The missing link: Economic exposure and pension plan risk. March 2012

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The missing link: Economic exposure and pension plan risk March 2012 FOR INSTITUTIONAL AND PROFESSIONAL INVESTOR USE ONLY NOT FOR RETAIL USE OR DISTRIBUTION

About J.P. Morgan Asset Management s Strategy Group This paper represents the latest instalment of our Global Strategic Research publication series from the Strategy Group at J.P. Morgan Asset Management. The Strategy Group partners with clients to develop objective, thoughtful solutions to the broad investment policy issues faced by corporate and public defined benefit pension plans, insurance companies, endowments and foundations. Our global team is one of J.P. Morgan s primary centres for thought leadership and advisory services for institutional clients in the areas of asset allocation, pension finance and risk management. The team s expertise is supported by powerful analytical capabilities for conducting asset/ liability, risk budgeting and optimal asset allocation analysis, in line with client-specific investment guidelines, risk tolerance and return requirements. In response to the changing needs of CFOs, treasurers and CIOs, our suite of tools has expanded to include corporate finance based risk management analytics for assessing and proactively managing the impact of the pension plan on the corporation as a whole. J.P. Morgan Asset Management For more than a century, institutional investors have turned to J.P. Morgan Asset Management to skillfully manage their investment assets. This legacy of trusted partnership has been built on a promise to put client interests ahead of our own, to generate original insight and to translate that insight into results. Today, our advice, insight and intellectual capital drive a growing array of innovative strategies that span U.S., international and global opportunities in equity, fixed income, real estate, private equity, hedge funds, infrastructure and asset allocation. This publication was produced by the Institutional Strategy Group at J.P. Morgan Asset Management.

Table of contents 1 Introduction: facing down factor risk 2 Joint plan and sponsor stresss 7 Extending the framework 9 Appendix 10 Glossary 11 Bibliography

IV The missing link: Economic exposure and PENSION PLAN risk I n t r o d u c t i o n : f a c i n g d o w n f a c t o r r i s k

Pension plan trustees are increasingly aware of the range of risks present in defined benefit pension plans. Volatile markets have led to volatile funding ratios, compounding the impact of falling interest rates and increasing longevity. This heightened awareness has led many plans to look at ways of managing these risks. Another key risk has proved more difficult to manage. The security of participants benefits is often dependent on the assumption that any shortfall in a pension plan s assets relative to its liabilities will be met by the company funding it, referred to here as the plan sponsor. Yet there is a risk that a plan sponsor may fail. If a plan s sponsor falls into insolvency when the plan is in deficit, then the plan s participants are at risk of receiving reduced pensions. The risk of sponsor insolvency is often closely linked to the performance of plan assets when firms are struggling, pension plan assets are more likely to be depressed. This link between the health of a sponsor s business and the funded status of its pension plan is as great a concern for the sponsor as for the plan participants. It creates the risk that when plan assets perform poorly, the need for funding to boost declining funded status will come at precisely the worst time for the sponsor. Funded status aside, a plan s poor investment performance could exaggerate poor performance in the sponsor s business as the corporate balance sheet must take into account plan investment results. While insulation from the performance of the sponsor s equity is provided by legislation, this provides incomplete protection. In this paper, we propose an approach to dealing with the risk that a sponsor may not be able to make up a shortfall in plan assets. We discuss a framework that can be used to develop a portfolio designed to protect against extreme adverse events for the sponsor while at the same time maintaining a particular target rate of return. Key to this approach is the measure used to describe the financial health of the sponsor. One obvious variable would be the sponsor s share price. However, since our framework is calibrated using historical data, there is a risk that this will reflect past idiosyncratic events. Further, the sponsor is unlikely to have experienced extreme stresses in the historical data, an example of survivorship bias. As an alternative, we therefore propose using an economic variable that can serve as a proxy for the risks faced by the firm. Essentially we think in terms of the economic exposure of the sponsor. The nature of this exposure varies from firm to firm for example, an aircraft manufacturer might be negatively exposed to extreme increases in the price of aluminium, while a firm that mines aluminium ore will be negatively exposed to its opposite: extreme decreases. Similarly, an airline might be negatively exposed to the risk that oil prices rise sharply, while an oil producer will be concerned about collapsing oil prices. In this paper, we use the example of an oil producer to show how an asset allocation to hedge sponsor risk could be constructed. We conclude that it is in general possible to construct a portfolio that allows investors to mitigate the risk of extreme adverse movements in a key variable in our example, the oil price without sacrificing expected returns or portfolio efficiency. J.P. Morgan asset management 1

