(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?
(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?
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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Please answer all 4 parts and provide all the steps.
Transcribed Image Text:(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?
Transcribed Image Text:(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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