Approaches to the Management of Financial Risks - Modern Banking

Though risk management was always central to the profitability of banks, its focus has changed over time. In the 1960s, the emphasis was on the efficient employment of funds for liabilities management. In the 1970s, with the onset of inflation in many western countries and volatile interest rates, the focus shifted to the management of interest rate risk and liquidity risk, with a bank’s credit risk usually managed by a separate department or division. Asset–liability management (ALM) is the proactive management of both sides of the balance sheet, with a special emphasis on the management of interest rate and liquidity risks. In the 1980s, risk management expanded to include the bank’s off-balance sheet operations, and the risks inherent therein. In the new century, managers are answerable not only to shareholders but to national and international regulators. The emphasis is on the use of models to produce reliable risk measures to direct capital to the activities that offer the best risk/return combination. Scenario and stress tests are employed to complement the models.

In this section, the traditional ALM function is reviewed but it also explores how new instruments have changed the risk management organisational structure within banks, to accommodate all the risks a modern bank incurs. In particular, it should be emphasised that while traditional risk management focused on a bank’s banking book (that is, on-balance sheet assets and liabilities), modern risk management has been extended to include the trading book, which consists mainly of off-balance sheet financial instruments. The financial instruments of a bank’s trading book are taken on either with a view to profiting from arbitrage, speculation or for the purposes of hedging. Financial instruments may also be used to execute a trade with a customer. The bank and trading books can be affected differently for a given change, say, in interest rates. A rise in interest rates may cause a reduction in the market value of off-balance sheet items, but a gain (in terms of economic value) on the banking book. Also, while the market value gain/loss on the trading book normally has an immediate effect on profits and capital, the effect on the banking book is likely to be realised over time.

Interest Rate Risk and Asset–Liability Management

Traditionally, the ALM group within a bank has been concerned with control of interest rate risk on the balance sheet. For some banks it may be equally or even more important to manage interest rate risk arising from off-balance sheet business, but it is instructive to look at the traditional methods and progress to the relatively new procedures. To provide an example of the complexities of interest rate risk management, consider a highly simplified case where a bank, newly licensed by the relevant regulatory authority, commences operations as follows.

  1. Liabilities consisting of one deposit product of £1000 and equity equal to £100, which gives the bank total capital of £1100. It plans to lend money to an unsecured borrower.
  2. The amount it can lend, given a risk assets ratio of 8%, is £1012.14

  3. The loan has a maturity of six months, when all interest and principal is payable (a ‘‘bullet’’ loan). It will be priced at the current market rate of interest, 7%, plus a spread of 3%. So the annual loan rate is 10% on 1 January 2000. The loan is assumed to be rolled over every six months at whatever the new market rate is, with an unchanged risk premium of 3%.
  4. A customer wishes to purchase the deposit product, a certificate of deposit (CD) on 1 January. The market rate is 7%, and because of highly competitive market conditions it is this rate which is paid on the CD. The bank has to decide what the maturity of the CD is going to be and once the maturity is set, the bank is committed to rolling over the CD at the same maturity.
  5. The ‘‘yield curve’’15 for the CD is assumed to be flat, that is, the same rate of 7% applies, independent of the maturity. On 1 February 1994 there is an unexpected one-off shift in the yield curve, to a new flat value of 9%, because the market interest rate rises, suddenly, to 9%. There are no further shifts during the year.
  6. Ignore all issues related to dividends and operating costs, with the exception of the requirement to conform to a risk assets ratio of 8%.

The ALM group may measure their performance in terms of net interest income (loan income less cost of deposit), the market value of equity (the market price of bank stock) or the economic equity ratio (new equity value/new loan value) for an unexpected change in interest rates. To the extent that changes in net interest income affect bank stock market valuations, the three measures will be very closely linked.

As was noted earlier, there is a 2% increase in market rates on 1 February 1994. To examine what happens to a number of bank performance measures, it is necessary to use a compounding formula to compute the monthly interest rate from the annual rates, because of the potential mismatch in the timing of cash flows for the six-month loan and the CD, the maturity of which is not determined.16 Thus, for the six-month loan, the monthly interest rate is 0.79741% when the annual rate is 10%, and 0.94888% when the annual rate is 12%. If interest rates rise by 2% on 1 February, the borrower pays monthly interest of £8.07 until 30 June (remember, the loan rate is fixed for six months), and £9.60 from 1 July.

