Methodology Update - June 2013

1 Introduction#

1.1  Background and purpose#

1.1.1. The Methodology for Risk-free Discount Rates and CPI Assumptions for Accounting Valuation Purposes is set out in a report dated July 2010 (Methodology report). The reason for providing a methodology and publishing central discount rates is to ensure consistency and efficiency across accounting valuations that are reported to the Government.

1.1.2. To establish risk-free rates and CPI assumptions for accounting valuations the Methodology involves determining three main components:

• The short-term assumptions which are derived mainly from observable market data.
• The long-term assumptions.
• The assumption for bridging the short and long-term.

1.1.3. We publish the risk-free yield curve following this methodology four times a year. The short term assumptions are updated at each publication date with reference to the market of New Zealand Government stock. The long-term assumptions are reviewed less frequently. For example the following are reviewed annually, for the 30 June year end valuations:

• Any adjustments required to the New Zealand government stock yield curve, eg by referencing bank SWAP rates.
• Any new information regarding the long-term CPI and discount rate assumption.
• Any new information regarding the bridging assumption.

1.1.4. Any new information on the long-term real-return assumption is updated every two years.

1.1.5. Significant changes in economic conditions or additional market instruments becoming available may result in an earlier review if appropriate.

1.1.6. A follow up report, Methodology for Risk-free Discount Rates and CPI Assumptions for Accounting Valuation Purposes - May 2012 Review of Long-term Assumptions, was published in July 2012 (May 2012 review). While the long-term economic assumptions remained the same as in the original Methodology, the bridging assumption was refined as a result of the May 2012 review. The bridging assumption bridges the end of the yield curve to the long-term rate and became subject to a maximum slope, thereby lengthening the smoothing period automatically in extreme circumstances.

1.1.7. This paper has been prepared to document the annual review for 30 June 2013.

1.2  Approach#

1.2.1. In order to review the long-term assumptions, the Treasury contracted PricewaterhouseCoopers (PwC) to review the following:

• Real long-term risk-free discount rates
• Nominal long-term risk-free discount rates
• Long-term inflation
• Bridging assumption
• Literature review.

1.2.2. This review is not intended to be a complete review of the methodology and should be read in conjunction with the Methodology report and May 2012 review. We have mainly focused on any new information regarding the long-term discount rate and CPI assumption and any new information regarding the bridging assumption.

1.2.3. As part of the process we have had discussions with Treasury economic forecasters, the Debt Management Office, the Accident Compensation Corporation and the Government Superannuation Fund.

1.3 Summary of findings#

1.3.1. This section sets out the changes to the Methodology and a summary of our findings. The three long-term assumptions in the Methodology (the long-term real risk-free rate, the long-term nominal risk-free rate and the long-term CPI assumption) are closely connected. Each of these elements is reviewed and judged individually in this paper. However, the combined view of all the elements is also an important aspect of judgement in selecting the appropriate assumptions.

Changes to the Methodology

1.3.2. The following changes have been made to the Methodology from 30 June 2013:

• The long-term nominal interest rate is reduced from 6.0% pa to 5.5% pa and the long-term real interest rate is reduced from 3.5% pa to 3.0% pa.
• The bridging period between market and long-term rates is extended from 5 years to 10 years and the maximum slope of the risk-free yield curve is reduced from 0.15% pa to 0.05% pa.
• The long-term CPI inflation rate of 2.5% pa is retained.
• The bridging approach for CPI will now be using the same approach as for the discount rates. The medium term inflation up until the end of the yield curve will be increased by 0.05% pa until the long-term assumption of 2.5% pa is reached.

Long-term rates

1.3.3. In the absence of any long-duration market data in New Zealand, judgment is required in selecting the long-term real and nominal risk-free rates. Current and recent historical real risk-free returns, returns on long-term New Zealand index-linked stock (if any), returns on relevant offshore index linked stock and economic theory are all relevant to selecting the long-term real risk-free discount rate.

1.3.4. In our view there is now evidence to reduce the real long-term risk-free discount rate assumption. We believe an acceptable range for the long-term real rate is now 2.0% pa to 3.5% pa (revised from a range of 2.5% to 4% at May 2012).

1.3.5. Market data indicates the 5 to 10 year forward rate for New Zealand government stock has stabilised in the 4.5% pa to 5.0% pa range. If the same differential between 10, 20 and 30 year government stock as in the US is assumed for hypothetical 20 and 30 year New Zealand government stock, the 20 to 30 year forward rate implied is about 5.5% pa and the 30 year spot rate implied is about 4.7% pa. This conclusion is also consistent when comparing the differentials between the 10 year stock and 30 year stock of both the UK and Japan.

