14
Funding, Margin, and Capital Costs

14.1 BANK FINANCING

Banks and other firms must fund their assets with various sources of financing. There are two main types of financing: debt and equity. In general, a bank's cost of this financing reflects the compensation that investors and depositors demand in exchange for funding the bank's activities. Banks have a range of possible sources of funding available to them, including retail funding (e.g. deposits) and wholesale funding (e.g. unsecured or secured bonds), as well as the bank's equity (capital) base.

The Modigliani–Miller (MM) theorem (Modigliani and Miller 1958) is a well-known result of capital structure theory. It states that, in an efficient market and in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, the value of a firm is unaffected by how that firm is financed. This, therefore, implies that the mix of equity and debt used to finance a bank is irrelevant. To some extent this can be seen in practice. For example, an increase in equity capital for a bank can be seen to lead to a reduction in risk and a corresponding lowering of the required return on equity.

Whilst a helpful result, the MM theorem is nevertheless based on some strong assumptions which do not hold in practice. This can lead to effects that may cause banks to find a particular capital structure more attractive. For example, the cost of default or financial distress may make equity financing appealing, whilst the tax deductibility of interest expenses would favour more debt financing.

The MM theorem suggests that banks should be indifferent to the proportion of equity capital they hold. Whilst high equity capital would reduce return in good times, it would also increase returns in bad times. This stabilisation of returns and reduction of risk would suggest that the ‘equity risk premium’ investors require in order to effectively provide capital would reduce, and the required return on capital should be lower. However, banks do generally consider equity capital to be expensive and believe they are most profitable when they operate at a high leverage with relatively low capital bases.

Correspondingly, the cost of bank failure can mean that having banks with larger capital bases is more socially advantageous, as the capital serves as a buffer that absorbs losses and reduces the probability of bank default. This, in turn, protects bank creditors and (in systems with explicit or implicit public guarantees) taxpayers. This is one reason for regulation to define minimum capital requirements for banks.

In general, the cost of funding is associated with various xVA terms (Figure 14.1), specifically funding value adjustment (FVA) and margin value adjustment (MVA) for the cost of debt financing (‘cost of funding’), and capital value adjustment (KVA) for the cost of equity financing (‘cost of capital’).

In general, banks consider funding and capital costs to be different components and assess their costs separately. This is only an approximation of the overall balance sheet financing required, due to the clear linkage and potential for an optimal balance sheet financing strategy in a world where not all of the MM assumptions hold.

Schematic illustration of funding and capital costs and their relationship to xVA terms. — **Figure 14.1** Simple illustration of funding and capital costs and their relationship to xVA terms.

Furthermore, the treatment of balance sheet financing costs via xVA adjustments may need simplifying in relation to the following aspects:

Different types of financing instruments. There are a multitude of funding sources in terms of both debt and equity funding.
- Debt funding. Retail deposits, unsecured wholesale funding (e.g. bonds), and secured wholesale funding (e.g. covered bonds).
- Equity funding. Common equity, contingent capital, preferred shares, and subordinated debt.
Marginal cost of financing. For assessing new transactions or businesses, it is the marginal cost of financing that represents the financing cost of the opportunity. However, this is rather hard to assess, and the current financing costs may be used as a proxy.
Financing should be asset specific. Related to the above, financing is asset specific. It should be cheaper to fund an asset with better credit quality and also to fund a more liquid asset (e.g. it might be possible to repo certain liquid securities). However, financing costs may not always be accurately assessed based on credit quality and liquidity.

Another important aspect is that regulation around capital, funding, and liquidity means that banks must comply with multiple metrics when financing their balance sheets. Different banks may be more or less sensitive to these metrics, and a single metric may be the primary determinant of costs (Table 14.1). For example, a bank may be leverage ratio constrained, even when having met its required total loss-absorbing capital (TLAC) ratio. A bank's debt funding strategy may not be consistent with the liquidity coverage ratio (LCR) or net stable funding ratio (NSFR), which may require additional funding of high-quality liquid assets (HQLAs) and/or longer-term funding. Some banks may be more or less sensitive to the various metrics due to their natural client base and financing (e.g. size of deposit base and general credit quality of borrowers). Furthermore, certain types of transactions (e.g. derivatives) may have certain behaviours with respect to the metrics which should ideally be captured. It may not be easy to assess how much additional capital, funding, and contingent liquidity should be represented in terms of assessing new opportunities.

Table 14.1 Key regulatory metrics for capital and funding.

Capital	Minimum capital ratios
	Total loss-absorbing capital
	Capital stress tests
	Leverage ratio
Funding	Liquidity coverage ratio
	Net stable funding ratio
	Liquidity stress tests

Since a bank finances itself via both debt and equity, the cost of each should be calculated based on its underlying costs, together with the type of transaction, identity of counterparty, and consideration of the above metrics. The cost of debt requires consideration regarding the underlying maturity and funding liabilities used (e.g. deposits and wholesale funding). The cost of such liabilities is to a large extent known (e.g. the spread from issuing a bond). The deductibility of tax on interest rates paid should also be a consideration. The cost of capital is more subjective since it is the return paid to shareholders, which is a policy decision by the bank, but it must deliver a satisfactory return from the shareholder point of view (or they will sell their shares). However, the cost of capital mainly arises from common equity and so, unlike debt funding, does not require the consideration of many different securities or maturities.

