# Interest rate risk

In finance, the interest rate risk is the risk that the interest rate associated with an interest- bearing financial product will deviate from the market interest rate due to future market developments .

## General

The interest rate risk results from the possibility of a change in market interest rates that is not expected a priori. It affects (financial) transactions with both fixed and variable interest rates .

In the case of fixed interest rates, the current market interest rate can deviate from the agreed fixed interest rate; in the case of variable interest rates, there is a risk that interest rate increases (for loans ) or interest rate reductions (for financial investments ) lead to additional interest costs (or a loss of income) compared to a comparable fixed interest rate. The interest rate risk thus turns out to be the negative deviation between the current and future realized net interest income caused by interest rate changes. Changes in interest rates are subject to subjective uncertainty. These are systematic risks that are correlated with aggregated economic variables and have a lasting impact on the welfare of economic agents. They can either be measured at present value or at current market values .

Interest rate risks play a decisive role not only for investors and borrowers, but also especially for credit institutions because of the maturity transformation . For credit institutions, interest rate risk is that the at unchanged interest rates to be achieved market value is not reached a financial product due to incoming interest rate changes.

## history

The state interest rate regulation that had existed in Germany since January 1937 ended with the repeal of the Interest Ordinance in April 1967. This stipulated maximum interest rates in the "Debit Interest Agreement" which the banks in the lending business should not exceed and in the " Credit Interest Agreement " the maximum remuneration for the deposit business , but which could also be undercut . Debit and credit interest remained stable, there was no need for adjustment or interest rate risks. After the interest rate was released in April 1967, debit and credit interest rates could freely adjust to market developments , which, however, created market risks for market participants and, in particular, interest rate risks.

## Analysis of the interest rate risk

### Influencing factors

The main influencing factors of the interest rate risk can be summarized in two general terms: On the one hand, the interest rate risk is dependent on the interest rate exposure (internal component) , and on the other hand on the market interest rate volatilities (external component) .

The interest rate exposure summarizes internal company factors such as the open fixed interest position, the maturities and the interest rate elasticity. The market interest rate volatilities represent changes in interest rates as well as changes in the interest rate structure. The more pronounced these two factors occur, i. In other words, the larger the fixed interest position is compared to the variable interest position, for example, or the more the interest rate level shifts, the higher the risk of changes in interest rates, all other things being equal.

The change in the interest rate level has little effect on the value of the position for bonds with a fixed coupon . However, changes in interest rates on fixed-rate bonds can lead to significant price changes. If these are held over a longer period of time, changes in interest rates have a significant impact on performance. The value of the bond goes down when the market rate rises. The redemption amounts (coupon and redemption) are invested at the new interest rate. If the interest rate rises, the amount resulting from the reinvestment of the repayment amounts also rises. The interest income from the coupons on the bond remains unchanged. If, on the other hand, a bond with a fixed coupon is held to maturity, there is only a small impact on the performance of the respective investment (since the amount of the coupon, i.e. the effective interest rate, does not change).

### Interest rate risk analysis instruments

The instruments for analyzing interest rate risk can be differentiated on the one hand according to whether they are primarily developed and used to analyze the risk of surplus interest income or the risk of present value. In addition, it is possible to differentiate between static and dynamic approaches. While the static approaches are related to the key date and generally only take into account the interest rate transactions already contracted on this key date, the dynamic approaches also integrate new and follow-up transactions into the analysis. The static instruments are therefore primarily aimed at operational business. Dynamic approaches, on the other hand, are particularly suitable for strategic risk analyzes.

### Net interest income or interest margin risks

If one looks at the long-term development of the interest margins of a large bank , a savings bank and a cooperative bank on the basis of the Bundesbank statistics, one observes strongly fluctuating interest margins over time.