1.3.6. We have decided that a 5.5% nominal and 3.0% real rate is appropriate for 30 June 2013 valuations because of the combination of the following:

• our view of the reduced range of the long-term real rate of 2.0% to 3.5%
• the New Zealand market data reflecting the lower stabilised nominal rate of the 5 to 10 year forward rate for government stock (stabilised in the 4.5% pa to 5.0% pa range), and
• the international data of differentials between 10 year stock and 30 year stock in the US, UK and Japan is an indication of the yield which would apply to a hypothetical New Zealand 30 year stock.

Bridging

1.3.7. Under the Methodology outlined in the May 2012 review the long-term rate applies 5 years after the end of the notional government stock yield curve, subject to a maximum yearly change by duration, or slope of 0.15% pa. There is evidence that this transition period is now too short.

1.3.8. We believe the bridging period between market and long-term rates should be extended from 5 years to 10 years and the maximum slope of the risk-free yield curve should be reduced from 0.15% pa to 0.05% pa. Setting a maximum slope automatically lengthens the bridging period in extreme circumstances when the yield curve is significantly different from the long-term rate. When the rate at the end of the yield curve is close to the long-term assumption, the slope of the bridging period is less relevant and the minimum transition period is used.

1.3.9. In concluding this we have put a reasonable amount of weighting on the recent papers from EIOPA and Mulquiney and Miller, which recommend the rate of reversion to real long-term real rates of return is slow and much longer than our current Methodology. The shape and the slope of the US curve also support this assumption.

1.3.10. We accept the selection of the transition period and the slope requires substantial judgement as there is a scarcity of conclusive supporting evidence.

1.3.11. We continued to support a straight line extrapolation of forward rates as in our view there is no reason to depart from the simplicity of a linear extrapolation.

Inflation

1.3.12. We believe the long-term inflation rate (CPI) should remain the same at 2.5% pa. CPI inflation has exhibited a long-term pattern of exceeding the mid-point of the RBNZ’s target range. Over the last 20 years, the average annual CPI has been 0.5% pa above the mid-point of the range. The consensus of forecasters indicates a slightly lower expectation in the medium term of 2.25% pa, closer to the mid-point of the inflation target. The inflation-linked stock also points to something around 2.25% pa.

1.3.13. The inflation assumption has to be set in conjunction with the nominal rate and the real return. Reducing the long-term CPI assumption by 0.25% pa would also require taking 0.25% pa from the long-term discount rate, otherwise the real yield will increase. On balance, in order to be consistent with the updated real and nominal rates, it is more appropriate to retain the current 2.5% assumption.

1.3.14. To be consistent with the nominal discount rates, the inflation assumption also needs a bridging assumption between the medium term inflation, which is informed by forecasts and market data, and the long-term rate.

1.3.15. We will use the same bridging approach as for the discount rates. The medium term inflation (expected to be about 2.2%) up until the end of the yield curve will be increased by 0.05% pa until the long-term assumption of 2.5% is reached.

2 Real long-term risk-free discount rates#

2.1  Introduction#

2.1.1. This section sets out the review of the real long-term real risk-free rate.

2.1.2. The real long-term risk-free rate is considered first because this is the primary driver of the value of cash flows that are inflated. In addition, it is reasonable to expect the real return to be robust to changes in long-term inflation outlook.

2.1.3. The real risk-free interest rate is the theoretical rate of return of an investment with zero risk, after taking into account the effects of inflation. The real risk-free rate represents the real return an investor would expect from an absolutely risk-free investment over a given period of time.

2.1.4. It was concluded in the Methodology report that the most suitable proxy for risk-free rates in New Zealand is the yield on government stock. Therefore, in the long term context, it is consistent that the resulting risk-free rate assumed is cross-checked against available market data of long-term real returns on government stock in New Zealand.

2.1.5. The Methodology report concluded that the long-term real return for New Zealand was in the range of between 3.0% pa and 4.0% pa, and selected 3.5% pa, being the mid-point of the range.

2.1.6. The May 2012 update commented that recent market developments raised considerable uncertainty in the future outlook and suggest that the bottom of the range had dropped, and a revised range was now 2.5% pa to 4.0% pa. However, although the range had widened, it was concluded that the combined evidence at that time was not yet compelling to conclude there had been a fundamental change in the very long term outlook. It was also agreed to reassess this assumption over 2012/13 in the light of an extra 6 to 12 months of market data and any other new information.

