Question

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4. Consider a bond of face value $1,000 with an annual coupon of 8.0% and 10 years to maturity and a present price of $877.11. Assume the yield curve is flat at 10%. a. Calculate the duration and convexity for this bond. b. Suppose your portfolio consists of this bond only and you want to immunize your interest risks. And suppose you can only buy or sell 1 zero-coupon bond. What should be the maturity of this zero-coupon bond? (Hint: consider now only - in the future, you can rebalance.)

Answer 1

Sheet1 Answer a) Colculation of Duration formula for Calculation of and convexity of the Bond Duration L + 2x e nx Interest & Redemption Aman ix Bo L Interest (tk) Interest t (1 kg)² Bo = Present Price se $877111 Interest - Coupon Amount ie $1000 X 84 = 80 k = Redemption n a Putting Yield to maturity i.e 10% ie o.1 Amount = 1000 number of years ie maturity - 10 above values in formula 2x Go lox (80 +1000) 70* (1.16 0.00114 / 72.73 + 132.23 + 180.32 + 218.56+ 248.27 + 270.95 + 287.37 +298.56+ 305.35+4163.87/ - 7.04 Years

Duration = Sheet -2 7.04 years Calculation of converity of Bond Converity of a bond Duration can be calculated through modified - modified Duration - Duration - where yTM & Yield to maturity le lor. modified Duration - 7.04 Itloy. = 7.04 a 6.4 7. means Convexity is 6.4 % Answer (6) - Immunization is an investment strategy used to minimize the interest rate risk o bond Investments by adjusting the portfolio duration to match the investor's investment time horizon. SCOPE

Sheet-3 for immunization Duration of Assets - Duration of liabilities Duration of Portfolio - Duration of zero Coupon bond Duration of Portfolio a 7.04 years Duration of 2000 Coupon bond = maturity of zero Coupon bond Duration of Portfolio - Duration of zero Coupon bond - 7,04 years = maturity of zero coupon bond there for maturity of zero coupon bond should be 7,04 Years for immunization. "