Portfolio Strategies - US

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1 Global 18 pages Bond Portfolio Analysis Portfolio Strategies - US Citigroup Pension Liability Index Revised Methodology We make two revisions to the procedure to calculate the Citigroup Pension Discount Curve and thus the Citigroup Pension Liability Index. The first change is to use market-weighted averages when applying the outlier filter in order to make month-to-month changes of the CPLI more reflective of market conditions. Martin Bernstein martin.bernstein@citi.com The second change is to simplify the process of combining the corporate spread curve with the Treasury curve by overlaying the spread curve over the Treasury spot curve. Over the past year, the CPLI calculated using the new methodology would have been 3.8bp lower on average than using the original methodology. The CPLI calculated using the new methodology exhibits a better correlation with a relevant market index than the original methodology exhibited. The preliminary year-end CPLI as of 12/28/2010, calculated using the new methodology is 5.76%. This compares to a preliminary year-end CPLI using the original methodology of 5.83%. Note that these are strictly preliminary and the final year-end CPLI could differ substantially from the preliminary CPLI. See Appendix A-1 for Analyst Certification, Important Disclosures and non-us research analyst disclosures. Citi Investment Research & Analysis is a division of Inc. (the "Firm"), which does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the Firm may have a conflict of interest that could affect the objectivity of this report. Investors should consider this report as only a single factor in making their investment decision.

2 Citigroup Pension Liability Index and Discount Curve We introduce a pair of revisions to the procedures for constructing the Citigroup Pension Liability Index (CPLI) and the Citigroup Pension Discount Curve (CPDC). We also present preliminary year-end CPLI and CPDC data using both the old methodology and the new methodology. These are strictly preliminary and could differ substantially from actual year-end numbers. The New Methodology The methodology we use to construct the Citigroup Pension Discount Curve (CPDC) and Citigroup Pension Liability Index (CPLI) has remained largely unchanged since the last time it was described in 1995 by Lawrence Bader and Y. Y. Ma. Today we present two changes to the procedures and show the impact of the changes to the CPDC and the CPLI over the past year. Original Methodology First, let s recap the original methodology. Simply, we construct the CPDC by combining two curves: the Citigroup Treasury Model Curve and a double-a corporate spread curve. The Treasury Model Curve is taken from the Yield Book as is, while the double-a corporate spread curve requires some processing. Creating the spread curve is a multistep process. 1. We start with the Citigroup Corporate Index and take corporate bonds rated Aa (Aa-, Aa, and Aa+) by Moody s and/or AA (AA-, AA and AA+) by S&P. 2. Next we eliminate callable bonds with less than three years of call protection and less than ten points between the earliest call price and the market price. 3. Then we divide the bonds into five maturity buckets: 1-3 year, 3-7 year, 7-15 year, year and 25+ year. 4. Within each bucket we apply an outlier filter that eliminates any bonds with a spread (calculated as the option-adjusted spread, or OAS, to the Treasury Model Curve) more than two standard deviations above the average spread within the bucket. 5. We calculate the market-weighted average spread of the remaining bonds in each bucket. 6. The spread curve is then interpolated between the averages from each bucket, assuming the averages are placed at the mid point of each bucket (except for the year bucket, in which case the average is placed at the 29.5-year point). The spread curve is combined with the Treasury Model Par Curve. The resulting double-a corporate par curve is converted to a spot curve and annualized. Methodology Change # 1 The Outlier Filter The first change was made to how we implement the outlier filter. The modification is intended to make month-over-month changes in the CPLI more 2

