity market neutral (uncorrelated) and short-biased (0.58). In analyses of a series of funds of funds not reported here, we found the correlation of dynamic beta programs to be negative and dynamic, much like that shown in figure 4. In short, this simple program could have helped all the funds of funds and portable-alpha strategies minimize drawdowns in 2008. With respect to private equity, David Deutsch, former chief investment officer at SDCERA, recognized as far back as 2006 that private equity and real estate essentially had a lot of embedded beta (one could even argue that these were levered exposures to the small-cap market). As a result, SDCERA developed and implemented its Beta Engine program with one additional twist. SDCERA applied its Beta Engine program to its entire portfolio—both the public market

TABLE 10: SUMMARY STATISTICS USING ASSET-LIABILITY MANAGEMENT PERSPECTIVE (JANUARY 2000−SEPTEMBER 2010) HFRI Weighted Composite 10-Year Duration

Portfolio I 10-Year Duration

Portfolio II 10-Year Duration

Risk Parity 10-Year Duration

Annualized Return

–3.15%

–2.90%

4.41%

0.40%

1.27%

Annualized Risk

8.88%

Macro 10-Year Duration

12.87%

17.11%

9.97%

11.26%

Return/Risk

–0.24

–0.17

0.44

0.04

0.14

Drawdown

–56.01%

–74.11%

–39.42%

–43.43%

–19.49%

50%

53%

64%

50%

47%

Drawdown as % Risk

Success Ratio

–435%

–433%

–395%

–386%

–220%

Correlation to Liability

–9%

–21%

31%

–22%

9%

TABLE 11: SUMMARY STATISTICS USING ASSET-LIABILITY MANAGEMENT PERSPECTIVE WITH DYNAMIC BETA (JANUARY 2000−SEPTEMBER 2010) HFRI Weighted Composite A 10-Year Duration

Portfolio IA 10-Year Duration

Portfolio IIA 10-Year Duration

Annualized Return

–2.58%

–2.33%

4.90%

0.94%

1.79%

Annualized Risk

Risk Parity A 10-Year Duration

12.41%

16.57%

9.63%

10.94%

8.83%

Return/Risk

–0.21

–0.14

0.51

0.09

0.20

Drawdown

–49.29%

–69.57%

–36.35%

–39.89%

–17.97%

50%

52%

64%

50%

50%

–397%

–420%

–377%

–365%

–203%

Success Ratio Drawdown as % Risk

© 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

8

Macro A 10-Year Duration

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and the private market exposures. In effect, the SDCERA recognition that private equity carried beta exposure, and ensuring that Beta Engine was negatively correlated to equity indexes, effectively ensured that the beta engine/dynamic beta program hedged the drawdown experienced in private equity in 2008 as well. So when most private equity investors were struggling with many general partners making capital calls at the worst possible time as their liquid portfolios were also beaten down, the dynamic beta program was generating attractive cash. Many investors in private equity, because of the delay in how valuations are updated for these investments, may believe that the correlation of private equity to public equity is low, but when the economic value of the underlying investments declines in line with smallcap stocks, implementing a dynamic beta program on the entire fund can help make illiquid investments more liquid and hedge their downside risk.

This is clearly shown by the fact that annualized risk, drawdown, and drawdown as a percentage of risk are lower in table 10 than in table 11. Table 10 also shows the appeal of a general risk-parity portfolio, where the levered bond position acts like a hedge against the liability, as shown by the positive correlation between the risk-parity and the liability stream. However, in all the examples, drawdown in solvency is nontrivial in absolute terms. For example, a drawdown in solvency in the risk-parity example implies a decline from 100-percent solvency to 61-percent solvency in 2008. This drawdown is offset partially by the return of the asset portfolio being greater than the return of the ten-year duration portfolio. However, the ideal ALM dynamic beta program would target a positive return (ideally above the cost of margin) with a positive correlation to liabilities and a negative correlation to the SAA.

The Asset-Liability Management Perspective

Dynamic Beta–Version 2.0

From an asset-liability management (ALM) perspective, a portfolio is successful only if it beats its true benchmark, which in the case of pension funds is the liability. For simplicity, we assume a pension fund portfolio has a ten-year duration achieved through a 23-percent allocation to thirty-year Treasuries and a 77-percent allocation to ten-year Treasuries. Table 10 shows the ALM perspective by presenting performance and risk statistics after subtracting the ten-year portfolio returns from the original reference portfolio returns. Table 11 shows similar statistics for returns of the portfolios with a 1-percent allocation to dynamic beta, also subtracting the ten-year duration return. Tables 10 and 11 show that due to its positive risk management impact on the asset portfolio, the dynamic beta program improves the solvency profile by generating higher returns as well as lowering ALM risks.

