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The Actuary The magazine of the Institute & Faculty of Actuaries
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Discount rates: Fighting for supremacy

Before the financial crisis, the banking and insurance industry had almost reached consensus on the appropriate way to value fixed cashflow promises, and the answer was an inter-bank rate called LIBOR. After a period of confusion during the crisis, the banks have settled on a new approach based on a rate called SONIA, which is typically below LIBOR. In this article we describe the rationale for the banks’ change of approach and consider whether the same arguments apply to insurers.

What are LIBOR and SONIA?
Banks with excess cash deposits routinely lend out to banks with excess loan assets at a fixed rate of interest. The agreed rate is a matter for negotiation between the parties, depending on the term of the deposit but also on the perceived creditworthiness of the borrowing bank. LIBOR and SONIA are both inter-bank rates. Table 1 compares the two rates. More information about both rates is available at www.bba.org.uk

What is the cause of the term premium?
LIBOR is typically but not always higher than SONIA, an effect known as the ‘term premium’. Due to the effect of discounting, banks moving from LIBOR to SONIA typically benefit from an increase in assets, which is largely offset by higher liabilities.

Figure 1 compares the two rates over the period 1996-2010. We can see that SONIA was historically much more volatile than LIBOR, but that this has stabilised in recent years.

Banks usually describe the difference between SONIA and LIBOR in terms of ‘committed funding’. The higher rate compensates LIBOR lenders for the inflexibility of a term deposit and reduced capacity to exploit other investment opportunities. The LIBOR borrower correspondingly avoids the inconvenience of daily refinancing and the possibility of increased borrowing costs following a downgrade.

Secondly, SONIA is based on actual transactions while LIBOR is an average of opinions. The opinions may be subject to reporting biases.

Thirdly, six-month LIBOR should also reflect expectations of changes to short-term rates over the six-month period.

Theoretically, these explanations could result in LIBOR being either higher or lower than SONIA. The LIBOR borrower also suffers a loss of flexibility to exploit new funding opportunities. Locking in a rate protects against higher future borrowing costs following a credit downgrade but also removes the possibility of cost-saving following an upgrade. The typical upward slope highlights the current asymmetric situation, where flexibility appears to be of greater value to lenders than borrowers, and prime banks are more concerned about downgrades than upgrades.

Actuaries might express these reasons differently, by analogy to the selection effect in mortality albeit over shorter timescales. Prime banks have benefited from the equivalent of insurance underwriting. For longer terms of deposit, the select effect gradually wears off.

Extending the short curves
Observing rates for terms up to six months is of little use for valuing 10- or 20-year liabilities. To extend the observed curve, most banks make reference to interest rate swap markets.

Interest swaps are a derivative instrument where two parties swap interest rate payments. Typically one party will make payments linked to a short rate such as LIBOR (floating rate) in exchange for receiving fixed interest payments from another party for a defined term that can be as long as 50 years, but is more typically 30 years or less. There is no need for either party to participate in deposits, either with each other or third parties, because the swap payments are calculated with reference to the published LIBOR, or other floating rate. The ‘fixed swap rate’ is the level of regular fixed payments that can be traded in the market for a stream of future LIBOR cashflows. We can think of the swap rate as being a market view of the average future LIBOR over the term of the swap contract.

There are similarly defined swaps relative to SONIA, but these have traded only very recently, with very few trades for terms beyond two years until 2008. Figure 2 shows historic differences between 10-year swap rates, comparing the effect of settlement against SONIA, three-month LIBOR and six-month LIBOR.

Why have banks moved to SONIA from LIBOR?
The trade in derivatives is now usually subject to collateralisation. For example, in the context of an option, the buyer pays a premium to the seller but at the same time the seller posts back the cash as collateral. The collateral position is updated daily, so it is inconvenient to commit to term deposits.

When the spreads between LIBOR and SONIA were predictable and small, and collateralisation was less widespread, banks usually valued their positions with reference to six-month LIBOR. This was never theoretically the perfect solution but had the practical advantage of a liquid swaps market to which discount curves could be calibrated. During the financial crisis, banks faced a widening and volatile shortfall between the rates actually earned on collateral and the assumed LIBOR.

As SONIA swaps became more widely traded, these provided a natural mechanism for banks to realign the return on collateral with the assumptions underlying their pricing models. However, liquidity can come and go. At the time of writing, SONIA swaps are liquid out to terms of two years with some activity out to 10 years. LIBOR swaps, in contrast, are liquid to 30 years with less frequently traded prices observed to 50 years.

Calibration options for insurance liabilities
All of this presents actuaries with new dilemmas in liability valuation and interest rate risk management. The reasons for changing bank practice do not relate directly to insurers’ liabilities. Insurers do not usually post cash collateral against promises to policyholders. However, the degree of credit risk embedded in LIBOR is now much more visible. There will continue to be questions over whether this spread should be allowed to reduce insurers’ stated liabilities.

Earlier this year, the CFO/CRO forum published a paper on risk-free rates, proposing a downward adjustment of 0.1% to six-month LIBOR rates to reflect the credit risk, intended to reflect an average spread over the cycle. In contrast, under current market conditions where 10-year swap spreads are close to 0.5%, an insurer moving from LIBOR to SONIA faces an increase of more than 5% in a stated 10-year liability. Given the limited liquidity of SONIA swaps, especially at longer terms, there is an understandable industry preference for LIBOR-based valuation.

Rather than focusing on deductions from LIBOR, insurers have shown more interest in possible additions, particularly in relation to illiquidity premiums.

Nevertheless, it does seem odd that, following the financial crisis, banks conclude that LIBOR discount rates were too high while insurers conclude that the same rates are too low. We can expect further changes as insights from the two industries are shared.

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Michael DeWeirdt is the head of capital markets and trading at Milliman in Chicago and Andrew D Smith is head of capital markets at Deloitte in London