Managing+Fixed-Income+Portfolios+Solution

Managing+Fixed-Income+Portfolios+Solution - FINA 221...

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1 FINA 221 Practice Problems Fall 2010 Managing Fixed-Income Portfolios (Suggested Solution) 1. True or False (a) Holding other factors constant, the Macaulay’s Duration of a bond is always increasing with the bond’s maturity. Solution: False. For deep discount bonds, the Macaulay’s Duration of a bond can be decreasing with the bond’s maturity. (b) Using Duration and Convexity to approximate bond price sensitivity to interest rate is more accurate than using Duration alone. Solution: True. The actual bond price sensitivity to interest rate is a not a linear relationship. Using Duration alone would give a straight-line approximation, while using both Duration and Convexity would give an approximation that is closer to the actual sensitivity. (c) The Macaulay’s Duration of a bond cannot be longer than the bond’s maturity. Solution: True. For zero-coupon bonds the Macaulay’s Duration equals the maturity. For coupon bonds the Macaulay’s Duration is shorter than the maturity. (d) If the Macaulay’s Duration is matched to the holding period, then reinvestment risk and price risk would still offset each other under any yield curve changes. Solution: False. When matching the Macaulay’s Duration to the holding period, reinvestment risk and price risk would offset each other only under small parallel changes in the yield curve. (Note: Please remember this fact, even though we have not analyzed non-parallel changes in the yield curve in our course.) 2. Managing Interest Rate Risk
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2 Suppose you purchase a five-year, 15% coupon bond (paid annually) with a yield-to-maturity of 9% per year. The face value of the bond is $1000. (a) Show that the duration of this bond is approximately equal to four years. Solution: First we calculate the bond price: ࡼ࢘࢏ࢉࢋ ൌ ࡯࢕࢛࢖࢕࢔ ൬૚െ ሺ૚൅࢘ሻ ൰൅ ࡲࢇࢉࢋ ࢂࢇ࢒࢛ࢋ $૚૞૙ ૙. ૙ૢ ሺ૚. ૙ૢሻ $૚૙૙૙ ሺ૚. ૙ૢሻ = $1233.379 Then we calculate the duration: ۲ܝܚ܉ܜܑܗܖ ൌ ෍ ܜ ൈ ࢚ୀ૚ ۱۴ ܜ /ሺ૚ ൅ ܡሻ ܜ ۾ܚܑ܋܍ ൌ૚ൈ ૚૞૙/ሺ૚. ૙ૢሻ ૚૛૜૜. ૜ૠૢ ൅૛ൈ ૚૞૙/ሺ૚. ૙ૢሻ ૚૛૜૜. ૜ૠૢ
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Managing+Fixed-Income+Portfolios+Solution - FINA 221...

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