THEORY & PRACTICE FOR FUND MANAGERS

T H E J O U R N A L O F THEORY & PRACTICE FOR FUND MANAGERS SUMMER 2012 Volume 21 Number 2 The Voices of Influence iijournals.com

LDI in a Risk Factor Framework DAN RANSENBERG, PHILIP HODGES, AND ANDY HUNT DAN RANSENBERG is a director at BlackRock Multi-Asset Client Solutions in San Francisco, CA. dan.ransenberg@blackrock.com PHILIP HODGES is a director at BlackRock Multi-Asset Client Solutions in San Francisco, CA. philip.hodges@blackrock.com ANDY HUNT is a managing director at BlackRock Multi- Asset Client Solutions in San Francisco, CA. andy.hunt@blackrock.com Pension plans do not need to accept more than a minimal level of investment risk. They can be funded purely from contributions. Yet we observe that most pension plans do choose to take high levels of investment risk in an effort to achieve investment returns in excess of their liability growth. Given that this is a discretionary act, it follows that before a pension plan can start to decide how to invest its assets, it should have a clear goal or focus. Defining success helps pension plans to determine the size and any constraints upon their investment risk budget. An example of such a goal may be to achieve and maintain a fully funded status within 10 years while minimizing contributions. In this article we begin by illustrating how a typical pension plan s asset class exposures have led to extreme funded status volatility over the past 15 years. While taking surplus risk is not necessarily bad, pension plans should seek to only take risks that are expected to help the pension plan achieve its goals. We outline three steps that can assist pension plans in spending the surplus risk budget wisely: Step 1 Identify rewarded risk factors and specify their return expectations. In this section, we identify factors grounded in economic rationale that drive returns across asset classes. We focus on a few of the dominant risk factors in a typical pension plan and outline a framework for determining forward-looking return expectations for these risk factors. Step 2 Understand what drives the pension surplus. In this section, we map the typical corporate plan asset and liability exposures into the risk factors identified in step 1, as well as additional actuarial exposures. Through this mapping, we establish a risk and return measurement framework that reflects the plan s assets and liabilities. Step 3 Improve investment efficiency by (a) diversifying rewarded risk exposures and (b) scaling risk exposures in the current market environment. In this section, we discuss spending the surplus risk budget to the rewarded risk factors in proportion to the contribution to the overall expected risk-adjusted return. We then test a typical pension plan s exposures versus three sample-improved portfolios using Ibbotson data that spans over 80 years of financial history from 1926 through 2010. Finally, we discuss the implications of the current low interest rate environment. We believe that the proposed surplus risk factor and risk budgeted approach to pension plan investment is a simple yet significant improvement to the approach that a typical pension plan takes today. We SUMMER 2012 THE JOURNAL OF INVESTING

believe this is how LDI strategies should be designed and implemented. TYPICAL PENSION PLAN ASSET CLASS EXPOSURES Exhibit 1 illustrates the typical U.S. corporate pension plan s asset, liability, and net surplus exposures. As pension liability cash flows are typically discounted by a statutory long corporate rate, pension plan liabilities can be modeled as a negative exposure to longduration corporate bonds. 1 Adding asset and liability exposures together, one can view net surplus exposures to each asset class. Of note is the size and direction of these exposures. Equities are a large positive exposure whereas long-duration bonds are a very large negative exposure (the positive exposure to bonds in the asset portfolio is eclipsed by the negative exposure of the liability portfolio). 2 As we have witnessed multiple times over the past decade (see Exhibit 2), these exposures create problems for pension plans in environments of poor economic growth, which ironically is when plan sponsors core businesses or tax revenue streams are likely to suffer as well. During these periods of tumult, equity values tend to fall while long-duration bonds rally. Unfortunately, a traditional pension plan portfolio is built with positive exposure to the former and negative exposure to the latter. The typical plan has therefore, in effect, doubled-down on its sensitivity to economic shocks, leaving it vulnerable and perhaps uncomfortably reliant on its plan sponsor. STEP 1: UNDERSTAND RISK FACTORS In developing a risk factor approach, our first task is to identify common factors that drive returns across the assets and the liabilities. In this section, we present the historical risk and return behavior of a few of the dominant risk factors in a typical pension plan and outline a framework for determining forward-looking return expectations for these risk factors. Understanding expected returns to risk factors is crucially important because, as we will see in the following section, the typical plan with an unhedged liability has a large negative exposure to real interest rate and inflation risks. Even though our research indicates that these risks are less well-rewarded than other factors E XHIBIT 1 Typical Pension Plan Exposures *Source: Pensions&Investments, BlackRock. For illustration purposes only assume the bonds have the same duration in years as the liability Size of liability expressed relative to the assets is 1/funded ration = 1/0.8 = 125%. LDI IN A RISK FACTOR FRAMEWORK SUMMER 2012

