Liability-Driven Investment Policy: Structuring the Hedging Portfolio

Transcription

1 Strategic Research November 2007 Liability-Driven Investment Policy: Structuring the Hedging Portfolio KURT WINKELMANN Managing Director and Head Global Investment Strategies (212) SCOTT MCDERMOTT Managing Director Global Investment Strategies (212) ALAIN KERNEIS Executive Director Global Investment Strategies 44 (20) YEVGENIA ZEMLYAKOVA Vice President Global Investment Strategies (917) SILVIA GLAUBACH Associate Global Investment Strategies (212) Executive Summary Liability-driven investing (LDI) strategies have attracted increased interest from plan sponsors in the past few years, driven in part by a new regulatory landscape. These strategies which view the plan s liability stream as its true benchmark have been implemented in several ways, from complete immunization (which eliminates interest rate risk but also virtually removes the potential for excess-return generation) to total portfolio solutions (when investors manage the pool of investable assets as two portfolios: hedging and return generation). To date, we have created a large body of work on LDI strategies, especially on the topic of development and implementation of total portfolio solutions. Most of our research papers have been devoted to the creation of the return-generating portfolio as well as the use of exotic beta asset classes in an effort to enhance potential returns. 1 In this paper, we discuss in more detail the tradeoffs investors face in designing a hedging portfolio. For example, we shed light on how investors should consider hedging the liabilities in their portfolios by using cash bonds, futures or interest rate swaps. Also, since many hedging solutions require the use of derivatives, we argue that investors must factor in the probability of exhausting collateral as a determinant in the size of the hedge. Furthermore, the level of hedging is also related to the amount of capital available for the hedging portfolio, which, in turn, is related to the target return for assets relative to liabilities. Thus, investors must consider the impact of the target return on the size of the hedge as well. We treat these considerations as a type of risk-budgeting problem. For example, the choice of hedging vehicle can be framed as how much basis risk (tracking error between the liabilities and the hedging portfolio) the investor is willing to tolerate, and what impact that basis risk has on the overall surplus volatility. While this paper does not suggest that there is a one-size-fits-all solution, it nevertheless concludes that relatively high proportions of the interest rate mismatch can be hedged with comparatively low effort. Looking ahead, managing the impact of the interest rate mismatch will be an increasingly important part of a plan sponsor s mandate. Understanding the tradeoffs associated with managing this part of the portfolio will help drive important parts of the investment decision-making process, including the structuring of an external hedging mandate. 1 See Winkelmann, K., McDermott S., Berger, A., Glaubach, S. (2006), Liability-Driven Investment Policy: Managing to the True Benchmark, GSAM; Winkelmann, K., Glaubach, S. (2006), Designing Efficient Return-Generating Portfolios: Tilting Away from Equilibrium toward Alpha and Exotic Beta; and Winkelmann, K., Berger, A., Glaubach, S., Zemlyakova, Y. (2006), The Future of Defined-Benefit Plans: Using LDI Policy to Adapt to New US Pension Regulation.

2 Liability-Driven Investing: A Total Portfolio Solution The investment and regulatory landscape for defined-benefit (DB) pension plans has changed dramatically over the past five years, prompting many investors to begin linking the performance of their asset portfolios more explicitly to the valuation of their liabilities. Such investment solutions have become known as liability-driven investing strategies. Specifically, new regulation has affected DB plan sponsors in three specific ways: Closely tying assets and liabilities to market values, Reducing (or eliminating) smoothing in the values of assets and liabilities, and Increasing the penalty (implicit or explicit) for underfunded status. All of these factors have the effect of driving pension investors to more explicitly manage the interest rate mismatch between their asset portfolios and their liabilities. This approach has two main benefits: 1) Reducing the mismatch can lower the potential for underfunding, and, consequently, can provide more security for plan beneficiaries; 2) The lower likelihood of underfunding diminishes the potential impact of pension funding on corporate earnings, and, therefore, provides a benefit for shareholders as well. However, reducing the impact of the interest rate mismatch does not solve everything. Investors would also like to see their asset portfolio grow. Thus, the real challenge in an LDI solution lies on balancing the tradeoffs between managing the interest rate mismatch and growing the value of assets. Traditionally, implementations of LDI strategies have ranged from complete immunization to total portfolio solutions. Other solutions have also included the implementation of extended-duration and portable-alpha strategies. 2 We have developed a strong body of research on LDI, particularly on the implementation of total portfolio solutions. In previous works, 3 we have shown how investors should think about setting up return-generating portfolios, and how the optimal portfolios should tilt towards mispriced asset classes (exotic beta) and applications of skill (alpha), among other things. In the remainder of this paper, we will turn our attention to the second portion of the total portfolio solution implementation, and define an optimal strategy for investors to set up a hedging portfolio. 2 Goldman Sachs Asset Management 2 Immunization strategies invest all plan assets in cash-flow matching bonds or a fixed income portfolio with benchmark duration equal to the duration of pension liabilities. The expected cash flows from the longer-duration bonds match the pension liability cash flows. A total portfolio solution uses a two-portfolio approach hedging and return-generating portfolios. This strategy dedicates a portion of assets to a strategic benchmark risk-matching the pension s liability. The remaining assets generate returns that are transported to the liability benchmark. Extended-duration strategies change the benchmark of all of the plan s existing fixed income investments to a longduration benchmark and extend duration of existing fixed income investments through the physical or synthetic ownership of bonds; while portable-alpha solutions transport active manager returns to a long-duration benchmark. 3 See Winkelmann, K., McDermott S., Berger, A., Glaubach, S. (2006), Liability-Driven Investment Policy: Managing to the True Benchmark, GSAM; Winkelmann, K., Glaubach, S. (2006), Designing Efficient Return-Generating Portfolios: Tilting Away from Equilibrium toward Alpha and Exotic Beta; and Winkelmann, K., Berger, A., Glaubach, S., Zemlyakova, Y. (2006), The Future of Defined-Benefit Plans: Using LDI Policy to Adapt to New US Pension Regulation.

