chapter 8; interest risk i

Interest Rate Risk I

Chapter 8

Copyright © 2010 McGraw-Hill Ryerson Ltd., All Rights Reserved..

Prepared by Lois Tullo, Schulich School of Business, York University

FINA 481 Fall 2015 A.Addas 2

Chapter Outline • This chapter looks at techniques used by FIs to

measure interest rate risk:– Monetary policy– Repricing model– Maturity model– Duration model– Term structure of interest rate risk– Theories of the term structure of interest

rates


Loanable Funds Theory

• Interest rates reflect supply and demand for loanable funds

• Shifts in supply or demand generate interest rate movements as market forces establish a new equilibrium


Determination of Equilibrium Interest Rates


Bank of Canada & Interest Rates

• Bank of Canada– Sets target ranges for inflation then adjusts the

overnight rate to achieve its inflation target.• Current target overnight rate = 0.5%

– Bank rate is the rate the BOC charges for one-day loans it makes to Fis

• Current bank rate = 0.75%– BOC pays attention to the action of other central

banks, mainly the Federal Reserve in the US.


CAD & US Central Bank Rates

Recent

http://www.tradingeconomics.com/canada/interest-rate


Central Bank and Interest Rates

• Target is primarily short term rates.– Focus on BOC overnight Rate in particular.

• Interest rate changes and volatility increasingly transmitted from country to country.– Statements by Fed Chair Ben Bernanke can have

dramatic effects on world interest rates• Notice May 2013



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United States Treasury Constant Maturity - 09/29/2015United States Treasury Constant Maturity - 7/28/2000United States Treasury Constant Maturity - 5/25/1990

Term

rate


Repricing Model• Repricing or funding gap model based on book value.• Repricing gap is the difference between the rate

sensitivity of each asset and the rate sensitivity of each liability: RSA - RSL.– Specifically it is the gap between the interest revenue

earned on assets and the interest paid on liabilities (called Net Interest Income) over a fixed time period

• Rate sensitivity means the interest rate paid or earned is liable to change over that time period


Repricing Model• If RSA < RSL => Refinancing risk• If RSA > RSL => Reinvestment risk

• Contrasts with market value-based maturity and duration models recommended by the Bank for International Settlements (BIS).


Maturity Buckets• Commercial banks must report repricing gaps

for assets and liabilities with maturities of:– One day.– More than one day to three months.– More than 3 three months to six months.– More than six months to twelve months.– More than one year to five years.– Over five years.


Maturity Buckets• Repricing will occur as a result of a rollover of

an asset or liability:– .e.g. a loan is paid off at or prior to maturity and the

funds are used to issue a new loan at current market rates


Repricing Gap Example


Applying the Repricing Model

• DNII = Change in Net Interest Income • DNIIi = (GAPi) DRi = (RSAi - RSLi) Dri

• GAPi = Dollar size of gap between BV of RSAa and RSLs in maturity bucket i


Applying the Repricing Model

Example: In the one day bucket, gap is -$10 million. If rates rise

by 1%, DNII(1) = (-$10 million) × .01 = -$100,000.


Applying the Repricing Model• Example II: We can also consider the cumulative 1-year gap,

DNII = (CGAPone year) DR = (-$15 million)(.01) = -$150,000.DR being the average interest rate change affecting

assets and liabilities that can be repriced within a year


Rate-Sensitive Assets• Table 8.2: a hypothetical balance sheet


Rate-Sensitive Assets• Example from (Table 8.2):

– Short-term consumer loans. If repriced at year-end, would just make one-year cutoff.

– 3-month T-bills repriced on maturity every 3 months.– 6-month T-bills repriced on maturity every 6 months.– 25-year floating-rate mortgages repriced (rate reset)

every 6 months.– => Total 1-year RSAa = $155 million– Remaining $115m not rate sensitive over 1 yr repricing horizon

(i.e. a change in interest rates will not affect the size of the interest revenue generated by these assets over the next year.


Rate-Sensitive Liabilities• RSLs bucketed in same manner as RSAs.• Demand deposits and passbook savings

accounts warrant special mention.– Generally considered rate-insensitive (act as core

deposits), but there are arguments for their inclusion as rate-sensitive liabilities because individuals may draw down their demand deposits


CGAP Ratio• May be useful to express CGAP in ratio form

as,CGAP/Assets.

– Provides direction of exposure and – Scale of the exposure.

• Example: – CGAP/A = $15 million / $270 million = 0.056, or 5.6

percent.