Informed rebalancing has attractive properties as a basic approach but numerous shortcomings as a delivery mechanism for dynamic beta. • The Dynamic Beta Program concept is relatively indifferent to the SAA (e.g., the SBCERA Dynamic Beta Program was not linked to the assets in specific portfolios used for comparison). Hence the assets selected for a better dynamic beta portfolio could be de-linked from the SAA, keeping the focus on negative correlation and positive targeted return from an assetonly perspective. This could allow for adding more assets (e.g., commodities, emerging markets, small caps, duration) to try to raise the Sharpe ratio while not giving up too much on correlations. • Further, arbitrary ranges imposed by the rebalancing policy also could be unnecessarily constraining. • The process could be run daily, the turnover need not be arbitrarily

linked to other passive rebalancing alternatives, and more factors could be added to the process to improve the Sharpe ratio of the dynamic beta program. Preliminary tests indicate that it may be possible to generate a Sharpe ratio that is comparable to the best of the HFRI Weighted Composite Index (or other hedge funds shown in table 9) or risk parity, but with a much more attractive drawdown than any of the strategies in table 9, while keeping a relatively high negative correlation (in the neighborhood of −0.3). Moreover, it can be shown that an efficiently structured program also can alter the distribution of returns more dramatically than shown in tables 7 and 8 through effective portfolio structuring and risk budgeting to such a program. Further, in additional work done in the context of corporate pension fund portfolios, it has been shown that the dynamic beta program can be designed to be positively correlated to the liability portfolio while maintaining the negative correlation to the asset portfolio, thereby dramatically improving the ALM risk profile. The key is that there is scope to improve this further with the optimal selection of rules that have an attractive Sharpe ratio by themselves, but also the attractive correlation to the reference portfolio(s). Does This Require InvestmentSavvy Staff? You may think that managing a dynamic beta program within a pension fund or endowment would require a large and expensive staff with extensive asset and research management experience, but we don’t think so. On average, asset management professionals are no smarter or bettertrained than the average pension fund or endowment investment professional. Success at SBCERA arose primarily through good governance: The board

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and the consultant recognized that rebalancing is a bet and hence needs to be owned, measured, monitored, and managed. This recognition led to the following process for SBCERA: 1. clear delegation of ownership of the rebalancing decisions to the investment team (in our experience, this clear delegation is the mostoften-missing item in investment policy statements); 2. specific assignment of responsibility to a single staff member with a colleague’s support; 3. research support for staff; and 4. adopting staff ’s request to move from cash-based rebalancing to futures-based rebalancing to capture efficiencies in process.

Rules such as these are in the public domain, in peer-reviewed journals. For example, Roberge and Moigne (2005) provide ten factors to dynamically allocate across stocks and bonds and was the basis of the initial SDCERA Beta Engine. It is well within the scope of the average pension fund investment officer. Hence, we conclude that developing and successfully implementing such a program requires good governance combined with motivating and supporting staff to make effective decisions. Why Dynamic Beta is Not the Same as Global Tactical Asset Allocation/Macro One might be tempted to think that the same goals can be achieved through a

macro strategy but, as shown in tables 3 and 4, the HFRI Macro index has an attractive Sharpe ratio but is positively correlated to the reference portfolio. Table 12 highlights how dynamic beta is similar in process but different in construction, objectives, and design from a traditional GTAA/Macro program. How Much to Allocate to Dynamic Beta How much risk should be allocated to a dynamic beta strategy from either an asset or an asset-liability perspective? Note that this is an allocation to a strategy, not to an asset, and it may be tempting to risk overallocating to a single product. An innovative chief investment officer can mitigate this risk by using multiple vendors with prod-

TABLE 12: COMPARING DYNAMIC BETA TO GTAA/MACRO AND RISK PARITY Risk Parity

GTAA/Macro

Dynamic Beta

Objective

Diversified portfolio of beta assets with low drawdowns relative to a typical portfolio

Diversified portfolio of assets with the highest possible Sharpe ratio with low portfolio drawdown

Assets Included

Global equity, bonds, commodities, and currencies

Mode of Investment

Global equity, bonds (including inflation linked), and commodities Assets are buckets based on regimes they perform well in; buckets are equally weighted on a relatively static basis (some may have triggers for risky periods); assets are levered/delevered to normal ize risks Fully funded and invested in cash instruments

Diversified portfolio of dynamic beta tilts with a high Sharpe ratio and low drawdown, but with the goal of lowering the solvency risk of the reference portfolio (either assets or assetsliabilities or even risk parity) Global equity, bonds, eurodollars, commodities, and currencies