3 Available Hedging Instruments Designing a liability hedging portfolio should start with the assessment of a number of available interest-rate-sensitive instruments. The root tradeoff investors face in selecting from these instruments is whether to use bonds (e.g., US Treasury bonds) or derivatives (e.g., swaps or futures). To evaluate this tradeoff, we examine the pros and cons of constructing a liability hedge with swaps, government/ credit bonds, and Treasury bonds. Exhibit 1 compares the available interest-rate-sensitive instruments. Exhibit 1 Investors should assess available interest-rate-sensitive instruments before setting up a hedging portfolio Pros Swaps Gov t/credit Sector Bonds, Indices Treasury Bonds, Indices Better yield curve sensitivity matching. Most appropriate for overlay or synthetic duration extension strategies. Potentially better match to corporate discount rates, which are generally based on AA-rated corporate yields. Most transparent. Most appropriate for immunization strategies. Cons Basis risk between swap rates and AA-rated corporate yields. Requires derivatives. May not be suitable for overlay or synthetic duration extension strategies. Index sectors may be a course representation of a specific liability stream. May not be suitable for overlay or synthetic duration extension strategies. Treasury yields are lower than AA-rated corporate yields. Implementation Examples Interest rate swaps Lehman 30-Year US Swap Lehman 20-Year US Swap Lehman 10-Year US Swap Lehman 5-Year US Swap Lehman 3-Year US Swap Lehman 2-Year US Swap Lehman 1-Year US Swap Portfolios of government and corporate bonds * Lehman Long Gov t/credit Index Lehman 5 10-Year Gov t/credit Index Lehman 1 5-Year Gov t/credit Index US Treasury Bonds * Lehman 30-Year Treasury Bellwether Index Lehman 10-Year Treasury Bellwether Index Lehman 5-Year Treasury Bellwether Index Lehman 3-Year Treasury Bellwether Index Lehman 2-Year Treasury Bellwether Index For illustrative purposes only. *Derivatives, like US Treasury futures and interest rate swaps, may be permitted but are not part of the benchmark. Source: Goldman Sachs Asset Management (GSAM) Benchmark swaps are available for various maturities and regions. In the US market, benchmark swap indices are available between 1 and 50 years of maturity, providing good yield curve sensitivity matching. Similarly, these indices are available between 1 and 50 years in the UK. Since swaps are synthetic instruments, they are not subject to specials, or supply constraints. Consequently, they can provide a capital-efficient way to manage an interest rate hedge. Swaps, however, introduce basis risk between swap rates and corporate discount rates. This basis risk can be relevant for determining the market value of the pension liability. For example, US pension regulations indicate that the funded status of a plan must be evaluated using AA-rated corporate yields. It s important to note that the broader investment grade bond market (and investment grade bond indices) has the potential to better match corporate discount rates. However, the corporate bond market is generally less liquid than the government bond market. Government bonds (and indices) represent a risk-free asset and are available at multiple maturities. However, investors who rely on government bonds are constrained by the available supply, which is typically more limited in longer maturities. This issue can be circumvented somewhat by the availability of a liquid futures market for government bonds. Goldman Sachs Asset Management 3

4 Creating the True LDI Benchmark: Yours! Once the potential hedging instruments have been identified, the implementation of a liability hedging portfolio must proceed with an analysis of the pension plan s cash flows. In this sense, the plan sponsor is responsible for understanding the structure of the liabilities, the size of future liability payments and the sources of risk (i.e., the forces driving changes in liability value). Consequently, the plan sponsor is also responsible for developing a tradable portfolio whose function is to mimic the plan s liability stream as established by its current cash-flow projections. In LDI terms, we look at this liability-mimicking portfolio as the plan s true benchmark, against which the performance of the remaining assets of the plan (e.g., the return-generating portfolio) should be compared. The composition and characteristics of this liability benchmark should be reassessed as often as cash-flow projections change so as to ensure it reflects the plan s latest actuarial assumptions. We illustrate the issues associated with developing the liability benchmark through the example in Exhibit 2, which highlights a hypothetical set of cash flows for a typical pension plan. We will use this example in the remainder of this paper. Exhibit 2 Pension liabilities are typically long-dated Representative Pension Liability Stream $ Millions The data shown are of a representative pension portfolio, are for informational purposes only and are not indicative of future portfolio characteristics/returns. Actual results may vary for each client due to specific client guidelines and other factors. One of the purposes of an LDI strategy is to explicitly consider the risk of the asset portfolio relative to the pension liabilities. We know that the valuations of asset portfolios change depending on the movements in equity and fixed income markets. But what market factors drive changes in value for pension liabilities? 4 Goldman Sachs Asset Management

5 Nominal pension liabilities are projections of future nominal cash flows. The present value of projected nominal cash flows is determined by discounting these cash flows with nominal interest rates. Thus, the principal driver of market risk for nominal pension liabilities is changes in interest rates (we will consider the impact of inflation later in this paper). This point is accentuated by regulatory requirements that pension liabilities be marked-to-market on a regular basis. Mark-tomarket requirements push plan sponsors to use an observable set of market interest rates to assess both value and risk in pension liabilities. With that in mind, our next step is to establish a portfolio of marketable instruments that best mimics the interest rate sensitivity of the liabilities. In other words, we need to create the portfolio that will become the benchmark for all investment-policy decisions. As shown previously, investors can select from three main sources of marketable instruments to construct the plan s liability benchmark (government/credit bonds, Treasury bonds and interest rate swaps). Out of the three, we believe that interest rate swaps provide the best and most flexible solution. There are many reasons why we like swaps best. First, the expansion in the swaps market as illustrated in Exhibit 3 has provided a liquid additional tool for investors to manage interest rate risk. Exhibit 3 The interest rate swap market has grown dramatically in the past five years Notional Amount Outstanding in US Interest Rate Swaps $ Trillions Source: Bank of International Settlements In addition, interest rate swaps offer a number of advantages that are not available in other interest-rate-sensitive products, namely: Swaps can be synchronized to pension cash flow dates; bonds cannot, Swaps can be customized to long-dated liabilities; bonds cannot, Swaps are easier to lever than bonds, and Swaps are available in longer maturities than bonds. This last point is well illustrated in Exhibit 4. The chart shows that over 50% of US Treasuries have a duration of five years or less. While the supply of long-duration Treasuries could grow in the future, the interest rate swaps market is likely to provide a better pool of interest-rate-sensitive instruments for the construction of a liability-mimicking benchmark. Goldman Sachs Asset Management 5