2.1.7. As stated in the Methodology, there is an absence of any direct and observable long-term yields to proxy a real risk-free rate in New Zealand, so judgement is required to set a single long-term real risk-free rate. Recent historical real risk-free returns, returns on long-term New Zealand index-linked stock, returns on relevant offshore index-linked stock and economic theory are all relevant to selecting the long-term real risk-free discount rate.

2.1.8. The latest analysis of the long-term real rate of return below is focused on new information since the May 2012 review and is summarised in two sections: market data and the Treasury fiscal forecast.

2.2 Market data#

New Zealand government stock rates compared to inflation

2.2.1. In reviewing the historical real risk-free rates, we have looked at the difference between interest rates and inflation rates in the past. There are a number of ways of considering this. The following chart shows the historical difference between the 10 year government stock yield at the start of a year and the average inflation experienced over the following ten years.

2.2.2. Up to March 2003, the gap has been calculated as the difference between the 10 year government stock yield and the average annual CPI inflation over the following 10 years.

2.2.3. After that, CPI inflation is averaged over the period to March 2013. For example, for the data point March 2011, this is the 10 yield government stock yield at the end of the month, less the average CPI inflation over the following two years.

Figure 1 - 10 year government stock yield less average inflation in following 10 years, to 31 March 2013

2.2.4. Since 1998, the difference between 10 year government stock yields and CPI has generally been between 3.0% pa and 4.5% pa.

2.2.5. Historical real risk-free returns are important inputs into making our judgement because they are a significant factor in setting investor’s expectations. In the absence of market data in the long term, current investor expectations become an important starting point. The period of history over which this assessment is made is critical. Whilst 20 year history above shows quite high rates, 100 year history indicates lower rates.

New Zealand index linked stock

2.2.6. Inflation linked stock can be useful evidence of the market’s view of real rates of return. A new inflation linked stock, maturing in 2025 was issued on 24 October 2012. There is approximately $3bn of this on issue, adding to the $2bn maturing in 2016. The NZ Debt Management Office plans to issue another $5bn in 2014 with a possible 2030 stock. This will increase the depth of the indexed market from around 7% of total Government debt to around 13%.

2.2.7. Since the date of issue and up to 16 May 2013, the (real) yield has varied between 1.1% pa and 1.8% pa. Note that this is the average return over the 12 year duration and is brought down by close to zero return for the early part of the yield curve, implying around 2.0% pa at the end of the curve.

2.2.8. This low (real) yield is not definitive evidence of a market expectation of real rates of return over the next 12 years, as it will be influenced by supply and demand pressures for both nominal and inflation linked stock. The inflation linked stock is currently under significant demand pressure from offshore investors, in particular UK Pension schemes with mandates to invest in inflation linked stock. For extrapolating the real yield forward, this 2.0% market observation gives a lower bound. Whilst it is difficult to estimate the impact of the current high demand, it is likely that this will not be permanent, giving some scope for the yields to increase.

US index linked stock

2.2.9. The two charts below show the 30 year and 20 year index linked stock yields quoted by the US Treasury. Data is only available from February 2010 for the 30 year stock.

Figure 2 - US 30 year index linked stock yields

2.2.10. The return on the 30 year index linked stock fell significantly in August 2011, to around 1.0% pa, and generally continued to fall from then until December 2012. In the early part of 2013, the yield rose above 0.5% pa from a minimum of 0.2% pa in December 2012. In the first three months of 2013, it traded at an average daily yield of 0.6% pa.

Figure 3 - US 20 year index linked stock yields

2.2.11. The 20 year US index linked stock traded below 0% during the latter part of 2012. It has risen again in 2013, and traded at an average daily rate of 0.2% pa in the first three months of 2013.

2.2.12. The difference between the 20 and 30 year rates implies a forward real rate between 20 and 30 years of approximately 1.5% pa.

2.2.13. The current yield is lower than historical US real yields, however the trends support the observations from New Zealand market data. It is still reasonable to expect that New Zealand real returns will attract a premium over US rates in the foreseeable future. It is difficult to quantify this but this observation supports a New Zealand real return between 20 and 30 years of 2.0% pa to 3.0% pa.

2.3 The Treasury fiscal forecasts#

2.3.1. We regularly forecast the New Zealand government fiscal position over 3 distinct time horizons:

• short term, one to 5 years (Forecast Period)
• medium term, 5 to 15 years (Projection Period)
• long term, 15 to 40 years. (Long-term Fiscal Model)

2.3.2. Relevant key inputs into these forecasts include:

• inflation rates (CPI and AWE)
• yield on 10 year government stock.