#### Interest spreads of selected banking groups in the period 1970 to 2000

Average Standard deviation Coefficient of variation 2.33% 0.56 percentage points 24% 3.18% 0.34 percentage points 11% 3.01% 0.30 percentage points 10%

While the interest margins of the savings banks and the cooperative banks showed a standard deviation of 0.30 to 0.34 percentage points during this period, it was just under 0.56 percentage points for the big banks. Obviously, the interest rate risk was more pronounced at the big banks. Considering the coefficient of variation as a relative control measure reinforces this impression.

#### Influencing factors and forms of net interest income risk

The essential interdependencies can be clarified with the help of a balance sheet analysis, whereby the connections also apply in the same way to the off-balance sheet business.

The entire interest business of a credit institution can be divided into two layers, which differ in terms of their adaptability to changes in market interest rates:

##### Fixed Income Transactions

These transactions include all positions that have a fixed, agreed and constant interest rate for a certain period of time .

##### Variable interest rate transactions

These interest rate transactions either have no fixed interest period or only a very short one. As a result, these transactions are partially or fully interest-sensitive.

Net interest income risks always arise when there is no matched fixed interest rates between the asset and liability items. Occurring mismatches lead to corresponding open positions in terms of amount or time.

The classic case of the net interest income risk is the so-called fixed interest rate risk . This arises when a fixed-interest block on the assets side is financed by a variable-interest-bearing position on the liabilities side of the balance sheet (risk with rising market interest rates) or, conversely, a variable-interest-bearing position on the assets side is financed by a fixed-interest position on the liabilities side (risk with falling market interest rates) .

#### Fixed interest balance sheet

The fixed interest balance sheet is an instrument with which interest rate risks can be identified and quantified. It was increasingly used in the 1970s, and particularly with the rise in interest rates at the beginning of the 1980s, to analyze the risk of changes in interest rates in credit institutions. As a result of the imbalances in individual institutions resulting from the high interest rate phase, the Federal Financial Supervisory Authority (BaFin) introduced the obligation for all banks to prepare fixed interest balance sheets.

In the fixed interest rate balance sheet, all asset and liability fixed interest positions are compared and the resulting open positions are determined for future periods. An open position, either as an asset surplus or a liability surplus , means an interest rate risk.

In accordance with BaFin, all transactions with a fixed interest rate of more than 180 days should normally be used as a basis for fixed-interest transactions. This balance sheet should also take into account non-interest-bearing non-interest-bearing assets and liabilities.

Usually, the fixed interest balance sheet takes into account a market interest rate increase of 1% when determining the surplus interest risk . I.e. the reported risk represents the amount in EUR that net interest income will decrease if the market interest rate rises by 1%.

##### Formal structure

The fixed interest balance sheet is part of the current account. The following table shows a fixed interest rate balance sheet with positive maturity transformation and the overall balance sheet, which also includes other business that is dependent on market interest rates.

assets liabilities
Closed fixed income position
Open fixed income position Fixed rate gap
Other business dependent on market interest rates

The fixed interest rate balance sheet has the disadvantage that a decrease compared to the original expectation can occur if there is a change in interest rates, although there is no fixed interest rate gap. The change comes from the other market-dependent business.

##### Example of a fixed interest rate balance sheet
volume Ø interest 2,300 8.0% 1,500 6.0% 1,500 2.0% 800 8.0% −8

Thus, in the above case, there is an interest surplus risk of 8 units.

##### criticism

Changes in interest rates can also have a negative impact on the result if there is a congruence of maturities (matching of the volumes with regard to the remaining maturity on the assets and liabilities side). This is due to the fact that the variable interest rates on the assets and liabilities side change differently.

As a rule, in practice there is an expansion of the fixed interest rate balance sheet through present value considerations. The risk of surplus interest income in the following periods is discounted using the relevant discount rate.

#### Interest rate gap analysis

Here the fixed interest stocks are shown at several points in time.

#### The interest elasticity concept

This concept, which was developed around the mid-1980s in particular by Rolfes (Rolfes, 1985), is based on the different interest rate responses in the variable interest business. One speaks here of interest rate elasticities. These therefore describe the adaptability of variable interest positions to changes in the market interest rate.

