Bonds A, B, C and D are zero-coupon bonds with par value $1,000 each and yields
ID: 2653614 • Letter: B
Question
Bonds A, B, C and D are zero-coupon bonds with par value $1,000 each and yields to maturity of 6 percent, 8 percent, 10 percent and 12 percent respectively. Bond A matures in one year, bond B in two, bond C in three and bond D in four years. Calculate the short rates r1, r2, r3 and r4. Suppose an agent buys bonds B, C and D, holds them for one year and then sells them all. Find the price the agent will be able to sell each of the three bonds at. Based on those prices, write expressions for the Holding Period Returns of each of the three bonds. Verify that the Holding Period Returns are the same.
Explanation / Answer
Calculate the short rates r1, r2, r3 and r4
r1 = 6%
r2 = (1+8%)^2/(1+6%) -1 = 10.04%
r3 = (1+10%)^3/ (1+8%)^2 - 1 = 14.11%
r4 = (1+12%)^4/ (1+10%)^3 - 1 = 18.22%
Suppose an agent buys bonds B, C and D, holds them for one year and then sells them all. Find the price the agent will be able to sell each of the three bonds at year 1
Bond B
Current Price = 1000/1.08^2 = $ 857.34
Price after one year = 1000/1.1004 = $ 908.76
Bond C
Current Price = 1000/1.10^3 = $ 751.31
Price after one year = 1000/(1.1004*1.1411) = $ 796.39
Bond D
Current Price = 1000/1.12^4 = $ 635.52
Price after one year = 1000/(1.1004*1.1411*1.1822) = $ 673.65
Verify that the Holding Period Returns are the same.
Bond B
Holding Period Returns = Price after one year /Current price - 1
Holding Period Returns = 908.76/857.34 - 1
Holding Period Returns = 6%
Bond C
Holding Period Returns = Price after one year /Current price - 1
Holding Period Returns = 796.39/751.31 - 1
Holding Period Returns = 6%
Bond D
Holding Period Returns = Price after one year /Current price - 1
Holding Period Returns = 673.65/635.52 - 1
Holding Period Returns = 6%