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Methodology for Risk-free Discount Rates and CPI Assumptions for Accounting Valuation Purposes

6  Long-Term Nominal Risk-Free Discount Rates

6.1  Introduction

6.1.1 This section sets out the Treasury's view of the ultimate long-term nominal risk-free rate. In this context long-term rates are rates for durations longer than the market yield curves available.

6.1.2 Our methodology is to determine a single long-term nominal risk-free rate from historical government bond yields and other available data.

6.1.3 As mentioned previously it is important that the nominal risk-free rate is a robust stand-alone assumption. This is important because the accounting standards place the most emphasis on the nominal risk-free rate. The standards require that the nominal risk-free rate is extrapolated from available market data. Minimal guidance is given on real rates of return and inflation assumptions in the standards.

6.1.4 Extrapolation is the process of constructing new market data points of longer duration than the current yield curve. This process enables us to form a hypothetical yield curve that matches the Government’s long duration assets and liabilities for accounting valuations.

6.1.5 Forming a full hypothetical yield curve is achieved in two stages. Firstly, using historical data of New Zealand government bonds we determine a single long-term risk-free rate. Secondly we consider the implications of extrapolating the short-term yield curve to the ultimate single long-term rate. This is a macroeconomic approach.

6.1.6 Interpolation describes the construct of the yield curve between known points. In this case, the known points are: (a) the final market rate on the current yield curve and (b) the ultimate long-term single assumption determined under this methodology. Our interpolation assumption (also referred to as “bridging”) is discussed in Section 8 of this paper.

6.1.7 We already established in Section 3 that government bond yields are the appropriate market reference to proxy risk-free rates in New Zealand for accounting valuations. Therefore, this section only considers extrapolation of the long-term government bond rates in New Zealand. However, the methodology would still apply if at some point in the future the base were to change to bank SWAP rates.

6.2  Summary

6.2.1 In the Treasury's view it is reasonable to extrapolate a single long-term forward interest rate beyond the available yields of government stock. The conclusion is that a reasonable long-term nominal interest rate is 6.0% pa.

6.2.2 The long-term nominal rate of 6.0% pa is consistent with the historical rates of government stock in New Zealand.

6.2.3 The three long term assumptions of nominal rate, real rate and CPI should all be consistent. The fact that the three assumptions are consistent within the methodology supports the choice of 6.0%.

6.2.4 In our view, the approach described below is also in compliance with accounting standards and meets best actuarial practice.

6.2.5 While we believe this long-term assumption is reasonable for the foreseeable future, we intend to periodically review it. Any change in this long-term assumption will need to be supported by evidence that the long-term CPI and real rates have fundamentally and permanently changed in New Zealand. This change must also be reflected in current market yields.

6.3  Options for setting long-term rates

6.3.1 There are a number of possible options available to project a long-term government bond rate. These include:

  • extrapolating the market yield curve using a constant spot rate
  • extrapolating the yield curve using a constant forward rate
  • extrapolating using the shape of the forward curve, and
  • using other information to inform the extrapolation.

6.3.2 The principles of extrapolation for the purposes of liability valuations should always be considered. In assessing the options above, we have also taken into account the latest international literature and guidance from the actuarial profession. In particular we have been following the recent proposals from the the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS).

6.3.3 The November 2009 paper from CEIOPS[2] stated that extrapolation should take account of:

  • realism, ie, it should be possible to earn this return in a risk-free manner, and
  • volatility in long-term discount rates that can lead to substantial changes in values of liabilities and consequent pro-cyclical effects. The choice of extrapolation should take account of the effect on financial stability.

6.3.4 The updatedMarch 2010 paper from CEIOPS expanded the discussion on extrapolation by proposing 11 principles for extrapolating the basis risk-free interest rate term structure. Of particular interest for our methodology are the principles numbered 3, 5, 6, 7 and 8 on page 25 of the CEIOPS’s document. All 11 principles are listed in paragraph 9.5.21of section 9 of this paper.

6.3.5 We have applied the extrapolation principles in the CEIOPS paper and in particular, focused on the principles that extrapolation should be:

  • theoretically and economically sound, and
  • based on forward rates converging from one, or a set of, last observed liquid market data points to an unconditional ultimate long-term forward rate, to be determined for each currency by macroeconomic methods.

Option 1 - Extrapolate the market yield curve using a constant spot rate

6.3.6 Extrapolating the curve using a constant spot rate is the simplest method and is effectively what is done when, for example, the 10 year government stock rate from the RBNZ is used unadjusted.

6.3.7 This is the approach adopted in The Commerce Commission's Approach to Estimating the Cost of Capital paper dated June 2009[3]. Their base risk-free rate is determined from the five year government stock rate. However, their methodology uses a single risk-free rate rather than a term structure. The Commerce Commission concluded that for their purposes a term structure is not required.