Joint plan and sponsor stress In this section, we present a framework which addresses the question of joint plan and sponsor stress within the context of a non-normal model of financial returns. Non-normality, a brief introduction There is an extensive academic literature on the non-normality of market returns and the associated impact on portfolio construction and risk measures, when compared with the mean-variance theory pioneered by Harry Markowitz in 1952. In the following analysis, we consider portfolio risk as measured through the non-normality of market returns model developed by J.P. Morgan Asset Management. 1 This model focuses on non-normality in simulating asset returns as influenced by three factors: Serial correlation: returns in different periods are not independent and identically distributed. Prior period returns influence the level of return in later periods. Fat left tails: negative returns are observed in greater magnitude and greater frequency than predicted by a normal distribution. Correlation breakdown: correlations between asset classes are not constant, but instead tend to converge during periods of market stress. Non-normality of market returns Ignoring non-normality can significantly understate downside portfolio risk in the worst of the worst case scenarios, potentially posing a solvency risk for the investor. An asset allocation incorporating non-normality can reduce the portfolio s volatility, improve its efficiency 2 and reduce its vulnerabilities to unpredictable and extreme negative market events. J.P. Morgan Asset Management has developed an asset allocation framework which incorporates the phenomena of non-normality in public and alternative investment markets into the asset allocation process. Our framework allows investors to structure a portfolio to take into account downside risk in a more robust fashion than traditional asset allocation frameworks based on the assumption of normality. 1 Sheikh, Abdullah and Hongtao Qiao. The Non-Normality of Market Returns, J.P. Morgan Asset Management (2009) 2 Habitually measured by means of the Sharpe Ratio, portfolio efficiency is here meant to represent portfolio return per unit of risk taken. 2 The missing link: Economic exposure and PENSION PLAN risk

joint plan and sponsor stress From VaR to CVaR to CRCVaR In line with previous work using the non-normality of market returns model, we make use of the Conditional Value at Risk (CVaR) measure of portfolio risk. The CVaR is calculated as the average portfolio return for a given level of confidence. For example, the CVaR95 would be defined as the average loss in a portfolio in the worst 5% of scenarios, based on forwardlooking computer-run simulations using the non-normality model. It contrasts with the more conventional Value at Risk VaR which solely measures return at the fifth percentile. The Cross-Return CVaR (CRCVaR) extends the Portfolio CVaR concept to consider the return on the portfolio relative to a given factor, such as an asset or other economic variable. The CRCVaR95 is calculated as the average portfolio return during the lowest 5% of factor returns. Exhibit 1 shows the key steps in this process: Exhibit 1: Steps to Calculate the Cross-Return CVaR95 Step 1: Simulate asset returns Step 2: Identify simulations in which worst 5% of asset returns occur Step 3: Identify portfolio returns for those simulations The returns of both the factor and the portfolio are simulated. The simulations in which the worst 5% of factor returns are identified. The average portfolio return in the simulations that correspond to the worst 5% of factor performances is calculated. The oil CRCVaR95 of a portfolio is the average portfolio return during the steepest 5% of annual oil price declines. It provides a link between the performance of this specific factor and its implications for the performance of the portfolio as a whole. Simulation 1 17 567... 9695 9923 500 Asset return 0.4345 0.6749 0.3432... 0.3224 0.5450 420.2122 Portfolio return 1.7432 1.4387 1.1650... 0.7342 0.2250 596.2122 Step 4: Average portfolio returns for these simulations to determine Cross-Return CVaR95 (Portfolio returns from Step 3) 5% * Total simulations Cross-Return CVaR95 Source: J.P. Morgan Asset Management. For illustration purposes only. Integrating Sponsor and Plan Risk CRCVaR allows for the consideration of the risk posed by joint plan and sponsor stress. The business of a pension plan sponsor whose financial health is positively linked to the returns on a particular asset is likely to slump under periods of low returns for the asset. Obviously it would be undesirable if the assets of the pension plan also performed badly at this time since the confluence of underperformance in both the sponsor s business and the plan s assets would restrict the ability of the sponsor to address any funding shortfall precisely when the need for pension contributions would be heightened. J.P. Morgan asset management 3

