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that the geometric mean is always equal to or less than the arithmetic mean, even if there are no losses, and the magnitude is dependent on the volatil-ity (standard deviation) of returns. Obviously, losses increase the magni-tude of the standard deviation signifi-cantly, so avoiding losses is paramount. But if equal arithmetic returns can be

Determining the geometric return is a bit complicated; however, there is an easy way to estimate the value. The estimate is the arithmetic return minus one-half of the variance (which is the standard deviation squared). The esti-mates in table 1 illustrate that the esti-mate is a good approximation. The most enlightening aspect of the estimate is

“D on’t put all your eggs in one basket” might be the oldest rule of investment

risk management. This adage suggests diversifying into multiple asset classes in your portfolio so when one goes down another might go up. It’s still the bedrock of most basic risk-management approaches and was first formalized in modern portfolio theory, created by Harry Markowitz, which seeks the low-est risk for allocations among multiple asset classes.

Techniques for managing portfolio risks have evolved since Markowitz and continue to evolve today. Post-modern portfolio theory, which focuses on downside risks, grew from modern portfolio theory (MPT). Value-at-Risk and conditional Value-at-Risk techniques were created. New approaches such as liability-driven investing and dynamic asset allocation methods are being used in pension investing. This article will discuss the pros and cons of these tech-niques and others to help advisors deal with volatility in pension portfolios.

The Math of Winning

One of the crueler vagaries of invest-ing is the effect that negative returns or returns below a target level have on try-ing to achieve a certain long-range rate of return. Table 1 shows the accumula-tion from a $10,000 investment at the end of three years under four scenarios that have the same arithmetic return.

As table 1 shows, the four scenarios accumulate to three different amounts. How can that be? The accumulated value of an investment is based on the geometric return on assets rather than the arithmetic average (mean)—the arithmetic return is misleading at best.

Risk Management Trends for Pension PlansBy L. Gregg Johnson, EA, MAAA, MSPA, CFA ®, and Michael Dieschbourg, CIMA ®

TABLE 1: COMPARISON OF ARITHMETIC AND GEOMETRIC PORTFOLIO RETURNS OF A $1,000 INVESTMENT

A B C D

Year 1 8% 8% 8% 8%

Year 2 8% 2% ‒8% 24%

Year 3 8% 14% 24% ‒8%

accumulated Wealth $12,597 $12,558 $12,321 $12,321

arithmetic return 8.0% 8.0% 8.0% 8.0%

Standard Deviation 0.0% 4.9% 13.1% 13.1%

Geometric return 8.0% 7.9% 7.2% 7.2%

Geometric return (est.) 8.0% 7.9% 7.1% 7.1%

FIGURE 1: RANGE AND STANDARD DEVIATION OF COMPOUND RETURNS

YearWorst Case Best Case Std. Dev.

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

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and practice. In practice there is.” The elegant and formal mathematics of MPT has relied too much on theory rather than the reality of market move-ments. Experience has proven that in practice, MPT does not deliver the promised results, particularly when they are needed the most.

Post-modern portfolio theory (PMPT) focuses on losses or downside risk to seek portfolios that will pro-vide the most return for any expected level of loss or to generally attempt to accurately measure the potential losses in a portfolio. Tail risk, or extreme loss scenarios, are measured using Value-at-Risk (VaR) to attempt to quantify how much a portfolio might lose in any specified period; or conditional Value-at-Risk (CVaR), which is the amount of loss expected given that a loss occurs. These measures were developed origi-nally for highly complex investment bank structures that included diverse instruments and also are utilized extensively in hedge fund risk manage-ment. Their application to investment portfolios is more suspect because of the fragile relationships of near-homog-enous asset classes. PMPT suffers from many of the same shortfalls as MPT.

Best Practices

Establishing best practices in building portfolios begins with the development of an objective process to establish goals and benchmarks of performance. Best practices should include the following steps:

Establish realistic goals within a risk budget. In establishing realistic goals, the investor or plan sponsor must articulate what is most important to the situation. The goals might be to achieve a consumer price index plus 3-percent annual return with no more than 10-percent volatility or, in the case of a pension plan sponsor, to achieve the highest funded ratio possible while taking no more than a 5-percent chance that the funded ratio will drop by 5 per-cent or more during any one year.

to deliver the returns you need. Static strategies actually may decrease the chances of attaining a fully funded plan.