It is assumed that the interest rates of the individual balance sheet items and banking products are linked to the money and capital market rates.

Mathematically represented, the interest elasticity is calculated as follows:

${\ displaystyle ZEL = {\ frac {PZ_ {t} -PZ_ {0}} {MZ_ {t} -MZ_ {0}}}}$

with = product interest in t, = product interest in period 0, = market interest rate in t, = market interest rate in period 0. ${\ displaystyle PZ_ {t}}$${\ displaystyle PZ_ {0}}$${\ displaystyle MZ_ {t}}$${\ displaystyle MZ_ {0}}$

However, since the level of the interest elasticities determined in this way depends very strongly on the two observation periods, it makes sense to calculate the elasticities with the help of regression analyzes.

##### Static elasticity balance

The basis for interest rate elasticity studies is regularly the static elasticity balance. It compares all asset and liability positions with their volumes and interest elasticities. In the basic model of the static elasticity balance, the entire interest rate risk is made up of two components : the fixed interest rate risk from the open fixed interest rate position and the variable interest rate risk .

###### Example of a static elasticity balance
Elasticity balance in million euros
assets volume Interest rate elasticity liabilities volume Interest rate elasticity
Cash reserves 200 0.00% Interbank liabilities 300 0.90%
Interbank claims 600 0.90% Sight deposits 200 0.00%
Overdrafts 1,500 0.80% Time deposits 1,100 0.70%
Short term loans 1,300 0.60% savings 2,400 0.40%
Bonds and Notes 300 0.00% Savings bonds 500 0.00%
Municipal loan 400 0.00% Bonds 300 0.00%
Mortgage loan 700 0.00% Equity 200 0.00%
Fixed Income Assets 1,400 0.00% Fixed Income Liabilities 1,000 0.00%
Total assets 5,000 0.504% Total liabilities 5,000 0.400%

In the remaining block of 3,600 million euros in variable business on the assets side, there is an average interest rate adjustment elasticity of 0.70%. The variable passive funds, on the other hand, only show an average elasticity of 0.50%. If the market interest rate increased by 1%, the interest income would increase more than the interest expenses. This would give the credit institution an opportunity to change interest rates.

${\ displaystyle ZAR = (ZEL_ {A} -ZEL_ {P}) \ cdot BS}$

with = interest elasticity active, = interest elasticity passive and = total assets. ${\ displaystyle ZEL_ {A}}$${\ displaystyle ZEL_ {P}}$${\ displaystyle BS}$

This gives the bank an opportunity to change interest rates of EUR 5.2 million.

##### Dynamic elasticity balance

The dynamic elasticity balance includes extensive strategic balance sheet and interest rate risk simulations. These are carried out with the help of PC solutions with limited effort, with corresponding programs being offered by management consulting companies as well as by individual banking associations.

These simulation calculations are based on the information from the fixed interest rate balance sheet and the static elasticity balance sheet.

Based on assumptions to be made, such as B. the future interest rate development, a variety of forecast problems arise.

##### criticism

The interest elasticities to be measured show no stability over time.

### Present value risks

Interest rate-related cash or market value risks come to the fore when looking at individual fixed-income securities through to securities portfolios. Here an impending rise in the market interest rate leads to an adjustment of the security price.

#### Price Risks of Fixed Income Securities

The price of a bond depends on factors such as B. the nominal interest and the remaining term .

In general, the market value (MW) of a fixed-income security can be calculated as follows:

${\ displaystyle MW = \ sum _ {t = 1} ^ {n} {\ frac {C} {(1 + r) ^ {t}}}}$

#### Duration analysis

The duration is a time value in years that specifies the period of time that is required for a fixed-income security so that the price and compound interest effects resulting from a change in interest rates are offset again and in which the original return is secured (see also duration ).