6 Exhibit 4 Over 50% of US Treasuries have duration of five years or less Duration Distribution of Treasury Market Market Cap Weight (%) Yr (Duration = 2 Yr) 3-5 Yr (Duration = 4 Yr) 5-7 Yr (Duration = 5 Yr) 7-10 Yr (Duration = 7 Yr) Yr (Duration = 9 Yr) 20+ Yr (Duration = 13 Yr) As of May Source: Lehman Live As an example, we built a portfolio of tradable swaps that mimics the liability stream shown earlier in Exhibit 2. The corresponding capital allocation breakdown to each node on the swaps curve is illustrated in Exhibit 5. In addition, we also show that not only does the benchmark mimic the liability stream s cash flows, it also has similar risk characteristics, such as duration and convexity. 4 Exhibit 5 A portfolio of tradable swaps mimics a pension plan s liability stream Maturity Notional Amount ($) Lehman 1-Year US Swap 12,824,898 Lehman 2-Year US Swap 14,287,206 Lehman 3-Year US Swap 24,158,684 Lehman 5-Year US Swap 68,928,044 Lehman 10-Year US Swap 160,998,757 Lehman 20-Year US Swap 256,587,518 Lehman 30-Year US Swap 315,639, ,424,193 Liability-Mimicking Liabilities Portfolio of Swaps Difference Duration Convexity For illustrative purposes only. However, duration and convexity only approximate the interest rate exposure of the liability stream, as these calculations implicitly assume that yield curves make only parallel moves. To understand the exposure of the liability stream more accurately to sources of interest rate risk such as the slope and curvature of the yield curve we must use other methods. 4 See Glossary for definition of terms. Also, see Appendix A for more detail on the construction of the benchmark portfolio. 6 Goldman Sachs Asset Management

7 Here s how we suggest one should approach this issue: since the benchmark replicates the liability stream in terms of exposures to key points on the swaps curve, we can calculate the volatility of returns and the correlation between the returns on each point on the swaps curve. Thus, the exposure to interest rate risk can be found by combining the swaps holdings in the benchmark with the estimated volatility and correlation for each of these key points on the swaps curve. Since pension liabilities are projections, we must also allow for some risk due to the mismatch between actuarial cash-flow projections and actual experience. We will call this risk the noise factor. Importantly, noise cannot be hedged by interest-rate-sensitive instruments. Once we incorporate noise, we can then calculate the total volatility of the liability stream. As a practical example, we break down the risk characteristics of our hypothetical liability stream in Exhibit 6. The total volatility of the liability stream is 9.8%, of which about 95.9% is due to the impact of interest rates and 4.1% is due to noise. Exhibit 6 Interest rate is the main source of risk in a typical liability stream Contribution to Cumulative Factors Total Variance Explanatory Power Level 95.7% 95.7% Slope 3.9% 99.6% Curvature 0.3% 99.9% Other Higher Order Factors 0.1% 100.0% Risk Characteristics of Liability Stream Interest Rate Risk 95.9% Unhedgeable Liability Risk (noise) * 4.1% Total 100.0% Total Risk ** 9.8% For illustrative purposes only. *Unhedgeable liability risk encompasses all actuarial assumptions not related to interest rates, including mortality and employee turnover. We assume 2% risk per 100% of liability present value. **Risk measured as the annualized standard deviation of the liability benchmark as a percent of plan liabilities. The exhibit also shows a decomposition of the interest rate risk. The data show that the dominant source of interest rate risk in long-duration pension liabilities is the impact of changes in the level of interest rates. This result is important, because it tells us that the big gains in hedging are likely to come from managing the impact of changes in the level of rates. 5 We will keep this result in mind as we consider alternative hedging strategies. 5 Most studies of interest rate risk suggest that there are three dominant interest rate risk factors: changes in the level of interest rates, changes in the slope of the yield curve and changes in the curvature of the yield curve. The effects of these three factors are captured when we represent the liability cash flows in terms of exposures to key points on the swaps curve. Also, these studies show that, as duration lengthens, the level effects become more pronounced. See Litterman R., Scheinkman J., Weiss L., Volatility and the Yield Curve, The Journal of Fixed Income, June Goldman Sachs Asset Management 7

8 Assets Distribution in a Total LDI Solution Context Once the liability benchmark is established, the next step in a total portfolio LDI solution is to assess the asset distribution between the hedging and the return-generating portfolio. But before we delve further into this topic, we would like to frame the discussion in the context of our previous work on LDI. In past papers, we described in detail that the role of a return-generating portfolio in a total portfolio LDI solution is to generate returns in excess of the liability benchmark. Moreover, we have also shown that this portfolio should be developed without significant bond holdings (in our approach to a total LDI solution, bonds and other interest-rate-sensitive products serve only the purpose of hedging interest rate exposure in liabilities). Finally, we have argued that the appropriate risk measure in a total portfolio LDI solution is the surplus volatility, and that the appropriate measure of portfolio efficiency is the Liability Adjusted Sharpe Ratio (LASR). As an example, Exhibit 7 shows the summary risk and return characteristics for an optimized return-generating portfolio. 6 Exhibit 7 Investors should seek return-generating portfolios with high Sharpe ratios Expected Total Asset Return 8.7% of which, risk-free rate 4.8% of which, market exposure return 1.9% of which, active manager return 2.0% Total Asset Risk * 8.0% market exposure risk 7.3% active manager risk 3.3% Total Asset Sharpe Ratio 0.49 passive Sharpe ratio 0.26 active information ratio 0.62 For illustrative purposes only. *Risk measured as the annualized standard deviation of returns. Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures. Accordingly, the capital allocations between the hedging and return-generating portfolios depend on the required target return, which, in turn, depends on the relationship between the current and the target funding ratio. For example, suppose a pension plan with $1.0 billion in assets and a funding ratio of 90% would like to restore fully funded status in four years. In this case, the target return of assets over liabilities would be approximately 2.5%. 7 Using our methodology (outlined in details in our previous literature 8 ), the LDI solution with an optimal LASR allocates 65% of the capital to the return-generating portfolio and 35% to the hedging portfolio. 6 See Appendix B for details on the capital allocations and risk budget. 7 Targets are subject to change and are current as of the date of this presentation. Targets are objectives and do not provide any assurance as to future results. 8 See Winkelmann, K., McDermott S., Berger, A., Glaubach, S. (2006), Liability-Driven Investment Policy: Managing to the True Benchmark, GSAM; Winkelmann, K., Glaubach, S. (2006), Designing Efficient Return-Generating Portfolios: Tilting Away from Equilibrium toward Alpha and Exotic Beta; and Winkelmann, K., Berger, A., Glaubach, S., Zemlyakova, Y. (2006), The Future of Defined-Benefit Plans: Using LDI Policy to Adapt to New US Pension Regulation. 8 Goldman Sachs Asset Management