E XHIBIT 2 Funding Ratio for a Typical U.S. Corporate Pension Plan Sources: Asset return: DataStream; asset allocation: Pensions&Investments as of 12/31/08; BlackRock; liability return: Bank of America Merrill Lynch (valued with AA rates). assume funding ratio 12/31/2006 = 100%. over long horizons, they still have significant positive expected returns. These substantial negative exposures to rewarded risk factors are a cost to the plan in long-term expected returns and, hence, investment efficiency. Step 1A: Identify Rewarded Risk Factors The typical empirical approach to building risk factor models involves identifying factors that are powerful at explaining variation in asset prices (see, e.g., Chen, Roll, and Ross [1986]; Fama and French [1992]; Chen, Novy-Marz, and Zhang [2010]). However, empirically derived factors are often not economically intuitive. Theoretical frameworks, such as arbitrage pricing theory (APT) (Ross [1976]), maintain that the expected excess return on any asset is a linear sum of the expected risk premia from its exposure to rewarded risk factors, but theory provides little help in determining candidates for rewarded risk factors. This article steps into this void and provides a tangible framework by identifying a simple set of factors that drive returns across asset classes, namely real interest rate risk, inflation risk, and economic growth risk. 3 While the selection of these factors from all possible factors is beyond the scope of this article, we believe that many investors would accept these factors as economically sensible. A challenge of this approach is that the risk factors themselves are not directly investable, and, thus, as a practical issue we must build investible portfolios, which we term factor mimicking portfolios or FMPs. These attempt to isolate each risk factor in turn. 4 Once the FMPs are defined, we can answer the following questions: Is the factor rewarded with a long-term positive risk premium? What are the correlations between these risks? What are the risk exposures of the liabilities? Which assets are exposed to which risks? How should we allocate between these risks in a plan? Exhibit 3 lists four risk factors and the FMP used to gain exposure to the associated risk premium. The FMPs are calculated by identifying assets that are sensitive to a particular risk factor, diversifying broadly between these assets, and then hedging away exposures to other risk factors. The factor portfolios discussed in this article SUMMER 2012 THE JOURNAL OF INVESTING

E XHIBIT 3 Description of Risk Factors are simplified versions of proprietary risk factor research by BlackRock. The mimicking portfolios are long short portfolios that can be used to understand the excess returns 5 to bearing each risk. For ease of comparison across risk factors, each FMP is scaled to target an ex ante risk level of 10%. Note that while these portfolios are designed to capture risk premia, they do not separate returns due to an ex ante risk premium from other sources of return. 6 In this respect, they do not differ from more conventional factors, such as those associated with equity size and value. We now examine the risk and return characteristics of each risk factor over the sample period from January E XHIBIT 4 Summary Statistics on Risk Factors: Which Risks Have Been Best Rewarded? Historical Performance from January 1990 to February 2011 1990 to February 2011. Exhibit 4 shows annualized returns, volatilities, and Sharpe ratios, as well as additional statistics that characterize the shape of the return distribution. The maximum drawdown is defined as the maximum cumulative loss in excess of cash during the sample period. During the sample period, each risk factor was rewarded with a positive risk premium in excess of cash. Real interest rate risk had the strongest risk-adjusted returns, while economic growth risk (whether accessed through credit spreads or equities) was least well rewarded. This is partly explained by the secular decline in real and nominal interest rates during the sample period, which was likely not expected, and therefore not priced into assets in 1990, and as a result the statistics probably overstate the premium for bearing real rate and inflation risks going forward. Investors should not be concerned solely with stand-alone return and stand-alone risk, but the environments in which losses occur, and their relationship with the rest of the portfolio and over time. This is explored in Appendix A, in which we also show that the returns to each risk factor, while overall positive, can differ considerably through time. A legitimate conclusion is that, unless investors have skill in forecasting these risk premia something that investors have struggled to demonstrate historically a diversified approach across rewarded risk factors is preferred to concentrated exposure to any single risk factor. LDI IN A RISK FACTOR FRAMEWORK SUMMER 2012

