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The Actuary The magazine of the Institute & Faculty of Actuaries

When long-term is too long

Peru Govindasamy looks at the liquidity and pricing consequences of developed market ultra long-term bonds 



Governments have, historically, issued bonds to enable them to meet their outgo when this exceeds their current revenue from taxes and duties. While unexpected events are a key lever of government debt issuance in the short-run, long-run issuance is largely driven by political factors. 

In November 2016, Austria issued an ultra long-term government bond of 70 years, maturing in November 2086. Austria is not the first European country to issue these ultra long-term bonds (see Figure 1).

Figure 1
Figure 1

Pricing and analysing an ultra-long instrument introduces an interest-rate challenge, as yield curves that extend past 20 to 30 years typically lack sufficient credibility to be used for pricing. This article explores the concept of the last liquid point (LLP), which is the point on the yield curve beyond which there is insufficient liquidity to value cash flows accurately. 

Rationale for ultra long-term bond issuance 

In the Eurozone, the European Central Bank (ECB) has adopted an accommodating stance, through zero and negative interest rate policies, to stimulate the European economy. As the ECB pushes interest rates to record low yields, issuers are extending the average maturity of their funding in order to lock in these low funding costs for as long as possible. A similar trend is noted in other developed markets.

The market for ultra long-term government debt 

Demand is primarily from pension funds (which are sometimes bound by their investment mandates to invest in government debt), insurance companies (which use these long-term instruments to match the liabilities on their policies) as well as other institutional and retail investors with sufficient risk appetite and a long enough investment horizon. 


A number of financial publications have highlighted the duration risk inherent to ultra long-term bonds. As issuers rush to issue this long-term debt, bond duration has increased to historic highs – the effective duration of the Bank of America’s (BoA) global government bond index hit a record high of 8.23 in 2016, from just 5 when the index started back in 1997. The modified duration (comparable with effective duration for option-free Treasury instruments) of the 70-year Austrian bond has been calculated at 43 by the Global Association of Risk Professionals (GARP, 2016). Practically, this resulted in a 3.5% loss for investors in this bond after global bond yields rose during the first week after issuance. 

However, to what extent can these duration and price figures be relied upon? 

As mentioned, yield curves spanning beyond 30 years are rarely published and even when published, are of questionable reliability. The European Insurance and Occupational Pensions Authority (EIOPA) has published the following guidance regarding LLPs for various currencies: 

Figure 2
Figure 2

When yield curves break down 

In order to value cashflows beyond the LLP, extrapolation approaches are used. These typically involve one of the following: 

  • Extrapolation with a focus on liability stability. This approach attempts to reduce the business impacts of volatility in order to produce a more stable yield curve. 
  • Extrapolation with a focus on market consistency. This approach is premised on market consistency and, as a result, is often recommended by regulatory authorities. In summary, this method aims to quantify the cost of transferring a liability within the context of the prevailing (immediate) market conditions. 


The implementation of both methods involves the following features and is illustrated in Figure 3

1. Selection of a starting point (on the known yield curve) for the extrapolation

2. Finding an appropriate proxy for the long-term rate (referred to as the ultimate (or unconditional) forward rate (UFR))

3. Determination of the path between points 1 and 2.

Figure 3
Figure 3


It is evident that the valuation techniques rely on the selection of both the starting point and the UFR as they drive the parameterisation of the extrapolation model. Since there is little established methodology to guide investors through this selection process, the entire valuation technique is, effectively, largely based on presumptions. This implies that even the duration figure quoted by GARP is illusory.

Firms may wish to select the above mentioned parameters with an objective of:

  • Achieving consistency across a group of subsidiary entities and/or similar markets
    If there is insufficient data to inform a starting yield curve value and/or UFR, it may be useful to follow that used in other entities within a group, especially if those entities are operating in similar markets. This may aid communicability and understanding of, as well as confidence in, the overall method. However, this should not be done at the expense of creating undue basis risk in the assumptions applied across the group.


  • Ensuring consistency with issued territorial guidance (e.g. from EIOPA)
    Prudential supervisors (both for insurers and banks) issue guidance on setting the UFR and starting yield for various territories (e.g. EIOPA has issued such guidance). Often, this guidance incorporates industry experience and expert perspectives, making it a reliable source.


  • Prioritising expert forecasts over currency
    It is sometimes the case that current data represents an outlier with respect to historical experience and/or most likely future experience. In these cases, it may be useful to prioritise expert perspectives over what current market data may be implying. Regressive models could also be used, perhaps with exponential weightings, to incorporate a more unbiased representation of past experience.


  • Achieving a certain velocity of convergence
    Depending on the term of the underlying instruments, it may be useful to consider setting the starting yield so that the extrapolation process converges to the UFR after a certain period (say 20 years).


There has also been research into using moving UFRs at different durations, for example a Smith-Wilson model using a moving UFR has been proposed. 

Implications for actuaries and investment 

Investors should exercise caution before investing in these instruments to ensure that their portfolios remain in line with their risk tolerances and investment strategies. Further, institutional investors (particularly banks and insurers subject to asset admissibility restrictions) should investigate more sophisticated methods of valuing these instruments, in order to accurately quantify the impacts (including liquidity, credit and future potential regulatory risks) on their balance sheets. 

Peru Govindasamy is a senior actuarial analyst at Liberty in South Africa