14.2 CAPITAL

14.2.1 Minimum Capital Ratios and Capital Costs

Capital (equity) has a number of different definitions:

it is the accounting value that remains after subtracting a bank's (fixed) liabilities from its assets;
it is what is owed to the bank's owners – the shareholders – after liquidating all the assets at their current value; and
it is the buffer that protects the bank from insolvency.

The cost of capital reflects the perceived risk of a company's equity to investors and the bank will seek to outperform this return via a defined return on capital (ROC). Whilst this cost is not an explicit and contractual payment, the ROC is a real cost of raising equity. Banks will make some assessment of the ROC on a given transaction given the underlying revenue and other costs. Historically, this assessment revolved around a bank's own assessment of its required capital, often known as economic capital.

Table 14.2 Regulatory capital requirements pre- and post-GFC.

		Pre-GFC	Post-GFC
Quantity	Minimum capital	8%	10.5%
	Countercyclical capital buffer	N/A	0–2.5%
	G-SIB surcharge		1–3.5%

Tests	Leverage ratio	N/A	Yes (3–6%)
	Stress tests		Yes

Type	Minimum CET1	2%	7%
	Minimum Tier 1	4%	9%
	Hybrid capital	Eligible	Ineligible

Prior to the global financial crisis (GFC), banks were subject to general regulatory standards requiring a minimum capital buffer equal to 8% of risk-weighted assets (RWAs). To protect the taxpayer against future bank bailouts, this minimum capital ratio has been gradually raised to 10.5%, with the inclusion of a mandatory capital conservation buffer of 2.5% (Table 14.2). Furthermore, there are potential additional requirements due to a countercyclical capital buffer and globally-systemically-important bank (G-SIB) surcharge. The TLAC of G-SIB banks must be at least 16% (rising to 18% from January 2022). Furthermore, the quality of the capital base is also required to be better, with more capital needing to be common equity and not other Tier 1, Tier 2, or hybrid securities. There is also a separate leverage ratio (LR) with a minimum of 3% (and higher for G-SIB banks) and stress tests that may become the binding constraints for some banks (in the event that they need to raise capital ratios further so as to meet these requirements).

The regulatory changes over the past few years have generally made banks focus less on economic capital and more on regulatory capital. This has arisen because the regulatory-defined minimum capital ratios are almost certainly higher than any economic capital requirements a bank may calculate. Regulatory capital, as defined by minimum capital ratios, the LR, and stress tests, is the binding constraint for most banks. The higher minimum regulatory capital ratios and need for Common Equity Tier 1 (CET1) capital (Section 4.2.2) have meant that banks have had to focus less on actual profits from their derivative activities and more on the ROC. Certain areas of a bank that have relatively high capital requirements may tend to focus more on the ROC. In general, even before recent regulation this was the case for some derivatives businesses.

Higher capital ratios have been contentious. On the one hand, they are supported by the risks associated with high bank leverage and the social costs of a financial crisis. Indeed, there are arguments that bank capital ratios should be even higher: the Minneapolis Plan calls for a minimum CET1 capital ratio of 23.5% of RWAs for the largest banks, achieved over a period of five years, with G-SIB banks then having to increase the ratio further to 38%. On the other hand, opponents of higher capital requirements argue that these may significantly increase the cost of bank credit and slow economic growth.

It is certainly now clear that when banks have to increase their capital ratios quickly, they are likely to constrain the supply of credit. The underlying transition costs can be lower when the capital adjustment is staggered (as has been the case) and/or takes place in the upswing of the credit cycle. Nevertheless, there is evidence that the equilibrium costs of higher bank capital are relatively small. This is supported by the MM theorem and can be seen since, for example, banks with weaker capital positions tend to face higher funding costs (Dagher et al. 2016).

Specific components such as the alpha factor (Section 13.4.5) and methodologies such as the standardised approach for counterparty credit risk (SA-CCR) (Section 13.4.3) create additional credit risk capital costs due to grossing up the value of a position, and can be particularly acute for certain transactions, such as in-the-money uncollateralised ones.¹ This may have led some banks, even pre-GFC, to focus more on capital costs in derivatives businesses. Furthermore, in addition to the overall capital ratios, post-GFC regulation has also raised the quantity of RWAs in some specific areas (that the capital ratios are calculated against). This has been particularly important for derivatives due to:

the introduction of a credit value adjustment (CVA) capital charge (Section 4.2.5);
the need to use stressed data when calibrating internal model method (IMM) models (Section 13.4.5);
the need to use a larger margin period of risk (MPoR) in certain situations (Section 13.4.5); and
the capitalisation of central counterparty default funds (Section 13.6.3).