Step 1B: Determining Forward-Looking Return Expectations for Risk Factors In determining expected future returns, there is a limit to the power of empirical data. Even if our returns are drawn from stationary normal distributions, the standard error in our estimate of the mean is equal to the volatility divided by the square root of the number of years of observations. Hence, given 20 years of data we can declare a Sharpe ratio to be statistically greater than zero (at a 5% significance level) only once it exceeds 0.44 a high bar. Furthermore, there is compelling empirical evidence that risk premia are not static but vary with time. Hence, the standard statistical tests are inappropriate, and historical average returns even less useful in forecasting future returns. As noted previously, we also need to recognize that long-term trends in valuations can significantly impact realized returns and must be controlled for before drawing inferences about relative returns. For example, our analysis covers a period in which 10-year U.S. Treasury interest rates declined from 8.2% to 3.6%, whereas high yield credit spreads began and ended the period around 4%. Given this, we expect the ex ante Sharpe ratio for interest rate risk to be lower than suggested by the empirical data, but we expect the empirical credit estimates to be a more reasonable estimate for the forward-looking Sharpe ratio for bearing credit risk. Given these forward-looking estimation issues, we suggest that investors weigh three considerations: 1. Theory. Financial and behavioral theory can help determine which risks should be best rewarded over time. 2. Empirical data. Empirical data (properly corrected for biases in the sample period) is useful to support or contradict theoretical and behavioral hypotheses. 3. Valuation and market environment. Investors may condition their long-term return expectations based on current valuations or other market insights. In many asset pricing models (see, e.g., the discussion of stochastic discount factor models in Cochrane [2001]), the risk premium depends on the covariance of returns with bad economic states. On this basis, we expect economic growth risks to earn higher long-term risk premia than real rate and inflation risks, which tend to be more diversifying in bad economic states (Appendix A). Additionally, since many investors are already short interest rate and inflation risks in their liability portfolios, 7 they should rationally demand a lower premium for holding these risks long, as they help to hedge existing short exposures. While these hypotheses make sense from a forward-looking perspective, we can also test their merits with historical data. To do this, we use historical data from 1926 in the U.S. (Morningstar [2011]), 1900 in the U.K. (Barclays [2011]), and 1980 in Japan and Germany. We are unable to separate real interest rate and inflation risk before the existence of active inflation linked bond markets, and hence we report returns to a nominal rates factor, which is a composite of the interest rate and inflation factors. Our analysis attempts to control for changes in valuation by isolating periods during which simple valuation metrics in the beginning and end of the sample period were similar. We call these valuation isobars. 8 For nominal rate risk, our valuation metric is nominal yield; for credit, we use the spread over Treasuries; and for equities the normalized price-to-earnings ratio. Average Sharpe ratios for nominal rate risk and economic growth risk (in equities and credit spreads) are summarized in Exhibit 5. E XHIBIT 5 Average Sharpe Ratios for Valuation Isobars We consider theory and empirical data next, and at the end of the article we briefly consider how to condition these expectations based on the current environment. Source: Blackrock, DataStream, Ibbotson, and Barclays Equity Gilt Study. SUMMER 2012 THE JOURNAL OF INVESTING

