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# EXCH07 - PRACTICE PROBLEMS CHAPTER 4 BOND MATHEMATICS A...

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PRACTICE PROBLEMS CHAPTER 4: BOND MATHEMATICS A word about BEY (i.e., Bond Equivalent Yield). T-bills use semi-annual compounding. So, for n < 365 2 , we use simple interest. Principle + interest is given by P (1 + y × n 365 ) = 100 at maturity. Solving for y gives y BEY = 100 P P × 365 n . For n = 365 2 , we have Principal + Interest = P (1 + y 2 ) Thereafter, i.e., for n > 365 2 , we use simple interest again: P (1 + y 2 )(1 + y × n 365 2 365 ) = 100, which is equivalent to the text’s equation on p. 132. We can use the quadratic equation to solve for y : BEY = − × × × + 2 365 365 2 2 365 100 2 365 2 1 1 1 n n n P n ( ) ( )( ) . Exercise 7.1: An investor buys a face amount \$1 million of a six-month (182 days) U.S. Treasury bill at a discount yield of 9.25%. What is the cost of purchasing these bills? Calculate the bond equivalent yield. Indicate clearly the formula you used and show all the steps in your calculations. Recalculate the bond equivalent yield if the T-bill has a maturity of 275 days. Exercise 7.2: On November 18, 1987, a 7 7 8 % U.S. T-bond maturing on May 15, 1990, was quoted for settlement on November 20, 1987. The last coupon was paid on November 15, 1987. The number of days between coupon payments is 182. The bond’s YTM is 7.91%. (a) What is the invoice price (cash price) of the T-bond? (b) What is the accrued interest on the T-bond? (c) What is the quoted price of the T-bond? (d) What is the exact duration of the T-bond? (e) What is the approximate convexity of the T-bond? (f) Re-do part (a) using the next coupon date; show that the prices are the same. Exercise 7.3: What is the price of a ten-year zero-coupon bond priced to yield 10% under each of the following assumptions? (a) Annual yield. (b) Semi-annual yield. (c) Monthly yield. (d) Daily yield. What is the continuous limit?

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