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3  Short-Term Risk-Free Rates

3.1  Introduction

3.1.1 This section describes the methodology and judgments that the Treasury made in determining the short-term risk-free discount rates for accounting valuations. In this context short-term means the period in which market yields are available in New Zealand to proxy risk-free rates (usually between 10 and 15 years).

3.2  Summary

3.2.1 In practice, the risk-free rate cannot be directly observed; it is usually proxied by the return on a very safe asset. When selecting the risk-free rate, the first step is to identify a suitable observable proxy and then to determine if any adjustments are required.

3.2.2 The Treasury's overall conclusion is that government stock with no adjustment is currently a suitable proxy for risk-free rates.

3.2.3 The methodology for establishing a short-term risk-free yield curve is:

  1. determine risk-free discount rates for the first year from the OCR and Treasury Bills and any stock maturing in this period
  2. determine a smoothed market forward rate curve from New Zealand government stock yields, and
  3. determine any adjustments required to the New Zealand government stock yields

3.2.4 At present, Treasury Bills are liquid and so Treasury Bill data, in our opinion, should contribute to the determination of risk-free discount rates for the first year without any adjustment. We do not expect that this will change and therefore, we have not considered in this paper any impacts of possible (but unlikely) future illiquidity issues on Treasury Bills.

3.2.5 Treasury Bills of up to six months can be used if forward rates for periods of up to six months are required. The overall shape of the yield curve when expressed in years is not particularly sensitive to the yields less than six months. The six month data point is particularly useful, as otherwise there is a potential large gap between the OCR and the first government stock maturity, which is currently 18 months duration.

3.2.6 When selecting to reference the market forward rate curve to New Zealand government stock we have been guided by the accounting standards and by generally accepted actuarial practice in New Zealand that government bonds are the most suitable risk-free proxy. The current market evidence also supports our view that the most suitable proxy to a New Zealand risk-free rate is yields on government stock.

3.2.7 However, we are aware from a review of international technical papers by the actuarial profession, that there are a number of sources of risk-free rates that an entity could use. These papers have also highlighted that there is considerable debate internationally on what the “best” basic risk-free rate source is and this can vary across jurisdictions. We are also aware that this debate has moved in response to bond market observations, particularly through the global financial crisis and during the recent sovereign bond crisis in some European countries.

3.2.8 After reviewing the international papers, as well as examining the current market in New Zealand, we have formed a view that the alternatives proposed, such as bank SWAPs or corporate bond rates minus risk adjustments, do not provide a more reliable and relevant proxy to risk-free rates in New Zealand.

3.2.9 The supply of government stock is forecast to increase significantly, and in our view this is a more appropriate starting point than bank SWAP rates. We recognise that in Europe the bank SWAP rate is regarded as a more appropriate starting point. However, they have the complication of multiple sovereigns issuing debt in a common currency which is not relevant in New Zealand. Therefore, this current European view is not automatically applicable to the New Zealand context.

3.2.10 We believe that in the current market, short-term risk-free discount rates can be reliably estimated through to the end of the government stock yield curve using the government stock and Treasury Bill data with no adjustment.

3.2.11 However, in the past, adjustments have been required to the New Zealand government stock yields to give short- term risk-free discount rates. We think that these adjustments have been, and continue to be appropriate in certain circumstances. This is particularly appropriate when a new bond issuance is very illiquid at valuation date. Therefore, our methodology requires an assessment for adjustments to the New Zealand government stock yields:

  1. assessing whether any adjustment is required by investigating other sources of information
  2. quantifying the scarcity discount or any other adjustment to government stock by investigating other sources of information
  3. quantifying the risk premium or any other adjustment to bank SWAP rates by investigating other sources of information, and
  4. attempting to reconcile the two adjustments (that is, government stock scarcity and bank SWAP risk premium) and making a judgment on the best approach considering the adequacy of the information available.