3 representative of actual market changes instead of the vagaries of the outlier filter. Old method: Within each maturity bucket, calculate the average spread and the standard deviation of the spreads. Eliminate those bonds with spreads more than two standard deviations above the average in the bucket. New Method: Within each maturity bucket, calculate the market-weighted average spread and the standard deviation of the spreads. Eliminate those bonds with spreads more than two standard deviations above the marketweighted average in the bucket. In the past, a small cohort of large issues in the year and 25+ year maturity buckets have had spreads close to the edge of the outlier filter. From month to month, the number of these bonds falling afoul of the filter could vary considerably. Because of their sizes, it only took a couple of bonds moving in or out of the universe to have a material impact on the CPDC and the CPLI. If a couple more bonds were caught by the filter and thus fell out of universe, it would lower the discount rate. Conversely, if a couple more bonds avoided the filter and came back into the universe, it would raise the discount rate. By switching from a straight average spread to a market-weighted average as the basis for the filter, we reduce the instance of large bonds entering and leaving the universe. As a result, the yield and spread of the updated CPLI exhibit a better correlation to the yield and spread of the Citigroup AAA/AA Corporate 10+ Index than the yield and spread of the old CPLI exhibit. Methodology Change # 2 Par versus Spot The second change we made involves the last part of the process: combining the Treasury and spread curves. This change is intended to make the process analytically more straight-forward and arguably more correct. Old method: Combine the OAS curve with the Treasury par curve to create a par double-a corporate curve. Then convert the resulting par curve into a spot curve. New Method: Combine the OAS curve with the Treasury spot curve to create a spot double-a corporate curve. The current method of adding the spread (OAS) curve to a par Treasury curve to create a par corporate curve and then converting this par curve to a spot corporate curve has produced some counterintuitive results. The most remarked-upon of these was occasionally causing part of the above median double-a curve to go below the corresponding part of the CPDC. There are perfectly good bond-math reasons why this happens, but it s still not a result we (or the many clients who called to point out the oddity) liked. By going straight to the spot curve, we eliminate the occasional reversal of parts of the above median curve and CPDC. Similarly, the new method makes it possible to do bespoke issuer-level exposure analysis of pension liabilities. The original method impeded this analysis, because of an effect similar to the reversal of parts of the above median curve and CPDC. In addition, it is arguably more correct to overlay an OAS curve over a spot curve than over a par curve, as OAS is calculated relative to spot rates, not par rates. Or, to put it another way, for a bond with no optionality the net present 3

4 value can be calculated by discounting each cash-flow by the sum of the OAS and the matching Treasury spot rate. In contrast, nominal spreads are calculated relative to Treasury par rates. Impact of the Methodology Changes In order to examine the impact the methodology change will have on the CPDC and CPLI we back-calculated the curve and index for each month from 12/31/09 through the preliminary 2010 year-end numbers. Figure 1 shows the CPLI calculated using both methods, in addition to the yield of the Citigroup AAA/AA Corporate 10+ Index (HG Index). The figure also displays the same comparison for the OASs of the CPLI methodologies and the HG Index. Figure 1. Yield and OAS Comparisons of Original and New CPLI and HG Index from 12/31/09 to 12/28/10. Yield (%) OAS (%) Date Original CPLI New CPLI HG Index Original CPLI New CPLI HG Index 12/28/ /30/ /31/ /30/ /31/ /31/ /30/ /31/ /30/ /31/ /28/ /31/ /31/ Original CPLI New CPLI Dif. Original CPLI New CPLI Dif. Average: Correlation to HG Index: On average over the past year, the CPLI calculated using the new methodology came in 3.8bp lower than the original methodology. The difference in the OASs was a similar 4.3bp lower. The correlations between the yields and OASs of the new CPLI and the HG Index are 0.99 and 0.96, respectively, while the correlations between the yields and OASs of the original CPLI and the HG Index are 0.96 and Figure 2 graphs the yields calculated using the two CPLI methodologies and the HG Index. In addition, we looked at how well the curves created using the original and new methodologies reflected the actual yields of bonds used to create the curves. Using market-weighted sum of squares to do the comparison, we found a negligible difference between the two methods. Some months the original method exhibited a better fidelity to the original yields, and other months the new methodology did a better job. Averaged over the year, there was no discernable difference. 4