Portfolio Theory

MPT was developed by Harry Markowitz in 1952 and uses expected return, standard deviation, and correla-tion estimates to produce the efficient frontier of asset allocations representing the highest return for any level of risk. The expected return, standard devia-tion, and correlations estimates can be generated from historical data or forward-looking anticipated estimates. However, the asset allocation outcomes are very sensitive to small changes in assumptions that lead to artificial asset class limits to prevent unreasonable allocations. The imposition of these limits makes the allocations generated almost pre-determined—the efficient frontier of the set of feasible portfolios with the desired return or risk is virtu-ally a straight line.

The limitations of MPT are best summarized in a quote attributed to computer scientist and educator Jan L. A. van de Snepscheut: “In theory there is no difference between theory

achieved in two portfolios, the portfolio with the lowest volatility always will accumulate to the most wealth.

Investment Risk

Many people have heard the adage that investment risk decreases with time—that achieving your investment goals will be easier the longer you stick with your asset allocation. While this statement is partially true, it misses a big issue.

If you are investing pension assets and attempting to achieve a certain rate of return, say 8 percent, and you select an asset allocation that historically pro-vides an expected return of that amount, the long-term compound (or geometric) return should approach that number. Figure 1 illustrates this concept.

However, as time increases, the uncertainty of your accumulated wealth increases as shown in figure 2. If you are the sponsor of a pension plan attempting to fund a liability, this means the uncer-tainty of the funded status of your plan increases with time. Attempting to fund your liability becomes a great deal more difficult than simply selecting an asset allocation and waiting for the long term

FIGURE 2: RANGE AND STANDARD DEVIATION OF WEALTH

$0

$250

$500

$750

$1,000

$1,250

$1,500

$1,750

$2,000

0 2 4 6 8 10

Year

Ass

ets

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ions

Worst Case Best Case Std. Dev.



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Return enhancers provide for the selection of managers or nontraditional classes where alpha ability can be demonstrated.

Inflation hedges accommodate benefits that are dependent, directly or indirectly, on inflation. Treasury inflation-protected securities (TIPS) or real assets typically are found in this bucket.

Direct hedges are used to hedge portfolio risk, equity, or fixed income, either tactically or for leaving on a hedge (such as a tail-risk hedge) at all times. Futures and options uses are growing rapidly and most investors have a choice of many hedging options previously not available to them.

Risk diversifiers come in many forms, and several are unique to pen-sion plans. The most fundamental risk diversifier is the fixed-income asset class. Because the risk in most portfo-lios is dominated by equity risk, adding fixed income—which typically has a correlation with equity of less than 0.50—is a common risk diversifier. In the past, fixed income has been the only real risk diversifier for many investors. Today, more asset classes are available to satisfy this function with specialized classes for some pension investors.

Risk diversifiers could be any asset class that exhibits a low correlation with the beta portfolio and whose correla-tion is not expected to approach 1.0 in anything but the most extreme circum-stances. Real estate is a good fit in this category. Absolute return appears to be an excellent risk diversifier and could be a very attractive alternative to fixed income. The key here is that it is futile to attempt to diversify equity risk with other equity classes—most equity cor-relations are at least 0.70 and it doesn’t take anything like a crisis for these cor-relations to approach 1.0. Therefore, all equity classes are included in the beta portfolio, a single return and risk mea-sure is used to represent them, and the real risk reducers are then introduced into the optimization.

Monitor progress. Performance is measured on achieving the goals out-lined in the process rather than focusing on the performance of any one manager or asset class.

Defining asset classes by function in a core-satellite approach is useful when considering the potential asset alloca-tions that are most likely to achieve one’s goals. Figure 3 shows how asset classes can be defined by function.