Since a certain fixed value results at the time of the duration independent of the occurring change in market interest rates, immunization against interest rate risks can be achieved with the aid of the duration .

#### Value-at-risk analyzes

Value at Risk

The procedures aimed at risk compensation, such as duration, must still recognize (residual) risks despite all the expansion stages. Since the uncertainty with regard to the influencing variables of a risk should also be better captured, a need for further developed methods for the analysis of price change risks already existed. Added to this was the growing interest in a suitable measure for measuring a bank's overall risk position . Therefore the concept of Value at Risk was developed.

Based on a downside-oriented concept of risk, which understands a risk as a negative deviation between the actual and expected result, the VaR risk measure is defined as the negative change in value of an asset position that, depending on an assumed distribution assumption, occurs at a maximum with a certain predetermined probability in a certain period can.

It thus represents a threshold value that the actual losses will not exceed with the given probability.

## Control of the interest rate risk

The contracting parties have developed various options for eliminating such interest rate risks. Interest rate risks can be partially or completely eliminated through risk reduction , risk transfer or risk avoidance . On the one hand, an interest rate risk can be excluded through contractual clauses in credit agreements or bond terms such as an interest sliding clause or an interest rate fixation period; on the other hand, interest rate derivatives such as interest rate swaps can be used to hedge interest rate risks as part of risk transfer.

The division of risk management into active and passive risk management measures can in principle also be transferred to the management of interest rate risk.

### Active versus passive treasury strategies

Active treasury strategies are characterized by deliberately entering into open interest positions or deviations from a defined benchmark , depending on specific interest rate forecasts , in order to achieve a higher return than the benchmark.

Passive treasury strategies , on the other hand, are rule-based strategies that are pursued independently of interest rate forecasts. An attempt is made to keep a given cash flow structure as constant as possible over long periods of time.

### Risk avoidance with risk limits

As part of active risk management, risk avoidance on the basis of limit systems must first be mentioned. In addition to limiting the overall bank risk , partial limits are usually also used to limit certain risk positions , such as B. the course change risk, used.

In practice, the risk limits are quantified using the value-at-risk concept explained above.

### Risk reduction and risk transfer through derivative instruments

In addition to balance sheet instruments for risk reduction and -überwälzung particular off-balance sheet derivative financial instruments are available.

The balance sheet control can take place in the customer as well as in the interbank business. On the customer side, however, it must be taken into account that customer acceptance is necessary, for example, to increase fixed interest rates in customer business. Since different demand patterns from the customer's point of view will arise due to economic cycles , it is probably difficult to implement the internally derived strategies for risk reduction and transfer.

It is therefore more promising for a bank to try to implement the defined strategy in interbank business.

#### Interest rate swaps

Interest rate swaps contain the exchange of two different interest payment obligations that relate to a uniform underlying nominal amount. Since only the interest payment obligation is exchanged and the nominal amount does not flow, there is no capital claim between the contractual partners .

#### Forward Rate Agreement

In a FRA two parties agree a fixed forward rate (forward rate) to a particular nominal value for a point in the future time period. In addition, they undertake to make compensatory payments if a fixed reference interest rate is above or below the agreed forward interest rate at the beginning of the future period.

#### Interest rate futures

Interest rate futures put the stock exchange equivalent of OTC forward rate agreements. They pose a real futures . In contrast to FRAs but not the will of interest between buyers and sellers, but the resulting from the interest rate agreed the paper. Ultimately, it is about the standardized buying / selling of a bond by appointment.

Interest rate futures are traded as standardized forward contracts on numerous futures exchanges. In Europe, these are in particular the Eurex in Frankfurt and the Liffe in London.

Bunds (BUND future), federal bonds (BOBL future), Treasury notes (Schatz future) and money market paper (one- and three-month Euribor futures) serve as the basis for buying bonds .

The most important features of a futures contract are:

• the specification of the underlying cash register instrument,
• the contract size,
• the regulations for the provision of security and the final invoice.

