Interest Rate Basis Risk

Paul Newson

This chapter will expand upon the topic of basis risk, which was briefly introduced in Chapter 3. Basis risk can be a significant risk for many banks, but is one that standard gap and value approaches will usually miss as, in effect, they focus solely on the date when items will re-price as opposed to how much they might re-price on that date.

Three sub-types – external basis, currency basis and tenor basis – will be examined in turn; the first two are reasonably straightforward, while the last is often misunderstood and requires a thorough awareness of what drives the shape of the yield curve; if this is unclear, the reader should refer to Chapter 2.


External reference rate basis risk describes the risk arising from the fact that different items, or products, on a bank’s balance sheet, even if perfectly matched in terms of re-pricing maturity, may nevertheless still re-price differently because they are explicitly or implicitly linked to different external rate indexes – for example, Libor and BBR.


Consider a bank that lends £100 million for five years at a rate always 2% higher than BBR, and funds this at one-month Libor. BBR and one-month Libor are both currently at 3% and the bank may be reasonably considered to be immune from changes to the “general” level of interest rates changes, provided any change is reflected in both BBR and one-month Libor (for simplicity, BBR may be considered as a rate that is normally only reset monthly).

If, however, either Libor goes up more than BBR or, alternatively, BBR goes down more than Libor, the bank will see an erosion of its margin as its funding cost will increase relative to the income it receives on its asset.

As with simple yield curve risk, basis risk may be hedged by means of derivatives – in this case by basis swaps, which are derivative instruments under which one party pays a variable rate of interest linked to one index (eg, Libor), and the other party pays a variable rate of interest linked to another index (eg, BBR).

The impact of the risk and how it can be mitigated by a basis swap is illustrated by Table 6.1, which considers what would happen in example 1 to one year’s net income if Libor suddenly rose from 3% to 4% but BBR stayed at 3%. This is compared to a situation where both rates rose to 4%. For simplicity, interest rate changes are assumed to take effect immediately and persist for one year – in practice, there would be some short delay.

Table 6.1 Income impact of a change in BBR relative to one-month Libor
£m Libor and BBR both remain at 3% Libor and BBR both rise to 4% Libor rises to 4% but BBR remains at 3%
Interest received 5 6 5
Interest paid (3) (4) (4)
Net income 2 2 1
Basis swap – paid (3) (4) (3)
Basis swap – received 3 4 4
Basis swap net 1
Overall NII 2 2 2

Table 6.1 demonstrates that the bank’s margin is not impacted by any general movement in all rates, but should one-month Libor increase by 1% relative to BBR it will lose £1 million of its anticipated NII. However, protection can be achieved by means of a basis swap whereby the bank pays BBR and receives Libor.

This example ignores any premium that might be payable on BBR/Libor basis swap; in normal market conditions this would be quite small as generally the two rates could be expected to remain very similar, but during the financial crisis of late 2008 Libor rose dramatically as BBR was cut, and although Libor and BBR have returned to within a few basis points of one another, BBR/Libor basis swaps can only be purchased at a premium reflecting the perceived risk of another major market dislocation.

Additionally, it should be noted that the BBR/Libor swap market is very thin and that most banks will actually use overnight index swap (OIS)/Libor swaps instead which are much more liquid. The OIS rate is computed by compounding the standard unsecured overnight interbank rate for the particular market – eg, Fed Funds in New York or the Sterling Overnight Index Average (SONIA) in London. While a bank that hedged its BBR/Libor basis risk with a OIS/Libor swap is theoretically just exchanging one basis risk for another, OIS and BBR do tend to be very closely correlated. BBR/ Libor basis risk is only one example of external basis risk; other examples include Libor/government basis risk, where a bank may have government bonds funded at Libor.

Finally, the term “basis risk” is also often employed to describe the basis between the bank’s own administered rate (SVR) and, say, Libor. This is covered in more detail in Chapter 7, but clearly it could not be hedged directly by any basis swap given that the level of the SVR is determined by the bank itself. However, if the bank considered that generally its own SVR would follow the path of BBR, a BBR/Libor swap might be considered a reasonable hedge.


This is the risk associated with the fact that the interest rates of individual currencies will, to a greater or lesser extent, probably move differently. A bank that simply converts its re-pricing mismatches into base currency and then models its risk as though all its positions were in that base currency might miss significant potential exposures.

It is important not to confuse currency basis risk with foreign exchange risk (the latter will be addressed in Chapter 9). Currency basis risk can most obviously arise when the currency of a variable rate asset differs from that of its funding. However, as described in Chapter 9, this also gives rise to foreign exchange rate risk, the hedging of which by means of currency swaps usually also removes the currency basis risk.

Less obvious is the currency basis risk that might exist in a situation where one business – managed as a whole – had products in various currencies, and although each is match-funded in respect of currency, some interest rate risk within individual currency positions might be left unhedged if it appeared to be offset in another currency position.