Although we cannot draw inferences about the relative Sharpe ratios for the real interest rate and inflation factors that comprise the nominal rates factor, we can still come to some conclusions about the sizes of each. Because its two sub-components are not perfectly correlated, the realized Sharpe ratio for the nominal rate factor will be higher than the average of the two component Sharpe ratios. The nominal rate figure, therefore, represents an upper limit on the average of our unavailable estimates of the Sharpe ratios for the real rate and inflation factors. We note that each type of risk is positively rewarded in each regional market after controlling for valuation changes. Also, consistent with our initial hypothesis, nominal interest rate risk has tended to offer lower riskadjusted returns than economic growth risks. Although the data is imperfect, it does support our theoretical hypothesis. We believe a reasonable conclusion is that long-term strategic surplus portfolio exposures should be balanced across rewarded risk factors, but should tilt away from factors such as interest rate and inflation risk that tend to be less well-rewarded in equilibrium. STEP 2: UNDERSTANDING WHAT DRIVES THE PENSION SURPLUS In this section, we revisit the typical corporate plan exposures illustrated in Exhibit 1. Only now we look at these exposures through the risk factor framework. Pension liabilities are a series of projected cash flows due to be paid to beneficiaries. These cash flows are calculated by the plan s actuary under a range of assumptions about the plan s membership (including longevity and other decrements) and the plan s rule (which governs the form and nature of the benefit promise). These projected liability cash flows are then discounted to a present value using a discounting process, usually one that keys off a market-derived yield curve. Both the treatment of the projection process and the discounting process infer the characteristics of the liabilities and lead to exposures to the risk factors under discussion: Pension liabilities impacted by experienced inflation, for instance via COLAs, are similar to inflation-linked bonds. The present value of these inflation-linked cash flows, therefore, has exposure to the real interest rate risk factor. Pension liabilities not impacted by experienced inflation are similar to nominal bonds. The value of nominal cash flows, therefore, has exposure to both the real interest rate risk factor and the inf lation risk factor. 9 If nominal liability cash flows are discounted using a corporate bond derived discount curve as is used for instance in many accounting and some funding requirements the liabilities will additionally gain exposures to the credit spread risk factor (see, e.g., Ransenberg and Hobbs [2011]). The projected liability cash flows also exhibit exposure to actuarial risk factors, such as longevity. For the remainder of this article, we model the pension liability as a nominal liability cash flow that is discounted with a corporate bond yield curve. Therefore, similar to a corporate bond, the pension liability modeled here has exposure to the following risk factors: real interest rates, inflation, and credit spreads with an additional exposure to an actuarial risk factor. As the pension liability is owed and not owned, these are negative exposures. To illustrate this point, Exhibit 6 shows an attribution of surplus return and surplus variance to the primary risk factors. Positive surplus return implies that exposure to this risk factor is expected to be rewarded (or that there is a cost to remove a risk factor exposure to actuarial risk). If a factor s surplus expected return contribution is negative and its surplus variance contribution is positive, this implies that the risk factor is both lowering the surplus expected return and increasing the surplus risk. In other words, removing the risk factor not only increases the plan s expected return, but decreases its surplus risk. Each risk factor is discussed further from a surplus perspective: Economic growth: equity. This is the pension plan s largest risk contributor, and the largest contributor to surplus return. The plan could benefit from diversifying this exposure among other return drivers, such as real rates, inf lation, and credit risks, to ensure more robust return generation across economic environments. Nevertheless, equities still LDI IN A RISK FACTOR FRAMEWORK SUMMER 2012