There is also the fact that there are a number of imminent regulatory changes impacting derivatives RWAs specifically, such as the SA-CCR (Section 13.4.3) and basic CVA/standardised CVA (BA-CVA/SA-CVA) (Section 13.4) approaches. Finally, there is the fact that derivative regulatory RWAs can be quite volatile due to positions moving in- and out-of-the-money (this will be shown in Section 19.3.2). All of this has led to the need to focus more heavily on capital costs for derivatives, often known as KVA.

14.2.2 Leverage Ratio

As discussed in Section 4.2.7, the LR is a measure that is intended to complement capital ratios by restricting a bank from being excessively leveraged (according to certain definitions of capital and exposure). The LR implies that exposure must – on average – be supported by a certain percentage of (Tier 1) capital. Of course, exposures will already be supported by some amount of capital based on various requirements (market risk, credit risk, operational risk, counterparty risk). If this amount of capital is less than the LR percentage ( images in Equation 5.3) then this could be defined as LR constraining business since it will tend to reduce the bank's LR.

An obvious solution to the above problem is to price the capital as the maximum of the normal capital requirements and the LR-implied requirement. However, if the bank is not LR constrained – shown by the case where images in Equation 5.4 – then this may be considered unnecessary.

Schematic illustration of charging capital requirements to originating businesses. — **Figure 14.2** Simple illustration of charging capital requirements to originating businesses.

14.2.3 Cost of Capital

Cost of capital is usually quantified via a benchmark percentage ROC that should ideally be achieved in order to pay a return to the investors who have provided the capital. Banks' derivatives businesses, like any other, are typically subject to capital hurdles due to the associated costs. The given ROC applied is an internal and somewhat subjective parameter, with around 8–10% being a commonly used base assumption. However, since profits generating an ROC will be taxed, an effective tax rate (for the region in question) will also be incorporated, leading to a higher effective rate. The number may be grossed up further by other costs, and so the gross ROC that banks aim for on their over-the-counter (OTC) derivative activities is probably more in the region of 15–20%. Traditionally, capital hurdles have represented guidelines but are now becoming more rigorously priced in via KVA (Chapter 19).

The increasing sophistication around quantifying costs (and benefits) such as CVA and FVA in banks and charging (paying) them to the originating business has also led to a push towards a more active KVA approach in line with this. It is therefore natural that the xVA desk may be responsible for correctly passing on the capital costs to a derivatives business unit (Figure 14.2).

Whilst it is certainly reasonable that the size of the capital requirements could be accurately calculated with reference to the underlying regulation, the cost component (ROC) remains a more subjective component that would need to be assessed on the basis of the minimum required return by shareholders. This should also consider MM-type considerations that a higher capital would, in turn, lead to a lower required return for shareholders. It may also consider other qualitative components, such as franchises and other relationships with the same clients. Ultimately, a bank may wish to look at the ROC by client (or even group of clients) and not impose the cost on all client activities separately. All of the above makes the correct assessment of the ROC more difficult and subjective. Banks may accept that the ROC for derivatives will be low but partially subsidised by revenues from other business with the same – or even different – clients.

14.3 FUNDING

14.3.1 Overview

Historically, banks and other financial institutions did not – explicitly – consider funding costs in the valuation of derivatives. This was for a number of inter-related reasons:

banks could fund rather easily via deposits or raising money in the wholesale market;
through the above, banks could fund at a rate close to Interbank Offered Rates (IBORs) or better, and an IBOR was viewed as being a close proxy for the risk-free rate; and
banks generally treated derivatives (from a funding point of view) as short-term assets and therefore considered only short-term funding costs where relevant.

Funding costs and associated funding risk were rarely considered in relation to derivatives, even those that were very long-dated.

Prior to the GFC, bank funding costs largely moved in line with ‘risk-free’ interest rates set by central banks. All of this changed with the onset of the GFC: some sources of funding evaporated rapidly, and other funding sources became materially more expensive. Some banks, such as those with low capital ratios or the inability to accept deposits and funded mainly via wholesale markets, were particularly sensitive to this increase.

Whilst funding costs have eased in the years since the GFC, they are still high compared to pre-crisis, and the market has experienced a regime shift and funding costs are now of greater importance. Additionally, some of the regulatory response to the crisis will make funding of positions, especially derivatives, increasingly costly. For example:

Liquidity coverage ratio. This requires banks to have sufficient HQLAs to withstand a 30-day stressed funding scenario and will restrict the use of short-term funding, again creating additional cost. Downgrade triggers, sometimes used in derivatives contracts, are especially penalised (Section 4.3.3).
Net stable funding ratio. This requires banks to use more stable sources of funding, which again will be more expensive. Derivatives suffer due to having a zero net funding benefit and other costs (Section 4.3.4).
The clearing mandate. The requirement to centrally clear standardised OTC derivatives will create significant funding costs due to the requirement to post initial margins and default funds to central counterparties (CCPs) (Section 4.4.1).
Bilateral margin rules. The requirements to post margin (collateral) against non-clearable OTC derivatives (Section 4.4.2) will increase funding requirements, again predominantly through initial margin.