At the core of all portfolios is the beta or market exposure class. This class consists of equity market exposures and other highly correlated asset classes. The portfolio is optimized based on return and risk expectations and any necessary allocation constraints. A single risk-and-return metric is deter-mined based on this allocation; it will be used in the remainder of the process and will help determine the allocation to the beta class.

The following satellite portfolios are then added:

Liquidity accommodates the near-term (5–7 years) benefit payments or cash outflows while maximizing return; satellite liquidity portfolios are updated annually.

Identify relevant risk metrics. In the process of setting goals, relevant risk measures usually are apparent. In the example above, minimum annual return and standard deviation are important to the first investor whereas funded ratio and stochastic probabili-ties are important to the second. Many plan sponsors are worried about the volatility of the contributions required by the plan so this is the relevant risk metric.

Measure current risk exposures. The relevant risk measures are quan-tified under the current or initially proposed asset allocation to establish a benchmark to use for determining improvements.

Evaluate alternatives to improve the risk profile. Alternative asset allo-cations are identified and risk metrics are measured to determine improve-ments from the initial allocation. An asset-liability modeling study is com-pleted to produce the metrics needed to evaluate the pension plan.

Implement solutions. The portfolio allocation needs to be dynamic at the asset allocation level, manager level, or both.

FIGURE 3: CORE-SATELLITE PORTFOLIO CONSTRUCTION OF ASSET CLASSES BY FUNCTION

BetaMarket

Exposure

Risk Diversifiers

DirectHedges

InflationHedge

Allocation

LiquidityAllocation

ReturnEnhancers


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The proper way to address interest-rate risk is to configure asset classes by function, as described above, then to investigate the effect of varying the allocation to the interest-matching fixed-income class by examining the effect on identified metrics through an asset-liability study in the best prac-tices process. Exposure to interest-rate risk can be clearly evaluated from the metrics and plan sponsors can make informed decisions about the risks they are willing to accept.

Dynamic Asset Allocation or Defined Benefit Glidepath

Another popular topic in pension investing is dynamic asset allocation, also called defined benefit glidepath. This approach seeks to achieve closely matched fixed-income assets to liabili-ties at the time the plan becomes well-funded. Acknowledging that return

fixed-income instruments of the same duration as liabilities, the movement of the assets and liabilities would be perfectly correlated and the plan always would remain 100-percent funded. This is the basis for LDI. (Insurance compa-nies have been doing this for years and call it “matching assets and liabilities.” Pension plan investors apparently wanted their own nomenclature.)

The proliferation of LDI applications among consultants has come to make LDI appear more of a product than just adding an interest-matching asset. Additionally, most consultants have indicated that LDI is used to “de-risk” a pension plan; however, LDI addresses only a single risk (interest-rate expo-sure) while many risks still remain in the assets and liabilities. LDI also seems to be presented as a solution to an underfunded pension plan. LDI itself cannot directly help the underfunding of a pension plan.

Because corporate pension plan liabilities are now marked-to-market, or measured at current yields, specialized instruments are available to lower their risk, primarily from decreases in inter-est rates. Public pension plans are not required to mark liabilities to market on the current yield curve, so none of these opportunities, nor liability-driven investing (see below), is a risk diversifier.

Liability-Driven Investing (LDI)

It is difficult to read about pension investing today without reading about LDI. The concept gained traction through the Pension Protection Act of 2006, which requires corporate pension plan liabilities—i.e., the present value of future benefit payments—to be deter-mined on current yields of investment-quality bonds. Because interest rates are so low, the liabilities of pension plans and the underfunding of plans (liabili-ties in excess of assets) are at histori-cally high levels.

