Adventures in Debentures

c Copyright ⃝ 2004 by Michael R. Gibbons

Adventures in Debentures

we can solve for y to obtain

Solutions to The Grammar of Fixed Income Securities
1. Part Part Part Part Part Part a. b. c. d. e. f. $100/(1.20)3 = $57.87. $100/(2)3 = $12.50. $100/(1)3 = $100. $100/(1.10)6 = $56.45. $100/(1.05)12 = $55.68. $100/e.20×3 = $54.88.

y= So yB = and yA =

2nLN nSN

1 + c/2 −1 . P/100

2 · 184 1 + .09125/2 − 1 = 2.991185% 105 103.6776495/100 2 · 184 1 + .09125/2 − 1 = 2.778233% . 105 103.7401495/100

2. Remember we are trying to find r such that the growth in our initial investment is the ˙ same as the growth from an alternative investment providing a rate of r(m). That is, find r ˙ Part a. Part b. Part c. Part d.
˙ ˙ such that er = (1 + r(m)/m)m so r = m ln(1 + r(m)/m). m = 1: ln(1.04) = 3.922%. m = 1: ln(1.20) = 18.232%. m = 4: 4 ln(1.05) = 19.516%. m = 1: ln(2) = 69.315%.

In addition, we have

Part b. Ignoring for the moment any restrictions on lot size, we note that a cash flow of $100 to be received on 12/31/92 and purchased on 9/17/92 is available either in the form of $100 par amount of the 12/31/92 bill or in the form of $100/(1+.09125/2) par amount of the 9 1/8’s of 12/31/92. (Indeed, since $100 par of the 9 1/8’s will pay off $(100 + 9.125/2) on 12/31/92, $100/(1 + .09125/2) par amount of the 9 1/8’s will pay off $100.) Can we buy this cash flow low through one instrument and sell it high through the other? We must see if the asked price of one of the instruments is lower than the bid price of the other. For the T -bill, we have computed from Example 14 the asked price: A PBILL ≈ 99.17 .
B PBILL = 100 1 − d

nSM 360

= 100 1 − .0288

105 360

≈ 99.15 .

3. Part a. Settlement is 9/17/92, the next coupon date is 12/31 the last coupon date is 6/30/92, therefore nSN = 105, nLS = 79, and nLN = 184. In addition, c = .09125. Accrued interest is