Consider a financial institution whose asset and liability both consist of coupon bonds only. The asset is a 10-year bond with face value $100 million, coupon rate 9.8% and yield 4%, while the liability is a 15-year bond with face value $100 million, coupon rate 8.2% and yield 4%. Both bonds pay coupon semiannually. Assume parallel yield shift. Required precision: 4 digits after decimal point for duration calculation; 2 digits after decimal point for dollar amount in million, e.g. $12.34 million; 4 digits after decimal point for percentage (coupon) rates, e.g. 1.2345%. (a) What are the market values of asset, liability and equity of this FI? What is its leverage-adjusted modified duration gap? (b) According to the duration model, what would the market value of equity be for a 10 basis points decrease in the yield? (c) To immunize itself from interest rate risk, the FI plans to restructure its asset bond by adjusting its face value and coupon rate, while keeping the bond's value (and hence the market value of asset), maturity and yield unchanged. What should be the new face value and coupon rate? (Hint: Write out and solve two equations, one for matching the market value of assets before and after the restructuring, and the other for eliminating the leverage-adjusted modified duration gap after the restructuring.)
Consider a financial institution whose asset and liability both consist of coupon bonds only. The asset is a 10-year bond with face value $100 million, coupon rate 9.8% and yield 4%, while the liability is a 15-year bond with face value $100 million, coupon rate 8.2% and yield 4%. Both bonds pay coupon semiannually. Assume parallel yield shift. Required precision: 4 digits after decimal point for duration calculation; 2 digits after decimal point for dollar amount in million, e.g. $12.34 million; 4 digits after decimal point for percentage (coupon) rates, e.g. 1.2345%. (a) What are the market values of asset, liability and equity of this FI? What is its leverage-adjusted modified duration gap? (b) According to the duration model, what would the market value of equity be for a 10 basis points decrease in the yield? (c) To immunize itself from interest rate risk, the FI plans to restructure its asset bond by adjusting its face value and coupon rate, while keeping the bond's value (and hence the market value of asset), maturity and yield unchanged. What should be the new face value and coupon rate? (Hint: Write out and solve two equations, one for matching the market value of assets before and after the restructuring, and the other for eliminating the leverage-adjusted modified duration gap after the restructuring.)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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(Immunization of FI) Consider a financial institution whose asset and liability both consist of coupon bonds only. The asset is a 10-year bond with face value $100 million, coupon rate 9.8% and yield 4%, while the liability is a 15-year bond with face value $100 million, coupon rate 8.2% and yield 4%. Both bonds pay coupon semiannually. Assume parallel yield shift. Required precision: 4 digits after decimal point for duration calculation; 2 digits after decimal point for dollar amount in million, e.g. $12.34 million; 4 digits after decimal point for percentage (coupon) rates, e.g. 1.2345%.
(a) What are the market values of asset, liability and equity of this FI? What is its leverage-adjusted modified duration gap?
(b) According to the duration model, what would the market value of equity be for a 10 basis points decrease in the yield?
(c) To immunize itself from interest rate risk, the FI plans to restructure its asset bond by adjusting its face value and coupon rate, while keeping the bond's value (and hence the market value of asset), maturity and yield unchanged. What should be the new face value and coupon rate? (Hint: Write out and solve two equations, one for matching the market value of assets before and after the restructuring, and the other for eliminating the leverage-adjusted modified duration gap after the restructuring.)
(d) Assume the immunization in (c) is successfully implemented. Immediately after the implementation, the yields of both bonds decrease from 4% to 3.9%. What are the market values of asset, liability and equity now?
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