2.3.3. We have recently published the Budget Economic and Fiscal Update 16 May 2013.

2.3.4. The short term forecasts use the rates implied by the current government stock yield curve and short term inflation forecasts. The latest Budget forecast predicts a rising 10-year stock rate over the forecast period (averaged for the March quarter) from 3.7% pa in 2013 to 5.2% pa in 2017 and CPI inflation rising from 0.9% pa in 2013 to 2.2% pa in 2017. This equates to a forecast real rate of return of 3.0% pa in 2017. The long-term forecasts, beyond the projection period, continue to use the assumption of 6.0% pa yield on government stock, a CPI of 2.0% pa, and an AWE of 3.5% pa.

2.3.5. These assumptions are largely unchanged from the Budget Economic and Fiscal Update published in May 2012.

2.4 Conclusion#

2.4.1. The updated market data section shows contrasting information. On the one hand, since 1998 the difference between 10 year government stock yields and CPI inflation has generally been between 3.0% pa and 4.5% pa. On the other hand, the recently issued New Zealand index linked government stock maturing in 2025 and the real risk-free returns on long terms stock in the US are yielding much lower than historical averages.

2.4.2. We are comfortable from our analysis to apply less weighting to the current returns of the index linked stock, for the reasons described above, but they still need to be factored into our assessment of a reasonable range for the real rate of return.

2.4.3. Economic forecasts are also an important factor in our Methodology when setting a long-term rate that is not directly observable from markets. Our Treasury long term fiscal model forecasts still use a yield on 10 year government stock of 6% pa beyond 18 years, and a CPI assumption of 2% pa, equivalent to a real return of 4% pa.

2.4.4. In our view there is enough evidence that an acceptable range for the long term real rate is now 2.0% pa to 3.5% pa. This is an updated change from our May 2012 view where we believed the range of the real long-term risk-free discount rate assumption was 2.5% pa to 4.0% pa. This change in view is due to a combination of further reductions in the market yields, a longer period of sustained lower rates, the availability of longer dated New Zealand inflation indexed stock and additional research being available.

2.4.5. As our view of both ends of the range has reduced, it follows this is likely to lead to a change in the real long-term risk-free discount rate assumption. The amount by which it should be reduced needs to be informed by the analysis carried out in other parts of this report, specifically the sections related to the long-term nominal rate and inflation assumptions.

3 Nominal long-term risk-free discount rates#

3.1  Introduction#

3.1.1. This section sets out the review of the long-term nominal risk-free rate. In this context, long-term rates are rates for durations longer than the New Zealand market yields available.

3.1.2. The nominal long-term rate is the second step in our analysis because it is the focus of accounting standards and can be cross-checked to historical market rates. It is important that the nominal risk-free rate is a robust stand-alone assumption. The standards require that the nominal risk-free rate is extrapolated[1] from available market data.

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

3.1.4. The latest analysis of the long-term nominal rate of return below is focused on new information and market data since the May 2012 review.

3.2 Market data#

Historical market yields on long-term New Zealand government stock

3.2.1. The following charts shows the historical market yields on 10 year New Zealand government stock and forward rates, where available. The first chart shows the period since March 1986 and the second chart gives more detail for the last two years. The charts show the monthly average yield of 10 year Government stock from the RBNZ website, with the yields annualised. The charts also show (yellow line) the implied forward rate between the 5 and 10 year stocks and, in the second chart, the (grey line) the implied forward rate between the 10 and 12 year stocks.

Figure 4 - New Zealand 10 year government stock yields - March 1986 to March 2013

Figure 5 - New Zealand 10 year government stock yields - March 2011 to March 2013

3.2.2. Between March 2011 and June 2012, the forward rates fell significantly, from 7.0% pa to 4.5% pa. Since then, they have generally stabilised in the 4.5% pa to 5.0% pa range. In the period from June 2012 to 31 March 2013 they have averaged about 4.5% pa. The forward rate on 18 April 2013 was 3.9% pa.

International observations

3.2.3. Germany, Japan, UK and USA all have 30 year bonds. This data could be useful to indicate the yield which would apply to a hypothetical New Zealand 30 year stock. Clearly a direct relationship would not be expected, as there are differences in the contractual terms, credit quality, expected economic conditions including expected inflation and exchange rate risk, and supply and demand. This data indicates the following differences between current yields on 30 and 10 year government stock.

* Data taken on 18 April 2013

3.2.4. This indicates significant consistency in the differences, except for Germany, with the differences being between 1.04% pa and 1.34% pa in each case.