For the deposit product, once the bank decides on the maturity of the deposit, it incurs interest rate risk. In this simple example, the size of the deposit (£1000) and loan (£1012)

The Effects of an Unexpected Rise in Interest Rates

The Effects of an Unexpected Rise in Interest Rates

The Effects of an Unexpected Rise in Interest Rates

An Unexpected Rise in Interest Rates

An Unexpected Rise in Interest Rates

similar. A three-month deposit will cut the discounted present value of the net assets by 1.15%. A six-month deposit would reduce the discounted present value of net assets by 0.76%, assuming the loan rate rises from 10% to 12% on 1 February. This is an example of a ‘‘liability’’ sensitive strategy, where liabilities reprice faster than assets, so net interest earnings fall with an increase in interest rates. If an asset sensitive strategy had been adopted, interest earnings would rise. It should be stressed that interest rate changes can affect the ‘‘economic value’’ of a bank in a way that is different from the short-term profit and loss accounts. The current earnings perspective will focus on the sensitivity of the profit and loss account in the short term (for example, a year) to a change in interest rates. Over the longer term, the effect on net economic value will be considered, where net economic valueis defined as the difference between the change in the present value of the bank’s assets and the present value of its liabilities, plus the net change in the present value of its off-balance sheet positions, for a given change in market interest rates. The difference between the two will be pronounced if marking to market instruments are not a major part of the bank’s portfolio.

The above cases refer to the interest rate risk caused by a shift in the yield curve, that is, yield curve repricing risk. There are other types of interest rate risk related to bank products. The interest rate is not necessarily determined by a market yield curve. For example, prime based loans and money market accounts may be linked to central bank or interbank rates, but it may not be a one-for-one relationship. Competition in the market and monetary policy will determine the extent to which this relationship is one-for-one.

However, even if it is not one-for-one, provided it is not volatile, there will be little in the way of additional risk. Also, banks will find the balance of their liabilities change in a period of fluctuating interest rates. For example, as interest rates rise, customers will be reluctant to hold cash in non-interest-bearing deposit accounts because of the rising opportunity cost of holding money in these accounts. In a period of falling rates, customers may shift deposits into other assets that yield a higher rate of return.

There can also be one-sided interest rate risk associated with bank products that have options attached to them, which gives rise to different types of customer behavior depending upon whether interest rates rise or fall. For example, prepayment risk arises with fixed rate mortgages. A prepayment18 option will result in different outcomes; if interest rates rise, mortgage prepayments decline and the expected average life of the portfolio increases. On the other hand, if rates fall, prepayment increases (because the fixed payments are less attractive) and the average life of the portfolio declines. In some countries (e.g. the UK), the borrower is charged a penalty for early repayment of a mortgage. In others, such as the USA, there is no penalty charge on prepayment of mortgages.

Gap Analysis

Gap analysis is the most well known ALM technique, normally used to manage interest rate risk, though it can also be used in liquidity risk management. The ‘‘gap’’ is the difference between interest sensitive assets and liabilities for a given time interval, say six months. In gap analysis, each of the bank’s asset and liability categories is classified according to the date the asset or liability is repriced, and ‘‘time buckets’’: groupings of assets or liabilities are placed in the buckets, normally overnight–3 months, >3–6 months, >6–12 months, and so on.

Analysts compute incremental and cumulative gap results. An incremental gap is defined as earning assets less funding sources in each time bucket; cumulative gaps are the cumulative subtotals of the incremental gaps. If total earning assets must equal total funding sources, then by definition, the incremental gaps must always total zero and therefore, the last cumulative gap must be zero. Analysts focus on the cumulative gaps for the different time frames. The above points are demonstrated in a simplified interest rate ladder, in Table above.

