MERCER YIELD CURVE - WHITE PAPER MYC EUROZONE 31 OCTOBER 2013

Transcription

1 MERCER YIELD CURVE - WHITE PAPER MYC EUROZONE 31 OCTOBER 2013

2 Mercer Pension Discount Yield Curve Eurozone Mercer has developed the Mercer Yield Curve (MYC) to help Finance Directors choose the most appropriate discount rate for their scheme. Mercer actuaries use this model to develop a discount rate that is specific to each scheme s liability profile and complies with IAS19 and FAS87 guidelines. The MYC consists of half-yearly spot (i.e. zero coupon) rates, developed from pricing and yield information on high quality corporate bonds. Step 1. Select bond universe. Details of corporate bonds in issue are obtained from Bloomberg, while the model uses bid-price corporate bond data provided by Datastream. Bid prices are generally available for all publicly traded corporate bonds, ensuring that we have the largest available pool of market information. While we would ideally like to have actual trading prices, the small number of actual trades for which pricing information would be available on any given measurement date would significantly reduce the number of bonds in our universe. Prior to May 2012, only bonds with at least 300 million in outstanding issue were included as this was used by Barclays Capital to determine the constituents of the Barclays Euro Aggregate index. Following the change to Bloomberg, this limit is no longer imposed and a lower 50 million limit is used. We include corporate bonds rated AA by at least one of the three main rating agencies, Standard & Poor s, Moody s and Fitch. Bonds selected are denominated in Euros. We exclude bonds that are callable, make-whole, sinkable, putable and those that have floating coupon rates. Although we could, in theory, adjust for embedded options in the excluded bonds, focusing on non-callable bonds gives us a homogenous data set for constructing the yield curve and eliminates the need for additional assumptions about the value of the embedded options. Zero coupon bonds are included, with their maturity term equal to that of a par bond with a coupon rate equal to the yield on the zero coupon bond. There is no doubt that there remains a deep market in Eurozone AA rated corporate bonds at most durations. However, the number of long AA rated bonds has reduced significantly over the past years and so, in order to improve the stability of the model, we incorporate additional yield information derived from A and AAA rated corporate bonds, where available. Analysis of historical spreads between the AA and A rated Markit iboxx Corporate bond indices shows that, with minor variations, spreads change throughout the range of maturities in a similar way, except for the over 10+ indices. (The AA 10+ index is much more volatile due to the very small MERCER 1

3 number of bonds in that index and the reductions in the numbers of these bonds at different times.) Appropriate yields for AA rated bonds at these longer maturities are determined by fitting curves to the constituents of the Barclays Euro Aggregate indices for A, AA and AAA corporate bonds; calculating the spreads, averaged over maturities 7 to 10 years, between the AA and the AAA or A curves; increasing the yields on the AAA rated bonds and reducing the yields on the A rated bonds with maturities over 15 years (in the Barclays indices) by these average spreads. Analysis of credit default swaps shows that there is little term structure to the spread after maturities of around 7-9 years. Where there is a variation in spreads, the variation is very small and the direction, i.e. increasing or decreasing with tenor, changes from month to month. The A and AAA rated bonds may be sourced from Bloomberg in future. Step 2. Determine best-fit regression lines of yield-tomaturity as a function of time to maturity and use regression equations to estimate the par coupon yield curve at selected maturities. Regression analysis is used to find the best fitting curve that links yield-to-maturity to time to maturity of the selected bond yields described above. The regression is based on a fourthdegree polynomial of yield-to-maturity as a function of the natural logarithm of time to maturity. This gives a good fit to the data at both long and short maturities. We determine the best fit using least squares regression, which minimizes the sum of the squares of the difference between the actual data points and the regression line. The regressed coupon yield curve is thus smoothly continuous along its entire length and represents an unbiased average of the observed market data that takes into account all the information for both a single maturity and across all maturities. Other curve fitting methodologies (splines, for example) require subjective judgment as to how the yield curve should be segmented and present the problem of discontinuities or other anomalies at the knot points between successive segments. In order to eliminate outliers, we exclude bonds where the yield-to-maturity is more than two standard errors from the regressed yield-to-maturity based on the initial calculation. The regression analysis is then rerun on the reduced data set to determine the final maturity yield curve. MERCER 2