9 We illustrate the efficiency generated by the total portfolio LDI solution in Exhibit 8. For comparison purposes, we show risk and return characteristics, and the surplus risk budget for our hypothetical LDI portfolio and for a typical portfolio with 65% allocated to global equity and 35% allocated to US fixed income. Exhibit 8 Total LDI solution tends to improve overall portfolio efficiency Typical Portfolio LDI Portfolio Surplus Risk * 14.5% 5.7% Risk from Investment Policy ** 46.5% 84.7% Net Interest Rate Risk 51.1% 0.0% Unhedgeable Liability Risk (noise) *** 2.4% 15.3% Excess Return over Liabilities 3.0% 2.6% Liability-Adjusted Sharpe Ratio (LASR) For illustrative purposes only. *Risk measured as the annualized standard deviation of pension surplus or deficit as a percent of plan assets. Asset-liability risk presented on a mark-to-market basis, neglecting the application of smoothing, if any, in the presentation of accounting results. **Includes all other assets in the portfolio except investment grade fixed income. ***Unhedgeable liability risk includes all actuarial assumptions not related to interest rates including mortality and employee turnover. We assume 2% risk per 100% of liability present value. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures. The surplus risk and the decomposition of surplus risk are important diagnostic tools. For example, we can see that the surplus risk decreases dramatically when we fully hedge all of the interest rate risk. With the typical portfolio, the surplus volatility is about 14.5%, while surplus volatility declines to 5.7% in the LDI solution. In addition, we can see that the impact of the interest rate mismatch is quite significant in the typical portfolio about 50% of the surplus volatility is attributed to the interest rate mismatch. By contrast (and by design), the impact of the interest rate mismatch is zero in the LDI solution. In fact, all of the surplus volatility in the LDI solution can be attributed to either investment decisions that generate excess returns or noise. Finally, the data also show that the LASR is substantially higher for the LDI solution 0.45 versus 0.21 in the typical portfolio. We will make additional use of the LASR and the surplus risk decomposition in our analysis of alternative hedging solutions. In particular, we will use the surplus risk decomposition to explore the tradeoffs between the impact of the interest rate mismatch, the level of hedging and the structure of the hedging program. Goldman Sachs Asset Management 9

10 Understanding the Tradeoffs in Setting Up Hedging Portfolios There are three basic tradeoffs that investors must work through in developing a hedging portfolio. These tradeoffs are important for two reasons: First, they help the plan sponsor understand the investment policy implications of the structure of the hedging portfolio. Second, they help the plan sponsor structure a mandate for external management of the hedging portfolio. These tradeoffs are: 1. The structure of the hedging portfolio relative to the liability benchmark, 2. The structure of the hedging portfolio relative to the overall surplus risk, and 3. The level of hedging relative to the impact of the interest rate mismatch and to the probability of collateral exhaustion. These tradeoffs should form an important part of the dialogue between the pension plan sponsor and their external managers. In the following sections, we will discuss each of the hedging tradeoffs in detail. 1. Structuring the Hedging Portfolio The root of this tradeoff is whether the actual hedging portfolio should deviate from the liability benchmark. We know this benchmark is designed to match interest rate risk characteristics of the liability stream, and, as a result, may hold a large number of interest rate swaps. However, an investor could decide to hold a smaller number of swaps (e.g., hold the 10-year and 30-year swaps), or to hold a combination of swaps and bonds, or to hold bonds and futures. Holding a portfolio that differs from the liability benchmark introduces a basis risk or tracking error. It is this basis risk that investors must consider when designing a hedging portfolio or structuring a mandate for external management. Exhibit 9 illustrates this point with four different hedging solutions relative to the liability benchmark. It shows the allocations to alternative hedging vehicles, and calculates the corresponding basis risk. The first portfolio is the liability benchmark itself, with a corresponding basis risk of zero. 9 The second and third portfolios show the impact of reducing the number of swaps held to five and then three, respectively. The fourth portfolio assesses the impact of using a combination of cash and Treasury futures. Exhibit 9 Investors can assess alternative ways of building a hedging portfolio versus the liability benchmark Liability Benchmark Alternative 1 Alternative 2 Alternative 3 in % (7 Swaps) (5 Swaps) (3 Swaps) (Treasury Futures) US Swap 1-Year US Swap 2-Year 1.7 US Swap 3-Year 2.8 US Swap 5-Year US Swap 10-Year US Swap 20-Year US Swap 30-Year US Treasury Bellwethers 10-Year 52.9 US Treasury Bellwethers 30-Year 47.1 Basis Risk to Liability Benchmark 0.0% 0.2% 3.0% For illustrative purposes only. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures. As expected, the basis risk increases as the hedging portfolio deviates from the liability benchmark. When only three points on the swaps curve are used, the basis risk is only 17 basis points. The relatively low basis risk can be attributed to the observation that, in our example, the principal source of interest rate risk in the liability benchmark is the impact of changes in the general level of interest rates. 9 Although the liability benchmark carries no basis risk, it still carries unhedgeable risks, or noise. 10 Goldman Sachs Asset Management