Leverage and Customization

No leverage and not customized to client needs

Trades can be either- directional or relative value, but most strategies are directional. Trades are diversified and chosen if (a) they are relatively uncorrelated to each other, and (b) they achieve a high Sharpe ratio. Funded or partially funded (if run as an overlay); largely futures and forwards but can include cash instruments Typically levered and not - customized to client needs

Static vs. Dynamic Role in Portfolio

Static approach

Dynamic approach

Highly correlated to reference portfolios so meant to be a substitute for the benchmark of the client because it is believed to be more efficient Asset-only focus; nothing to do with liabilities

Source of uncorrelated alpha—allows clients to raise portfolio return for a given risk

Strategy

Asset-Liability Considerations

Asset-only focus; nothing to do with liabilities

Trades are relative value and bucketed into core beta decisions: (a) stocks vs. bonds vs. commodities; (b) currencies; (c) intra-stocks; and (d) intra-commodities. Modules tend to be uncorrelated, but focus is on factors that generate excess returns that are negatively correlated to the reference portfolio. Unfunded, because it can be executed with just futures, forwards, and options; frees up cash to be kept aside for liquidity management Net exposure is zero. Program can -be customized to any reference portfolio and risk level. Gross exposure (sum of long- and short positions) depends on the target risk level (e.g., can be as high as 3x notional assets under management for 10% annual risk) Dynamic approach; correlation to the reference portfolio is also dynamic Can lower risk of the total portfolio, specifically lowering drawdown. If negative correlation with positive return is achieved, want - to allocate a lot to this strategy Can be shown to lower solvency risk

© 2009 Investment Management Consultants Association Inc. Reprinted with permission. © 2011 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved.

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ucts that aren’t strongly correlated. This can be achieved with vendors that emphasize different economic, valuation, sentiment, seasonality, and momentum factors in the design of their programs. Application to Non-U.S. Investors In other preliminary and unpublished research, we have found indications that the program designed for U.S. pension funds can have attractive risk-management-enhancing properties for even Australian plans (from an asset-only perspective), Dutch pension plans (from both an asset-only and asset-liability perspective where the fund had applied a funded-status based dynamic de-risking SAA), Japanese plans (from an asset-only perspective), and Canadian plans (from an asset-only perspective). However, one would argue that funds in different geographical locations would be well-served to design customized programs for their specific portfolio structures.

them. All errors are the authors’ alone. The authors thank Donald Kendig of Santa Barbara County Employees’ Retirement System, Michael Dieschbourg of Broadmark Asset Management, and colleagues at AlphaEngine Global Investment Solutions for valuable comments. They also thank an anonymous reviewer for suggestions that greatly improved the paper.

“dynamic rebalancing” by different clients) or absolute return programs. 3

See Kunz (2011) for an excellent definition of risk parity and a review of its pros and cons. See the Journal of Investing (spring 2011, volume 20, number 1) for a special section on risk parity with a number of papers that discuss the pros and cons of these strategies along with an attempt to define them clearly in the context of a robust theory.

Timo thy B ar r e tt , C FA ® , i s dir e c to r o f p e n si o n in v e s tm e n t s , w o rl d w id e , E a st man Ko d ak C o mp any. C o n t a c t him a t t im o thy.b ar r e tt@ ko d ak .c o m .

4

In the classic “risk-based” approach, assets are broadly reclassified into risk buckets as if the reclassification reduces the risk of the overall portfolio. The system’s new asset allocation puts assets into five new classifications:

D onald P ierce , C FA®, i s chief inve st ment off icer of S an B er nardino Count y Employ e e s Retirement Associ ation . C ont act him at dpierce@sbcera .org.

(a) growth—public and private equity; (b) income—Treasury and other fixed-income securities; (c) real assets—real estate, infrastructure, and forestland; (d) liquidity—which includes cash and government bonds such as

Jame s Perr y, C AI A , is senior inve stment off icer at San Bernardino County Employee s Retirement Association. Contact him at jperr y@sbcera .org.