Table above separates the assets and liabilities of a bank’s balance sheet into groups with cash flows that are either sensitive or insensitive to changes in interest rates. An asset or liability is said to be interest rate sensitiveif cash flows from the asset or liability change in the same direction as a change in interest rates. The ‘‘gap’’ (see Table above) is the sterling amount by which rate sensitive assets (RSA) > rate sensitive liabilities (RSL). A negative gapmeans RSA < RSL; a positive gap means RSA > RSL. The gap ratiois defined as RSA/RSL. If the gap ratio is one, then the rate sensitivity of assets and liabilities is matched, and the sterling gap is zero.

Most banks have a positive gap, that is, rate sensitive assets exceed rate sensitive liabilities, because most banks borrow long and lend short, so their assets will mature later than their liabilities. For example, a bank will have rate sensitive deposits, which can be withdrawn any time, but the majority of its rate sensitive loans are not due to be paid back anywhere from a year up to 25 years in the case of a mortgage.

Suppose a bank has a positive gap (RSA > RSL). Then a rise in interest rates will cause a bank to have asset returns rising faster than the cost of liabilities, but if interest rates fall, liability costs will rise faster than asset returns.

Gap Analysis for Interest Rate Risk (£m)

Gap Analysis for Interest Rate Risk (£m)

The bigger the maturity gap, the more a bank’s net worth will be affected by a change in interest rates. Suppose the bank wants to immuniseitself, i.e. hedge against this type of interest rate risk. If it structures the banking book such that the weighted average of RSA equals the weighted average of RSL, so MA − ML = 0, then it will substantially reduce, but not eliminate, interest rate risk on the banking book.

The bank is not fully hedged against; it ignores the following.

  • The extent to which a bank is geared or leveraged, that is, the extent to which loans are funded by deposits (as opposed to equity).
  • Duration – to be discussed below.

The maturity gap analysis presented above provides the ALM group with a picture of overall balance sheet mismatches. While this type of analysis still takes place in most banks, it is used in conjunction with other risk management tools, for a number of reasons.

  1. Mismatches that fall within each time bucket are ignored. Returning to the case study examples, suppose the deposit product had a term of 3.5 months, so that it was repriced after this time. The loan will not be repriced until after six months, making the >3–6 month time bucket liability sensitive, though in the gap analysis it appears to be asset sensitive, because the loan was £1012, funded by a £1000 deposit and £100 in equity; equity is in the ‘‘not stated’’ time bucket because it has no stated maturity.
  2. Interest rates on deposit accounts, some loans and credit card receivables are not solely determined by the market interest rates. Some banks offer ‘‘free’’ bank services with a current account but compensate for it by paying a lower rate.
  3. It ignores the bank’s exposure to prepayment risk, the risk that long-term fixed rate mortgages and loans will be repaid early if interest rates fall.
  4. Some bank products, such as non-maturity accounts, non-market rate accounts and off-balance sheet items, cannot be handled in a gap analysis framework, though part of this problem has been overcome through duration gap analysis (see below).

Duration Analysis

Duration analysis expands on the gap analysis presented above by taking duration into account. Again, the objective is to consider the impact on shareholders’ equity if a risk-free rate, for all maturities, rises or falls, but takes the procedure one step further. Duration analysis allows for the possibility that the average life (duration) of an asset or liability differs from their respective maturities. Suppose the maturity of a loan is six months and the bank opts to match this asset with a six-month CD. If part of the loan is repaid each month, then the duration of the loan will differ from its maturity. For the CD, duration is identical to maturity if depositors are paid a lump sum at the end of the six months. However, if only part of the loan is repaid each month, and depositors are paid a lump sum, a duration gap is created, exposing the bank to interest rate risk.