3.2.5. As New Zealand is a smaller economy than any of the above, a higher differential would be expected. Also, New Zealand does not have the massive pension schemes and annuity schemes present in the other economies to drive demand for long dated government stock. For these reason, we believe it would be reasonable to take the upper end of the range, ie 1.34% pa, or higher. A 1.34% pa differential would imply a 30 year government bond in New Zealand would currently yield 4.7% pa[2].

3.2.6. A 4.7% pa 30 year government bond yield implies a 5.4% pa forward rate between 10 and 30 years.

3.2.7. Historic 10 and 30 year bond data is readily available for the US. If the same approach is used with just US data, ie adding the differential rate between the US 30 year bond and the US 10 year bond as at that time to the New Zealand 10 year bond rate, the implied 30 year bond rates over the last 20 years would have been as follows (breaks in the chart are periods where the US 20 year bond or the US 30 year bond was not trading).

Figure 6 - Notional New Zealand 20 and 30 year bond yield (based on US differential)

3.2.8. The forward rates implied by these are shown in the following chart (breaks in the chart are periods where the US 20 year bond or the US 30 year bond was not trading).

Figure 7 - Notional New Zealand 10 to 20 and 20 to 30 year forward rates (based on US differential)

3.2.9. This indicated that the 20 to 30 year forward rates implied by this method have been between 5.0% pa and 6.0% pa for the last 18 months and averaged 5.5% pa. At 31 March 2013 they were 5.5% pa. Again, it could be argued that given the differences between the US and New Zealand economies, this method should underestimate the New Zealand forward rates.

Comparison to bank swap yields

3.2.10. The purpose of this section is to check that the spread between government bond and bank SWAP rates is still in the normal range of around 0.4% to 0.5%. We conclude that the spread is in the normal range and that no adjustment is required.

3.2.11. Bank SWAP rates are the commonly used to price a variety of interest rate swap instruments between two parties. The purpose of this section is to determine if any adjustment is required to government bond yields to determine the true risk-free rates. The reason for considering such adjustments is based on the theory that the true risk-free rate lies somewhere between the market for government stock and bank SWAPs.

3.2.12. As mentioned in the Methodology report, there are two viable options for obtaining market data on risk free rates. The first option is to use government stock plus a scarcity adjustment, and the second option is to use bank SWAPS less a risk adjustment. The SWAP spread is a good measure of the sum of the upwards adjustment to government stock (the scarcity adjustment) and the downwards adjustment to bank SWAP rates (the risk adjustment).

3.2.13. The following chart shows the SWAP spread over the last thirteen years.

Figure 8 - 10 year bank swap spread

3.2.14. From August 2010 to May 2011, the swap spread was below zero, ie the 10 year government bond was trading at above the 10 year bank swap. The spread averaged 0.33% for the 12 months to March 2013.

3.2.15. Recent 10 year bank swap spreads have been in the range expected, indicating no adjustment is currently required to the government stock yield due to inconsistencies with bank swap rates.

Analysis of overseas differentials

3.2.16. The shortness of the NZ yield curve makes extrapolating market data particularly challenging. Other markets have longer yield curves to 30 years. The shape of these yield curves from 10 to 30 years is useful additional information to use to extrapolate the New Zealand curve. The US spot rates and derived forward rates are shown in the chart below.

Figure 9 - US Treasury - spot and forward rates 30 April 2013

3.2.17. The graph clearly shows that the forward rates continue to increase beyond 10 years. The difference between the 30 year forward rate and the 10 year forward rate is 0.65%.

3.3  Conclusion#

3.3.1. In our view, the combination of market data over the last 12 months (both historic yields and current yields on long-term New Zealand government stock and what is inferred from a hypothetical New Zealand 30 year bond reference to international data) indicates there has now been a fundamental and significant shift from our current long-term assumption of 6% pa nominal rate to something lower. In making this judgment, we are persuaded by the following factors:

• Since June 2012, the 5 to 10 year forward rate for New Zealand government stock has been volatile but has averaged about 4.5% pa
• Spot rates for 10 and 30 year government stock for Japan, UK and USA imply a 30 year government bond in New Zealand would currently yield 4.7% pa (18 April 2013)
• If the same differential between 10, 20 and 30 year government stock as in the US is assumed, the 20 to 30 year forward rate implied recently is between 5.0% and 5.5% pa. It could be argued that, given the differences between the US and New Zealand economies, this method should underestimate the New Zealand forward rates.

3.3.2. We have also noted that recent 10 year bank swap spreads have been in the range expected, indicating no adjustment is currently required to the government stock yield due to inconsistencies with bank swap rates.

4 Long-term inflation#

4.1 Introduction#

4.1.1. Long-term inflation is the third step of the three connected components. The long-term inflation is determined as the long-term risk-free rate less the nominal risk-free rate. Consequently, a single long-term inflation assumption is derived for accounting valuations. The current long-term inflation assumption is 2.5% pa.