#### Interest rate options

In addition to the financial instruments mentioned above, other instruments are also suitable for hedging against interest rate or market price risks:

• Cap : Protection against rising interest rates
• Floor : Protection against falling interest rates
• Collar : Fixing an upper and lower interest rate limit

## Regulation of the interest rate risk

A distinction is made between interest rate risks in the banking book and the trading book .

### Interest rate risks in the banking book

Interest rate risks in the banking book are not regulated in Principle 1 ; this also applies to Basel II , although this can be taken into account in pillar 2.

To support Pillar 2, the Basel Committee (2004) established “Principles for the Management and Supervision of Interest Rate Risks”, in which, among other things, the term outlier banks is defined. This includes those banks for which a standard interest rate shock or its equivalent (e.g. a 200 basis point interest rate shock for exposures in G10 currencies) results in a present value loss in the banking book of more than 20% of the liable capital (tier 1 and tier 2 capital ) leads. The national banking supervisors should be particularly careful with outlier institutions with regard to the adequate level of regulatory capital.

The supervisory treatment of interest rate risks in the banking book was regulated until November 2011 in circular 07/2007 (BA) of BaFin, which was replaced on 9 November 2011 by circular 11/2011 (BA). The rules for internal control of the interest rate risk in the banking book can be found in the minimum requirements for risk management (MaRisk) .

For the German banking system, the interest rate risk in the banking book was determined by the Deutsche Bundesbank and BaFin for the first time in 2005/2006 as part of a voluntary survey among German banks. However, the detailed results of this interest rate risk survey have not yet been published.

The Basel Committee (2004) has also drawn up a standardized model framework that can be used to quantify the interest rate risk in the banking book of banks using external (accounting) variables on the part of the national supervisory authorities. Similar models are already being used in other countries such as the USA (Economic Value Model, EVM). More sophisticated models include the Office of Thrift Supervision's Net Portfolio Vaue Model (NPV) or the Time Series Accounting-Based Model (TAM) , which was used to analyze the interest rate risk of German banks.

### Interest rate risk in the trading book

In the case of interest rate risks in the trading book, a net interest position must first be determined. This is generally the case with market price risks. It results from interest-related securities and cash positions , securities-related derivatives and market interest rate derivatives.

In the case of interest-dependent securities and cash positions , opposing positions are netted. It is the net interest position in the same securities.

In the case of securities- related derivatives , the securities-related component is netted with opposing positions.

The market interest-related components of the securities- related derivatives are netted in the same way as the market interest-related derivatives . This applies to largely corresponding positions .

### Capital requirements for general exchange rate risks

#### Duration method

${\ displaystyle \ Delta C_ {0} = - D_ {m} \ cdot C_ {0} \ cdot \ Delta i \}$
• ${\ displaystyle \ Delta C_ {0}}$: Change in market value
• ${\ displaystyle D_ {m}}$: modified duration
• ${\ displaystyle C_ {0}}$: Market value
• ${\ displaystyle \ Delta i}$: Change in interest rate
##### Determination of the partial credit amount for the general interest rate risk
• Net interest positions are classified into maturity bands according to their duration. Then the corresponding course change is calculated.
##### Offsetting within maturity bands

Closed bank positions have a 5% weight

##### Netting within maturity zones

There are three maturity zones: a short-term with a duration of less than a year, a medium-term with a duration of less than 3.6 years and a long-term with a duration of over 3.6 years. A closed position receives a 40% weight if it is short, and a 30% weight if it is medium and long.

##### Netting between the respective maturity zones

Then the open positions are netted. For short and medium, a closed zone balance of 40% applies, for medium and long, if it is open in the medium term.

##### Open positions

Backing of the remaining open position with 100%.

An unbalanced duration balance can be compensated by the following measures:

• by taking on liabilities with high duration and investing assets with low duration, this also applies to new contracts
• through the use of suitable derivatives

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