11 The basis risk between the hedging portfolio and the liability benchmark increases when futures and bonds are used (in this example, we have approximated a US Treasury futures position with 10-year and 30-year bellwether bonds). Now, the basis risk includes the impact of the basis risk between futures (or bonds) and swaps, as well as the more general impact of changes in the level of interest rates. These figures are relevant for investors who are looking to structure a mandate for an external manager to hedge the liability stream. In this context, the plan sponsor would provide the external manager with the liability benchmark and an investment opportunity set, consisting of bonds, swaps and futures. Finally, the plan sponsor would provide a tracking error target relative to the liability benchmark. The degree to which the manager uses the flexibility afforded by a broad investment opportunity set would be driven by the magnitude of the tracking error target. 2. Overall Surplus Risk Considerations Of course, pension investors are also investing in an effort to generate return in excess of the liability benchmark. Thus, the basis risk generated by the structure of the hedging portfolio should be considered in the context of the overall surplus risk. The overall surplus risk, in turn, depends on the risk level of the return-generating portfolio. An investor may be willing to tolerate an imperfect hedge as long as the impact on total surplus volatility is quite small. Exhibit 10 illustrates this point by calculating the surplus volatility for each of the portfolios shown in Exhibit Exhibit 10 Basis risk in hedging portfolio should be reflected in the risk budget for the aggregate portfolio Liability Benchmark Alternative 1 Alternative 2 Alternative 3 in % (7 Swaps) (5 Swaps) (3 Swaps) (Treasury Futures) 65% Allocation to Return-Generating Portfolio Surplus Risk * Risk from Investment Policy Net Interest Rate Risk Unhedgeable Liability Risk (noise) ** % Allocation to Return-Generating Portfolio Surplus Risk * Risk from Investment Policy Net Interest Rate Risk Unhedgeable Liability Risk (noise) ** For illustrative purposes only. *Risk measured as the annualized standard deviation of pension surplus or deficit as a percent of plan assets. Asset-liability risk presented on a mark-to-market basis, neglecting the application of smoothing, if any, in the presentation of accounting results. **Unhedgeable liability risk includes all actuarial assumptions not related to interest rates including mortality and employee turnover. We assume 2% risk per 100% of liability present value. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures. As shown, the choice of the hedging structure has a negligible impact when the number of swaps is reduced. At either capital allocation, reducing the number of swaps from seven to three has virtually no impact on the total surplus risk, and only a negligible impact on the contribution of interest rate risk to surplus volatility. The negligible contribution from the interest rate mismatch occurs because reducing the number of swaps introduces higher order interest rate effects (e.g., the impact of slope and curvature), and these are relatively unimportant for a long duration pension liability. 10 The surplus volatility shown in Exhibit 10 uses the same return-generating portfolio of Exhibit 6, together with the assumption that 35% of the total capital is allocated to the hedging portfolio. In addition to the surplus volatility, Exhibit 10 shows the contribution to surplus volatility from the basis risk arising from the mismatch between the hedging portfolio and the liability benchmark. Finally, for comparison purposes, Exhibit 10 also shows the same statistics when the capital allocation to the return-generating portfolio is 50%. Goldman Sachs Asset Management 11

12 Surplus volatility does go up somewhat when Treasury futures are used rather than swaps. Furthermore, the impact of the net interest rate risk also increases. Both effects are attributable to the basis risk between swaps and futures, not fundamental interest rate factors. These issues become important considerations when setting the target tracking error for an external manager. An investor who would like to reduce the impact of the basis risk between futures and swaps should decrease the tracking error target relative to the liability benchmark. This analysis leads us to two main conclusions: First, investors who are concerned about generating significant excess returns relative to liabilities have significant flexibility in designing a hedging portfolio. Second, investors who are less concerned about generating excess returns should probably place more emphasis in the construction of the hedging portfolio, and in reducing the tracking error targets for their external mandates. 3. Impact of Interest Rate Mismatch and Probability of Collateral Exhaustion The next important issue that deserves attention is determining the size of the hedge. In other words, at what point do the benefits from hedging decline so significantly that they become less useful? To answer this question, we need to identify an economic cost of interest rate hedging (beyond explicit transactions and management costs). Since fully implementing a liability hedge will involve the use of derivatives, the cost question can be re-framed in terms of the probability of collateral exhaustion. Let s look at the benefits and costs of alternative hedging portfolios in turn. Exhibit 11 (next page) uses our hypothetical portfolio s previously mentioned allocations to describe the benefits of hedging in terms of the impact on the marginal contribution to surplus volatility. To analyze the hedging portfolio, we start with a portfolio that is fully invested in a long-duration bond index (approximately hedging 30% of the interest rate risk in liabilities). Subsequent hedging portfolios are constructed by pledging cash collateral for a swaps overlay portfolio. The swaps overlay portfolio is constructed with a combination of short-duration and long-duration swaps it s the liability benchmark. The table shows that as the allocation to the swaps overlay portfolio increases, the surplus volatility decreases. Also, the contribution to surplus volatility from interest rate exposure decreases, and the LASR increases. Furthermore, we see that the most significant improvements in the LASR occur with the first three allocations to the overlay portfolio (60% hedge). Subsequent allocations to the overlay portfolio improve the LASR, but do so at a diminishing rate. To implement the swaps overlay portfolio, we need to pledge collateral and use leverage. The more we hedge interest rate risk, the more leverage we need. So, if interest rates increase, we will have to pay out of collateral. Thus, the price for hedging the interest rate mismatch and pledging cash as collateral can be quantified as the chance that we will exhaust the pledged collateral. This price will increase as more leverage is used. Exhibit 11 illustrates this point with two sets of statistics. The first shows the number of standard deviations that interest rates will have to move before collateral is exhausted. For example, when the collateral is pledged to hedge only 20% of the interest rate risk, then there is sufficient collateral for a 14-plus standard-deviation move in rates. By contrast, when the collateral is pledged for a full hedge, then there is sufficient collateral to cover about a three standard-deviation move in rates. The second translates the magnitude of the interest rate moves into probabilities of exhausting collateral. Looking again at the 20% hedge, there is an imperceptibly small probability that collateral will be exhausted over one-, three- and five-year horizons. By contrast, when all of the interest rate risk is hedged, there is an imperceptibly small chance that collateral will be exhausted over a one-year horizon. However, over a five-year horizon, there is almost a 4% chance that all of the collateral will be used. 12 Goldman Sachs Asset Management