All of the above has led banks to become much more aware of the need to quantify and manage funding costs alongside more traditional areas such as counterparty risk. In derivatives businesses, such funding is usually defined by the need to post and receive margin. Since variation margin is a two-way payment, this gives rise to both costs and benefits, which are generally defined within FVA. Initial margin – due to the required segregation – gives rise only to funding costs which are associated with MVA. Both FVA and MVA create a clear need to define funding curves, just as credit curves are required for CVA.

It may be hard to separate general funding costs from the need to hold HQLAs in order to meet requirements such as the LCR. This is because holding a large HQLA buffer may reduce funding costs overall, and it may not be completely clear how much of the HQLA should be apportioned to a given business. Likewise, the NSFR may cause a bank to fund its balance sheet more conservatively, but it may not be able to define precisely the additional cost of doing this. Such costs may, therefore, be borne implicitly across the bank or transfer pricing more heterogeneously (Section 14.3.6). However, there are components (e.g. the need to pre-fund ratings downgrades under the LCR) that may be easier to capture heterogeneously and charge to the originating business.

Schematic illustration of charging and remunerating funding requirements to originating businesses. — **Figure 14.3** Simple illustration of charging and remunerating funding requirements to originating businesses.

Most banks have funds transfer pricing (FTP) frameworks (Figure 14.3). The Treasury charges business units that require funding to buy assets, and remunerates business units that attract funds via liabilities. The internal price of funding is based on the market price for funds for the relevant maturity and currency, and is traditionally transferred on an accrual basis. The Treasury then manages aggregate mismatches in the balance sheet through an asset-liability management (ALM) strategy.

A problem with derivatives in the above set-up is that they can be both assets and liabilities and therefore represent both costs and benefits. Furthermore, since derivatives are typically mark-to-market (MTM), it makes sense to do the same with the associated funding costs and benefits, rather than just accruing them over time. It therefore makes sense for the xVA desk to act as an intermediary between the derivatives business and the treasury to appropriate, own, manage, and transfer the costs and benefits of funding. The precise relationship between the treasury and the xVA desk will be important and discussed in more detail in Section 21.3.1.

Recent years have seen the incorporation of funding costs into the pricing and valuation of uncollateralised derivatives trades. Aside from anecdotal evidence and the observation of clearing levels, the clearest manifestation of FVA is via Markit's Totem consensus pricing service (Section 5.3.5). Generally, FVA is an adjustment alongside CVA that accounts for the net funding cost or benefit of the trade in question. Banks have generally moved from charging funding on an accrual basis to a more upfront FVA approach (Figure 14.4). Key catalysts for this have been significantly-increased costs of funding and the requirement to rely less on short-term funding.

FVA has, therefore, become a key component of the clearing price for derivatives and will be routinely priced into uncollateralised (and potentially some collateralised) trades by most banks (Chapter 18), especially those that are long-dated (Figure 14.5). Banks may also pay special attention to cases such as one-way margin agreements or in-the-money portfolios.

Although this will be discussed in more detail in Section 18.2.5, it is useful to characterise the approximate relationship between CVA, debt value adjustment (DVA), and FVA (Figure 14.6). FVA is generally made up of funding cost adjustment (FCA) and funding benefit adjustment (FBA). This is analogous to bilateral CVA (BCVA) (Section 17.3.3) which consists of CVA and DVA. CVA and FCA are related to expected positive exposure (EPE), whilst DVA and FBA arise from expected negative exposure (ENE). A threshold in a margin agreement should have the effect of reducing FCA and FBA (just as it does for CVA and DVA). Note that this may be asymmetric: for example, it would be expected that a one-way margin agreement acting against a party would remove their FBA (since they must post margin against any negative value) but leave the FCA unaffected.

Pie chart depicts the market practice on pricing funding. — **Figure 14.4** Market practice on pricing funding.

Source: Deloitte Solum CVA Survey (2013).

Pie chart depicts the market practice on pricing FVA into trades. — **Figure 14.5** Market practice on pricing FVA into trades.

Source: Solum FVA Survey (2014).

Graph depicts the relationship between bilateral CVA and FVA. The dotted lines represent thresholds in the margin agreement for each party. — **Figure 14.6** Illustration of the relationship between bilateral CVA (CVA and DVA) and FVA (FCA and FBA). The dotted lines represent thresholds in the margin agreement for each party.

Note that FVA may present an immediate discrepancy between pricing and valuation. For pricing purposes, a bank would presumably wish to use its own funding costs, but for accounting purposes, the exit price implies that the bank should rather reference a market cost of funding.

Some have argued that FVA should not be considered in the pricing or valuation of derivatives.² The industry has largely ignored such arguments, which imply significant structural changes to the current treatment of funding.³ Indeed, these arguments are now more in relation to the accounting treatment of FVA than to the consideration of funding when pricing.⁴

14.3.2 Cost of Funding

The cost of funding of derivatives could be linked to (at least) three inter-related aspects:

uncollateralised market values;
cash flows; and
margin flows.

It is important to capture all relevant aspects but also to avoid double-counting. For example, an in-the-money uncollateralised derivatives portfolio will generally require margin to be posted on the hedges. Furthermore, cash flow payments on collateralised derivatives will be largely offset by margin flows in the opposite direction. Given that most bank's derivatives books are mainly hedged from a market risk point of view, the main source of funding requirements on a day-to-day basis will be margin moves. The assessment of margin will usually, therefore, be the primary determinant of funding costs (and benefits). However, it is also important to capture large cash flows (e.g. novating into a large in-the-money derivatives portfolio) and uncollateralised market values (e.g. a relatively profitable transaction).