5 Figure 2. Yields of New and Original CPLIs and HG Index, from 12/31/09 to 12/28/ Original CPLI New CPLI Corp. AAA/AA 10+ Index 6.00 CPLI Yields (%) Citigroup Corporate AAA/AA 10+ Yield (%) 4.75 Dec-09 Jan-10 Feb-10 Mar-10 Apr-10 May -10 Jun-10 Jul-10 Aug-10 Sep-10 Oct-10 Nov -10 Dec-10 Date 4.50 Of course, we are not just interested in the overall CPLI. We also compared the average CPDC for the year in Figure 1. On average, the new method tended to produce its lowest yields relative to the original method in the year area and slightly higher yields at the very long end of the curve. Figure 3. Original and New CPDCs, Average from 12/31/09 to 12/28/10. Average CPDC (12/31/09-12/28/10) Average CPDC (12/31/09-12/28/10) Year Original New Difference Year Original New Difference

6 In Appendix 1 we show the original and new CPLI and CPDC as well as the differences between the two for each month from 12/31/09 to 12/28/10. We repeat the exercise in Appendix 2 for the Citigroup Above Median Double-A curve and index. Note that the 12/28/10 is not the official year-end data. It is strictly preliminary and the official year-end numbers could differ substantially from the 12/28/10 numbers Year-end Preliminary Data We present this year, as we did last year, preliminary year-end data. This year it takes on added importance, as we also roll out the new methodology. To reiterate (ad-nauseum), these numbers are strictly preliminary, and the official year-end numbers could differ substantially from the preliminary ones. Figure 4. Preliminary 12/28/10 Citigroup Pension Liability Index and Citigroup Pension Discount Curve. Preliminary Citigroup Pension Liability Index New Version Old Version Disount Rate 5.76% Discount Rate 5.83% Duration 16.1 Duration 16.0 Preliminary Citigroup Pension Discount Curve New Version Old Version Year Rate Year Rate Year Rate Year Rate

7 Figure 5. Preliminary 12/28/10 Citigroup Above Median Double-A Index and Citigroup Above Median Double-A Curve. Preliminary Citigroup Above Median Double-A Index New Version Old Version Disount Rate 5.93% Discount Rate 5.92% Duration 15.8 Duration 15.8 Preliminary Citigroup Above Median Double-A Curve New Version Old Version Year Rate Year Rate Year Rate Year Rate

8 Appendix 1 We present the past year of both the new and original versions of the Citigroup Pension Liability Index and Citigroup Pension Discount Curve. We also show the month-by-month differences between the two versions. Figure 6. New and Original CPLI Data, from 12/31/09 to 12/28/10. New Citigroup Pension Liability Index 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/09 Discount Rate 5.76% 5.45% 5.42% 5.14% 5.04% 5.41% 5.47% 5.82% 5.79% 6.05% 5.99% 5.93% 5.98% Duration Monthly Return -4.54% 0.02% -4.24% -1.24% 7.03% 1.39% 6.42% -0.05% 4.80% -0.50% -0.41% 1.27% Year to Date Ret. 9.93% 14.48% 14.46% 18.71% 19.96% 12.91% 11.52% 5.10% 5.15% 0.35% 0.85% 1.27% Original Citigroup Pension Liability Index 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/09 Discount Rate 5.83% 5.44% 5.59% 5.16% 4.97% 5.47% 5.45% 5.83% 5.92% 6.14% 6.00% 5.98% 5.96% Duration Monthly Return -5.65% 2.84% -6.40% -2.69% 9.19% 0.15% 6.76% 1.96% 4.08% -1.66% 0.19% 0.25% Year to Date Ret. 8.16% 14.63% 11.46% 19.08% 22.37% 12.07% 11.90% 4.82% 2.80% -1.22% 0.45% 0.25% Difference 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/09 Discount Rate -0.07% 0.01% -0.16% -0.02% 0.06% -0.06% 0.02% 0.00% -0.13% -0.09% -0.01% -0.05% 0.01% Duration Monthly Return 1.10% -2.82% 2.16% 1.44% -2.15% 1.24% -0.34% -2.01% 0.72% 1.16% -0.61% 1.01% Year to Date Ret. 1.44% 0.19% 3.33% 0.79% -0.99% 1.33% -0.05% 0.29% 2.36% 1.57% 0.40% 1.01% 8

