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Unformatted text preview: Interest Rate Risk the Maturity Model and the Duration Model 62 Overview This lecture defines and explores various sources of interest rate risk. We discuss the concept of the maturity model as one way of measuring interest rate risk. Using the maturity model as the only interest rate risk measurement tool might give rise to significant problems. Then we discuss a particular interest rate risk measurement and management model: duration. We discuss the general calculation of duration and the calculations for selected types of securities, such as consol bonds. We examine the relationship between the duration of a security and various securities features, such as the coupon rate. We use duration to immunize future payments as well as the whole balance sheet of an FI. Finally, we examine the weaknesses of duration to measure and manage interest rate risk. 63 What is interest rate risk? The structure of a fixedincome security: Principle (face) value Time to maturity Coupon rate Interest rate (yield) Valuation: 1 1 1 (1 ) Pr * Pr (1 ) (1 ) N t t t N t N t CF P R incipal CouponRate incipal Coupon R R = = = ∑ + + = + ∑ + + Movements in interest rate will cause fluctuation in prices. 54 Interest rate risk and maturity Example: Consider three fixedincome securities, A, B and C. All securities pay an annual coupon of $100 (10% coupon rate) and the principal of $1,000 at the maturity. The remaining time to maturity is 1 year for A, 2 years for B, and 3 years for C. What are the prices of the securities if current interest rates are 10%? Solution: Security A: Security B: Security C: 1 1,100 $1,000 1.1 A P = = 1 2 100 1,100 $1,000 1.1 (1.1) B P = + = 1 2 3 100 100 1,100 $1,000 1.1 (1.1) (1.1) C P = + + = 55 Interest rate risk and maturity What happens if interest rates on all securities simultaneously rise by 1% to 11% p.a.? Solution: Security A: Security B: Security C: 2 1,100 $991.0 1.11 0.9% A A P P = = ∆ =  2 2 100 1,100 $982.9 1.11 (1.11) 1.71% B B P P = + = ∆ =  2 2 3 100 100 1,100 $975.6 1.11 (1.11) (1.11) 2.44% C C P P = + + = ∆ =  56 Interest rate risk and maturity Interest rate risk: the market value rises ( falls ) if interest rates fall ( rise ), The use of maturity as a measure of the degree of interest rate risk The longer the maturity, the greater the fall or rise in market value for any given interest rate increase or decrease . The fall in the value of longerterm securities increases at a diminishing rate for any given increase in interest rates. R P ... R P R P ∆ ∆ < < ∆ ∆ < ∆ ∆ 30 2 1 P R ∆ < ∆ 3 2 2 1 P P P P R R R R ∆ ∆ ∆ ∆ < ∆ ∆ ∆ ∆ 57 Maturity as a measure of interest rate risk for a portfolio of assets and liabilities Where: M i = the weightedaverage maturity of an FI’s assets (liabilities), i = A or L , W ij = the importance of each asset (liability) in the asset (liability) portfolio as measured by the market value of that asset (liability)...
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 Three '11
 Lee
 Interest Rates, Interest, Interest Rate, Bond duration, rate risk

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