joint plan and sponsor stress Protecting a long-term portfolio against asset price risk The following section shows how the CRCVaR measure of factor-specific risk can be integrated into the process of making asset allocation decisions. We continue with our example of a firm subject to the risk of falling oil prices. We first consider whether it is possible to increase protection at the total portfolio level. We then consider the equity allocation in isolation, before looking at whether it is possible to achieve the same return and overall equity index risk while reducing the oil price risk. Our analysis is based upon 100,000 simulations of the non-normality model, on a one-year basis. Similar results should apply to a longer investment timeframe. Exhibit 2 shows in its first column a representative pension plan, with a 55% allocation to equities, a 30% allocation to fixed income and a 15% allocation to alternative asset classes. The funding level is calculated as the ratio of the pension plan assets to the liabilities, with long Treasury bonds being used as a proxy for liabilities. The assumed starting funding level is 100% for ease of comparison. Below the portfolio allocations in Exhibit 2, the portfolio s expected return is reported, along with the portfolio CVaR95, the expected return of the portfolio in the worst 5% of portfolio returns, and the portfolio oil CRCVaR95 return, the expected return of the portfolio in the worst 5% of years for oil prices. The benchmark portfolio, as shown in the first column, maintains a positive return of 0.6% in the worst five percent of oil years, as shown by the oil CRCVaR95. The 0.6% return suggests that a fall in oil prices would be detrimental to the portfolio, as it is markedly lower than the portfolio s 4.6% expected return. Using the oil CRCVaR framework, we can consider whether the downside protection can be enhanced while maintaining reasonable relative portfolio efficiency. We determine portfolio efficiency by comparing the overall average portfolio return (the expected return) and the average portfolio returns in the 5% worst case scenarios its CVaR95. The second column reallocates the benchmark portfolio, reducing exposure to developed world equity and increasing exposure to emerging market equity and debt, U.S. debt and several alternative asset classes. This reallocation maintains reasonable relative portfolio efficiency, through a stable expected return and an increase in Portfolio CVaR95 of 1.3%. More importantly, the oil CRCVaR95 funded status shows that the plan s funding level would have improved during periods of low oil prices, increasing of 2.4%, from 96.9% to 99.3%. Exhibit 2: Reallocation between asset classes to strengthen downside protection Asset class Benchmark (%) Passive reallocation to target CRCVaR95 (%) Intermediate Treasury 20.0 20.0 Long Treasury 5.0 10.0 U.S. High Yield 5.0 7.5 EMD 0.0 2.5 Total Fixed Income 30.0 40.0 U.S. Equity 40.0 35.0 World ex-u.s. Equity 15.0 10.0 Emerging Markets 0.0 2.5 Total Equity 55.0 47.5 Fund of Hedge Funds 5.0 2.5 Private Equity 5.0 2.5 Commodities 5.0 0.0 Direct Real Estate 0.0 5.0 Leveraged Loan 0.0 2.5 Total Alternatives 15.0 12.5 Total allocation 100.0 100.0 Expected return 4.6 4.6 Portfolio CVaR95-18.7-17.0 Portfolio funding level 103.8 103.8 Oil CRCVaR95 return 0.6 2.9 Oil CRCVaR95 funding level 96.9 99.3 Source: J.P. Morgan Asset Management. For illustration purposes only. 4 The missing link: Economic exposure and PENSION PLAN risk