E XHIBIT 6 Risk Factor View of Typical Pension Plan Surplus Return and Risk Attribution play a useful, positive role in most pension plan risk budgets. Real interest rates plus inflation. A typical pension plan s second largest risk exposure is to long-duration nominal rates (real rates and implied inflation). Being net short this factor, however, contributes negatively to surplus return. Reducing the plan s negative exposure to these risk factors increases the plan s expected surplus return and decreases the plan s surplus volatility. Economic growth: credit. The liability-induced net short credit exposure is a net drag on fund return, but it also contributes negatively to portfolio variance. This is because the negative credit exposure helps to diversify the large positive economic growth exposure elsewhere in the portfolio. Reducing the plan s negative exposure to credit risk increases the plan s expected surplus return but also increases the surplus risk. Many investors will, therefore, conclude that hedging the interest rate component of the liability is more important than hedging the credit component. Actuarial. Pension liabilities are often subject to significant actuarial risks, such as longevity risk, disability risk, and retirement age risk. For pension plans, retaining this risk factor contributes positively to surplus return because there is a significant cost to transferring this risk to an insurance company. In other words, the expected surplus return would be lower after removing this risk. STEP 3: BUILDING A BETTER LDI PORTFOLIO Pension plans can build a better LDI portfolio, that is, one that is focused on maximizing surplus investment efficiency, by diversifying rewarded risk exposures, and spending risk in proportion to the strength of the view of how attractive each risk is compared to other opportunities. Step 3A: Improving Investment Efficiency by Removing Unrewarded Risks and Diversifying Rewarded Risks In Exhibit 5, we presented long-term Sharpe ratios for the three dominant risk factors in a typical plan: nominal rates (real rates plus inflation), credit spreads, and equities. Given these assumptions, the portfolio that maximizes surplus expected return while minimizing surplus volatility should have long exposure to each of these risk factors. We can also ask: if the surplus portfolio that investors currently hold is efficient (maxi- SUMMER 2012 THE JOURNAL OF INVESTING

mizes surplus return per unit of surplus volatility), what does that imply about their return expectations for each risk factor, and how does that compare with historical evidence? The process of deriving implied returns (or Sharpe ratios) from presumed-efficient portfolios is described in detail in Grinold [1996]. Exhibit 7 shows the implied Sharpe ratios for two portfolios: the typical plan (detailed in Exhibits 1 and 6) and a 60/40 equity/aggregate bond portfolio. 10 The final row restates the empirically derived Sharpe ratios from Exhibit 5. Three points are worth emphasizing: The typical plan is only efficient on a surplus basis if the Sharpe ratio for nominal rate risk is considerably negative, that is, nominal government bonds significantly underperform cash. For this to be a sensible long-term strategic portfolio, one must expect either consistently rising long-term interest rates or a normally inverted yield curve. The typical plan is also more optimistic on the risk-adjusted returns available from investing in equities than the historical record suggests. Even a surplus portfolio that has 40% capital exposure to long credit is more pessimistic on long-run nominal bond returns than the historical record (controlled for valuation changes) suggests. Exhibit 8 illustrates the capital allocation and risk factor exposures for three sample portfolios that we have tested with Ibbotson data that goes back to 1926 and spans a very wide range of economic environments. Pension liabilities are modeled as a short position in long credit bonds. Each of the portfolios has been calibrated to have the same historic return since 1926. Portfolios two and three have asset leverage to reduce surplus volatility. The plan is assumed to be fully funded at inception in 1926: Portfolio 1 s capital allocation is 60% equities and 40% long-duration corporate bonds. Equities and long government bonds map to the risk factors as expected and long credit bonds and liabilities map to both economic growth credit and the real rates and inflation risk factors. The result is the typical long equity, short credit, rates, and inflation risk exposures we often see from pension plans. Portfolio 2 builds on portfolio 1 by reducing equity exposure and hedging all liability nominal rate risk via leveraged Treasury bonds. As highlighted in the exhibit, the surplus portfolio has zero exposure to real rates and inflation. Portfolio 3 goes one step further, producing a surplus portfolio that has positive exposure to interest rate risk, inflation risk, and economic growth risk, and negative exposure to cash. It does this by further reducing equity exposure and utilizing leverage in the asset portfolio to achieve positive exposures to each risk factor (on top of hedging all liability risks). The quantity of equity risk has been scaled such that each portfolio has the same historic return and similar forward-looking returns. Exhibit 9 illustrates the historical funded ratio risk for each of these three portfolios since 1926. Risk here is defined as a one-in-ten downside event. 11 For example, in a one-in-ten downside negative year for pension plans, E XHIBIT 7 Implied Risk Factor Sharpe Ratios on the Assumption that the Surplus Portfolio is Efficient Source: Blackrock, DataStream, and Ibbotson. LDI IN A RISK FACTOR FRAMEWORK SUMMER 2012