4 Step 3. Convert par coupon yield curve into the equivalent zero coupon spot rate curve. We convert the regressed maturity yield curve into a spot rate curve using the technique known as bootstrapping, which assumes that the price of a coupon bond for a given maturity equals the present value of the underlying bond cash flows using zero-coupon spot rates. This principle is equivalent to requiring that there cannot be any arbitrage opportunities to make risk-free profits. In making this conversion, we assume that the regressed coupon yield at each maturity date represented a coupon-paying bond trading at par. We also convert the bond-equivalent (compounded semi-annually) yields to effective annual yields during this process. Step 4. Extrapolate the curve where sufficient data is not available. The spot rate at time 0.5 is determined by holding the spread between the corporate bond spot rate and the AAA-rated Euro treasury spot rate constant from time 1 to time 0.5. From time 1, spot rates derived from the regression are used until the duration equal to the average maturity term for the last five available corporate yields, with a maximum of 30 years (assumed to be more stable than using the longest maturity term only). The spot rates from that duration onwards until time 50 are determined by holding the spread above AAA-rated Euro treasury spot rates constant. These spot rates will be reviewed against the yields on any longterm zero coupon bonds to ensure consistency. It is not expected that the MYC will match the yields, but significant discrepancies may flag the need for an adjustment. Step 5. Match pension (or retiree medical) cash flow to the spot rates. Scheme cash flows can be produced by the Mercer valuation system for each year into the future until no more benefit payments are expected to be paid (typically after 70 to 80 years). These cash flows can be entered into the MYC where they are matched to the appropriate spot rates and discounted back to the measurement date. The cash flows after 50 years are discounted assuming the spot rate remains constant from that point onwards. MERCER 3

5 Step 6. Determine single equivalent discount rate. Once the present value of the cash flows as of the measurement date has been determined, a single equivalent discount rate is calculated. Sample rates for 5-yearly durations are available, as are rates for some sample age classifications typical of the liability profiles of Eurozone pension plans. Both these can be used as a guide to selecting the single discount rate if scheme-specific cash flows are unavailable. Discount rates for sample plans The scheme profiles have been derived from the cashflows of Eurozone schemes. It is difficult to categorise the profiles in terms of liabilities as these can differ considerably from one country to another. For example, in Belgium, pension liabilities are for lump sums only, while in the Netherlands pensions in payment are increased with limited price increases or with discretionary increases. The provision in Ireland is similar, with non-increasing pensions being most common, but with a significant minority providing increases on a guaranteed or discretionary basis, either linked to inflation or a fixed annual percentage. MERCER 4

6 The sample scheme profiles, with a description of the scheme liabilities which could fall into that category, are shown in the table below. Note that young, younger and older refer to the relative duration of the liabilities of the members in that country, not just their actual ages. Scheme profile Approximate duration (years) at 31 August 2013 Possible description based on scheme liabilities Very short 2.5 Belgium very short liabilities Short 5 Belgium short liabilities Retiree 12 Pensioner only or mainly pensioner German scheme Shorter intermediate 15 Ireland (20% older deferreds, 80% pensioners) Netherlands (20% older deferreds, 80% pensioners) or mixed German scheme Intermediate 21 Ireland (30% older actives, 20% deferreds, 50% pensioners) Netherlands (25% older actives, 30% deferreds, 45% pensioners) Longer intermediate 25 Ireland (50% younger actives, 25% deferreds, 25% pensioners) Netherlands (65% younger actives, 25% deferreds, 10% pensioners) Long 30 Ireland (85%young actives and 15% young deferreds, few pensioners) Netherlands (80% young actives, 20% deferreds) MERCER 5

7 Mercer Limited is authorised and regulated by the Financial Conduct Authority Registered in England No Registered Office: 1 Tower Place West, Tower Place, London EC3R 5BU Mercer Limited Westgate House, 52 Westgate Chichester PO19 3HF +44 (0)