joint plan and sponsor stress Constructing a hedge against economic exposure Following from our analysis of the relationships between financial assets and the oil price, we now consider the extent to which the sectoral components of the S&P 500 Index are exposed to oil CRCVaR risk. A high exposure to oil CRCVaR risk would suggest that we could improve the performance of the portfolio not just by reallocation away from equities, as in Exhibit 2, but by altering the allocation to the underlying sectoral components of the S&P 500. 3 Exhibit 3: Market Value weighting of the S&P 500 Index Sector MV weighting (%) Energy 12.5 Materials 3.5 Industrials 10.5 Consumer Discretionary 10.8 Consumer Staples 11.3 Health Care 11.5 Financials 13.5 Information technology 19.8 Telecoms 3.0 Utilities 3.8 Total 100.0 Source: Thomson Reuters Datastream, J.P. Morgan Asset Management. For illustration purposes only. Forward-looking equity sector return assumptions To ensure that our analysis in this section is forward looking, we rely on J.P. Morgan s forward looking Long-Term Capital Market Assumptions for each broad asset class. When modelling returns for the sectoral constituents of the equity index, however, it is unrealistic to assume that each sector s expected return will match that of the index. Some equity sectors are more volatile than others or more highly correlated to others. We allow for this difference among the equity sectors by drawing on a framework first described by William Sharpe in 1974, which combines expected broad market returns based on long-term market views with observed asset class volatilities, plus correlations and market weights, to obtain expected returns for each individual asset class or, in this case, equity sector. 4 (For a fuller description of our methodology, please refer to the Appendix) The return performance on the market-weighted portfolio, detailed in the first column of Exhibit 4, is influenced by the weightings in sectors which exhibit a strong relationship with oil. Even a simple but aggressive re-weighting among the equity sectors, detailed in the second column, can have a marked effect on the oil CRCVaR95, raising it from 5.1% to 11.0%, albeit with an increase in tail risk. This re-weighting has increased expected return by 0.4%, while increasing the risk of loss, the portfolio CVaR95 by 3.8%. In other words, it is possible to reduce oil price exposure by an investment in U.S. equity without significantly sacrificing return, or dramatically increasing overall risk taken. 3 Weightings calculated as at November 14, 2011. Source: Thomson Reuters Datastream 4 For a full description of this approach, please refer to William Sharpe, Imputing Security Returns from Portfolio Composition, The Journal of Financial and Quantitative Analysis, Volume 9, Number 3 (June 1974), pages 463-472 J.P. Morgan asset management 5

joint plan and sponsor stress Exhibit 4: Reallocation of equity sectors to strengthen downside protection Sector MV weighting (%) CRCVaR95 targeted reallocation (%) Energy 12.5 0.8 Materials 3.5 4.6 Industrials 10.5 10.7 Consumer Discretionary 10.8 22.3 Consumer Staples 11.3 10.9 Health Care 11.5 3.4 Financials 13.5 39.8 Information Technology 19.8 0.9 Telecoms 3.0 5.0 Utilities 3.8 1.6 Total 100.0 100.0 Expected return 6.2 6.6 Portfolio CVaR95-26.4-30.2 Oil CRCVaR95 return 5.1 11.0 Source: J.P. Morgan Asset Management. For illustration purposes only. Considering now this impact at the portfolio level, Exhibit 5 shows in the first column the same representative benchmark U.S. pension plan as used in the above analysis. (Note that the allocation to U.S. equity sectors is equivalent to a total allocation of 40%, using the market value weights stated above). The following column displays a portfolio with the same simple but aggressive equity reallocation used in Exhibit 2. It also reduces the total equity allocation to 35%, redistributing the balance to emerging market assets. This portfolio demonstrates modifications to the benchmark asset allocation which strengthen downside protection, with an increase in oil CRCVaR95 funding level of 4.4%, while providing attractive relative portfolio efficiency, with an increase in expected return of 0.1% and an increase in Portfolio CVaR95 of 0.9%. Exhibit 5: Reallocation with the U.S. equity allocation to strengthen downside protection Benchmark CRCVaR95 targeted with active Asset class (%) U.S. Equity allocation (%) Intermediate Treasury 20.0 20.0 Long Treasury 5.0 10.0 U.S. High Yield 5.0 7.5 EMD 0.0 2.5 Total Fixed Income 30.0 40.0 U.S. Equity Energy 5.0 0.3 Materials 1.4 1.6 Industrials 4.2 3.7 Consumer Discretionary 4.3 7.8 Consumer Staples 4.5 3.8 Health Care 4.6 1.2 Financials 5.4 13.9 Information Technology 7.9 0.3 Telecoms 1.2 1.8 Utilities 1.5 0.6 Total U.S. Equities 40.0 35.0 World ex-u.s. Equity 15.0 10.0 Emerging Markets 0.0 2.5 Total Equity 55.0 47.5 Fund of Hedge Funds 5.0 2.5 Private Equity 5.0 2.5 Commodities 5.0 0.0 Direct Real Estate 0.0 5.0 Leveraged Loan 0.0 2.5 Total Alternatives 15.0 12.5 Total allocation 100.0 100.0 Expected return 4.6 4.7 Portfolio CVaR95-18.7-17.8 Portfolio funding level 103.8 104.0 Oil CRCVaR95 return 0.6 5.0 Oil CRCVaR95 funding level 96.9 101.3 Source: J.P. Morgan Asset Management. For illustration purposes only. An oil CRCVaR95 funding level lower than 100% demonstrates that the benchmark portfolio was poorly protected against declines in the oil price. The two targeted portfolios provide an example of the application of the framework to understand and mitigate funding risk in the face of joint plan and sponsor stress. Through this approach, portfolio return has been maintained at roughly equivalent levels, while portfolio CVaR95 and oil CRCVaR95 funding levels have both been increased. 6 The missing link: Economic exposure and PENSION PLAN risk