Duration is the present value weighted average term to repricing, and was originally applied to bonds with coupons, correcting for the impurity of a bond: true duration is less than the bond’s term to maturity. The duration of an ‘‘impure’’ bond (that is, one with a coupon) is expressed as follows:

Duration =T{1−[coupon size/(MV×r)]}+[(1 + r)/r][1−(DPVR/MV)]----(I)

where:
T: time to redemption
r: market (nominal) interest rate
MV: market value
DPVR: discounted present value of redemption

For example, suppose the problem is to compute the duration of a 10-year £100.00 bond with a fixed £5.00 coupon. The coupon is paid annually, the first one at the end of the first year of the investment, and the last one at the time the bond is redeemed. The current market price for the bond is obtained by computing the present value, using the formula

(c/r)[1−(1 + r)T]+RT(1+r)T ---------(II)

where:
c: coupon value (£5.00)
r: market interest rate, with a horizontal term structure, assumed to be 10%
T: date of redemption
RT: amount redeemed (£100.00)

In the example, the current market price of the bond is:

£100(1.1)−10+£50[1−(1.1)−10] = £50[1+(1.1)−10] = £69.277

There is a cash flow associated with the bond, and the idea is to discount each cash flow to the present value. To compute the duration, the formula from equation (I) is used:

Duration = 10[1−(£5/£6.9277)]+(1.1/0.1){1 −[£100(1.1)−10/£69.277]} = 7.661 years19

As can be seen from the example, duration analysis emphasises market value, as opposed to book value in gap analysis. All cash flows are included in the computation, and there is no need to choose a time frame, unlike gap analysis.

Duration analysis has been widened to include other assets and liabilities on a bank’s balance sheet with flexible interest rates, and paid by borrowers or to depositors at some point in the future. In these cases, the duration of the equity is computed as:

DE=[(MVA× DA)(MVL/DL)(MVA−MVL)----(III)

where:
DE: duration of equity
DA: duration of rate sensitive assets
DL: duration of rate sensitive liabilities
MVA: market value of asset
MVL: market value of liability

The computed duration of equity is used to analyse the effect of a change in interest rates on the value of the bank, because it will approximate a zero coupon bond with the given duration.20 The greater a bank’s duration mismatch, the greater the exposure of the bank to unexpected changes in interest rates.

Duration Gap Analysis

Duration gap analysis estimates a bank’s overall interest rate exposure on the balance sheet, taking into account that duration gaps are present. The key question is, in the presence of a duration gap, how is the value of shareholders equity affected for a given change in interest rates?

The duration of the assets and liabilities are matched, instead of matching time until repricing, as in standard gap analysis. The on- and off-balance sheet interest sensitive positions of the bank are placed in time bands, based on the maturity of the instrument.

The position in each time band is netted, and the net position is weighted by an estimate of its duration, where duration measures the price sensitivity of fixed rate instruments with different maturities to changes in interest rates. If the duration of designated deposits and liabilities are matched, then the duration gap on that part of the balance sheet is zero.

This part of the balance sheet is said to be immunised against unexpected changes in the interest rate. In this way, immunisation can be used to obtain a fixed yield for a certain period of time because both sides of the balance sheet are protected from interest rate risk.

Note, however, that the protection is less than 100%, because market yields can change in the middle of an investment period, and other risks are still present, such as credit risk.

Furthermore, the duration measure used assumes a linear relationship between interest rates and asset value. In fact the relationship is normally convex. The greater the convexity of the interest rate–asset value relationship, the less useful is the simple duration measure.

Hence, the use of duration to measure interest rate sensitivity should be limited to small changes in the interest rate.

Saunders (2002)21 shows how a duration model can be used to measure the overall gap of the bank’s exposure to interest rate risk, i.e. the duration gap. Begin by summing up the bank’s duration of, respectively, its assets and liabilities portfolio.

DA: the market value weighted average of the individual durations of each asset in the portfolio
DL: the market value weighted average of the individual durations of each liability

δE = δA δL-----(IV)

where:

δE: the change in net worth of the bank
δA: the change in market value of assets for a given change in interest rates
δL: the change in market value of liabilities for a given change in interest rates

Saunders (2002, pp. 208–211) shows the net worth of the bank can be expressed as:

δE = −(adjusted duration gap) × asset size × interest rate shock

where

interest rate shock = δR/(1 + R)

where R is the yield to maturity, and will change, for example, as a result of a change in the interest rate set by the central bank:

adjusted duration gap = duration gap DA − GDL

where DL is adjusted for the proportion of assets funded by liabilities (e.g. deposits, or other borrowed funds) rather than equity. That is, DL is adjusted for gearing or leverage:

G = L/A, where A is total assets and L is the bank’s liabilities, excluding equity.