3.2.12 Our current view is that given the NZ DMO’s current bond programme over the next 5 to 10 years (announced in the May 2010 Budget Update), it is unlikely that any adjustments will be required to government bond issuances as was the case in the past. However, we will remain vigilant for changes in activity in government bond trading which may indicate there is an anomaly in the market rate that requires an adjustment to determine a basic risk-free rate. In particular we will be vigilant of new government tranches that may be issued just before or on valuation dates that may show signs of illiquidity or prices out of line with the rest of the market. Our proposed smoothing process will allow for this by weighting the various stocks by the amount on issue. Consequently a new, small volume stock will receive a lower weighting in the fitting of the yield curve. This was the case with the 2021 government bond tranche issued in May 2009.

3.2.13 We believe that short-term risk-free rates should be expressed as forward rates and the yield curve smoothed because this is automatically hypothecates a portfolio of risk-free assets that matches the duration and timing of the liability cash-flows. The details of the curve fitting and smoothing are described in Appendix 2.

3.3  Analysis

3.3.1 The following analysis is divided into four topics:

  • The risk-free rates for terms of less than one year.
  • Market data for terms of more than one year (including a discussion on the various market data options over one year including our conclusion on the most appropriate risk-free option in New Zealand).
  • Bank SWAPS compared to government stock.
  • Market adjustments (including an assessment of adjustments to government stock rates).
  • Illustrative examples using current market data.
  • The outlook for the New Zealand government stock market.

3.4  Risk-Free Rates for Terms of Less than One Year

3.4.1 Risk-free rates for terms of less than one year are available from the OCR and Treasury Bills. Reuters and Bloomberg quote rates for Treasury Bills of the following durations:

  • One month
  • Two month
  • Three month
  • Six month

3.4.2 At present, Treasury Bills are liquid and so Treasury Bill data can be used to determine risk-free discount rates for the first year without any adjustment. At present there is no expectation that this will change.

3.5  Market Data for Terms of More than One Year

3.5.1 In an ideal world, market data on risk-free rates should be available directly from market observations. In practice we have limited observations from markets that may have shortcomings. We therefore need to consider how to best determine risk-free rates from available market data.

3.5.2 From our review of the international literature and discussions with New Zealand actuaries, we are aware that there are a number of different sources for risk-free rates, including:

  • government stock rates
  • government stock rates plus an adjustment for scarcity
  • SWAP rates minus an adjustment for risk
  • SWAP rates, and
  • corporate bond rates minus an adjustment.

3.5.3 The two most liquid markets for New Zealand fixed interest are the bank SWAP market and the New Zealand government stock markets. The spread between the yields shown by these two markets can be caused by a number of factors, including:

  • an extra risk addition to the yield for SWAPS;
  • a liquidity addition to the yield for SWAPS, and
  • a market scarcity deduction from the yield for government stock.

3.5.4 The corporate bond market in New Zealand is nowhere near as extensive as other countries and the available stock covers a wide range of credit ratings. It is generally accepted that New Zealand does not have a high quality corporate bond market. For this reason we have eliminated corporate bonds as a viable option as a reference to risk-free rates in New Zealand.

3.5.5 Furthermore, even if we did believe the corporate bond market was a viable starting point, the adjustment required for removing risk is not straight forward to determine and requires reference to other “risk-free” assets. For these reasons, we have not investigated this option further. The decision between the first four options then comes down to decomposing why the government stock rates are different from the bank SWAP rates and arriving at the most appropriate point between the two.

3.5.6 Government stock rates and bank SWAP rates without considering any adjustments described in the options above are not, in our opinion, viable options in New Zealand. These instruments have been prone to yield anomalies in the past when stresses are put on the market. Whilst currently such market stresses are not a significant issue, it may be in the future.