Extending the framework The framework can be applied to examine further implications of joint plan and sponsor stress. In the following section, two applications are briefly explored: exposures to an upside move in an asset and exposures to other resource or non-resource asset classes, or another economic variable. Exposure to upside moves in an asset class The CRCVaR measure can be easily adapted to consider circumstances when the plan sponsor s business is negatively exposed to changes in asset prices, the opposite question to that posed in our oil case study. For example, the impact of oil prices on a trucking company might well be the opposite of their impact on an oil concern. A spike in oil prices, which would benefit the oil concern, could expose the trucker to joint plan/sponsor stress. The CRCVaR measure of interest for the trucker then would be the CRCVaR05, the average portfolio return in the highest 5% of annual oil price increases. Targeting an oil CRCVaR05 by itself is relatively simple, but of interest is whether the trucker s plan performance can be improved while maintaining reasonable relative portfolio efficiency. The first column in Exhibit 6 demonstrates the performance of the same benchmark portfolio as used in the oil CRCVaR95 case study on an oil CRCVaR05 basis. The second column shows the performance of the portfolio, which was targeted at improving oil CRCVaR95 and in the third column an adjustment to this portfolio to target oil CRCVaR05. J.P. Morgan asset management 7

extending the framework Exhibit 6: Reallocation to strengthen upside protection Asset class Benchmark (%) CRCVaR95 targeted (%) CRCVaR05 targeted (%) Intermediate Treasury 20.0 20.0 22.5 Long Treasury 5.0 10.0 5.0 U.S. High Yield 5.0 7.5 2.5 EMD 0.0 2.5 0.0 Total Fixed Income 30.0 40.0 30.0 U.S. Equity Energy 5.0 0.3 13.0 Materials 1.4 1.6 2.7 Industrials 4.2 3.7 3.4 Consumer Discretionary 4.3 7.8 4.4 Consumer Staples 4.5 3.8 2.8 Health Care 4.6 1.2 0.9 Financials 5.4 13.9 1.5 Information Technology 7.9 0.3 10.1 Telecoms 1.2 1.8 0.3 Utilities 1.5 0.6 1.0 Total U.S. Equities 40.0 35.0 40.0 World ex-u.s. Equity 15.0 10.0 15.0 Emerging Markets 0.0 2.5 0.0 Total Equity 55.0 47.5 55.0 Fund of Hedge Funds 5.0 2.5 5.0 Private Equity 5.0 2.5 5.0 Commodities 5.0 0.0 5.0 Direct Real Estate 0.0 5.0 0.0 Leveraged Loan 0.0 2.5 0.0 Total Alternatives 15.0 12.5 15.0 Exposure to other resource or non-resource asset classes This framework can be applied to any asset, or combination of assets, to which a sponsor s business may be highly exposed. For example, exposure for a commercial or retail bank could be proxied by constructing an asset from a short cash and long corporate bond exposure. A non-exhaustive list of other examples is shown in Exhibit 7. Beyond this, the risk associated with changes to macroeconomic variables such as inflation, growth and the interest rate may also be considered. Exhibit 7: Other applications of the framework Sector MV weighting (%) Vehicle manufacturers Airlines Health care Utilities Banks Basic industries Transport General Manufacturing Natural resources Economic cyclicality, commodity baskets, consumer demand, maritime assets Oil prices, global growth Growth from emerging market demand Natural gas, oil, coal, maritime assets Short rates and long rates, credit spreads, emerging markets Basic materials (metal ores, etc.), global growth Oil prices, global growth Commodities, global growth, emerging markets growth, wage strength Natural resources, e.g. oil, natural gas, aluminum etc. Source: J.P. Morgan Asset Management. For illustration purposes only. Total allocation 100.0 100.0 100.0 Expected return 4.6 4.7 4.6 Portfolio CVaR95-18.7-17.8-18.8 Portfolio funding level 103.8 104.0 103.8 Oil CRCVaR05 return 9.5 4.6 11.9 Oil CRCVaR05 funding level 111.7 106.8 114.1 Source: J.P. Morgan Asset Management. For illustration purposes only. The CRCVaR05-targeted portfolio would improve performance in high oil price environments while maintaining the efficiency of the benchmark portfolio. On the other hand, the CRCVaR95- targeted portfolio, while performing seemingly well in low oil price environments, would lag the benchmark in high oil price environments. Conclusion: breaking the missing link In this paper we show that investors are generally able to construct portfolios that allow them to mitigate the risk of extreme adverse movements in a key variable the impact of oil prices on oil producers and consumers was our example without sacrificing expected return or portfolio efficiency. Beyond this, we develop a framework to measure how resilient an existing pension plan portfolio is to extreme adverse moves in a variable of concern and we present an approach to portfolio construction that aims to reduce economic exposure risk without reducing portfolio returns or portfolio efficiency. 8 The missing link: Economic exposure and PENSION PLAN risk

