Question

17. Imagine you are investing for one year and are considering three different bonds, each with a $1000 face value: A one-year treasury bill. A two-year zero coupon Treasury. A ten-year zero coupon Treasury. Today, each bond has a 4% yield to maturity. For each of the following scenarios, compute the return you'd get on each of the three bonds under consideration. A) Yields increase to 5%. B) Yields fall to 2%. Show all calculations.

Answer 1

Solution along with Calculation Current Market Price 0 1 year Treasury boll Price = face Value xl 1 + YTM = $1000 1' = $961:54 1.04 ©_2 year Zero Coupon Treadway Price = $1000 *[ 17 = $1000 x 0.92456 = $ 924:56 Jo year Zero Coupon Trocarry Price = $1000 * 1]" 1.04 - $1000 0.67556 = $675.56

A. if Yield (YTM) Pncreases to 5% (After 1 year) 0 1 year T. bill Value = $ 10o being the face value, as it matures after a year. 2 2 year 2. C. Treasury 7 (Remaining life) price a face value of = $1000 Gos DR YTM = $1000 x 0.95238 - $ 952-38 ② 10 yen Z.C.T. Price = $1000 x L 1.05 = $1000 x 0.64461 = $646.61

B. if Yield (YTM) falls to 2% (After 1 year) I year To Biu. Value = $ 100 (face Value, as it matures) 2 2 Year Zero Coupon Treasury Price = $1000 [ 17 = $(coo * 0.98039 = $ 980:39 > 10 years I. C. Troadwy. Price = $(coor ] Ll.oz. = $1000 x 0.83675 = $836.75

- Return under (A) Return = Price after I year - Current Market Price Return (%) = Return . x 100 Current market price 0 1 year T. BIU Return = $1000 - $961.45 = $38.55 Return (%) = $28.55 $961.45 = 4.01% ar 4% ©_2year Z.C. Treasury Return = $952.38 - $924.56 Retuary $27.82 = 3% $924.56 = $27.82 ③ 10 years Zic. Treasury Return = $646.61- $675.56 = $-30.95 (Loss Return () $-30.95 = -4.58% (Loss) $675.56

Return under (B) 0 1 year To bill Return = $1000 - $961.4S Return (2.) = $38.55 $961.45 = 4% $38.55. @ 2 year Z.c. Treasury Return = $980.39 - $924.56 = $55.83 Return (%) = $55.83 $924.56 = 6:04% ar 6% ③ 10 year IC. Treasury Return = $836175 - $.675.56 = $161.19. Return (%) = $161-19 = 23.86% $6756561

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