6.3.8 While this has the benefits of being simple, it ignores some information about the term structure of the rates; consequently it is not theoretically correct and would not result in smooth forward rates. However, this method would result in a similar outcome to smoothing down to a long-term rate, in that the forward rate beyond the end of the yield curve would be lower than the last observed forward rate.

Option 2 - Extrapolate the yield curve using a constant forward rate

6.3.9 Extrapolating the yield curve using a constant forward rate, based on the last market point, is technically more correct than using a constant spot rate. However, this fundamentally assumes that the longest observation is valid forever with no real justification.

6.3.10 In New Zealand the government bond market yields are only available for 10-12 years in duration and the yield curve has a history of volatility. Where a constant discount rate, based on the last market point in the curve, is used to discount cash out flow durations exceeding 50 years, the value of the obligation is very sensitive to any small change in rate. A significant change in the value of an asset or liability, caused by a small amount of market volatility in the yield curve, may be misleading when there has been no change in the underlying cash flows expectations. .

6.3.11 In our view, using the constant forward rate, based on the last market point is contrary to the principles of the CEIOPS recent papers. For example the CEIOPS proposal states the choice of extrapolation should take account of the effect on financial stability of the obligation being valued. Extrapolation should also be theoretically and economically sound. In our view, the markets view of the forward yield in 10 or 12 years does not necessarily provide a sound theoretical or economic basis to apply to longer durations of cash flows for accounting valuations.

6.3.12 For the reasons stated above option 2 is considered not appropriate for the Treasury’s methodology.

Option 3 - Extrapolate using the shape of the forward curve

6.3.13 This option supposes that there is sufficient information within the forward rate yield curve to determine what the shape of the yield curve is beyond the last market point. A number of theories have been proposed to perform this extrapolation. The idea is that this will give guidance on whether the curve should keep going up, stay constant or come down. Considering the prior shape of the yield curve requires considerable judgement and to the best of our knowledge has not been used successfully. We also doubt that the New Zealand yield curve has enough data points to enable any meaningful analysis of shape.

Option 4 - Use other information to inform the extrapolation

6.3.14 In our view, considering the historical government bond yields, along with any other relevant information available is the most appropriate way to determine an extrapolated long-term yield. That is, applying a macroeconomic approach to extrapolation, in our view, is the most rational option. Therefore, the final paragraphs in this section are focused on doing this.

6.4  Historical Market Yields on Long-Term New Zealand Government Stock

6.4.1 The following graph shows the historical market yields on 10 year New Zealand government stock. The graph shows the monthly average of 10 year notional stock from the RBNZ website, with the yields annualised. The graph also shows (dotted line) the implied forward rate between the 5 and 10 year stocks. This line departs from the market rate as the yield curve becomes steeper, either positively or negatively.

10 year Government Stock to April 2010
10 year Government Stock to April 2010.

6.4.2 There are a couple of significant dates in the period covered by the graph. In 1989/90 the RBNZ explicitly changed its focus to targeting inflation, gradually bringing it under control. Their actions led to interest rates falling and becoming less volatile. The Official Cash Rate (OCR) was introduced in 1999 and is the RBNZ's primary tool in controlling inflation.

6.4.3 The table below shows the average 10 year stock yields as well as comparative CPI, real and GDP figures for various periods through to April 2010.

Averages 5 year 10 year 15 year 20 year
10 yr stock 6.0% 6.2% 6.5% 7.1%
5 to 10 year forward 6.0% 6.3% 6.6% 7.2%
CPI 2.9% 2.7% 2.2% 2.2%
Implied real return 3.1% 3.5% 4.3% 4.9%
GDP growth 0.3% 1.2% 2.0% 2.5%

6.4.4 The last ten years is the most consistent in terms of monetary policy, and over this period the 10 year stock rate has averaged 6.2%, 3.5% greater than inflation over the same period. The 5 to 10 year forward rates have averaged very similar figure. The historical analysis above supports the Treasury's assumption of a 6% long-term government bond yield.

6.5  International Observations

6.5.1 Although we are extrapolating the New Zealand bond data we believe it is appropriate to look at Australia and US bond rates to test the reasonableness of our 6% assumption. The following graphs compare New Zealand, Australia and US Bond rates.

NZ, AU and US 10 yr bond rates
NZ, AU and US 10 yr bond rates.
Source: Reserve Bank of New Zealand, Datastream

6.5.2 The long-term US Rates at the time of writing this report are:

10 year 3.57%

20 year 4.23%

30 year 4.41%

30 year indexed 1.85%

6.5.3 In order to compare international rates, and test the reasonableness of our assumption, there needs to be some consistency between the inflation environments. The US rates quoted above imply an inflation outlook of 2.6% pa, which is consistent with the inflation assumption discussed earlier of 2.5% pa.

6.5.4 The implied forward rates on the US bonds from 10 to 30 years are approximately 4.8% pa. As discussed in paragraph 5.6.4 of section 5 of this paper, addition of a country risk premium of 1.0% pa for New Zealand would indicate notional forward rates for New Zealand of 5.8% pa for between 10 and 30 years.

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