Risk free yield curves Brian Kipps

Risk-free interest rate workshop
Brian Kipps
Swaps vs. Bonds: Theoretical considerations
In evaluating an ideal “risk free” yield curve one should consider the characteristics required from such
a curve:
• Observable
Transparent, quoted in the open market, easily validated
• Objective
No bias in the curve or data used in constructing the curve. Typically this is achieved in cases where
there are a significant amount of contributors
• No/low credit risk
Projected cashflows should be discounted at a rate which implies that there is certainty on the
occurrence of such cashflow
• Liquidity across term structure
Liquidity indicates the reliability of the observed prices/rates and whether observed rates are
achievable. In the valuation of long-term liabilities it is important that there is liquidity across the term
structure of the yield curve due to the sensitivity of long-dated cashflows to interest rates.
• Arm’s length requirement
Typically used in defining a fair value: should indicate the price or value at which such valued
cashflows could be bought/sold in the financial markets.
Swaps vs. Bonds: Theoretical considerations (cont)
Ideal characteristics
No/Low credit Risk
Liquid across term structure
Arm’s length transaction
But let’s be clear: there is no true risk free curve – governments default despite the ability to print
cash and raise taxes (that is why SA local currency debt is only A- on international scale), and
collateralised swap transactions can lose money if a bank defaults and you can’t close out the
transaction quickly enough and collateral proves insufficient (jump risk)
What we really need is a practical approach to the risk free rate and to move on to some of the
more important stuff
Swaps vs. Bonds: Practical implications
Using a specific risk free curve in the insurance industry could have significant implications for local
financial markets:
Government relies on the bond market for funding, especially in the back end which is where
long term insurers invest although bank support through B3 as well as real money investors will
arguably absorb the supply should the swap curve be preferred
Corporates and banks rely on the swap market for funding and risk transfer through the
derivatives market, again long term insurers play an important role here
And since neither curve is truly risk free, why do something that has wider unintended
consequences on the real economy?
First prize is that insurers are allowed to use either the swap curve or the bond curve in valuing
different tranches of business as this will ensure minimal impact on or disruption to the financial
There may need to be rules to prevent abuse of this e.g. upfront election per tranche of business
(not unlike an accounting election), and capital implications for assuming bond/swap basis risk in
risk management activities
Swaps vs. Bonds: Practical implications (cont)
It is also very important to consider the illiquidity premium as part of our risk free rate discussion
Remember a bond is funded (your money is at risk), whilst a swap is unfunded (no cash put down)
and collateralised under CSA
A bond (adjusted for credit risk) is comparable to a bank deposit (adjusted for a bank’s credit risk),
and not a swap
Bank deposits pay significantly over Jibar to attract term funding, the majority of which is
compensation for illiquidity (banks need to pay investors a premium to lock up their funding so
they have a stable deposit base to on-lend to corporates)
A bank raising funding through senior debt (marked against government bonds), or through
institutional deposits (marked against Jibar) is generally ambivalent between the two sources –
they are priced to be largely equivalent, and in fact a bank will generally swap its senior debt funding
into Jibar once it is raised anyway
What this means is that there is a big market force (bank funding) ensuring that the government
bond and (credit adjusted) deposit markets are kept in line
Supply and demand dynamics of the two markets means this does not always hold, but there is a
link between the two of them
Swaps vs. Bonds: Practical implications (cont)
In the event that a single risk free curve is forced upon the insurance industry, then in our opinion
the swap curve is preferable:
Closer to credit risk free: CSAs internationally moving to zero threshold, cash collateralised
Convergence of banking and insurance: if we want to reduce regulatory inconsistencies,
then we need to adopt the swap curve – why should a 5yr amortising deposit have a different
value to a 5yr term certain annuity?
For the economy: supports corporates looking to fix their funding, whilst B3 and real money
investors will continue to support government funding efforts
For fixed income liabilities: Interest rate risk is an unrewarded risk; credit risk is a rewarded
risk. Swaps allow flexibility to hedge interest rate risk, but optimise allocation to credit risky
assets – beneficial to policyholder returns and/or shareholder ROE
For hedging of investment guarantees: Some exposures cannot be hedged on the bond
curve – no swaptions, zero coupon instruments, and funding implications would force you into a
rolling bond forward strategy which is expensive (which will impact policyholder pricing and
benefit provision) and is dependent on the bond-repo market at every roll date
Arms length: if the intention is to create a market consistent liability, the market consists of
other life companies and banks (which use the swap curve) – not the government
Illiquidity premium
Illiquidity premium = compensation for locking your money in for a long period of time
For an annuitant, he is lending his money to the life company for a long period of time and deserves
compensation for this – this can be achieved by investing his money in matching assets which earn
an illiquidity premium e.g. long-dated bonds, loans
An illiquidity premium is merely one constituent of the overall risk premium defined as the total
return on an asset in excess of the risk free return
Total risk premium
Total risk premium
Total return on asset
Excess risk premium
Profits demanded by
Idiosyncratic default risk
Compensation for firmspecific credit risk.
Systemic default risk premium
Compensation for non
firm-specific credit risk.
Illiquidity premium
Risk free return
Credit spreads are generally defined as
the spread over risk-free on a credit risky
asset. Credit spreads are not in their
entirety compensation for expected loss –
they also compensate the investor for
illiquidity, profit (to cover CoC)
Compensation for
potential lack of liquidity.
Bond or swap rate.
Illiquidity premium (cont)
So how do we approximate this illiquidity premium, since on its own it is not easily observable...
Ideally the illiquidity premium is calculated from the market, not from the assets you hold – this is
old school actuarial thinking
A practical suggestion:
If using the swap curve, look at bank funding rates and adjust for bank’s credit risk
If using government curve, apply something similar to current matching premium calculation
but calculated on a universe of applicable bonds, not just the ones you happen to hold, and
adjusted using expected loss rather than random number like 25%
One of the problems with the current matching premium approach is that because it assumes
one risk free (swap) curve, it also captures bond/swap basis in the matching premium if you invest in
This has nothing to do with illiquidity
To avoid this, either disallow these assets from the matching premium calculation (not ideal), or
strip out the bond/swap basis from the matching premium AND hold capital against the basis
Does this really need to be prescribed, or just some principles agreed?
Extrapolation methodologies
In valuing long dated liabilities it is inevitable that these will extend beyond the observable part of the
yield curve (roughly 30yrs)
The key principles that should be applied in extrapolating a yield curve are:
Where there is useful data, use it (e.g. back-end of observable curve)
Ideally no complicated theoretical model which is hard to understand and creates
unnecessary “noise” in capital calculations and earnings
Convergence to an ultimate forward rate is a sensible approach although care should be
taken not to put too much reliance on a few points on the observable yield curve: could lead to
market distortions
Ideally the extrapolated part of the curve needs to be linked to the observable yield curve and
updated dynamically
Ideal outcome would be for insurers to apply discretion as long as methodologies are consistently
applied, sensible, and (potentially) disclosed

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