13 Exhibit 11 As the allocation to the swaps overlay hedging portfolio increases, the surplus volatility decreases Hedge with Long Duration Bond Hedge with Swaps Overlay Hedge 30% Hedge 20% Hedge 40% Hedge 60% Hedge 80% Hedge 100% of Liabilities of Liabilities of Liabilities of Liabilities of Liabilities of Liabilities Surplus Risk * 10.3% 10.6% 8.9% 7.4% 6.2% 5.7% Excess Return over Liabilities 2.4% 2.5% 2.5% 2.5% 2.5% 2.6% Liability-Adjusted Sharpe Ratio (LASR) Surplus Risk, as % of Assets 10.3% 10.6% 8.9% 7.4% 6.2% 5.7% Due to Risky Assets 5.6% 5.6% 5.5% 5.4% 5.3% 5.2% Due to Risky Liabilities 8.6% 9.1% 7.0% 5.0% 3.2% 2.2% Risk from Investment Policy 30.0% 27.3% 38.0% 53.7% 73.0% 84.7% Net Interest Rate Risk 65.3% 68.3% 55.8% 37.2% 14.2% 0.0% Unhedgeable Liability Risk (noise) ** 4.7% 4.4% 6.3% 9.1% 12.8% 15.3% Collateral, as % of Assets 35% 35% 35% 35% 35% Number of Standard-Deviation Rises in Interest Rates Covered by Collateral *** Probability of Exhausting Collateral (%) In 1 Month **** In 3 Months **** In 1 Year **** In 3 Years **** In 5 Years **** For illustrative purposes only. *Risk measured as the annualized standard deviation of pension surplus or deficit as a percent of plan assets. Asset-liability risk presented on a mark-to-market basis, neglecting the application of smoothing, if any, in the presentation of accounting results. **Unhedgeable liability risk includes all actuarial assumptions not related to interest rates including mortality and employee turnover. We assume 2% risk per 100% of liability present value. ***Assumes a 1% interest rate volatility. ****Probability calculations assume a normal distribution of returns. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures. Thus, the tradeoffs that investors face in setting the size of the hedging program are between reducing the impact of the interest rate mismatch on surplus volatility (thereby decreasing surplus volatility and improving portfolio efficiency) and increasing the probability of collateral exhaustion. One way for the plan sponsor to resolve this tension is to pin down the level of collateral exhaustion with which they are comfortable. From this figure, the plan sponsor can then work backwards to determine the level of the hedge, and the corresponding effects on both surplus volatility and the contribution of the interest rate mismatch to surplus volatility. In our example, a plan sponsor may decide that they are comfortable with no more than a 50 basis-point chance that collateral is exhausted over a five-year horizon. This figure would then correspond to hedging 60% of the interest rate mismatch and a surplus volatility of 7.4%. The remaining interest rate mismatch would account for 37% of the surplus volatility One remaining question is whether plan sponsors can rely on potential efficiency improvements from the return-generating portfolio. We believe no further efficiencies can be gained if the return-generating portfolio has been optimized and the capital allocated to it has been chosen to achieve the target return. That said, investors should remain attuned to the potential future development of new strategies, which, over time, could further improve the return-generating portfolio. Goldman Sachs Asset Management 13

14 Real Liabilities: Considering the Impact of Inflation Until this point, our discussion has focused on nominal liabilities. We have assumed that all liability projections are for fixed nominal payments nominal payments are fixed and real values of future liabilities vary with the path of future inflation. This assumption also lets us take advantage of a very liquid nominal interest rate swaps market to construct a liability benchmark and implement a hedging program. However, some liability streams are expressed in real terms, not nominal terms. In this case, it is future real payments that are fixed, and future nominal payments vary with the actual path of inflation. In practice, one can think of this structure as a nominal cash flow projection plus an adjustment for uncertain future levels of inflation. Conceptually, the switch from nominal to real cash flows will have an impact on how we think about the mark-to-market risk associated with future cash flows. At one level, the risk of real cash flows is measured as the response in the value of the real cash flow to changes in the real interest rate. In practice, however, real cash flows should be seen as representing a fixed nominal cash flow (that incorporates an inflation projection) plus an adjustment for future shocks to inflation (i.e., deviations from the inflation projection). From this perspective, the market risk of a future real cash flow is simply the market risk of the future nominal cash flow plus the market risk of the inflation adjustment. In addition, there will be an adjustment for any diversification benefits between nominal interest rates and inflation (if they exist). The introduction of an inflation adjustment impacts both the structure of the liability benchmark portfolio and the actual hedging portfolio. We can think of the liability benchmark as consisting of two parts: the first reflects the certain nominal cash flows, while the second acts to replicate the adjustment for future inflation. Practically, the liability benchmark is simultaneous positions in a nominal interest rate swaps portfolio (as in the preceding discussion) and in an inflation swap portfolio. The first replicates the impact on the market value of liabilities of changes in nominal interest rates (i.e., the effect of nominal interest rates on the certain nominal cash flows). The second replicates the impact on the market value of liabilities of changes in inflation. Exhibit 12 (next page) illustrates the impact of the switch to real cash flows by taking sample nominal cash flows and adjusting them to reflect the inflation component. 12 The adjustment assumes an inflation rate of 3.0%. As shown, introducing an automatic inflation adjustment shifts the pattern of the nominal cash flows up. Similarly, if deflation occurred, then nominal payments would be adjusted down Since many UK pension plans have inflation-linked liabilities, we have constructed an example of the cash flows for a representative UK pension plan for this portion of our analysis. 13 In practice, many inflation adjustments have both caps and floors. The cap acts to dampen the impact of the inflation adjustment for higher inflation rates and the floor acts to dampen the impact of the deflation adjustment. Analysis of inflation caps and floors is beyond the scope of this paper. 14 Goldman Sachs Asset Management

