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# Measuring and Managing Interest Rate Risks

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Critically evaluate the re-pricing model, maturity model and duration model that are used by financial institutions for measuring and managing interest rate risk. Your answer should also indicate the method preferred by the BIS and the reasons why this is the case. Interest risk is the possibility of unexpected adverse changes in interest revenues and expenses. It can be shown that interest rate changes are unpredictable almost 100%. They depend on monetary policy; supply and demand, inflation etc. These in turn depend on many other factors. So how do financial institutions manage the risk of fluctuating interest rates give that they cannot predict it? The immunization of a portfolio against interest rate risk means that the portfolio will neither gain nor lose value if interest rates change. In this essay we will look at some of the different models used by financial institutions for managing interest rate risk. They are the re-pricing model, the maturity model and the duration model. We will describe them and evaluate the comparative advantages and disadvantages each model assumes. Firstly we consider the re-pricing model. It is a balance sheet where assets and liabilities are grouped according to the time periods in which the different assets and liabilities are rate sensitive. Assets or liabilities are rate sensitive within a given time period if the values of each are subject to receiving a different interest rate should market rates change. These groupings are referred to as ‘maturity buckets’. Then ‘Gap analysis’ is conducted where the rate sensitive liabilities are subtracted from rate sensitive assets for each maturity bucket. This is called the GAP. It can be shown that GAP * interest change = net interest income (or profit) change or the interest margin. We can also calculate the cumulative gap(CGAP) by adding up the gaps in the brackets over a period of time, for example 1 year. As long as CGAP&lt;0, there exists a net negative effect of a rate increase on net interest income. For each moment in time CGAP * interest change indicates how much higher or lower at that moment the net interest income is. The idea is that the risk can be managed by reducing gaps in individual maturity ‘buckets’ towards zero by using different combinations of assets and liabilities of different maturities. The advantage of this model is that is simple to use. The disadvantages are that it is static. That is, it only uses current balances without taking into account possible growth or changes in activities. It captures a specific moment in time as if nothing else would change, but there will be a change because interest rate fluctuation continues. In addition the model assumes that all rate sensitive assets and liabilities follow the change in market interest rates 100% at their moment of re-pricing which is not always the case. Short-term assets may change faster than long-term assets and some financial contracts limit rate adjustment. If the chosen maturity buckets are too long, the re-pricing model may produce inaccurate results because there may be large differences in the time to re-pricing for different securities within each maturity bucket. Similarly, the maturity gap for a bank is the average maturity of the assets minus the average maturity of the liabilities within each maturity bracket. For a given change in interest rates, fixed-rate assets with longer-term maturities will have greater changes in price than assets with shorter maturities. We can immunise the balance sheet by matching the maturities of assets and liabilities. From the standpoint of the maturity model, if the average maturity of assets is 1.5 years and the average maturity of liabilities is 1.5 years, and then the FI has no interest rate risk exposure. A major shortcoming of the maturity and the re-pricing model is its neglect of reinvestment income on interim cash flows and the timing of the cash flows is likely to differ between the assets and liabilities. A duration model uses the maturity or re-pricing schedule but applies sensitivity weights to each time band. Such weights are based on estimates of the duration of the assets and liabilities that fall into each time band. Duration is a measure of the percentage change in the economic value of a position that will occur given a small change in the level of interest rates under the simplifying assumptions that changes in value are proportional to changes in the level of interest rates and that the timing of payments is fixed. An average duration is assumed for the assets and liabilities within each maturity bracket. The average durations are then multiplied by an assumed change in interest rates to construct a weight for each time band. The weighted gaps are aggregated across time bands to produce an estimate of the change in net interest income for the bank. The BIS, an international organisation for central banks and other agencies in pursuit of monetary and financial stability, regularly publishes reviews and guidelines for financial institutions. It advises that estimates derived from a standard duration approach may provide an good approximation of a bank’s exposure to in interest rates for relatively non-complex banks. However, for more complex banks it advises modified models that relax some assumptions of the standard duration model such as the linearity between percentage changes in value and percentage change in market interest rate and the assumption that cash flows are fixed, which is an important limitation of standard duration models. Foe example an institution could estimate the effect of changing market rates by calculating the precise duration of each asset and liability and then deriving the net interest income for the bank. The answer is the based on more accurate duration measures. More complex models are available, such as various simulations based on predicting the future interest rate movement using Monte Carlo simulations and which take into account various other factor such as consumer behavior, for example, and attempts to model it. The BIS warns that these models, while more comprehensive require more care and are only as good as the assumptions used. They advise effective management and frequent re-assessment of assumptions underlying the model. Sources. https://www.frbsf.org/publications/economics/letter/2004/el2004-26.html https://www.few.eur.nl/few/people/smant/a1609/notes/c4_fininst2-riskintr.pdf https://www.bis.org/publ/bcbs108.pdf

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