3.5.7 The issue of markets under stress is not unique to New Zealand and has been the subject of considerable international debate, particular during the recent global financial crisis. While adjustments may not be necessary at every valuation date, to future proof our methodology we have anticipated that any starting position whether it is government bonds or bank SWAPS, should be reviewed for adjustment for scarcity and risk respectively.

3.5.8 Therefore, in our view there are only two viable approaches in New Zealand, Firstly government stock plus a scarcity adjustment, or secondly bank swaps less a risk adjustment. There is potentially considerable uncertainty around determining the quantum of both of these adjustments. The next part of this section discusses these two main options and the reliability of both scarcity and risk adjustments depending on the starting point.

3.6  Bank SWAPS compared to Government Stock

3.6.1 Bank SWAP rates are the commonly used description of the quoted market rates used to price a variety of interest rate swap instruments between two parties. In this paper we only consider the quoted market in NZ dollars and refer to the rates as bank SWAP rates.

3.6.2 The purpose of this section is to determine if Bank SWAP rates adjusted for risk are a viable alternative source to government stock adjusted for scarcity, for determining a basic risk-free rate. This comparison also gives us useful information on the size of adjustments required.

3.6.3 Currently, while this choice is simplified because the bank SWAP spread is close to zero and no adjustment is required to either, we recognise that this may not always be the case. Therefore, our decision needs to be based on principles that can endure beyond the current bank SWAP spread observations.

3.6.4 The difference between bank SWAP rates and government stock is known as the bank SWAP spread. It is extremely difficult to accurately decompose the spread into its components. However, the following observations can be made about the historic size of the spread shown in the graph below:

  • From 2005 until the Global Financial Crisis (GFC), the spread increased. This was largely due to the fact that there was a large demand for government stock and limited availability as a lot of stock was tightly held and the New Zealand Government were paying off debt, driving the yields down.
  • After the GFC, bank SWAPs were effectively government guaranteed for a period and the New Zealand government stock market also become significantly more liquid. The spread reduced to close to zero.
Bank SWAP spread
Bank SWAP spread.

3.6.5 The graph above shows that the bank SWAP spread is currently close to zero and has been for over a year. 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). Because the sum is zero, we can conclude that both the scarcity and the risk adjustments are also zero.

3.6.6 This initial analysis shows the current equivalence of the two methods, but does not provide any clear answers on a robust methodology in the longer term. It is useful to further explore the adjustments that may be required in the future.

3.7  Market Adjustments 

3.7.1 The reason for making market adjustments is based on the theory that the true risk-free rate lies somewhere between the market for government stock and bank SWAPs.

3.7.2 Based on this theory the two relevant adjustments are:

  • a scarcity discount adjustment to apply to government stock rates (will increase the yield), and
  • a credit risk adjustment to apply to bank SWAP rates (will reduce the yield).

3.7.3 A third possible adjustment is a liquidity adjustment to reflect the liquidity nature of insurance liabilities for accounting purposes. We believe this adjustment is not relevant for the purposes of the Financial Statements of the Government. The theory behind this adjustment is discussed at the end of this section.

3.7.4 As discussed above, the most useful market information on the two most relevant adjustments is the SWAP spread, which will give guidance on the total of these two adjustments but not the split between the two.

3.7.5 In New Zealand, the true risk-free rate will normally lie somewhere between the government stock rates and the bank SWAP rates. The true risk-free rate will normally be at or above the government stock rate, as government stocks are tightly held, leading to a scarcity premium. The bank SWAP market is more liquid than the government stock market, but arguably attracts a credit risk premium. An adjustment will move the government stock rates up towards the bank SWAP rates, or alternatively the bank SWAP rates down towards the government stock rates.

Process for adjusting market data

3.7.6 The following is an appropriate process to be adopted when assessing any required adjustments to market data:

  1. Assess whether any adjustment is required by investigating other sources of information.
  2. Quantify the scarcity discount or any other adjustment to government stock by investigating other sources of information.
  3. Quantify the risk premium or any other adjustment to bank SWAP rates by investigating other sources of information.
  4. Attempt to reconcile the two adjustments (scarcity discount and risk premium) and make a judgment on the best approach considering the adequacy of the information available.
  5. Consider the liquidity adjustment and whether this can be justified from the nature of the liabilities.

