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PS6Solutions_09

# PS6Solutions_09 - Solutions to*NEW Problem Set 6...

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Solutions to **NEW** Problem Set 6 Investments Prof. Pierre-Olivier Weill 1. Suppose you buy a seven-year zero-coupon Treasury bond, with a face value of \$1000, at a price P 0 = \$600. Answer the following questions: (a) What is the yield to maturity (YTM) on the bond? (assume annual compounding) Solution: By definition the YTM of the bond is equal to parenleftbigg 1000 600 parenrightbigg 1 / 7 - 1 = 7 . 57% (b) Suppose that, in year t = 1, the YTM of the bond increases to 10% and remains equal to 10% until year t = 7. i. Calculate your annualized holding period return if you buy the bond in year t = 0 and sell it in year t = 1. ii. Calculate the annualized holding period return if you buy the bond in year t = 1 and sell it in year t = 7. iii. Calculate your annualized holding period return if you buy the bond in year t = 0 and sell it in year t = 2. Solution: If, in year t = 1, the YTM is equal to 10%, then the price of the bond is P 1 = 1000 (1 + 0 . 1) 6 = \$564 . 4739 , keeping in mind that, at t = 1, there are only 6 years left to maturity. Similarly, the price in year t = 2 is equal to P 2 = 1000 (1 + 0 . 1) 5 = \$620 . 9213 . Lastly, the price in year 7 is always equal to \$1000. Thus the annualized holding period return from buying the bond at t = 0 and selling at t = 1 is P 1 P 0 - 1 = 564 . 4739 600 - 1 = - 5 . 92% .

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