9 Figure 7. New Version of Citigroup Pension Discount Curve, Annualized Spot Yields 12/31/09 to 12/28/10. New Citigroup Pension Discount Curve Years 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/

10 Figure 8. Original Version of Citigroup Pension Discount Curve, Annualized Spot Yields 12/31/09 to 12/28/10. Original Citigroup Pension Discount Curve Years 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/

11 Figure 9. New - Original Versions of Citigroup Pension Discount Curve, Annualized Spot Yields 12/31/09 to 12/28/10. New Original Citigroup Pension Discount Curve Years 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/

12 Appendix 2 We present the past year of both the new and original versions of the Citigroup Above Median Double-A Index and Citigroup Above Median Double-A Curve. We also show the month-by-month differences between the two versions. Note that this is a discount curve based on similar methodology and data to that of the Citigroup Pension Discount Curve, while constraining the universe of AA bonds to those with an above median option adjusted spread within their maturity band. By construction, this curve is not representative of the AA market discount rates and hence is not necessarily directly applicable to the discounting of pension liabilities Figure 10. New and Original Citigroup Above Median Double-A Index Data, from 12/31/09 to 12/28/10. New Citigroup Above Median Double-A Index 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/09 Discount Rate 5.93% 5.66% 5.63% 5.34% 5.27% 5.62% 5.71% 6.07% 5.96% 6.23% 6.20% 6.10% 6.19% Duration Monthly Return -5.53% -0.05% -4.13% -0.74% 6.50% 1.89% 6.38% -1.23% 4.92% 0.10% -1.00% 1.79% Year to Date Ret. 8.89% 14.43% 14.48% 18.62% 19.37% 12.85% 10.96% 4.58% 5.81% 0.89% 0.79% 1.79% Original Citigroup Above Median Double-A Index 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/09 Discount Rate 5.92% 5.54% 5.73% 5.29% 5.08% 5.62% 5.58% 5.94% 6.01% 6.25% 6.18% 6.07% 6.12% Duration Monthly Return -5.46% 3.55% -6.54% -3.02% 9.83% -0.07% 6.38% 1.56% 4.36% -0.52% -1.24% 1.33% Year to Date Ret. 9.30% 15.61% 11.64% 19.45% 23.17% 12.15% 12.23% 5.50% 3.88% -0.46% 0.07% 1.33% Difference 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/09 Discount Rate 0.01% 0.12% -0.10% 0.06% 0.19% 0.01% 0.13% 0.13% -0.05% -0.02% 0.02% 0.04% 0.06% Duration Monthly Return -0.07% -3.61% 2.41% 2.28% -3.32% 1.96% 0.00% -2.78% 0.56% 0.62% 0.24% 0.47% Year to Date Ret % -1.18% 2.84% -0.83% -3.81% 0.70% -1.26% -0.91% 1.93% 1.35% 0.73% 0.47% 12

13 Figure 11. New Version of Citigroup Above Median Double-A Discount Curve, Annualized Spot Yields 12/31/09 to 12/28/10. New Citigroup Above Median Double-A Discount Curve Years 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/

14 Figure 12. Original Version of Citigroup Above Median Double-A Discount Curve, Annualized Spot Yields 12/31/09 to 12/28/10. Original Citigroup Above Median Double-A Discount Curve Years 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/

15 Figure 13. New - Original Versions of Citigroup Above Median Double-A Discount Curve, Annualized Spot Yields 12/31/09 to 12/28/10. New - Original Citigroup Above Median Double-A Discount Curve Years 12/28/10 11/30/10 10/31/10 9/30/10 8/31/10 7/31/10 6/30/10 5/31/10 4/30/10 3/31/10 2/28/10 1/31/10 12/31/

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