15 Exhibit 12 Introducing an automatic inflation-adjustment mechanism shifts the pattern of the nominal cash flows up Cash Flows ( Millions) 120 Real Cash Flows 100 Nominal Cash Flows For illustrative purposes only. In Exhibit 13, the inflation swaps portfolio assumes that nominal cash flows adjust to exactly match changes in inflation. 14 Exhibit 13 The structure of the liability benchmark consists of positions in nominal swaps and in inflation-linked swaps Notional Amount ( ) Maturity Nominal Swaps * Inflation-Linked Swaps ** 1-Year Swap 110,112,621 5,939,646 2-Year Swap 102,465,686 8,249,342 3-Year Swap 97,713,535 10,378,631 4-Year Swap 88,526,480 12,162,761 5-Year Swap 84,803,456 13,781,897 6-Year Swap 80,764,550 15,095,580 7-Year Swap 77,224,824 16,262,835 8-Year Swap 73,854,907 17,251,270 9-Year Swap 70,389,134 18,013, Year Swap 97,306,238 27,006, Year Swap 145,910,430 46,567, Year Swap 192,073,617 72,459, Year Swap 186,096,936 86,172, Year Swap 125,699,159 67,391, Year Swap 121,422,873 87,411,793 Total 1,654,364, ,143,687 For illustrative purposes only. *Modeled using ICAP Zero Coupon Swap Indices. **Modeled using Bloomberg UK RPI Indices. 14 In actual practice, inflation adjustments are often smoothed and can have caps and floors. Goldman Sachs Asset Management 15

16 Now that we have the positions in the two hedging portfolios, we can next assess the mark-to-market risk in the liability benchmark. As in the case of fixed nominal cash flows, the risk in the nominal interest rate hedging portfolio will depend on the nominal duration of the liability stream and the volatility of nominal interest rate movements. The risk in the inflation hedging part of the portfolio will depend on the nominal duration and the volatility of inflation. Finally, the total risk of the liability benchmark will be influenced by any diversification effects between nominal interest rates and inflation. Exhibit 14 shows the risk characteristics for the liability benchmark with and without the adjustment for inflation. Introducing the inflation adjustment increases the volatility of the liability benchmark. However, the impact of the adjustment is small relative to the fixed nominal cash flow exposure. 15 Exhibit 14 Introducing inflation adjustment slightly increases the volatility of the liability benchmark Risk Characteristics of the New Liability Benchmark Interest Rate Risk from Nominal Swaps 85.8% Interest Rate Risk from Inflation-Linked Swaps 4.3% Unhedgeable Liability Risk (noise) * 9.9% Total 100.0% Total Risk ** 6.4% Risk from Nominal Swaps 5.8% Risk from Inflation Swaps 0.9% For illustrative purposes only. *Unhedgeable liability risk includes all actuarial assumptions not related to interest rates including mortality and employee turnover. We assume 2% risk per 100% of liability present value. **Risk measured as the annualized standard deviation of the liability benchmark as a percent of plan liabilities. So far, our discussion has assumed that the liability benchmark is constructed from nominal interest rate swaps and inflation swaps. This is convenient because it views the liability stream as a fixed nominal payment plus a series of uncertain inflation adjustments. Alternatively, we could have treated the liability stream as a known series of real cash flows, and constructed the liability benchmark as a series of exposures to real interest rates (i.e., calculated the liability benchmark with real government bonds). We decided not to take that road for two reasons: First, inflation smoothing is used in the calculation of yields on real government bonds, and this smoothing is unlikely to match the inflation adjustments present in most real liabilities. Second, we considered the availability of real bonds in the market. Put simply, the supply of real government bonds is quite limited, both relative to the nominal bond market and along the curve. Exhibit 15 illustrates this point by showing the market values at selected term structure points for each of the major real government bond markets. In this context, investors who create liability benchmarks with real bonds are quite limited in terms of the options available to them relative to using inflation swaps. In summary, introducing real liabilities adds a complication, but a surmountable one. The path to creating a liability benchmark is to treat the aggregate portfolio as a sum of a nominal interest rate hedging portfolio and an inflation hedging portfolio. Once that is done, the issues become the same as for the nominal hedging portfolio. 15 It is worth noting that a more volatile inflation process would increase the contribution of the inflation component to the risk of the liability stream. 16 Goldman Sachs Asset Management

17 Exhibit 15 Supply of inflation-linked government bonds is limited Market Value of Inflation-Linked and Nominal Bonds Inflation Linked Nominal $ Billions 10,000 8,000 6,000 4,000 2,000 0 US UK Euro Source: Barclays Capital Conclusion More and more investors around the world are adopting total LDI solutions. These solutions treat the liability stream as the plan s true benchmark, and consequently consider all risk and return characteristics relative to the liability stream. In this context, the aggregate investment portfolio is perceived as a hedging portfolio and a return-generating portfolio. This type of structure is not unduly complicated by the use of real instead of nominal liabilities. Specifically, this paper explored the tradeoffs investors face when designing a hedging portfolio. Our structure has separated the hedging issue into two separate portfolios: the first is a portfolio that mimics the risk characteristics of the liabilities, which we ve called the liability benchmark. The second is the actual hedging portfolio, whose design is based on the liability benchmark. We find that investors have considerable flexibility in reducing the number of hedging instruments used when the target return (relative to the liability stream) is large. By contrast, when the target return (relative to the liability stream) is small, then investors are well served by expanding the number of hedging instruments in their hedging programs. This flexibility can be reflected in the tracking error target given to external managers with hedging mandates. Goldman Sachs Asset Management 17