E XHIBIT 8 Three Surplus Portfolios with the Same Return Since 1926 a traditional portfolio (portfolio 1) would have suffered a 12% drawdown in funded ratio whereas a diversified risk factor portfolio (portfolio 3) would have only suffered a 6% drawdown in funded ratio. We can also see that increasing the time horizon from one to five years increases the risk difference between the portfolios. In summary, over this period a traditional pension plan portfolio (portfolio 1) has had significantly more risk than the comparison portfolios, while generating no additional return over liabilities. The most appealing portfolio over this period was portfolio 3, which maintained positive surplus exposure across the rewarded risk factors. Step 3B: Scaling Risk Exposures in the Current Market Environment In the risk factor framework, an ideal long-term portfolio balances positive surplus exposure across rewarded risk factors. This is a good starting point, but investors may have views about expected returns conditional on the current valuation, sentiment, or cyclical environments. These can readily be incorporated into the risk factor based LDI portfolio. For instance, a pension plan might construct market indicators that proxy the size of the expected return, or risk premium, for E XHIBIT 9 Historical Drawdown on Funded Ratios One in Ten Downside Event (1926 2010) SUMMER 2012 THE JOURNAL OF INVESTING

each risk factor. For example, a credit risk premium indicator can be built to measure the extent to which credit spreads overcompensate for expected default losses, or an inflation risk indicator could measure the extent to which breakeven spreads overcompensate for expected inflation. These views, conditioned on their size and the conviction held, can be used to craft an optimal (tactical) portfolio in a conventional manner, with the resulting portfolio tilting toward higher expected return opportunities. Without discussing the authors tactical positions and views, we note that most pension plans today are implicitly taking a view that returns for bearing interest rate risk may be lower than historical averages, or even negative. Moreover, they have adopted a very large bet in this regard, which suggests that they are quite confident about this. While this view and position can be supported from time to time, we suspect that the persistence of this implied view over the past several decades more likely stems from an under appreciation of the risk factors at work within the pension plan asset and liability portfolio. SUMMARY AND CONCLUSION In this article we have introduced a preferred framework for building efficient pension plan portfolios a risk factor approach to LDI. This approach focuses on surplus risk disaggregated into risk factors. A pension plan should reduce (hedge) risk factors that are negatively rewarded, and focus on only taking on positive exposure to risks that bear reward. These risk exposures should be scaled in accordance to their expected rewards and, specifically, their contribution to surplus investment efficiency (surplus return per unit of surplus risk). Such a risk factor approach to LDI can help limit unintended surplus risk and increase surplus expected reward in other words, it can improve investment efficiency. The application of this approach enables pension plan decision makers to build more risk-managed and more efficient pension portfolios. It enables a clearer picture to be painted of what is driving risk, and hence aids and informs investment decision making. We believe the output will be wiser spending of a plan s investment risk budget, which is the essence of a good liability-driven investment portfolio. A PPENDIX A UNDERSTANDING THE INTERACTION BETWEEN FACTOR-MIMICKING PORTFOLIOS OVER TIME Exhibit A-1 shows correlations between the five risk factors. Most of the full-sample correlations are below 0.2, indicating that the risk premia are diversifying over long investment horizons. While the correlations between risk factors are fairly stable throughout the sample period, investors should be very careful before assuming that negative correlations, such as those between inflation and economic growth risk, will persist. This negative correlation reflects an estimate from a period of declining inflation uncertainty and substantial economic growth uncertainty. Investors should be aware that when inflation risks dominate (such as the 1970s in the U.S.), the inflation growth correlation tends to be positive, while it tends to be negative when growth risks dominate (such as the 2000s). E XHIBIT A-1 Correlations between Risk Factors Note: Full sample from January 1990 to February 2011. Source: Bloomberg, BlackRock. LDI IN A RISK FACTOR FRAMEWORK SUMMER 2012