APPENDIX AppendiX Reverse optimisation procedure for sectoral expected returns Following William Sharpe s (1974) article, we adopted the following procedure for determining the expected return of the S&P 500 Index equity subsectors. Let X i denote the relative market value weighting of subsector i, for i = 1,..., 10, and let E i denote the expected return on subsector i. Also let C ij denote the covariance between returns on equity subsectors i and j. We begin by assuming that the X i, i = 1,..., 10 are selected in such a way as to maximise subject to M linear constaints where where λ is a constant, for k = 1,..., M and N = 10 and The Lagrangean function of this maximisation problem is defined as Setting derivatives to zero for i = 1,..., 10, we obtain Finally, the expected return for each subsector is given by J.P. Morgan asset management 9

GLOSSARY Glossary A defined benefit (DB) pension plan is a pension arrangement where the pensions payable are defined in terms of a member s salary and time spent as a member of the plan. Most DB pension plans are balance of cost plans, meaning that members contributions are fixed and the difference between these contributions and the amount required to fund benefits is paid for by the pension plan sponsor. The plan sponsor is the business entity which is responsible for funding the pension plan. Typically, the members of a pension plan are former and current employees of the sponsor or the sponsor s predecessor companies. Even though the pension plan is a legally separate entity to the sponsor, these members depend on the sponsor s ability to meet any shortfall in the pension fund if the liabilities exceed the assets. The funding level is the ratio of the pension plan assets to the pension plan liabilities. The pension plan assets less the liabilities is known as the surplus if it is positive and the deficit if it is negative The CVaR95 of a portfolio is the average loss of the portfolio in the worst 5% of outcomes. This is a measure of the potential loss of the portfolio in a worst case scenario. The Cross-Return CVaR95 (CRCVaR95) of a portfolio is the average portfolio return during the lowest 5% of returns for the particular asset or factor considered. This is a measure of the economic or sectoral risk taken by the portfolio. The oil CRCVaR95 of a portfolio is the average portfolio return during the lowest 5% of returns for oil. This is a measure of the oil price risk taken by the portfolio, and is a particular case of Cross-Return CVaR95. 10 The missing link: Economic exposure and PENSION PLAN risk

BIBLIOGRAPHY Bibliography Brigden, A., Clare, A., Driver, R., McKersie, M. and Selvaggi, M., Coping with Uncertainty and the Importance of the Sponsor s Covenant, ABI Research Paper Number 9, 2008. Cowling, C.A., Godon, T.J., Speed, C.A. Funding Defined Benefit Pension Plans, British Actuarial Journal (2005). McCarthy, D. and Miles, D. Optimal Portfolio Allocation for Pension Funds in the Presence of Background Risk, monograph, May 2007. Merton, R.C. Allocating Shareholder Capital to Pension Plans, Journal of Applied Corporate Finance, vol. 18 (1), pp. 15-24., 2006 Sharpe, W. Imputing Security Returns from Portfolio Composition, The Journal of Financial and Quantitative Analysis, Volume 9, Number 3 (June 1974), pages 463-472. Sheikh, A. and Qiao, H. The Non-Normality of Market Returns, J.P. Morgan Asset Management (2009). J.P. Morgan asset management 11

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