For example, a UK bank’s European retail business unit might raise fixed term Swiss franc deposits and use these to fund a variable rate Swiss franc mortgages. It might also raise euro variable rate deposits and use these to fund euro fixed rate mortgages. The Swiss franc business is exposed to Swiss franc rates falling, while the euro business is exposed to euro rates rising. If, however, the business’s risk metrics looked solely at the combined position expressed in sterling, it might conclude that there was no significant risk position, but this would only be true if Swiss franc and euro interest rate changes were always perfectly correlated. Theoretically, currency swaps – with no exchange of principal – could hedge this risk, but a simpler and more transparent approach would be to manage each currency separately and to hedge each using IRSs in that currency.

Currency basis risk can also arise where a bank has foreign subsidiaries or branches that are separately capitalised (again, see Chapter 9). The final considerations under this heading are how risk appetite and limits should be calibrated in a multi-currency bank, and how risk positions should be aggregated.

The first question to address is whether – regardless of metric selected – standardised shocks, such as 100bp up and down, can be applied to all currencies. Theoretically, the answer must be “no” as the relative likelihood of two interest rates always moving exactly in line with one another will be zero, so the shocks almost by definition will not be of equal severity. However, the trouble is that the effort required to try to derive shocks that are totally consistent, in a relative sense, may not in practice enhance the control framework, and could in fact make it more obscure. The purpose of standard shocks in a banking book is more about highlighting potential risks rather than quantifying with total precision their actual impact. Consistency and transparency may serve this objective better than continual minor revisions based on statistical analysis. That said, a bank operating in many currencies may wish to apply some level of differentiation to currency groups – if, for example, a 100bp shock were applied to major currencies such as sterling, the euro and the US dollar, a higher shock such as 250bp might possibly be applied to more volatile emerging markets currencies on the grounds that the two scenarios are of approximately equal likelihood.

Regardless of whether the same shocks or different standard shocks are applied to different currencies, the question still arises of how total risk should be computed – ie, how risks in separate currencies should be aggregated in terms of base currency. Even if a bank manages the interest rate of each material currency separately within individual limits or triggers, there will bound to be some residual interest rate risk and, when these are added together, it is likely that, unless all businesses happen to be positioned the same way, some offsetting will occur that will reduce aggregate risk as reported both internally and externally. Whether this actually matters is possibly something of a moot point. From a control perspective, if there is a simple additive limit/trigger structure in place, then comfort can be drawn from the fact that even if each individual business were fully utilised and in the same direction, then total appetite still could not be exceeded and any reduction at a total level from fortuitous offsetting is irrelevant. On the other hand, a bank does need to understand its total quantum of risk, so implicitly assuming all currencies are 100% positively correlated may lead to a material understatement.

One approach to obviating this aggregation problem would simply be to add the absolute risk values together allowing no offset, but this would then imply all currencies were 100% negatively correlated, and so could result in an equally material overstatement of aggregate risk.

Another approach is to apply what is termed a “disallowance factor”. This means, for example, in the case of a gap value metric, not simply adding together each gap position in a given tenor bucket, but rather imposing a restriction on the offset allowed between different currencies. For instance, if in the three-month bucket there was a positive gap of £100 million and a £100 million (equivalent) negative gap in US dollars, then the offsetting US dollars gap position might be reduced by 20% to give a combined net gap position of £20 million (as opposed to zero). Such an approach, however, would require the maintenance of a matrix of disallowance factors between currencies based on some observation of actual correlations, and the rules for offsetting in the case of several currencies could become complex and lacking in transparency.

Overall, a proportionate approach needs to be adopted depending on the materiality of the currency basis risk that exists. In a banking book, where it is assumed there is no positive appetite for IRRBB, the surest way is to close risk as it arises at the individual currency level.


Tenor basis risk is the risk that deals or positions, despite re-pricing on the same date, being in the same currency and being linked to the same benchmark (eg, Libor), could nevertheless still re-price differently due to the fact that, when they re-price, they do so for different periods or tenors, and that this could have an adverse impact on the bank.

Consider a five-year fixed rate asset funded by a three-month Libor deposit. As explained in Chapter 5, a position of this type would typically be hedged by entering into a five-year IRS whereby the bank paid a fixed rate and received a floating rate. Let us assume, however, that the floating leg of the swap, rather than resetting every three months, reset every six months. The initial gap report would be as shown in Table 6.2.

This would show the bank at risk of an immediate rise in rates, and this makes sense since, if rates did rise, the deposit would reprice upwards in three months time while the protection afforded by the swap would only take effect in six months time, leaving the bank exposed for the intervening three months. However, this is simple open mismatch risk, which is not the same as tenor basis risk.