E XHIBIT A-2 Correlations between Risk Factors in Good and Bad Economic States Note: Full sample from January 1990 to February 2011. Source: Bloomberg, BlackRock. E XHIBIT A-3 Risk Factor Returns Notes: Factor returns are annualized returns to investible portfolios that mimic the fundamental risk factors. All factors target an ex ante risk level of 10%. Source: Bloomberg, BlackRock. Exhibit A-2 shows risk factor correlations conditional on joint negative (lower left) or positive (upper right) returns greater than one standard deviation from the sample mean. 12 We can think of the joint positive states as good environments for the risk factors, and, by loose extension, as good economic states. Similarly, we think of the joint negative states as bad states. Note that inflation risk has tended to be diversifying in bad economic states. We outline the implications of this later. Exhibit A-3 summarizes the returns to each risk factor over distinct six-year periods. It illustrates that the reward for bearing each systematic risk has typically been positive but has appeared to fluctuate considerably over time. The upshot is a recognition that either our predictive ability as defined through these FMPs is low, or the factor risk premia are unstable, or both. ENDNOTES 1 Plus additional actuarial risks, such as longevity risk. More details on liability risks can be found in the Step 2 section. 2 It is interesting to note that nearly all pension plans have negative surplus exposure to long-duration bonds and yet nearly all pension plans assume that bonds offer a positive, long-term expected return over cash at least this is assumed SUMMER 2012 THE JOURNAL OF INVESTING

in the calculation of their EROA in pension accounts. By utilizing synthetic instruments, most pension plans could remove much of the negative surplus exposure to long-duration bonds and increase their plan s total expected return over cash. 3 Additional rewarded risk factors identified by Black- Rock include political uncertainty and liquidity risk. These are not discussed in this paper. 4 The construction of the FMPs, as with the selection of the targeted risk factors themselves, is an area where econometrics and investor beliefs need to be blended. 5 In excess of the risk-free rate. In this article, we use the one-month T-bill rate as the risk-free rate. 6 For example, the inflation FMP captures both an inflation premium and any differences between realized and expected inflation. 7 They are essentially short a nominal bond. 8 There is more than one way of achieving this. We have used a process that averages all periods of more than five years of data for which the start and end valuation points were deemed comparable. 9 Note that we have defined the inflation risk factor as the risk that the investor is not rewarded when inflation spikes. Therefore, a nominal bond (or liability value) has exposure to the inflation risk factor whereas an inflationlinked bond (or liability value) does not have exposure to the inflation risk factor. 10 The analysis uses a historical risk factor covariance matrix, constructed using equally weighted monthly data from 1990 to 2011, and Sharpe ratio estimates are scaled such that each portfolio has an expected return of one-month T-bills plus 5%. 11 Overlapping data periods are utilized to perform calculations. 12 A threshold of one standard deviation is chosen over more extreme outcomes to increase the statistical significance of the results. REFERENCES Barclays. Barclays Equity Gilt Study. 2011. Chen, L., R. Novy-Marx, and L. Zhang. An Alternative Three-Factor Model. Working paper 15940, National Bureau of Economic Research, April 2010. Chen, N.-F., R. Roll, and S.A. Ross. Economic Forces and the Stock Market. Journal of Business, Vol. 59, No. 3 (July 1986). Cochrane, J.H. Asset Pricing. Princeton University Press, 2001. Fama, E.F., and K.R. French. The Cross-Section of Expected Stock Returns. Journal of Finance, Vol. 47, No. 2 (June 1992). Grinold, R.C. Domestic Grapes from Imported Wine. The Journal of Portfolio Management, Special Issue (December 1996), pp. 29-40. Morningstar. Ibbotson SBBI Classic Yearbook. 2011. Ransenberg, D., and J. Hobbs. Overcoming Credit Downgrades: Four Ways to Improve Your Liability Hedge. Investment Insights, Vol. 14, No. 2 (April 2011). Ross, S.A. The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory, Vol. 13, No. 3 (December 1976), pp. 341-360. To order reprints of this article, please contact Dewey Palmieri at dpalmieri@iijournals.com or 212-224-3675. LDI IN A RISK FACTOR FRAMEWORK SUMMER 2012