Question

Elliot Karlin is a 35-year-old bank executive who has just inherited a large sum of money. Having spent several years in the bank's investments department, he's well aware of the concept of duration and decides to apply it to his bond portfolio. In particular, Elliot intends to use $1 million of his inheritance to purchase 4 U.S. Treasury bonds: 1. An 8.61%, 13-year bond that's priced at $1,095.54 to yield 7.45%. 2. A 7.789%, 15-year bond that's priced at $1020.34 to yield 7.56%. 3. A 20-year stripped Treasury (zero coupon) that's priced at $199.28 to yield 8.23%. 4. A 24-year, 7.49% bond that's priced at $965.54 to yield 7.81%. Note that these bonds are semiannual compounding bonds. a. Find the duration and the modified duration of each bond. b. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds. c. Find the duration of the portfolio if Elliot puts $330,000 each into bonds 1 and 3 and $170,000 each into bonds 2 and 4. d. Which portfolio—bor —should Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as possible? Explain. From which portfolio does he stand to make more in annual interest income? Which portfolio would you recommend, and why?

Answer 1

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =13x2

Bond Price =∑ [(8.61*1000/200)/(1 + 7.45/200)^k]     +   1000/(1 + 7.45/200)^13x2

k=1

Bond Price = 1095.54

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,095.54)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	43.05	1.04	41.50	41.50
2	43.05	1.08	40.01	80.03
3	43.05	1.12	38.58	115.73
4	43.05	1.16	37.19	148.76
5	43.05	1.20	35.86	179.28
6	43.05	1.25	34.57	207.41
7	43.05	1.29	33.33	233.29
8	43.05	1.34	32.13	257.04
9	43.05	1.39	30.98	278.78
10	43.05	1.44	29.86	298.63
11	43.05	1.50	28.79	316.70
12	43.05	1.55	27.76	333.08
13	43.05	1.61	26.76	347.88
14	43.05	1.67	25.80	361.19
15	43.05	1.73	24.87	373.09
16	43.05	1.80	23.98	383.67
17	43.05	1.86	23.12	393.01
18	43.05	1.93	22.29	401.18
19	43.05	2.00	21.49	408.26
20	43.05	2.08	20.72	414.32
21	43.05	2.16	19.97	419.41
22	43.05	2.24	19.25	423.60
23	43.05	2.32	18.56	426.95
24	43.05	2.41	17.90	429.52
25	43.05	2.50	17.25	431.35
26	1,043.05	2.59	403.03	10,478.74
			Total	18,182.41

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=18182.41/(1095.54*2)

=8.29

Modified duration = Macaulay duration/(1+YTM)

=8.3/(1+0.0745)

=8.000

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =15x2

Bond Price =∑ [(7.789*1000/200)/(1 + 7.56/200)^k]     +   1000/(1 + 7.56/200)^15x2

k=1

Bond Price = 1020.34

Period Cash Flow Discounting factor =(1+YTM/number of coupon payments in the year) “period PV Cash Flow Duration Calc =PV =cashflow/disc cashflow*period ounting factor ($1,020.34) 1.04 1.08 38.95 38.95 38.95 1.12 1.16 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.56 1.62 1.68 1.74 1.81 1.88 1.95 2.02 38.95 37.53 36.16 34.84 33.57 32.35 31.17 30.04 28.94 27.89 26.87 25.89 24.95 24.04 23.17 22.32 21.51 20.73 19.97 19.24 18.54 17.87 17.22 16.59 15.99 15.40 14.84 14.30 13.78 13.28 341.34 37.53 72.32 104.53 134.29 161.75 187.03 210.26 231.54 251.00 268.73 284.84 299.41 312.55 324.33 334.84 344.15 352.35 359.48 365.63 370.86 375.22 378.77 381.56 383.65 385.08 385.90 386.14 385.86 385.08 10.240.09 18,694.77 38.95 38.95 38.95 2.53 2.72 2.83 2.93 3.04 38.95 1,038.95 Total

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=18694.77/(1020.34*2)

=9.16

Modified duration = Macaulay duration/(1+YTM)

=9.16/(1+0.0756)

=8.83

Please ask remaining parts seperately