Now that liabilities of corporate pen-sion plans are inversely related to interest rates, there exists an opportunity to directly match the movements of assets and liabilities. For example, if a plan were 100-percent funded and invested only in

TABLE 2: DYNAMIC ASSET ALLOCATION BASED ON PLAN FUNDED STATUS

ClassLess than

80% Funded80%‒90%

Funded90%‒100%

Funded100%‒110%

FundedMore than 110%

Funded

Cash 5% 5% 5% 5% 5%

Fixed Income 35% 45% 60% 70% 80%

real estate 10% 5% 5% 5% 0%

Large-Cap equity 15% 15% 10% 10% 10%

Mid-Cap equity 10% 10% 5% 5% 5%

Small-Cap equity 5% 5% 5% 0% 0%

International equity 10% 10% 5% 5% 0%

Private equity 10% 5% 5% 0% 0%

expected return 7.8% 6.9% 5.8% 5.0% 4.2%

Standard Deviation 11.8% 8.9% 6.4% 4.9% 5.1%

Projected Contributions over 20 Years

95th Percentile $404,478,630



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“ The proli feration of LDI applications

among consultants has come to make LDI

appear more of a product than just adding an

interest-matching asset. ”



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returns is the surest path to having the resources to distribute required amounts to pensioners.

L . Greg g Johnson , E A , M AAA , MSPA , CFA® , i s manag ing pr incipal o f Pension Applicat ions . He earned a BBA with honors in actuar ial sc ience f rom the Univer si ty o f Te xas and a Master s o f Finance f rom Georg ia State Univer si ty. Contact him at lg reg g johnson@pen-apps .com.

Michael Dieschbourg, CIMA®, i s managing director at BROADMARK Asset Management . He earned a BBA from Loyola University of Chicago and serves on IMC A’s Board of Directors as well as the editorial boards of Investments & Wealth Monitor and the Journal of Investment Consulting . Contact him at mdieschbourg@broadmarkasset .com.

happening primarily because the com-monly accepted static approach to asset allocation and asset management is not working. Indeed, the static approach is based on a number of assumptions and theories that all too often are proving false in common practice. Consequently, the math of losing is forcing a move to a more dynamic approach that focuses more on success than on theory. The key to the success of this dynamic approach is a collaborative effort among all inter-ested parties, plan boards, consultants, actuaries, and investment managers to achieve the liability objective of the plan rather than market-focused goals. Better tools for describing portfolio behav-ior will help. But the most important improvement is the establishment of a new core that seeks to avoid large drawdowns while still maintaining equity exposure. The avoidance of large drawdowns while maintaining adequate

is important when the plan is under-funded and that some investment risk will be taken to help achieve improved funding, the roadmap or glidepath for asset allocation will be based on the funded status of the plan. Plans with lower funded status will have higher allocations to beta or alpha-generating assets, gradually moving to matching fixed-income investments as funded status improves. An asset-liability study can optimize the glidepath based on a metric identified by the plan sponsor, and this optimized glidepath will be included in the investment policy state-ment. Table 2 illustrates an example of a glidepath based on funded status.

Conclusion

The funding crisis in pension plans is causing plan administrators, consultants, and asset managers to rethink traditional approaches to return and risk. This is

Mina, J. 2005. Risk Budgeting for Pension Plans. RiskMetrics Journal 6, no. 1: 9–34.

Russell Investments. 2012. De-risking Risk: Investors Making Progress on Risk Management, But Still Face Challenges in Governance. Russell Investments and Pensions & Investments, Part 2. http://sup-plement.pionline.com/risk-trending/_pdf/PI_Russell_De-risking_Risk_Pt2.pdf.

Schmid, M. A., and Q. Nguyen. 2012. A Total Enterprise Approach to Endowment Management. The NMS Exchange: Investment Bulletin for the Endowment & Foundation Community (January).

Disclaimer: This document is issued by Russell Investment Management Pty Ltd ABN53 068 338 974, AFS Licence 247185 (RIM). It provides general information for wholesale investors only and has not been prepared having regard to your objectives, financial situation, or needs. Before making an investment decision, you need to consider whether this information is appropriate to your objectives, financial situation, or needs. This information has been compiled from sources considered to be reliable, but is not guaranteed. Past performance

is not a reliable indicator of future performance. Nothing contained in this material is intended to constitute legal, tax, securities, or investment advice, nor an opinion regarding the appropriateness of any investment, nor a solicitation of any type. Copyright © 2012 Russell Investments. All rights reserved. This material is proprietary and may not be reproduced, transferred, or distributed in any form without prior written permission from RIM.

Gillespie–CurwoodContinued from page 11

Johnson–DieschbourgContinued from page 15


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