18 Appendix A Cash Flow Replication The liability benchmark is calculated by taking each projected liability cash flow and finding a portfolio of equivalent swaps. One of the issues is that the liability payment dates are very unlikely to exactly match the benchmark swap rates. Thus, the issue is to construct a portfolio of swaps that preserves both the value and the duration of the liability stream. Suppose that we have three payment dates, t<t <t, and suppose that a liability cash flow occurs at date t. Furthermore, suppose that there are two nominal zero-coupon swaps, one maturing at date t and the other at date t. Let the discount rate from zero to t be r, and the forward rate between t and t be f. Our objective is to determine the percentages of the value of the liability cash flow to allocate to the zero-coupon swaps maturing at t and t. We would like to do so in such a way to preserve the value and the interest rate sensitivity. Let w be the percentage of the value allocated to the zero maturing at date t and w be the allocation to the zero maturing at date t, and let the liability cash flow occurring at date t be denoted L. With this notation, the allocation w and w are given as follows: w = Le -f(t -t) [(t -t )/(t -t)] w = Le f(t -t) [(t -t)/(t -t)] Note that while these weights preserve both value and duration, they do not preserve convexity. Trying to preserve convexity would be difficult, as the resulting system of equations would be over-identified (i.e., three equations and two unknowns). Appendix B Optimal Return-Generating Portfolio This appendix shows the capital allocations and risk budget for an optimized return-generating portfolio. The portfolio was constructed using the process outlined in our paper titled Liability- Driven Investment Policy: Managing to the True Benchmark. Exhibit 1 A return-generating portfolio tends to focus on uncorrelated sources of alpha, exotic beta and beta Capital Allocations Risk Budget Cash for Completion, 1.0% US Small Cap Equity, 8.9% GTAA Overlay, 7.2% EAFE Equity, 5.7% Emerging Equity, 3.0% All Other Risk, 0.9% GTAA Overlay, 3.2% Hedge Funds, 2.2% US Large Cap Equity, 8.2% US Small Cap Equity, 16.7% Hedge Funds, 39.6% US High Yield, 13.8% Emerging Debt, 1% US Public Real Estate, 5.7% Private Equity, 12.9% Commodities, 1.2% Private Equity, 28.7% US Public Real Estate, 4.7% Emerging Debt, 0.9% EAFE Equity, 21.6% Emerging Equity, 6.0% US High Yield, 7.0% All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures. 18 Goldman Sachs Asset Management

19 Glossary of Terms Alpha: Expected return not explained by movements in the market. Alpha is usually measured as the excess return of an investment above its benchmark. A positive alpha is the extra return awarded to the investor for taking active risk, instead of accepting the market return. Active Risk: The risk associated with deviations from a passive benchmark. The deviations from the benchmark are the active weights, which reflect the manager s views on where value can be added. The return associated with these views is the active return. The standard deviation of this return is the active risk. Beta: Measures how much exposure the portfolio, or security, has to the market. A beta of 1.0 indicates that, all else equal, the portfolio will have the same return as the market. A beta higher than 1.0 indicates that the portfolio (or security) will have a higher return than the market, while a beta lower less than 1.0 indicates that the portfolio (or security) will have a lower return than the market (all other factors held constant). In this case, the other factors are the active risk. Black-Litterman model: The Black-Litterman model treats expected returns (on asset classes or active strategies) as a blend between equilibrium returns and investor-specific views. Users of the model can vary how much weight is placed on their views, and how much confidence is expressed in one view relative to another. Capital Asset Pricing Model (CAPM): The CAPM is an equilibrium model that expresses all asset returns in terms of their covariance with the market. Completion Programs: A completion program is a strategy intended to give a portfolio a consistent set of exposures over time. For example, an equity completion program might target a 30% portfolio exposure to large cap US equity. If, at the end of a certain month, the portfolio s equity holdings were only 27% (perhaps due to market volatility), the completion program would add back 3% equity exposure to give the portfolio 30% exposure over the next month. These programs are generally implemented with futures. A duration completion strategy is designed to give the portfolio a constant duration over time. Convexity: Measures the change in duration vis-à-vis the change in interest rate. Correlation: A statistical measure of the co-movement between two variables. A positive correlation indicates that the two variables move together, while a negative correlation indicates that they move in opposite directions. The value of a correlation can range from -1 to +1. A correlation of zero means that the two variables are independent of one another. Covariance: In statistics, it describes the correlation between two variables multiplied by the standard deviation for each of the variables. Covariance Matrix: A collection of many covariances in a matrix form. Duration: The approximate percent by which a future liability s market value will change if the yield changes by 100 bps (one percentage point). Efficient Frontier: The set of investment portfolios that maximizes the expected rate of return at any given level of portfolio risk. A portfolio below the frontier is not efficient because, for the same risk, it is possible to achieve greater expected return. Goldman Sachs Asset Management 19

20 Equilibrium: A theoretical state of the world where supply equals demand. All prices reflect fair value, and there is no opportunity to outperform the market (i.e., no alpha). Excess Return: The measurement of a portfolio s return minus the return of the risk-free rate. Achieving excess return implies you have attained a return above what you would have made if you invested in cash. Exotic Beta: Exotic beta is a market exposure that is expected to earn higher returns than it would normally be predicted by the CPAM over a relatively long future horizon. Information Ratio (IR): The return of a portfolio relative to its benchmark divided by the tracking error. A higher number is better, indicating that the portfolio manager was able to achieve more excess return for each unit of active risk. The IR is particularly helpful in comparing managers with different returns and different levels of risk. Mark-to-Market Framework: A framework in which assets and/or liabilities are assessed at their true market value at regular intervals for regulatory or accounting purposes. This can be contrasted with a framework where assets (and/or liabilities) are always valued at their initial purchase price or where some actuarial smoothing methodology is used to value them. Market Risk: The portion of an investment s risk coincides with the market and, therefore, cannot be eliminated by diversification. It is also known as systematic risk. In most balanced portfolios, the market risk is driven by exposure to overall equity market returns, and is measured by the beta. Market Risk Premium: The difference between the expected return on a market portfolio and the risk-free rate. Risk-Free Rate: The rate of return on an asset that has no risk. For example, when we have a short time horizon, we might use three-month LIBOR. When we have a long-time horizon, we might use the ten-year Treasury yield as the risk-free rate. Sharpe Ratio: A measure of the risk adjusted return of the portfolio. Similar to an IR, the Sharpe ratio is measured by subtracting the risk-free rate of return from the return of the portfolio and dividing by the portfolio s standard deviation. A higher number indicates that the portfolio was able to achieve more return for each unit of risk taken. Smoothing: A methodology for valuing assets (and/or liabilities) whereby changes in value are realized gradually over time rather than immediately recorded. For example, a $1 billion portfolio that lost 20% of its value ($200 million) in one year might be able to smooth that loss by recognizing a $50 million loss in each of the next four years, rather than immediately reducing its value to $800 million. Standard Deviation: In statistics, it measures the dispersion of a variable around its mean value. In a normal distribution, about 66% of the observations can be expected to be within +/- 1 standard deviation of the mean, and about 96% of the observations can expected to be within +/- 2 standard deviations of the mean. Tracking Error: The standard deviation of a portfolio s return relative to a benchmark (usually the representative index). Volatility: Usually taken to mean the standard deviation of portfolio returns. 20 Goldman Sachs Asset Management