It also makes sense to charge a business for funding on a net, or portfolio, basis. This means that funding benefits (e.g. receiving margin or a negative market value) will tend to offset funding costs. However, there is also the question of what to do if the total funding position is beneficial for a given business. There may be inherent asymmetry: a net derivative asset will probably be considered to require long-term unsecured funding, but a net derivative liability may not be considered to represent an equivalent benefit. The NSFR treatment of derivatives also reflects this view, where net derivative assets incur a 100% required stable funding (RSF) charge, whereas net derivatives liabilities represent 0% available stable funding (ASF). Indeed, it may be appropriate to incorporate derivatives more fully in the ALM process so that, for example, short-term derivatives liabilities are not considered as fully funding longer-term derivatives assets. These aspects are at the heart of the definition of FVA and will be discussed in more detail in Section 18.3.2.

There is also the need to incorporate correctly the costs arising from contingent funding. The LCR forces banks to hold HQLAs against potential liquidity shocks. Such HQLAs will produce relatively low returns which will not offset the funding costs. Furthermore, any returns from HQLAs will likely be due to the inherent credit and liquidity risk and should not, therefore, be seen as reducing the underlying funding cost. A good FTP framework will allocate contingent liquidity costs to the originating businesses.

The cost of funding differs from the cost of capital (Section 14.2.1) in a number of ways:

it can be partially observed via the spreads of securities (e.g. bonds) trading in the secondary market and issuance levels in the primary market;
whilst more observable, it arises from multiple different instruments with different characteristics (secured/unsecured, maturity, and availability); and
it is not asset specific, and so whereas capital charges differ across transactions and clients, the cost of a unit of funding may be seen as the same, irrespective of the use of the funding.

In general, the funding cost of a bank may be seen as the combination of four components (Figure 14.7):

Risk-free rates. Central banks implement monetary policy by setting their own short-term borrowing and lending rates, which in turn define short-term market interest rates. These interest rates can be viewed as ‘risk free’ given that the risk of the central bank defaulting is generally considered to be very low. Longer-term rates reflect market participants' expectations of future central bank policy. Because risk-free rates are a common component of funding costs for all types of bank funding, it is common to refer to a bank's ‘funding spreads’ as the difference between funding costs and an appropriate risk-free rate at a given maturity.

Figure 14.7 Illustration of the funding cost for a bank.
IBOR-OIS basis. This is the difference between the most reasonable proxy for the risk-free rate (overnight indexed spread, OIS) and the reference for defining funding spreads (typically an IBOR). This component has existed for technical reasons and may disappear with the transition away from IBORs (Section 14.3.4).
Credit risk premium. When buying bank debt, investors will demand compensation for bearing the credit risk that the bank may default on its debt. The credit risk premium will be largely for more risky and less well-capitalised banks. An individual bank's credit risk premium may increase if investors consider it to be riskier. The credit risk premium of the banking sector may increase if investors believe that all banks are more risky. The credit risk premium will also depend on the maturity of the borrowing and other characteristics such as whether it is unsecured or secured, with the latter being lower credit risk.
Liquidity risk premium. Investors will also factor in liquidity when they decide on the price they will pay and/or the return they will demand for an investment. Investors will demand compensation in the form of a liquidity risk premium in exchange for investing in illiquid assets. A key determinant of the liquidity risk premium is the maturity of an asset, with longer-dated assets requiring a higher return than shorter-dated ones. This is demanded in return for the inconvenience of not being able to access these funds for a longer period of time. Liquidity risk premiums may depend on both idiosyncratic and macro risk factors. The idiosyncratic component may depend on factors such as how frequently a bank's debt is traded in secondary markets. The macro component may be driven by confidence in the banking sector in general.

In the above, the funding cost of the bank is represented as the sum of all components. The credit default swap (CDS) market may be expected to include all components except the liquidity risk premium, which would, therefore, be observable via the so-called CDS-bond basis. The additional liquidity premium would compensate a bondholder for potential illiquidity when selling a bond (Longstaff et al. 2005). This represents (by convention) a negative CDS-bond basis (bond spreads higher than CDS spreads), although this does not necessarily have to be the case, nor has it always been the case historically.

14.3.3 The Risk-free Rate, IBOR, and OIS

Historically, IBORs were thought to be largely free of credit risk due to the extremely small default probabilities of banks and short tenor (three or six months).⁵ An alternative risk-free proxy has been the yields of triple-A treasury bonds, again considered to be largely free of credit risk due to the extremely high-quality rating of the sovereign issuer. IBORs were generally thought to be preferable to treasury bonds due to better liquidity, the lack of problems with technical factors (such as repo specialness and tax issues), and the close links between IBORs and funding costs. Hence, pre-2008, the market standard discount (or funding) curve was the three- or six-month IBOR curve.⁶

The OIS rate is generally the (unsecured) interest rate that banks use to borrow and lend from one another in the overnight market. There are conceptual similarities between OIS and IBORs. Both are unsecured, and whilst the former reflects a single-day time horizon, the latter is longer (e.g. three months). Furthermore, OIS rates are averages from actual transactions, whereas an IBOR is just the average (with the highest and lowest submissions removed) of banks' stated opinions.