4.1.2. In this section we update the historical analysis in the context of New Zealand’s economic environment.

4.1.3. Many of the Crown’s obligations or assets valued using estimated future cash payments and receipts are sensitive to various inflation assumptions, including CPI. This is particularly true for estimated future cash flows over long durations, such as the Crown’s ACC claims liabilities and GSF pension obligations, which are just as sensitive to inflation rates as they are to discount rates, because of the compounding nature of both. Below is a summary and analysis of our view of an appropriate long-term CPI assumption for accounting valuations to be reported to the Treasury.

4.2 Market data#

Inflation over the last 20 years

4.2.1. CPI inflation in New Zealand has been relatively stable since the introduction of the Reserve Bank Act with inflation targets (1989/90). CPI inflation has been impacted by the introduction of GST in 1986, its subsequent increase from 10% to 12.5% (1989) and then further increase from 12.5% to 15% (2010).

4.2.2. The RBNZ inflation targets have been:

• from March 1990 0% pa to 2% pa, mid-point 1.0% pa
• from Sept 1996 0% pa to 3% pa, mid-point 1.5% pa
• from Dec 2002 1% pa to 3% pa, mid-point 2.0% pa

4.2.3. In this analysis on inflation, the effect of a GST change should be backed out. It is generally accepted that GST is a step change and is unlikely to impact on longer term inflation expectations. In the following analysis, we have removed the 2% impact of GST on CPI inflation due to the increase in GST from 12.5% to 15% in October 2010. The earlier GST rate increase (in 1986) does not impact the analysis as it was made before RBNZ established inflation targets.

4.2.4. The chart below shows the year-by-year progression of annual CPI plotted next to the target mid-point.

Figure 10 - CPI compared to target midpoint

4.2.5. The actual inflation has more often been above the mid-point than below, being below seven years out of the last 23 years.

4.2.6. The following histogram shows the historical inflation rates, as measured by CPI, from March 2003, after the inflation target was revised to between 1% pa and 3% pa, and March 2013. The inflation rates are rolling annual rates for each quarter during this period.

Figure 11 - Annual Inflation History

4.2.7. The bars in yellow represent the times when the annual inflation was within the target range. The red bars represent the times that the target has been outside of the range. Again this shows that CPI increases have been above the range more often than they have been below.

4.2.8. The actual average CPI in periods to March 2013, compared to the mid-point of the RBNZ range, have been:

* Numbers may not add due to rounding

4.2.9. CPI has been low in 2013, as shown in Figure 10, which has brought down the average CPIs.

4.2.10. Looking at a longer period, CPI has generally been higher than the mid-point target. The table above shows that the average inflation for the last 10 to 20 years has exceeded the mid-point by 0.4% pa to 0.5% pa.

New Zealand index linked government stock

4.2.11. Inflation linked government stock can be useful evidence of the market’s view of real rates of return. An inflation linked bond, maturing in 2025 was issued on 24 October 2012. The inflation expectation implied by the yield on this bond is currently 2.2% pa (as at 30 April 2013).

4.2.12. This is not definitive evidence of a market expectation over the next 12 years, as it will be influenced by supply and demand pressures for both nominal and inflation linked stock. The inflation linked bond is currently under significant demand pressure from offshore investors, in particular UK Pension schemes with mandates to invest in inflation linked stock.

4.2.13. In addition, the market is still small in global terms and can be easily moved by a large investor and so, until the market develops further and there are other index linked points on the yield curve, the index linked stock should not be used as the only determinant of inflation to 2025.

4.2.14. The break-even inflation for the 2025 index linked government stock will be taken into consideration when determining the appropriate average inflation until 2025.

4.2.15. For valuations at dates other than 30 June, the index linked stock could be usefully used to inform adjustments to the inflation assumptions.

Reserve Bank influence

4.2.16. New Reserve Bank Governor, Graeme Wheeler released a statement in December 2012, indicating that the inflation target is the midpoint of the range 1% - 3%, ie 2% pa. “Monetary policy remains focused on keeping future average inflation near the 2 percent target midpoint.”

4.2.17. This is a change in focus, in that the target is now more tightly defined as being 2% on average, as opposed to 1% pa to 3% pa. This many reduce the inflation in the long term, but the actual inflation over time is still likely be skewed positively, as there is more upward pressure on prices than downward ie we are unlikely to have negative inflation. This means that the long term average CPI inflation will still likely be greater than 2.0% pa.