Assess whether any adjustment is required

3.7.7 The first step is to investigate if there is any reason for government stock to be adjusted. The clearest signal will be obtained from the bank SWAP spread. If there is no or minimal spread (ie, both sets of rates are essentially the same), then no adjustment is possible or required. The market is telling us that there is no scarcity of government stock and minimal extra risk in bank SWAP rates. Consequently, when these rates are similar, we can be confident that the overall level of the government stock curve is reasonable and needs no adjustment.

3.7.8 Currently the SWAP spread is minimal or even negative so no adjustment is required. This is supported by the increased liquidity and supply of government stock, implying that it is unlikely that a premium is being paid for government stock.

Scarcity discount

3.7.9 Firstly, to support the need for a scarcity adjustment, volumes of trading, volumes available, buy sell spreads or price volatility can be looked at to assess if there have been any changes in the market liquidity. This situation occurred in 2007 and 2008 in New Zealand, where there was evidence of a shortage of government stock, including the presence of a large bank SWAP spread. Another indicator was the yield on debt used by sovereign backed organisations in New Zealand dollars, for example the World Bank. The difference in yield between government stock and these could not be explained adequately by risk and liquidity.

3.7.10 It not straightforward to evaluate the size of the market adjustment required. There are a number of sources available, including international fixed interest. It is possible to generate a synthetic US Treasury security in New Zealand dollars by using cross currency SWAPS. The cross currency SWAPS are reasonably robust as they are an important component or by-product of the global market for bank SWAPS. The difference between the synthetic US Treasury yield curve in NZ dollars and the government stock yield curve gives an indication of the extent of any adjustment required. This method was used for the ACC outstanding claims liability valuation in June 2008, when the bank SWAP spread was greater than 1.0%.

3.7.11 If adjustments are required in future, then a range of options will need to be considered.

Risk premium

3.7.12 The adjustment to bank SWAPs to reflect the risk is also complex and relies on judgement. There is a fairly well developed methodology for decomposing the yields on corporate bonds into components such as default risk, uncertainty of default risk and liquidity. This analysis can be extended to bank SWAP rates where the default risk has two components. The first component is the default risk of the instrument itself which is limited to the coupon payments; the second component is the default risk on the 90 day bank bill that is included in the yields used to price the SWAPS.

Reconcile the two adjustments

3.7.13 Ideally the two methods and starting points: government stock plus scarcity or bank SWAP less risk will give the same answer. In order to determine which will provide the most robust answer, a judgement needs to be made on the stability of the adjustments and the likely outlook for each market in terms of supply, liquidity and trading.

3.7.14 If both methods are judged to be equally robust, then government stock is the preferred starting point. This is on the basis that some of the accounting standards refer to government stock explicitly, whereas none refer to bank SWAPS.

3.7.15 Currently the outlook for the government stock market is for significantly more supply. There seems to be no reason why the scarcity adjustment should change in the short term. Consequently, until there is evidence otherwise, the Treasury concludes that government stock is the appropriate starting point.

Liquidity adjustments

3.7.16 Another possible adjustment currently being debated is a liquidity adjustment to reflect the liquidity nature of insurance liabilities. The insurance accounting standard states that the nature of the liability should be considered, and the argument is that liquidity is part of the nature. The argument is that if insurance liabilities are illiquid, then the entity responsible for settling the liability can invest in illiquid risk-free assets that will return a slightly higher yield. The criteria for considering this adjustment is that the liabilities must be certain and not able to be redeemed immediately at no cost. In Europe the proposal is for there to be different degrees of liability liquidity.