Before the GFC, the basis between OIS and IBORs was tight (less than 10 basis points). However, the crisis caused the IBOR-OIS basis to widen dramatically, as can be seen from Figure 14.8 for Fed Funds and the USD three-month London Interbank Offered Rate (LIBOR). Whilst the basis is much tighter than during the worst point of the GFC, it is still material. This effect can be seen in other ways, such as via basis swap spreads, which represent the exchange of rates in the same currency. For example, the three-month Euro Interbank Offered Rate (EURIBOR) versus the six-month EURIBOR basis swap spread went from less than 1 bp to over 40 bps in October 2008 after the Lehman Brothers bankruptcy. This represents the additional unsecured credit risk in the six-month tenor versus the three-month tenor. When banks were perceived as risk free, such differences did not exist, but as soon as this myth dissolved, basis swap spreads blew up dramatically. The difference or ‘spread’ between the IBORs and OIS rates is an important measure of risk and liquidity. A higher spread is typically interpreted as an indication of decreased willingness to lend by major banks. Whilst this basis has tightened in recent years, the use of IBORs as a ubiquitous risk-free rate is considered wrong.

The historical situation where IBORs were seen as a good proxy for the risk-free rate drove this rate to be used as a common funding reference in transactions such as loans, deposits, floating-rate notes, and derivatives. The use of IBORs as a reference represents a problem in a market where an IBOR cannot be reasonably used as a proxy for the risk-free rate. In derivatives, another problem with the use of IBORs in defining funding is that collateralised derivatives usually specify the relevant OIS for the remuneration of cash margin. The presence of the IBOR-OIS basis, therefore, causes a technical problem in terms of defining funding and xVA adjustment.

Schematic illustration of the historical relationship in US dollars between OIS and three-month LIBOR. The top graph shows the respective levels and the bottom line shows the difference between the two. — **Figure 14.8** Illustration of the historical relationship in US dollars between OIS (Fed Funds) and three-month LIBOR. The top graph shows the respective levels, whilst the bottom line shows the difference between the two.

Source: Bloomberg, reproduced with permission. www.bloomberg.com.

Due to their short tenor and unbiased submission process, OIS rates would seem to be a more logical risk-free rate. The daily tenor of such transactions means they should carry a minimal amount of credit risk. The transition away from IBORs will, therefore, simplify the definition and application of xVA adjustments.

14.3.4 IBOR Transition

First published in 1986, LIBOR fixings and other related IBORs have been important reference rates in the derivatives market. Historically, IBOR rates have been used as a measure of credit risk, since they reflect the confidence banks have in each other's credit quality. IBOR rates are also hardwired into many areas of the financial markets as a reference rate. An IBOR is typically constructed by taking quotes from a range of banks on how much they would be charged in interest to borrow money on a short-term basis from another bank. The outliers are excluded and an average is taken. LIBOR rates have historically been published across five currencies and over a range of tenors. LIBOR fixings are intended to represent the interest rate charged on short-term (unsecured) loans made between banks. IBORs are very important to financial markets due to the fact they are extensively referenced in derivative, bond, and loan documentation, and in a wide range of consumer borrowing and lending instruments such as deposits, mortgages, and loans.

IBOR rates represent indicative unsecured lending between banks, and they are the rates charged (determined daily) for banks to borrow from other banks, usually for terms of three months on an uncollateralised basis. An IBOR is risky in the sense that the lending bank loans cash to the borrowing bank on an unsecured basis, albeit for a relatively short period. An IBOR is supposed to represent an average interest rate that a bank would be charged if borrowing from other such banks.

An IBOR was always understood not to be truly risk free, but was seen as a robust benchmark with a relevant grounding in the extensive market of interbank lending, which prior to the GFC was seen as very low risk. In the aftermath of the GFC, there was a series of fixing scandals in relation to IBORs which damaged their reputation as being objective benchmarks.⁷ Furthermore, at the same time, activity in the market on which IBORs are based – unsecured interbank term borrowing – declined substantially. This was partly in response to regulation (such as NSFR) that treated interbank borrowing as unstable.

In February 2013, the G20 commissioned the Financial Stability Board (FSB) to review the major interest rate benchmarks, as a result of concerns regarding the reliability and robustness of these IBOR benchmarks. The FSB (2014) recommended their general replacement with so-called risk-free rates (RFRs). Whilst IBOR rates will not be banned, regulators globally have given a clear signal that firms should transition away from IBORs towards alternative overnight RFRs.

Table 14.3 Example RFRs.