Market forecasts

4.2.18. The following table summarises these published forecasts of CPI inflation. Actual CPI inflation to March 13 (12 months), from Statistics New Zealand was 0.9%.

4.2.19. While these projections generally do not go beyond five years, they indicate an expected inflation rate, in 4 to 7 years time of 2.2% pa to 2.4% pa.

4.3 Conclusion#

4.3.1. In our view the above analysis indicates a long term inflation assumption of 2.25% pa to 2.5% pa would be reasonable. We are comfortable with this range because:

• CPI inflation has exhibited a long-term pattern of exceeding the mid-point of the RBNZ's target range. Over the last 20 years, the average annual CPI has been 0.5% pa above the mid-point of the range.
• The breakeven inflation over the next 12 years, implied by the yield on the inflation linked bond maturing in 2025 bond is 2.2% pa. Market inflation expectations may differ from the breakeven inflation due to market the market view of the value of the inflation guarantee versus nominal yield uncertainty and liquidity adjustments.
• Statements made by the new Governor of the Reserve Bank imply in that the inflation target is now more tightly defined as being 2% pa on average, as opposed to 1% pa to 3% pa. This many reduce the inflation slightly in the long term.
• Market forecasts indicate an expected inflation rate, in 5 to 7 years time of 2.2% pa to 2.4% pa.

4.3.2. In addition, there are arguments that the increasing proportion of older people in the New Zealand population trends will drive down inflation in the longer term.

5 Bridging assumption#

5.1  Introduction#

5.1.1. This section covers a review of the bridging assumption which is required to bridge the short-term market rates to the long-term assumed rate. This includes a decision of the appropriate period over which to smooth the bridge.

5.1.2. We recognise the bridge is one of the most subjective areas of the methodology. The accounting standards do not contemplate this requirement and therefore we have used research and discussion papers to outline the broad principles of extrapolation in the Methodology.

5.1.3. At the time of the original Methodology was set, there were several options considered for smoothing the forward rates at the end of the yield curve into the long-term rate. The conclusion at the time was to smooth to a date five years after the maturity date for the longest dated government stock (end of the yield curve).

5.1.4. In May 2012 a review of this approach was required because of the significant difference between the forward rates at the end of the yield curve and the long term assumption. At that time the slope of the smoothing was 1.6% spread over five years and this was considered too steep.

5.1.5. In May 2012 the methodology was updated to address the steepness by setting a maximum slope which would automatically lengthen in extreme circumstances. The smoothing period of five years was retained, subject to a maximum slope of 0.15%. For the May 2012 yield curve, the maximum slope applied and this was equivalent to a smoothing period of 10.67 years compared to five under the original approach.

5.1.6. Since May 2012 new papers have been issued on this topic. We have also looked at the shape of US yield curves to help inform our analysis of the bridging methodology.

5.2 Recent studies#

5.2.1. Papers by Mulquiney and Miller (November 2012 and May 2013) and EIOPA referred to in the next section argue that the smoothing period should be significantly longer than currently adopted.

5.2.2. The three main conclusions from Mulquiney and Miller were:

• There is reasonable international market evidence for reversion to a flat long term forward rate
• The rate of reversion is slow, and
• Linear path reversion is plausible, with other approaches possible.

5.2.3. The EIOPA papers consider a global approach to setting long term discount rates, and made recommendations on long term rate and bridging methodology.

5.2.4. Refer to the Literature section for more details on both these papers.

5.2.5. Both papers recommend periods of more like 40 years to reach the long term rate, which is a significant longer period than the current Methodology. The current Methodology slope of 0.15% pa gets to the long term rate of 6% pa in between 10 and 13 years.

5.2.6. Currently we use a straight line extrapolation of forward rates. Both studies suggest there are other more technically justifiable curves that can be fitted, however there is no consensus on the best method. Also, a different shape to the extrapolated curve does not have a material impact on the result and consequently, in our view, there is no reason to depart from the simplicity of a linear extrapolation.

5.3 US Treasury forward rates#

5.3.1. The graph below shows the US curve referred to in section 3.2. The forward rates increase by 0.61% pa from 10 years to 20 years and by 0.65% pa from 10 years to 30 years suggesting a slope of between 0.03% pa and 0.06%pa. The graph shows a forward rate with a slope of 0.05% pa.

Figure 12 - Fitted US Treasury Yield Curve 30 April 2013

5.3.2. The US yield curve is steeper than the New Zealand yield curve which increases the slope of the yield curve at early durations. The slope of 0.05% pa translated to the NZ yield curve therefore seems a reasonable upper bound to adopt between 10 and 30 years.

