You hold a portfolio of $40 million in 1-year zero-coupon Government bonds and $60 million in...

 

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You hold a portfolio of $40 million in 1-year zero-coupon Government bonds and $60 million in 10-year Government bonds. The yield curve is flat with yields to maturity on all Government bonds of 6% per year. The 10-year Government bonds are currently trading at their par value. You decide to switch to a portfolio of corporate debt, consisting of $30 million of BBB-rated securities yielding 7.5% per year and $70 million of distressed debt yielding 9.5% per year. The investment-grade debt pays semi-annual coupons of $1 million for your $30 million investment and the term to maturity is 6 years. The distressed debt is not expected to pay coupons, but will make a single payment at expiry should there be no further defaults. It has a term to maturity of 3 years. Immediately after your switch to corporate bonds, the yield on Government bonds decreases to 5% per year, and all credit spreads tighten by 0.5% (Assume semi-annual compounding) (a) (15 marks) Calculate the Modified Duration and Convexity for your new portfolio. Estimate the new value of your portfolio following these interest rate changes. (b) (15 marks) Repeat (a) using effective Modified Duration and effective Convexity. (c) (15 marks) Suppose you maintained your position in Government bonds. Estimate the value of your portfolio following these interest rate changes. You hold a portfolio of $40 million in 1-year zero-coupon Government bonds and $60 million in 10-year Government bonds. The yield curve is flat with yields to maturity on all Government bonds of 6% per year. The 10-year Government bonds are currently trading at their par value. You decide to switch to a portfolio of corporate debt, consisting of $30 million of BBB-rated securities yielding 7.5% per year and $70 million of distressed debt yielding 9.5% per year. The investment-grade debt pays semi-annual coupons of $1 million for your $30 million investment and the term to maturity is 6 years. The distressed debt is not expected to pay coupons, but will make a single payment at expiry should there be no further defaults. It has a term to maturity of 3 years. Immediately after your switch to corporate bonds, the yield on Government bonds decreases to 5% per year, and all credit spreads tighten by 0.5% (Assume semi-annual compounding) (a) (15 marks) Calculate the Modified Duration and Convexity for your new portfolio. Estimate the new value of your portfolio following these interest rate changes. (b) (15 marks) Repeat (a) using effective Modified Duration and effective Convexity. (c) (15 marks) Suppose you maintained your position in Government bonds. Estimate the value of your portfolio following these interest rate changes.

Answer rating: 100% (QA)

a The Modified Duration and Convexity for your new portfolio are as follows Modified Duration 375 ye... View the full answer