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Duration-enhancing overlay strategies for defined benefit pension plans

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Abstract

Many large corporate and public pension trusts remain underfunded since the 2001–2002 recessionary periods. These plans are challenged by global demographic trends and the recent slowing economic conditions. We show that a special overlay strategy can improve performance and reduce risks by adding duration to the portfolio. The approach combines elements of liability-driven investing and asset liability management. Versions of the strategy are evaluated via historical data. In addition, the strategy is tested with a widely employed, forward-looking economic projection system.

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Notes

  1. See Consigli and Dempster (1998), Mulvey and Ziemba (1998), Muralidhar and van der Wouden (1999), Ziemba (2003), Fabozzi et al (2004) and Zenios and Ziemba (2006).

  2. Towers-Perrin liability index has a duration of 12.6 years.

  3. For the period of 1982–2000, the liability growth rates are extrapolated based on the Towers-Perrin liability construction rules. Growth rates for 2001–2007 are directed obtained from the Towers-Perrin liability index.

  4. We also conduct the same tests employing the 30-year government bond index as a different proxy for the liability. The tests yield similar results as the tests with Towers-Perrin liability index (see Appendix A).

  5. Two issues arise upon formulating the model into a convex problem. First, as we employ the fixed-mix rule under multi-period setting (n=5, 10), the final wealth becomes a polynomial of order n, which is a non-convex function. Second, most of the problems include constraints related to funding ratio. As it is defined as the ratio of wealth to outstanding liability, the problems become non-convex.

  6. We employ OptQuest as the solver, which is embedded in the Crystal Ball software package.

  7. When the funding ratio falls below a threshold level, the sponsoring company is generally obliged to make contributions to make up for the deficit within the following 6-year period.

  8. This is to ensure that the funding ratio is always above 0.8.

  9. In most cases, DB pension plans do not take short positions on core assets except via hedge funds and related asset categories.

References

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Author information

Authors and Affiliations

  1. Operations Research and Financial Engineering Department, Bendheim Center for Finance, Princeton University, New Jersey, USA

    John M Mulvey

Authors
  1. John M Mulvey
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  2. Woo Chang Kim
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  3. Yi Ma
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Corresponding author

Correspondence to John M Mulvey.

Appendices

Appendix A

TEST RESULTS WITH 30-YEAR GOVERNMENT BOND INDEX AS A PROXY FOR LIABILITIES

See Tables A1, A2 and A3.

Table a1 Performance of key strategies over 1982–2007 with 30-year bond index as liability
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Table a2 Performance of 60-40 strategies after applying DEO with 30-yr bond index as liability
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Table a3 Performance of 70-30 strategies after applying DEO with 30-year bond index as liablilty
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Appendix B

ADDITIONAL RESULTS ON EMPIRICAL TESTS WITH ALM MODELS

We discuss the positive effects of DEO using various performance-risk measures. The main results indicate that employing a moderate level of DEO can improve the performance-risk trade-off as in ‘Empirical results with a forward-looking scenario generator (CAP:Link)’ section.

Importantly, institutional managers tend to focus on short-term performance as their performance is evaluated based on short- to mid-term investment outcomes, although the ultimate objective is to achieve long-term goals. Therefore, in order to ensure a successful implementation of DEO in practice, it is imperative to examine the investment outcomes with a shorter time horizon as well. Fortunately, the test results show that one can still achieve superior investment performance by applying a moderate level of DEO for a shorter time horizon (T=5).

ADDITIONAL ALM MODEL (1)

The return and the volatility of core assets are employed as the performance-risk measure pair. Numbers in red next to the points on efficient frontiers are the DM values (see Figure B1 and Table B1).

Table b1 Performance-risk measures for ALM models
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Figure B1
figure 4

Efficient frontiers of ALM models.

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ADDITIONAL ALM MODEL (2)

The return and the volatility of core assets are employed as the performance-risk measure pair. A constraint on duration matching ratio is introduced (DM⩾0.9). Numbers in red next to the points on efficient frontiers are the DM values (see Figure B2 and Table B2).

Table b2 Performance-risk measures for ALM models
Full size table
Figure B2
figure 5

Efficient frontiers of ALM models.

Full size image

ADDITIONAL ALM MODEL (3)

The funding ratio and its volatility are employed as the performance-risk measure pair. Numbers in red next to the points on efficient frontiers are the DM values (see Figure B3 and Table B3).

Table b3 Performance-risk measures for ALM models
Full size table
Figure B3
figure 6

Efficient frontiers of ALM models.

Full size image

ADDITIONAL ALM MODEL (4)

The funding ratio and its volatility are employed as the performance-risk measure pair. A constraint on duration matching ratio is introduced (DM⩾0.9). Numbers in red next to the points on efficient frontiers are the DM values (see Figure B4 and Table B4).

Table b4 Performance-risk measures for ALM models
Full size table
Figure B4
figure 7

Efficient frontiers of ALM models.

Full size image

ADDITIONAL ALM MODEL (5)

The economic value (Final Surplus – Total Contributions) and its expected shortfall at 95 per cent level are employed as the performance-risk measure pair. A constraint on duration matching ratio is introduced (DM⩾0.9). Numbers in red next to the points on efficient frontiers are the DM values (see Figure B5 and Table B5).

Table b5 Performance-risk measures for ALM models
Full size table
Figure B5
figure 8

Efficient frontiers of ALM models.

Full size image

ADDITIONAL ALM MODEL (6)

An example of ALM models with different levels of DEO strategies (0–250 per cent) is illustrated for a shorter time period (T=5). The economic value (Final Surplus – Total Contributions) and its expected shortfall at 95 per cent level are employed as the performance-risk measure pair. Numbers in red next to the points on efficient frontiers are the DM values. Consistent with the historical test results with a long–term horizon, applying 100–150 per cent of DEO can increase the duration of core assets enough to match that of the liability for a shorter period (see Figure B6 and Table B6).

Table b6 Performance-risk measures for ALM models
Full size table
Figure B6
figure 9

Efficient frontiers of ALM models.

Full size image

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Mulvey, J., Kim, W. & Ma, Y. Duration-enhancing overlay strategies for defined benefit pension plans. J Asset Manag 11, 136–162 (2010). https://doi.org/10.1057/jam.2010.10

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