5.4 Comparison of different long-term rates and slopes#

5.4.1. The following chart shows the risk free rates for 30 April 2013, using the current method of smoothing at a maximum slope of 0.15% pa and a long-term rate of 6.0% pa, shown by the dotted yellow line, compared to a maximum slope of 0.05% pa and a series of different long term rates (LTR).

Figure 13 - Comparison of the spot rates curve using different slopes and long term forward rates

5.4.2. Other alternatives to a linear transition, such as various fitted curves, or a fixed period rather than a slope will also only make a marginal difference to the result.

Figure 14 - Comparison of the forward rates curve (30 April 2013) using different slopes and long term forward rates

5.4.3. The long term rate is reached under the different long term rate options at term 30, 40 and 50.

5.5 Conclusion#

5.5.1. Current international thinking and the slope of the US suggest that the length of the transition period should be considerably longer than our currently methodology. We think it’s appropriate to consider changing the methodology and lengthening the bridging period further because:

• The papers published on this subject suggest a transition period of about 40 years is reasonable.
• We can derive a slope from 10 to 30 years from US market data, and a reasonable slope is 0.05%.
• There is no information available beyond 30 years and it is reasonable to extend the slope of the transition beyond 30 years as well.
• The long-term rate should be reach at duration 30, 40 and 50 depending on the long term rate selected.

5.5.2. The bridging assumption also needs to be considered in conjunction with the long term rate and lengthening the bridging assumption is an alternative to reducing the long term rate.

5.5.3. This assumption still retains a great deal of subjectivity, and we accept that a number of different recommendations are viable.

5.5.4. We continued to support a straight line extrapolation of forward rates, as in our view there is no reason to depart from the simplicity of a linear extrapolation. Although other more technically justifiable curves can be fitted, there is no consensus on the best method and a different shape to the extrapolated curve does not have a material impact on the result. It should also be noted that further reductions in slope or extensions in the transition period will have a decreasing marginal impact.

6 Literature review#

6.1  Introduction#

6.1.1. Below we summarised two recent papers which we have referred to in the above analysis. One by Mulquiney & Miller and the other by EIPOA. The overall approach indicated in these is similar to that currently adopted by Treasury, albeit the length of the bridging assumption is much longer than Treasury’s original methodology.

6.2  Mulquiney & Miller#

6.2.1. Mulquiney & Miller (November 2012 and May 2013) presented a paper at the Actuaries Institute’s General Insurance Seminar. They had a number of conclusions including:

• There is reasonable international market evidence for reversion to a flat long term forward rate. This rate is reached via extrapolation from the end of the observable yield curve.
• The rate of reversion is slow. We believe term 40 is about the minimum point to reversion based on the bond markets examined, with a central estimate closer to term 60. This conclusion rests on the assumption that the unconditional forward rate has been stable over the period 1998 to 2012.
• Linear path reversion is plausible, with other approaches possible. Non-linear paths may have implications for term at which the long term rate can be reached.

6.3  EIOPA#

6.3.1. The European Insurance and Occupational Pensions Authority (EIOPA) are currently in the middle of a Solvency II Long-term Guarantee Assessment, where are they will collect qualitative and quantitative information from the insurance industry and supervisory authorities on the effects of the Long-term Guarantee (LTG) package[3]. On 25 January 2013, they released a technical document, “LTG Assessment Technical Specifications Part II”. There are a number of points relating to the risk-free rates:

• Swap mid rates will be used in the determination of the basic risk-free interest rate term structure.
• There needs to be an adjustment for credit risk and basis risk. For the purpose of the LTG assessment, the adjustment is applied as a fixed deduction across all maturities of the observed swap term structure.
• A framework is currently under development for the credit risk adjustment for government stock. For the purpose of the LTG, it is proposed not to implement a credit risk adjustment for government stock that deviate from the one applied to swaps.
• The methodology used to interpolate between the finite number of liquid market data points and the extrapolation in to the ultimate forward rate (UFR) is the Smith-Wilson method.
• The UFR is a percentage rate that the forward curve converges to and is a function of the long-term expectations of the inflation rate and the long-term average of the short-term real rate. It is expected that this value is stable over time and only change due to changes in long-term expectations.
• For the purpose of the LTG assessment, it is assumed that the UFR for each currency is equal to 4.2% pa - this is made up of an expectation of 2.2% pa long-term growth and 2.0% pa inflation.
• The LTG assessment asks participants to consider the impact of two different speeds of convergence to the URF:
  • convergence in 10 years from the last liquid data point
  • convergence in 40 years from the last liquid data point
  • the last liquid data point is generally taken as prior to the last data point.