Market rate method

The market interest rate method (MZM) is a method for identifying sources of success in bank calculations . It determines the profit contribution of an interest rate transaction compared to an alternative market interest rate ( opportunity ). Each banking transaction is contrasted with a capital market transaction with the same maturity behavior ( maturity congruence ) as an opportunity transaction . According to the principle of opportunity, instead of lending to a customer, the money could be invested in the capital market . Instead of accepting savings, the bank could borrow the money it needs for refinancing on the money and capital market (GKM).

Basic idea and objective

The main objective of the market interest rate method is to identify sources of success in the bank's value range and to determine the earnings contributions from individual transactions (on the assets and liabilities side). The individual transaction-related valuation is carried out using alternative GKM transactions.

Compared to traditional methods

While assets and liabilities are always linked horizontally in traditional methods ( pool method, stratified balance method ) , with the market interest rate method the money and capital market is pushed between the assets and liabilities side and serves as a benchmark for the earnings contribution of both lending and deposit business .

Split of earnings contributions

This also enables the profit contributions to be split into a condition contribution and a structure contribution. The former illustrates the level of net interest income from the individual transactions and corresponds to a so-called gross margin. The latter illustrates the additional profits that result from maturity transformation . Maturity transformation generally means the revolving short-term refinancing of long-term loans.

starting point

The market interest method is based on current investment theory . The decision criterion in perfect markets under security is the net present value (NPV). The investment to be valued is valued with an equivalent portfolio of financial stocks from the money and capital markets.

Segmentation of markets

However, the markets are segmented:

• A complete and perfect money and capital market prevails on the interbank market (which is a requirement of classical investment theory, but is not a premise of the market interest rate method, because this is based solely on the assumption of a money and credit market on which GKM papers are risk-free )
• However, bank customers only have indirect access through a financial intermediary . The financial intermediary demands a market access premium, the conditional contribution value .

The contribution from maturity transformation results from financing long-term loans through short-term, revolving deposits.

method

The market interest method separates the success from the better conditions in customer business compared to the money and capital markets (the condition contribution ) from the success from the maturity transformation (the structural contribution ).

Condition contribution / condition margin

The condition margin is:

• the condition margin of a lending transaction is equal to the difference between its interest rate and the capital market interest rate with the same deadline
• the condition margin of a deposit transaction is equal to the difference between the capital market interest rate with the same deadline and the interest rate of the deposit transaction.

Example:

• GKM interest rate for 2 years: 7%
• Loan for 2 years: 9% Condition margin: 2% ${\displaystyle \rightarrow }$
• Deposit 2 years: 4% condition margin 3% ${\displaystyle \rightarrow }$

Structural contribution / structural margin

A structural margin arises with maturities in congruent investment and refinancing.

Exemplary representation of the conditional contribution and the structural contribution (active)

Example:

• Debit interest 9%, credit interest 4%
• GKM interest rate for 2 years: 7%
• GKM interest rate for 1 year: 6%

Volume: 1000

• Loan for 2 years: Debit interest (2 years) - GKM interest (2 years) = condition margin (active): 9% -7% = + 2%

${\displaystyle \rightarrow }$Conditional margin (active) Volume = Conditional contribution (active) 0.02 1000 = 20 ${\displaystyle \Rightarrow }$

• Deposit 1 year: GKM interest (1 year) - credit interest (1 year) = condition margin (passive): 6% -4% = + 2%

${\displaystyle \rightarrow }$Conditional margin (passive) Volume = Conditional contribution (passive) 0.02 1000 = 20 ${\displaystyle \Rightarrow }$

• ${\displaystyle \rightarrow }$GKM 2 years (7%) - GKM 1 year (6%) = +1% corresponds to the structural margin. ${\displaystyle \Rightarrow }$

Structural margin volume = structural contribution = 10

Debit interest 9% volume = interest income = 90

Credit interest 4% volume = interest expense = 40

Interest income - interest expense = net interest income = 50 = structural contribution + conditional contribution (ak) + conditional contribution (pa)

Calculation of the present value condition contributions

E.g .: loan amount 100, 2 years term, interest 10% p. a. Repayment 50% p. a.

