Skip to main content
The Actuary: The magazine of the Institute and Faculty of Actuaries - return to the homepage Logo of The Actuary website
  • Search
  • Visit The Actuary Magazine on Facebook
  • Visit The Actuary Magazine on LinkedIn
  • Visit @TheActuaryMag on Twitter
Visit the website of the Institute and Faculty of Actuaries Logo of the Institute and Faculty of Actuaries

Main navigation

  • News
  • Features
    • General Features
    • Interviews
    • Students
    • Opinion
  • Topics
  • Knowledge
    • Business Skills
    • Careers
    • Events
    • Predictions by The Actuary
    • Whitepapers
    • Moody's - Climate Risk Insurers series
    • Webinars
    • Podcasts
  • Jobs
  • IFoA
    • CEO Comment
    • IFoA News
    • People & Social News
    • President Comment
  • Archive
Quick links:
  • Home
  • The Actuary Issues
  • June 2018
06
General Features

When long-term is too long

Open-access content Friday 1st June 2018 — updated 1.27pm, Wednesday 6th May 2020

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

2

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

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. 

Duration 

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

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

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

This article appeared in our June 2018 issue of The Actuary.
Click here to view this issue
Filed in
06
Also filed in
General Features
Topics
General Insurance

You might also like...

Share
  • Twitter
  • Facebook
  • Linked in
  • Mail
  • Print

Latest Jobs

New Fast-Growing Team - Actuarial Systems Development

London (Greater)
Excellent Salary Package
Reference
143762

Actuarial Pension Consultant – Scotland/Remote – Up to £90,000 plus bonus

Edinburgh / Glasgow / Remote working
Up to £90,000 + Bonus
Reference
143761

Part Qualified Pensions Actuary– Specialised Pensions Consultancy - Scotland/Remote - Up to £70,000

Edinburgh / Glasgow / Remote working
Up to £70,000 + Bonus
Reference
143760
See all jobs »
 
 

Today's top reads

 
 

Sign up to our newsletter

News, jobs and updates

Sign up

Subscribe to The Actuary

Receive the print edition straight to your door

Subscribe
Spread-iPad-slantB-june.png

Topics

  • Data Science
  • Investment
  • Risk & ERM
  • Pensions
  • Environment
  • Soft skills
  • General Insurance
  • Regulation Standards
  • Health care
  • Technology
  • Reinsurance
  • Global
  • Life insurance
​
FOLLOW US
The Actuary on LinkedIn
@TheActuaryMag on Twitter
Facebook: The Actuary Magazine
CONTACT US
The Actuary
Tel: (+44) 020 7880 6200
​

IFoA

About IFoA
Become an actuary
IFoA Events
About membership

Information

Privacy Policy
Terms & Conditions
Cookie Policy
Think Green

Get in touch

Contact us
Advertise with us
Subscribe to The Actuary Magazine
Contribute

The Actuary Jobs

Actuarial job search
Pensions jobs
General insurance jobs
Solvency II jobs

© 2023 The Actuary. The Actuary is published on behalf of the Institute and Faculty of Actuaries by Redactive Publishing Limited. All rights reserved. Reproduction of any part is not allowed without written permission.

Redactive Media Group Ltd, 71-75 Shelton Street, London WC2H 9JQ