Equal Rate Changes on RSAs, RSLs

• Example: Suppose rates rise 1% for RSAs and RSLs. Expected annual change in NII,

DNII = CGAP × D R= $15 million × .01= $150,000

• With positive CGAP, rates and NII move in the same direction.

• Change proportional to CGAP.


Equal Rate Changes on RSAs, RSLs


Unequal Changes in Rates• If changes in rates on RSAs and RSLs are not

equal, the spread changes. In this case, DNII = (RSA × D RRSA ) - (RSL × D RRSL )


Unequal Rate Change Example

• Spread effect example: RSA rate rises by 1.2% and RSL rate rises by 1.0%

DNII = D interest revenue - D interest expense = ($155 million × 1.2%) - ($155 million × 1.0%)

= $310,000


Example of Rate Changes


Interest Rate vs. Spread Changes


Restructuring Assets & Liabilities

• The FI can restructure its assets and liabilities, on or off the balance sheet, to benefit from projected interest rate changes.– Positive gap: increase in rates increases NII– Negative gap: decrease in rates increases NII


Weaknesses of Repricing Model• Weaknesses:

– Over-aggregation• Distribution of assets & liabilities within individual

buckets is not considered. Mismatches within buckets can be substantial.

– Ignores effects of runoffs• Bank continuously originates and retires consumer and

mortgage loans. Runoffs may be rate-sensitive.– Ignores market value effects and off-balance sheet (

OBS) cash flows.

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The Over Aggregation Problem(Figure 8-3)

FINA 481 Fall 2015 A.Addas

32

The Run-Off Problem

Runoff Periodic cash flow of interest and principal amortization payments on long-term assets, such as conventional mortgages, that can be reinvested at market rates.


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Off Balance Sheet Items

RSAs and RSLs used in the basic re-pricing model include only the assets and liabilities listed on the balance sheet. Changes in interest rates will affect the cash flows on many off-balance-sheet (OBS) instruments as well.



The Maturity Model• Explicitly incorporates market value effects.• For fixed-income assets and liabilities:

– Rise (fall) in interest rates leads to fall (rise) in market price.

– The longer the maturity, the greater the effect of interest rate changes on market price.

– Fall in value of longer-term securities increases at diminishing rate for given increase in interest rates.


Maturity of Portfolio• Maturity of portfolio of assets (liabilities)

equals weighted average of maturities of individual components of the portfolio.

• Principles stated on previous slide apply to portfolio as well as to individual assets or liabilities.

• Typically, maturity gap, MA - ML > 0 for most banks and thrifts.


Effects of Interest Rate Changes

• Size of the gap determines the size of interest rate change that would drive net worth to zero.

• Immunization and effect of setting MA - ML = 0.


Maturities and Interest Rate Exposure

• If MA - ML = 0, is the FI immunized?– Extreme example: Suppose liabilities consist of 1-

year zero coupon bond with face value $100. Assets consist of 1-year loan, which pays back $99.99 shortly after origination, and 1¢ at the end of the year. Both have maturities of 1 year.

– Not immunized, although maturity gap equals zero.

– Reason: Differences in duration** **(See Chapter 9)


Maturity Model• Leverage also affects ability to eliminate

interest rate risk using maturity model.– Example:

Assets: $100 million in one-year 10-percent bonds, funded with $90 million in one-year 10-percent deposits (and equity).

Maturity gap is zero but exposure to interest rate risk is not zero.


Duration• The average life of an asset or liability.• The weighted-average time to maturity using

present value of the cash flows, relative to the total present value of the asset or liability as weights.


Term Structure of Interest Rates

Time to Maturity

Time to Maturity

Time to Maturity

Time to Maturity

YTMYTM


Unbiased Expectations Theory• Yield curve reflects market’s expectations of

future short-term rates.• Long-term rates are geometric average of

current and expected short-term rates._ _ ~ ~

RN = [(1+R1)(1+E(r2))…(1+E(rN))]1/N - 1


Market Segmentation Theory

• Investors have specific needs in terms of maturity.

• Yield curve reflects intersection of demand and supply of individual maturities.


Liquidity Premium Theory

• Allows for future uncertainty.• Premium required to hold long-term.

The Relationship Between the Liquidity Premium and Expectations Theory


Chapter Summary• This chapter looked at techniques used by FIs

to measure interest rate risk:– Monetary policy– Repricing model– Maturity model– Duration model– Term structure of interest rate risk– Theories of the term structure of interest rates


Pertinent Websites• For information related to central bank policy,

visit:Bank for International Settlements: www.bis.orgFederal Reserve Bank: www.federalreserve.gov

http://www.bis.org/

http://www.federalreserve.gov/

chapter 8; interest risk i

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