3.7.17 It has been noted that the Australian Prudential Regulation Authority (APRA) has considered this same question for the purposes of capital reporting and their interpretation is that, for regulatory purposes, only lifetime annuities qualify for a liquidity adjustment.

3.7.18 In the Treasury’s view the settlement of our insurance liabilities are too uncertain to be regarded as illiquid. Therefore, for the purposes of the Government’s financial reporting under NZ IFRS, we do not think it is appropriate to make a liquidity adjustment to any starting point at this stage. This is currently a relatively new area of debate and may need to be reassessed as the international position is updated.

3.8  Illustrative Examples with Current Market Data

3.8.1 To put the preceding discussion in context it is useful to describe the current market and show illustrative market rates.

Government Stock

3.8.2 The current New Zealand government stock on issue is as follows.

Current New Zealand Government Stock maturities on issue (at 31 March 2010)
Maturity Coupon Total Issue
Available (net of
15-Nov-2011 6.00% 8,137 6,442
15-Apr-2013 6.50% 7,870 6,392
15-Apr-2015 6.00% 6,275 5,094
15-Dec-2017 6.00% 7,436 5,962
15-May-2021 6.00% 4,080 3,494

CPI indexed


1,521 1,171
Total   35,319 28,555

3.8.3 The yield curve of government stock, as at 11 May 2010, is shown below.

Yield Curve 11 May 2010
Yield Curve 11 May 2010.

3.8.4 In the graph above, the top two lines are forward rates, raw and smoothed. The lower lines are the spot rates for actual stock, including coupons, plotted against average duration (note the coupons reduce the average duration of the stock), and the derived zero coupon curve plotted against raw duration. In this example Treasury Bills have not been included in the data.

3.8.5 When there is a negative yield curve, the forward rates will be below the spot rates, as if the whole graph had been flipped upside down.

3.8.6 Note that in the graph above there is some evidence of forward rates peaking and then reducing for longer terms.

3.8.7 We have cross-checked the yield curves with those derived by NZ DMO and they are consistent. The yield curves have not yet incorporated the Treasury Bills, and for this reason they are slightly different to the NZ DMO's curves in the short term.

3.8.8 Information on the curve fitting methodology used is set out in Appendix 2.

Bank SWAPs

3.8.9 The bank SWAP yield curve for the same date is shown below.

Yield Curve 11 May 2010
Yield Curve 11 May 2010.

3.8.10 The bank SWAP forward rate curve has longer term observations than government stock, namely at 12, 15 and 20 years. There is limited trading on the 20 year SWAP and the 15 year SWAP is probably the longest reliable duration.

3.9  Outlook for the New Zealand Government Stock Market

3.9.1 The New Zealand Government has significant and growing debt forecasts in the medium term and consequently a significant amount of government stock is expected to be issued in the medium term.

3.9.2 Presently, the NZ DMO is intending to maintain a reference 10 year government stock over the near future. It is expected that this will be achieved by issuing a 12 year stock every 2 years. In addition, other government stocks may be issued to maintain a yield curve that ideally has a maturity at least every two years.

3.9.3 The latest information from the NZ DMO reflects Budget 2010 (released 20 May 2010) and includes forecast bond programmes of $10.5 billion in 2011/12, $10 billion in 2012/13 and $6 billion in 2013/14.

3.9.4 Key features of this include the fact that the NZ DMO is actively considering reintroducing inflation-indexed bonds during 2010/11, as well as issuing a 2019 nominal bond which will fill the gap between the current 2017 and 2021 bonds.[1]

3.9.5 The implications of these plans are that:

  • the liquidity of government stock markets is likely to improve and yield adjustments are unlikely to be needed in the near future
  • new issues with a term of less than 12 years will not change any methodology but will add an extra data point, and
  • new issues of longer dated indexed stock, particularly longer than ten years, will provide additional information on longer term real yields. This should not affect the methodology but may mean that the parameters for long-term real rates will need to be reviewed.
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