Table 6.2 Gap showing open mismatch at inception
Re-pricing maturity 0–3m 3m–6m 6m–12m 1y–2y 2y–3y 3y–4y 4y–5y Total
Loans             100 100
Deposits (100)             (100)
IRS pay             (100) (100)
IRS   100           100
Net gap (100) 100         0 0

Consider now what the situation would be in three months time – ie, just after the deposit has re-priced (see Table 6.3).

Table 6.3 Gap showing no open mismatch after 3 months
Re-pricing maturity 0–3m 3m–6m 6m–12m 1y–2y 2y–3y 3y–4y 4y–5y Total
Loans             100 100
Deposits (100)             (100)
IRS pay             (100) (100)
IRS 100             100
Net gap 0           0 0

This would suggest that the position was now subject to no interest rate risk, because the deposit and the floating leg of the swap now have the same residual re-pricing maturity – this is due only to the passage of time. However, would it be correct to infer that the bank at this point is truly immune to any change in interest rates that might occur in the next three months? Logically, this can only be the case if it can be demonstrated that the net income impact of the two items re-pricing will be equivalent economically, and will thus offset one another despite the fact that each will reset for a different tenor (ie, the swap leg will reset for six months while the deposit will reset for three months).

The answer is that the different re-pricing tenors of the two items will not matter provided any rate change is the result either of a change to the current overnight rate or a market expectation of a future change to that rate. As to why this is the case may it not be entirely obvious, so the impact of both scenarios will be explored in a little more detail. Let us assume, first, that the current yield curve is flat at 5% for all tenors, which implies there is currently no market expectation of any changes to the overnight/BBR rate, and then consider the two scenarios in turn.

A parallel shift

Assume a parallel shift of 1% down. This implies a sudden (and unexpected) fall in the current overnight rate but nevertheless a market belief that there will be no further changes. Rates for all tenors thus fall from 5% to 4%.

Consequently, both the variable cost of the deposit and the variable rate received on the swap leg will fall by 1%. Clearly, it does not matter that the two items re-price for different periods as the change in rate is the same for all tenors.

A non-parallel shift

Assume a change to the curve driven solely by an expectation that in three months’ time the overnight rate will fall by 1% to 4%. The three-month rate will stay the same at 5% but the six-month rate will decrease to approximately 4.5% since, by virtue of the no-arbitrage argument outlined in Chapter 2, the cost of six-month money must equal the cost of three-month money plus the forward/forward cost of three-month money in three months’ time.

The impact on the bank will be as follows. The cost of the deposit – which resets for three months – will stay the same, but the variable rate on the swap leg will fall to 4.5%. The bank will thus lose 0.5% over the next three months (deposit at 5% and the swap at 4.5%), but when the deposit resets it will be at 4% with the swap still at 4.5%, so the bank will gain 0.5% over the second three months, and will therefore be flat over the whole six months.

Therefore, even in the case of a non-parallel shift, the different tenors of items re-pricing on the same date can be shown to be irrelevant provided that the change in the shape of the yield curve is driven solely by expectations about the future level of interest rates.

The underlying reason for the irrelevance of the tenor of future resets to the quantification of simple yield curve risk is that normal yield curve construction assumes that the spot rate for any given tenor must equal the effective rate for a shorter tenor plus today’s forward rate for the remaining period. This arbitrage-free model is, however, predicated on the assumption that market participants are entirely indifferent to tenor.

In practice, of course, market expectations of future moves in interest rates are not the sole drivers of price variation between tenors. An additional element is termed the “tenor spread”, which exists essentially because cash instruments (loans and deposits) command a premium in respect of both credit risk and liquidity, and this premium is naturally higher the longer the tenor of instrument. If the IRS market existed totally in isolation, swap prices would probably not attract any tenor spread as a swap involves no credit risk on the principal amount and has minimal liquidity impact; however, the swap and cash markets are of course closely related (otherwise arbitrage profits could be made) so tenor basis spread works its way into the price level of all interest rate instruments, and is normally quoted as a relative spread between two tenors – eg, three month versus six month.

The tenor of any re-pricing item is therefore important from a risk perspective, but the issue is not so much its current level – that will already be within the price of whatever instruments the bank holds – but rather how much it might change between now and the next reset. Returning to the example above, if we assume that instead of the yield curve being flat there was some degree of upward slope resulting from tenor basis, the bank would be exposed to a narrowing of the three-month versus six-month spread as this would decrease the rate on the swap relative to the cost of the deposit – ie, at the moment any tenor spread would benefit the bank as it would be receiving the six-month tenor and paying the three-month, so a reduction in this spread will reduce this benefit.