Cash flows
time	${\displaystyle t_{0}}$	${\displaystyle t_{1}}$	${\displaystyle t_{2}}$
Financial title 1	'-1	'1.06
Financial title 2	'-1	0.07	1.07
credit	'-100	60	55

An equivalent portfolio is a portfolio with equal repayment in and as out of the loan. ${\displaystyle t_{1}}$ ${\displaystyle t_{2}}$

Solution of the system of equations

${\displaystyle 1{,}06x_{1}+0{,}07x_{2}=60}$

${\displaystyle 0x_{1}+1{,}07x_{2}=55}$

The conditional contribution value of the loan is equal to the difference between the payments from this equivalent portfolio and the loan at the time : ${\displaystyle t_{0}}$

${\displaystyle x_{1}+x_{2}-100=C_{0}}$

Extension of the equation to include the payment settlement through the liquidity-effective withdrawal of the KB cash value ${\displaystyle C_{0}}$

${\displaystyle C_{0}-x_{1}-x_{2}=-100}$

If the investment and refinancing interest rates are equal to the GKM interest rates, one can record in such a way that the customers bring in the necessary repayments. But you only have to pay 100. remains as the present value of the condition contribution. ${\displaystyle 100+C_{0}}$ ${\displaystyle C_{0}}$

The maturity transformation is an essential difference to the current investment theory.

mechanism

The difference between the customer interest and the opportunity interest, i.e. H. the interest condition contribution forms the interest on the opportunity business. The complementary differences summed up over the assets and liabilities side form the structural contribution. The structural contribution describes the success that the bank achieves as a result of the maturity transformation. However, a one-sided excess deadline always means a market risk. The yield curve can move in an unexpected direction over time, which can adversely affect the bank's performance. These market risks can be eliminated within the framework of balance sheet structure management using appropriate derivative instruments. In return, however, the costs of this protection will more or less consume the structural contribution.

Alternative option for calculating the present value of the condition contribution

The assumptions of the state preference theory are adopted, whereby in their simple case a future point in time can have several states. A pure security pays 1 monetary unit in one state. The price in is then the state price . ${\displaystyle t_{0}}$

With the market interest rate method, we instead consider several future points in time with secure payments (abstractly the same). A pure security (zero bond with different maturities) then pays 1 monetary unit at a time. The state prices are interpreted as discount factors.

Calculation of the net present value

The prices of the securities, spot interest rates and forward interest rates are used for this purpose. Discount factors can be derived from this (discount structure).

There are 3 methods:

• ${\displaystyle {\text{Zahlungsstrom Kredit in }}t_{1}\cdot AF_{01}+{\text{Zahlungsstrom Kredit }}t_{2}\cdot AF_{02}-{\text{Zahlungsstrom in }}t_{0}=C_{0}}$
• Matrices

${\displaystyle {\begin{pmatrix}1&-1&-1\\0&1{,}06&0{,}07\\0&0&1{,}07\end{pmatrix}}\cdot {C_{0} \choose x}={\begin{pmatrix}ZSt_{0}\\ZSt_{1}\\ZSt_{2}\end{pmatrix}}}$

• Inverse

${\displaystyle {C_{0} \choose x}={\begin{pmatrix}1&AF_{01}&AF_{02}\\0&AF_{01}&0{,}07\\0&0&1{,}07\end{pmatrix}}\cdot {\begin{pmatrix}ZSt_{0}\\ZSt_{1}\\ZSt_{2}\end{pmatrix}}}$

The elements of the first line of the inverse coefficient matrix indicate the price of the "pure securities" (synthetically generated zero bonds) from the point of view of the starting point, which pay out in 1 MU and in all other points in time 0 monetary units. The number n corresponds to the column number. The first line of the inverse represents the discount rates. ${\displaystyle t_{n}}$

Periodic condition contribution

There are two options:

• Withdrawal of the condition contribution at the time ${\displaystyle t_{0}}$
• Distribution of the effective condition margin on the time axis

Periodic condition contributions : condition margin · undiscounted capital balance of the individual periods.

Effective condition margin = condition contribution / annuity basis; it serves to distribute the capital effectively tied up over the individual maturity periods.

Annuity base : Sum of the present values ​​of the capital base

Capital base : sequence of the effective capital balances, d. H. the bound capital of the individual periods.

Calculation of the pension base
time	${\displaystyle t_{0}}$	${\displaystyle t_{1}}$	${\displaystyle t_{2}}$
Capital base		100	50
Discount factors		0.943	0.873
Cash values		94.3	43.6
Annuity base	137.98

• With a KB present value of 4.61, this results in an effective condition margin of 3.34%.
• This results in the periodic condition contributions: 3.35 (100 · 0.0334) and 1.67 (50 · 0.0334).
• Discounted, this results in the condition contribution value: 4.61 (3.34 0.943 + 1.67 0.873).

Term transformation and structural contribution

With a normal interest rate structure, banks can generate additional profits through revolving short-term refinancing of long-term loans . Revolving means that the deposits are accepted again and again after the repayment and that new funds flow into the bank again and again.

It must therefore be between the part of the net interest income:

• through conditioning and
• by speculating on a favorable interest rate development

can be distinguished.