Thus:

δE = −[DA − GDL] × A × δR/(1 + R) -----(V)

Example:

Assume DA = 4 years and DL = 2 years.

Assets on the balance sheet are £200 million; liabilities consist of £150 million of borrowed funds and £50 million of equity. So L/A = 150/200 = 0.75 and GDL = (0.75)(2) = 1.5. Suppose the bank expects interest rates to rise by 0.5% from 5% to 5.5%. Then _R = 0.005 and (1 + R) = 1.05, so δR/(1 + R) = 0.00476.

So δE = −(4 − 1.5) × £200 000 000 × 0.00476 = −£2 380 000 or − £2.4 million.

Thus, as a result of an increase in interest rates, the net worth of equity holders will fall by £2.4 million. The Basel Committee recommends that banks using the standardized approach for market risk also adopt this method for monitoring their interest rate exposure.

Liquidity Risk and Asset–Liability Management

The ALM group in a traditional bank is also responsible for the management of liquidity risk. As defined earlier, it is the risk that a bank is unable to meet its liabilities when they fall due. Liquidity risk is normally associated with the liabilities side of the balance sheet when depositors unexpectedly withdraw their financial claims. Assuming the liquidity preferences of a bank’s customers are roughly constant, the problem usually arises if there is a run on the bank as depositors try to withdraw their cash. A bank liquidity crisis is normally triggered either by a loss of confidence in the bank or because of poor management practices, or the bank is a victim of a loss of confidence in the financial system, caused, possibly, by the failure of another bank. However, if the bank experiences an unusually high deposit withdrawal rate, and lacks the cash or is unable to borrow the money quickly, it is faced with liquidating its longer-term investments, possibly in a market where other banks and investment houses are also selling, pushing down prices.

A bank can also experience liquidity problems on the asset side of the balance sheet, caused by large numbers of unexpected loan defaults. Banks have also been caught out granting credit lines which they do not expect to be drawn down, but which are subsequently used by the borrowers. If an economy goes into recession relatively quickly, these banks may see firms drawing down their credit lines all at once, which will put pressure on their liquidity. There is also liquidity risk linked to off-balance sheet transactions, and to a slow-down or collapse in the payments system.

If a bank does experience liquidity problems, the central bank is usually willing to lend to them at some penal rate, which is costly for the bank. Also, the central bank will have to be reasonably certain that the problem is one of illiquidity and not insolvency. Banks will borrow funds on the interbank markets or from other sources before they approach the central bank, but again, this is costly for the bank, and undermines its profitability.

The objective of liquidity risk management should be to avoid a situation where the net liquid assets are negative. Gap analysis can be used to manage this type of risk. The gap is defined in terms of net liquid assets: the difference between net liquid assets and volatile liabilities. Liquidity gap analysis is similar to the maturity ladder for interest rate risk, but items from the balance sheet are placed on a ladder according to the expected time the cash flow (which may be an outflow or an inflow) is generated. Net mismatched positions are accumulated through time to produce a cumulative net mismatch position. The bank can monitor the amount of cash which will become available over time, without having to liquidate assets early, at penal rates.

Liquidity Funding – Maturity Ladder Approach (£000)

Liquidity Funding – Maturity Ladder Approach (£000)∗

The Bank of International Settlements (2000) has outlined a maturity ladder approach, which consists of monitoring all cash inflows and outflows, and computing the net funds required. A simple version of this type of ladder appears in Table above.

The ALM group in a bank is not normally responsible for risk management in other areas, though how risk management is organised does vary from bank to bank. In some banks, the ALM group has been replaced by a division with overall responsibility for risk management, but credit risk continues to be managed separately. Increasingly, 21st century banks have a division with overall responsibility for coordinating risk management.

The management of interest rate risk has moved beyond the traditional gap and duration analysis because banks have increased their off-balance sheet business and the use of derivatives.


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