Treasuries; and (e) inflation—commodities and inflation-linked bonds. 5

For simplicity we assume liabilities that are nominal and hence easily proxied by nominal fixed income instruments. This does not

Conclusions Most strategic asset allocations confuse strategic asset allocation with static asset allocation, resulting in embedded risk. A dynamic beta program allows innovative investors to manage primary beta risk and lower the volatility and/ or drawdown of the reference portfolio, whether it is asset or asset-liability focused. This requires a program uniquely designed to tactically tilt the beta, earn a positive return, but be negatively correlated to the reference portfolio. This is well within the grasp of the average investor. The frequency of execution can be as low as monthly and these programs can be designed to make tilts on just the typical assets in an average SAA. In short, investors that engage in the development, implementation, and execution of dynamic beta programs can get paid to manage risk.   Acknowledgments This article represents the personal opinions of the authors and does not reflect the views of the organizations that employ

Arun Muralidhar, PhD, is chairman and founder, AlphaEng ine Global Inve stment Solutions , LLC . Contact him at a smuralidhar@alphaeng ine .net .

Endnotes 1

fundamentally change any of the arguments made here, but it might require a different set of economic factors to be used in a dynamic beta program than those used by SBCERA. 6

The drawdown is the measure of the decline

the allocation to equities to funded status

from an historical peak in cumulative perfor-

to serve as a quasi put option on funded

mance and hence provides a measure of how

status. However, these methods are being

bad cumulative performance could be. We

adopted only more recently; the success

refer to it as “yield-to-fire” because it pro-

of the ABN AMRO fund in 2008 using a

vides an estimate of how much and for how

similar mechanism shows their efficacy. The

long a fund/chief investment officer (CIO)

method in Muralidhar (1999) is similar to

can underperform before the CIO is fired.

that of Mercer (2009). Muralidhar (2011a)

Note that once a drawdown is achieved, the

demonstrates why this approach—called

return required to get the fund back to the original asset value is higher than the draw-

naïve de-risking—is inadequate. 7

down. For example, a $100 fund that declines get back to $100. We thank Michael Diesch-

The authors thank Michael Dieschbourg from Broadmark Asset Management for

50 percent requires a 100-percent return to

2

Muralidhar (1999) made the case for tying

figure 3. 8

The data on the risk-parity portfolio is the

bourg for this observation.

pro forma performance of a risk-parity port-

We use “dynamic beta program” as the over-

folio offered by a vendor that is broadly rep-

arching term to refer to any programs that

resentative of the core concepts of risk parity.

are dynamic and involve decisions on beta

Given that risk parity is a strategy, other

assets. These programs include rebalanc-

variations of this performance are possible,

ing programs (referred to as “intelligent

each of which will need to be subjected to the

rebalancing,” “beta engine,” “tactical beta,” or

same analysis to generalize these conclusions.

© 2011 Investment © 2009 Investment Management Management Consultants Consultants Association Association Inc. Reprinted Inc. Reprinted with permission. with permission. All rights reserved.

Volume 12 | Number 2 | 2011

11

9

10

Drawdown measures the peak-to-trough decline in

buy is related to an attractive price level, as measured

performance. Because it provides an indication of

by analytical standards. Similarly, the investor must

the decline of solvency, it is the most appropriate

take his cue to sell primarily not from so-called tech-

measure for evaluating the risk to the ability of an

nical market signals but from an advance in the price

De-Risking Solution. London, UK:

institutional investor to meet obligations.

level beyond a point justified by objective standards

Mercer Limited. http://www.mercer.com/

However, it is easy to show the fallacy of using the

of value.’ This is nothing more than a value-based,

services/mercer-dynamic-de-risking-

mean-reversion argument as the basis for constant

active asset allocation strategy. Of course, in order

rebalancing in a multi-asset portfolio. Muralidhar

to pursue a value-driven approach, patience and a

(2011a) points out the flaws in Swensen’s approach:

willingness to be contrarian are required.”

•  There is evidence in a number of simple observa-

presentation. See also Roberge and Moigne (2005)

tions: (i) it does not provide any evidence of the

for an example of a peer-reviewed journal article

the arbitrary claim of mean reversion; (ii) if arbitrary.

gram has generated an annualized 77 basis points of excess and this result has been validated by the

revert, then a more intelligent mean-reverting

independent implementation agent.

that is more intelligent than a naïve range-based or “real time” rebalancing strategy; (iii) what is relevant

White Paper, May 2010, Boston, MA. http://www. gmo.com. Muralidhar, A. 1999. Innovations in Pension Fund Management. Palo Alto, CA: Stanford University Press. ———. 2011a. A SMART Approach to Portfolio Management: An Innovative Paradigm for Managing Risk. Great Falls, VA: Royal Fern Publishing. ———. 2011b. “Delegated Decisions and the Capital Relative Asset Pricing Model,”

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11

Asset Allocation ≠ Static Asset Allocation. GMO

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This article was published in a special issue of the Journal of Investment Consulting that focused on the pension crisis. To purchase reprints of this article or other articles, visit http://www.imca.org/main/do/The_ Journal.

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