Period 1

Structural contribution in period 1 = (net interest income) - (net interest income if maturities match)

Period 2

Structural contribution in period 2 depends on the then applicable refinancing conditions. This is the interest rate on the newly raised liabilities.

The refinancing rate can

• either correspond to the implicit forward interest rate
• or deviate from the implicit forward rate.

Result

• The implied forward interest rate simply means a profit shift between the periods.

Another interest rate means a present value of the structural contribution not equal to 0

The implicit forward interest rate serves as a benchmark for maturity transformation decisions.

We accept revolving refinancing with one-year GKM funds and the withdrawal of condition contributions

${\displaystyle {\text{Strukturbeitrag}}={\text{Zinsüberschuss}}-{\text{Zinsüberschuss bei fristenkongruenter Refinanzierung}}}$

Influence of the yield curve (ZSK)

The interest rate structure influences the structural contribution as follows:

• With normal ZSK, banks can initially generate additional profits through revolving short-term refinancing of long-term loans (positive structural contribution today)
• flat ZSK: no structural contribution
• inverse ZSK: negative structural contribution

Refinancing not with matching maturities

When it comes to the effects of refinancing that does not match maturities, a distinction must be made between two cases:

1. The refinancing rate corresponds exactly to the implicit forward interest rate, which is calculated from the interest rate structure at point in time . ${\displaystyle t_{0}}$
2. The refinancing costs differ from the implicit forward interest rate. The present value of the structural contributions is usually not equal to zero.

Security about future interest rates

To be sure, the future spot interest rates must correspond to the respective current implicit forward interest rates . If this condition were violated, there would be an arbitrage opportunity . If the condition is valid, the present value of the structure contributions is always zero ( consistency condition ). This means that maturity transformation only shifts profits between the periods, but does not generate additional earnings contributions.

${\displaystyle SB_{n}}$: Structural contribution in period ${\displaystyle t_{n}}$

${\displaystyle AF_{n}}$: Discount factor in period ${\displaystyle t_{n}}$

The validity of the consistency condition therefore includes:

${\displaystyle SB_{1}\cdot AF_{1}+SB_{2}\cdot AF_{2}=0}$

Alternative:

Structural contribution in the period from the refinancing of 100,000 euros results from the one-year investment in refinancing over the third bond that is relative to maturity-congruent refinancing. ${\displaystyle t_{3}}$ ${\displaystyle t_{2}}$

Post calculation

The post calculation includes a control function. It reveals fundamental calculation errors. It gives indications of inefficiencies through z. B. periodic target / actual comparisons. Post calculation of the interest result, e.g. B. relevant in Treasury to determine the maturity transformation result. The post calculation is not necessary to determine the success of the customer advisor. The condition contribution is only determined by the GKM interest rates at the time of the transaction. The customer advisor is not responsible for future interest rate changes. The condition contribution therefore remains unaffected.

criticism

theory

The starting point of the market interest method is the current investment theory , in which the investment to be valued is formed by an equivalent portfolio of financial market stocks from the money and capital markets.

• liquid market
• no transaction costs
• no differences in the determination of the interest rate structure from swap markets and from coupon bonds

The market interest rate method is a model that is idealized in several respects, but this is in the nature of a model. The contradiction to other models does not necessarily mean that this is unusable.

practice

Application problems for the market interest method arise from the requirements of the overall bank management

• Measures to control the interest rate risk
• Measures to control liquidity
• Limitation of equity

and from various market imperfections. Examples are

• Bid-ask spreads : divided capital market
• regulatory restrictions
• as well as for the valuation of variable interest rate transactions: only applicable to fixed rate transactions or until the next adjustment date.

Requirements for banking results information

Separation of sources of success is ensured by separating the condition contribution and structural contribution in the market interest method.

The data used within the market interest method are sufficiently up-to-date (GKM rates) and correspondingly objective. These are market prices.

Since the condition contribution of a customer transaction is only determined by the GKM interest rates observed at the time of the transaction, the same condition contribution results in the pre- and post-calculation when using the corresponding interest rates.

The market interest method uses GKM transactions for valuation. In principle, these can also be carried out. A problem arises insofar as the market interest method assumes a perfect and “exciting” money and capital market. In reality, e.g. B. Term and volume restrictions exist.

The information on the results of the market interest method is factually correct; however, they do not contain all information relevant to the valuation, since only the respective individual transaction (only cash flow related) and not the entire customer relationship is considered.

The market interest method does not make particularly high demands in terms of computation.

The idea of ​​the market rate method is understandable. By comparing the interest rates of the customer transactions with the GKM interest rates to be announced, the calculation of the condition contribution is easy to understand. The same applies to the term transformation contribution.