Currency	RFR	Abbreviation
USD	Secured Overnight Financing Rate	SOFR
JPY	Tokyo Overnight Average Rate	TONAR
GBP	Sterling Overnight Index Average	Reformed SONIA
CHF	Swiss Average Rate Overnight	SARON
EUR	Euro Short Term Rate	ESTER

RFRs are generally overnight secured or unsecured rates and are defined on a currency-by-currency basis, with no uniform definition nor method for their calculation used across all currencies. They are generally required to represent actual market funding rates based on reliable data. They should also be robust to changes in market structure and subject to appropriate controls and governance. Some examples are shown in Table 14.3. For example, the Sterling Overnight Index Average is calculated as the weighted average of the interest rates charged for all unsecured loans (of more than £25m) reported by market participants in the London market.

Unlike IBORs, RFRs do not – generally – reflect the credit risk of the borrowing institution, since they are intended to be risk free. The other main difference is that RFRs have no term structure (yet, although term RFRs are not yet being proposed) as they only reference overnight rates, unlike IBORs, which are defined by various terms. RFR-based transactions will accrue interest over the relevant time period and, by necessity, will be calculated in arrears.

The transition to RDRs is complex and requires significant work given the vast number of transactions specifying IBOR rates. Current fallbacks to IBOR (such as using the last known rate) only envisage that a rate is temporarily unavailable rather than permanently withdrawn. If this ‘same rate’ persisted indefinitely then it could be very disadvantageous to one party during a period of significant interest rate change. The industry is, therefore, working on better transition mechanisms for each RDR. Since RDRs are generally lower than the IBORs they replace, this would imply replacing the IBOR reference in a contract with the relevant RDR plus a spread. However, since the spread between IBOR and RDR rates is not fixed, this would not lead to economically equivalent contracts.

Despite the transitional changes, the move to RFRs will simplify derivatives and the definition of funding costs by removing IBOR-OIS basis risks currently seen in collateralised trades. It will also tend to align the margin remuneration rate more closely with the standard reference rate (although it is unclear whether the margin remuneration rates will be standardised to the defined RFR in all regions).

14.3.5 Funding Spreads

Derivatives, due to their dynamic nature and the funding approach of banks, are not term funded. Traditionally, the funding has been generally considered to be short term, but regulation (e.g. LCR and NSFR) is pushing banks to rely less on short-term funding.

In general, the funding spread or term liquidity premium (TLP) will define the relevant funding curve for a bank. In terms of quantifying this funding curve, a starting point would be the range of funding sources used by a bank, such as:

deposits (e.g. current accounts);
unsecured money market (e.g. commercial paper);
secured money market (e.g. repo);
unsecured capital market (e.g. bonds); and
secured capital market (e.g. covered bonds).

The above have different positives and negatives in terms of their characteristics, such as cost, duration (contractual or behavioural), and availability. These are often subjective judgements: for example, customer deposits have a very short term (typically one day). However, they are typically quite ‘sticky’, in that a bank's deposit base will not reduce substantially over a short period (especially due to depositor guarantee schemes that may reduce the chance of a bank ‘run’). This can be seen as a ‘behavioural adjustment’, where the statistical maturity is not the same as the contractual maturity. Whilst this provides a reasonably stable and cheap source of funding, it may be difficult for banks to increase funding in this way by attracting more deposits, and some banks – for example, investment banks – cannot rely on a natural deposit base as a source of funding.

Furthermore, secured funding can only be achieved with sufficient liquid assets to use as margin, and the money market funding is short term (e.g. commercial paper has a fixed maturity of no more than 270 days). This leaves unsecured capital market funding as the most obvious benchmark for assessing new funding costs, since this would be the obvious place for a bank to raise money if required. There is also the question of whether to look at secondary or primary markets. The secondary market defines the current long-term unsecured funding cost, but the primary market may represent a more realistic basis for the marginal cost of raising new funding.

It may also be that CDS quotes are useful indicators of the funding costs of banks. Whilst they do not represent issuance levels, they may generally be more liquid than the secondary bond market.

Derivatives assets can be effectively used for margin for other derivatives liabilities (through netting), but they cannot be used as security against borrowing (e.g. repoed). This also suggests that an unsecured term funding rate would be more applicable for assessing the underlying funding costs.

Another consideration is the term: although to some extent funding should be priced according to its maturity and the underlying cost of borrowing money, it may be acceptable not to charge as if all assets were to be term funded. This may be implemented qualitatively by a flattening of the funding (TLP) curve. NSFR regulation should be a consideration on this point as a bank would only improve its NSFR by issuing funding beyond one year, and would presumably look significantly beyond this in order to create a stable NSFR. Hence, even short-term assets may need to be charged longer-term funding costs.

A bank's FTP curve for internal pricing of funding will, therefore, be set on a blended basis with all of the above considerations taken into account. Ultimately, the assessment of a funding curve will be – like the credit curve mapping in Section 12.2 – subjective and open to debate.

Graph depicts the cost of funding in different currencies and the cross-currency basis. — **Figure 14.9** Illustration of cost of funding in different currencies and the cross-currency basis.

In terms of defining costs of funding in different currencies, a bank may issue in either a single currency or multiple currencies. It may, therefore, be possible to define the TLP curve in different currencies directly (Figure 14.9). Alternatively, a bank may need to use the foreign exchange (FX) markets to transfer funding via cross-currency basis swaps. These two methods should produce broadly similar results. Another post-GFC effect is that funding in certain currencies can be materially more expensive than others.