Tenor basis risk is separate and additional to ordinary yield curve risk, and can only be quantified by analysing re-pricing items not only by reset date but also by their tenor – then, typically, some adverse move in the tenor basis spread is modelled to arrive at a potential P&L impact. In theory, an NII sensitivity model should be able to incorporate this risk directly as the tenor of the re-pricing item will be known and all that needs to be added to the particular scenario is a change to the current spread. Simple value models, which revalue only the net gap position, cannot capture this risk, however, due to their construction.

Tenor basis spread risk can be hedged by means of tenor basis swaps. These are instruments whereby, for a given period of time, one party pays the floating rate for one tenor and receives the floating rate for another tenor. In a perfect world, with little credit or liquidity risk between banks, such instruments would be largely worthless and would hence command little or no premium. Indeed, before the 2007–08 financial crisis, tenor basis swaps only cost a few basis points as opposed to a typical price latterly of 20–30bp, the current premium reflecting not only the current level of tenor spread but also expectations as to how this might change over the duration of the swap. A bank buying such an instrument can effectively lock into the current level of the tenor basis spread it is paying (or receiving) and thus immunise itself from further changes, but, as will be explained in the next section, mechanically hedging this, or indeed any form of basis risk, can in a banking book be problematic unless there is complete certainty about the future volume of the underlying customer products that give rise to the position.

Tenor spread risk is often misunderstood, largely because the term itself is not fully descriptive. As a result, there is a natural tendency to imagine that the word “tenor” is being used in the sense of residual tenor to next reset, whereas it is the tenor of the following reset that creates the potential risk. Also, any tenor basis risk position automatically creates simple yield curve risk as well, so people can confuse the two – for instance, at certain points a three-month versus a six-month position will additionally result in an open gap position when the residual re-pricing maturities of the two component are unmatched, but when they are in line it disappears. A better, albeit clumsier, term might be “tenor of future resets risk”.

Finally, it might be wondered why banks have tenor basis risk positions in their banking books at all. The reason is probably that it is largely accidental, and that until the financial crisis it was a risk that few outside of a derivatives trading area would even have heard of. Simple mismatch hedging is usually done at the product level based on a standard gap report, with the bulk of the visible risk being closed by picking any seemingly appropriate and reasonably priced fixed/floating swap; less attention is usually paid to whether it resets monthly, three monthly or six monthly, and traditionally six-monthly resetting swaps are the most liquid and hence the cheapest. At the individual swap level, the risk is likely to be negligible, but unless the overall position is monitored, significant positions can accumulate.


All the types of basis risk described above can usually be hedged by means of basis swaps, which are floating/floating instruments whereby the bank, for a fixed premium, can effectively lock into the current market expectations as to the level of the particular basis for a given period of time – say, two, three or four years – and thus be immune to further changes.

However, such a hedging strategy is only fully effective if the length of the underlying exposure is known with certainty. For example, in the case an IRS portfolio where a bank over the years may have acquired supposedly offsetting positions but with floating legs resetting for different tenors, tenor basis swaps would provide a good hedge as the underlying swaps will be contractual and the overall length of the tenor mismatch will simply equal the length of these underlying swaps.

If, however, one or either side of a basis risk position contains positions that are not contractual, the hedge could actually end up creating risk. Consider the BBR/Libor basis risk created by writing BBR-linked mortgages. As customers will generally have the right to repay at any point, a decision has to be made about the length of the required basis risk protection. This is where the real risk lies since it is entirely dependent on assumptions about customer behaviour and thus the future volumes of the mortgage product, and this itself may be a function of both how rates actually move and how customers think they might move in the future. Thus, in a low rate environment where the expectation is for rates to rise, customers may find fixed rate products more attractive than variable rates, and thus a bank thinking it is prudently hedging its basis risk may end up over-hedged and thus exposed to the obverse of the risk it thought it was closing.

Similarly, in the case of tenor basis risk, tenor basis swaps only fully neutralise risk in respect of items whose future re-pricing profile is certain. If, however, the tenor mismatch comprises elements such as simple short-term cash funding, then there is less certainty over the tenor of future deals as this will depend on market conditions and the bank’s overall ability to secure funding at its chosen tenor.


External reference rate basis risk is the risk of two benchmark rates such as Libor and BBR changing relative to one another, and a bank is exposed if it has assets linked to one and liabilities to the other.

Currency basis risk is the risk of an overall, and otherwise matched, position having different currency components that are not matched within themselves, and where the interest rates relating to the individual currencies then move differently to one another.

Tenor basis risk is the risk that positions, although re-pricing on the same day, may nevertheless re-price differently for different tenors, and that the interest rates for these different tenors move for reasons unconnected with expectations about the future level of interest rates.

Most basis risk can be hedged by transacting appropriate basis swaps, but this hedging is only effective if the length of the required protection is known with certainty; where the underlying position comprises customer products, this is unlikely to be true, so some residual risk will remain and hedging may well increase risk should these underlying balances change.

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