As noted previously, funding costs are asset specific. For example, a high-quality treasury bond can be repoed fairly easily, and it is, therefore, the financing cost via the repo market (haircut and spread) that is relevant. The existence of the repo market means that it is not necessary to consider the cost of borrowing money on an unsecured basis to buy the bond (which would be considerably higher). The funding of an asset should also depend on the credit quality of the asset itself, as lenders will charge funding rates that inevitably depend on the quality of the balance sheet of the borrower. For example, a bank trading with a triple-A counterparty should have lower marginal funding costs than if it were doing the same business with a lower-rated counterparty, since it will have a more beneficial effect on the credit spread premium in Figure 14.7. Whilst it is not practical to have many separate funding curves, it may be relevant to adjust FTP policy in certain cases (e.g. triple-A counterparties) so as to create the right incentive.

Given that funding references margin, the underlying remuneration will also be an important consideration. Typically, cash margin will be remunerated in the associated overnight rate in the relevant currency (e.g. Fed Funds). Since this will typically align as a good proxy for the risk-free rate in Figure 14.7, this creates self-consistency. However, if remuneration of margin is less than OIS (e.g. in the case of cash initial margin posted to a CCP), then the overall funding cost should be higher: even funding at OIS may be seen as costly. Indeed, segregation may be seen to create additional funding costs: initial margin received may be costly to segregate and may not earn a return.

Where there is clear value in the margin management process, such as being able to post non-cash margin and/or having a choice over the type of cash/securities, this may be seen as an additional cost (benefit) when receiving (posting) margin. The relevant haircuts in different markets (derivatives through the margin agreement and the current levels in the repo market) must also be factored in. Such benefits may be defined more explicitly as collateral value adjustments (ColVA) outside the main funding framework.

14.3.6 NSFR and LCR

Suppose a bank has an NSFR of 95% as a result of 950 ASF and 1,000 RSF. Assume that the bank has a desired NSFR of 105% and so raises additional long-term funding of 125 in five-year bonds with an average ASF ratio of 80%⁸ and retires short-term debt with an ASF of 0%. This results in a higher cost of funding of 100 bps, this being the difference between the rate on the new long-term debt compared to the retired short-term debt. It may seem natural for the bank to charge the additional cost of the funding on a pro rata basis to businesses with RSF requirements, the logic being that the reason for raising the new funding was solely to improve the NSFR. This will clearly penalise businesses with high RSF compared to their natural funding costs.

Some RSFs – a good example being the charge for 20% of derivatives liabilities – do not require any normal funding (e.g. cash is not required). It may be argued that charging for these components may feel unnatural and may penalise an RSF-generating business that does not require additional funding, potentially to the detriment of shareholders. On the other hand, not charging the RSF will tend to deteriorate the bank's NSFR. An NSFR invariance pricing approach will lead to charges for components such as the 20% liability RSF charge. This will be discussed in more detail in Section 18.3.4.

A similar effect will occur with respect to the LCR and the need to hold HQLAs for various contingent liquidity stress events. To the extent that this requires additional funding beyond the normal strategy, this additional cost of HQLA should probably be transfer priced. If this is not the case, then new business will tend to deteriorate the bank's LCR as the incremental cost of additional HQLA will not be priced. A good example of this is the need to fund margin requirements (e.g. posting initial margin) for a three-notch rating downgrade. It is unlikely that, in the absence of the LCR, any funding would be put in place for this contingent liquidity. An LCR invariance pricing policy may, therefore, transfer price the full cost of funding the additional HQLA requirement. However, this does assume that there are no other benefits to having a strong LCR, such as lower funding or capital costs.

14.3.7 Accounting

Since FVA and MVA are reported in the financial statements of banks, it is also relevant to consider the cost of funding that would be used for such adjustments. As discussed in Section 5.3.3, from an accounting point of view, it is the exit price that drives the valuation, and entity-specific components cannot be included. It follows that the funding curve should reference the cost of funding of other market participants. There is also the question of whether the full contractual maturity of a transaction should be used, or some shorter period based on the fact that the transaction could be exited early if required. However, this could become difficult since an entity might argue that it would tactically exit certain transactions with parties with different funding costs depending on the characteristics of the transaction at the time (e.g. whether it is in-the-money and the tenor).

All the above points have left market participants, accountants, and regulators in much debate over defining the cost of funding. Some of the questions that arise when incorporating funding into pricing are:

the instruments a funding cost should be calibrated to (e.g. primary issuance, secondary bond trading, CDS quotes, or internal assessment of the cost of funding);
whether a party should use its own cost of funding, the cost of funding of a counterparty (with whom it might exit the transaction if required), or a curve that is blended based on the cost of funding of market participants in general; and
whether term funding should be assumed using the final contractual maturity of a transaction, or if a shorter tenor should be assumed, based on the fact that term funding is not required and/or that the transaction may be terminated early.

This will be discussed in more detail in Section 18.2.7.