Answer To: Group Exercise 5 - Interest Rate Swap (Lecture 9) Find the data presented in “Group Exercise 5”...
Sanjeev answered on Apr 19 2021
Group Exercise 5
Source: https://www.macrotrends.net/1433/historical-libor-rates-chart
date 1M 3M 6M 12M Group Exercise 5 - Interest Rate Swap (Lecture 9) Find the data presented in “Group Exercise 5” sheet in the Excel file. There are 4 LIBOR (London InterBank Offer Rate) rates for different maturities (1-month, 3-month, 6-month and 12-month). On 1/1/1990, there was a plain interest rate Swap whose floating leg payments are to be 3-month Libor rate at the beginning of each period. Both fixed and floating leg payments are to be made in March, June, September and December and thus the first floating leg interest rate was set to be 8.38% when the Swap was initiated on 1/1/1990. The nominal (notional) principal of this swap is $10,000,000.
3/1/90 8.38 8.5 8.69 8.94
6/1/90 8.31 8.38 8.38 8.44
9/1/90 8.27 8.31 8.31 8.44
12/1/90 7.63 7.58 7.56 7.56
3/1/91 6.31 6.38 6.56 7
6/1/91 6.06 6.19 6.56 7
9/1/91 5.44 5.63 5.63 5.75 5-1. If there were no premiums set for this Swap (Swap spread = 0. This means each fixed and floating leg party will pay the coupons from each side). When the yield on 1/1/1990 was 8%, calculate the fixed interest rate of this Swap and the market value of the long position of the Swap on 1/1/1990.
12/1/91 4.31 4.25 4.23 4.31
3/1/92 4.25 4.37 4.51 5.06
6/1/92 3.94 3.94 4.06 4.31
9/1/92 3.19 3.27 3.27 3.38 5-2. Using the historical LIBOR, calculate the profit (or loss) of the fixed leg on each coupon payment date. Draw the graph.
12/1/92 3.31 3.44 3.63 4.06
3/1/93 3.19 3.25 3.38 3.63 5-3. Suppose on 1/1/1990, 3-month forward LIBIOR rates were all set for the next 30 years (this is a very strong assumption) yet the swap contract was made. Calculate the price of a bond of which principal is $10,000,000 and coupon rate is the same as your answer in 5-1 (coupon is paid just like the fixed leg of the swap.) on each coupon date. Plot this along with the profit and loss of the fixed leg in 5-2. Discuss the level of duration of the fixed leg of the swap compared with this coupon bond. Discuss the level of duration of the floating leg of the swap
6/1/93 3.19 3.31 3.51 3.75
9/1/93 3.19 3.38 3.38 3.56
12/1/93 3.25 3.38 3.5 3.81
3/1/94 3.69 3.94 4.25 4.75
6/1/94 4.56 4.88 5.25 5.81
9/1/94 5.06 5.5 5.75 6.31
12/1/94 6 6.5 7 7.75
3/1/95 6.13 6.25 6.5 6.81
6/1/95 6.13 6.06 6 5.98
9/1/95 5.88 5.95 5.95 6
12/1/95 5.69 5.63 5.51 5.43
3/1/96 5.44 5.47 5.5 5.72
6/1/96 5.5 5.58 5.79 6.13
9/1/96 5.43 5.63 5.73 5.99
12/1/96 5.5 5.56 5.6 5.79
3/1/97 5.69 5.77 5.94 6.27
6/1/97 6.06 5.9 5.69 5.48
9/1/97 5.66 5.77 5.84 6
12/1/97 5.72 5.81 5.84 5.97
3/1/98 5.69 5.71 5.75 5.89
6/1/98 5.66 5.72 5.78 5.84
9/1/98 5.38 5.31 5.25 5.06
12/1/98 5.06 5.07 5.07 5.1
3/1/99 4.94 5 5.06 5.25
6/1/99 5.24 5.37 5.65 5.84
9/1/99 5.4 6.08 5.96 6.04
12/1/99 5.83 6 6.13 6.5
3/1/00 6.13 6.29 6.53 6.94
6/1/00 6.64 6.77 7 7.18
9/1/00 6.62 6.81 6.76 6.8
12/1/00 6.56 6.4 6.2 6
3/1/01 5.08 4.88 4.71 4.67
6/1/01 3.86 3.84 3.91 4.18
9/1/01 2.63 2.59 2.52 2.64
12/1/01 1.87 1.88 1.98 2.44
3/1/02 1.88 2.03 2.33 3
6/1/02 1.84 1.86 1.96 2.29
9/1/02 1.81 1.79 1.71 1.73
12/1/02 1.38 1.38 1.38 1.45
3/1/03 1.3 1.28 1.23 1.28
6/1/03 1.12 1.12 1.12 1.19
9/1/03 1.12 1.16 1.18 1.3
12/1/03 1.12 1.15 1.22 1.46
3/1/04 1.09 1.11 1.16 1.35
6/1/04 1.37 1.61 1.94 2.46
9/1/04 1.84 2.02 2.2 2.48
12/1/04 2.4 2.56 2.78 3.1
3/1/05 2.87 3.12 3.4 3.85
6/1/05 3.34 3.52 3.71 3.88
9/1/05 3.86 4.07 4.23 4.44
12/1/05 4.39 4.54 4.7 4.84
3/1/06 4.83 5 5.14 5.29
6/1/06 5.33 5.48 5.59 5.69
9/1/06 5.32 5.37 5.37 5.3
12/1/06 5.32 5.36 5.37 5.33
3/1/07 5.32 5.35 5.33 5.22
6/1/07 5.32 5.36 5.39 5.43
9/1/07 5.12 5.23 5.13 4.9
12/1/07 4.6 4.7 4.6 4.22
3/1/08 2.7 2.69 2.61 2.49
6/1/08 2.46 2.78 3.11 3.31
9/1/08 3.93 4.05 3.98 3.96
12/1/08 0.44 1.43 1.75 2
3/1/09 0.5 1.19 1.74 1.97
6/1/09 0.31 0.6 1.11 1.61
9/1/09 0.25 0.29 0.63 1.26
12/1/09 0.23 0.25 0.43 0.98
3/1/10 0.25 0.29 0.44 0.92
6/1/10 0.35 0.53 0.75 1.17
9/1/10 0.26 0.29 0.46 0.78
12/1/10 0.26 0.3 0.46 0.78
3/1/11 0.24 0.3 0.46 0.78
6/1/11 0.19 0.25 0.4 0.73
9/1/11 0.24 0.37 0.56 0.87
12/1/11 0.3 0.58 0.81 1.13
3/1/12 0.24 0.47 0.73 1.05
6/1/12 0.25 0.46 0.73 1.07
9/1/12 0.21 0.36 0.64 0.97
12/1/12 0.21 0.31 0.51 0.84
3/1/13 0.2 0.28 0.45 0.73
6/1/13 0.2 0.27 0.41 0.69
9/1/13 0.18 0.25 0.37 0.63
12/1/13 0.17 0.25 0.35 0.58
3/1/14 0.15 0.23 0.33 0.56
6/1/14 0.16 0.23 0.33 0.55
9/1/14 0.16 0.24 0.33 0.58
12/1/14 0.17 0.26 0.36 0.63
3/1/15 0.18 0.27 0.4 0.69
6/1/15 0.19 0.28 0.45 0.77
9/1/15 0.19 0.33 0.53 0.85
12/1/15 0.43 0.61 0.85 1.18
3/1/16 0.44 0.63 0.9 1.21
6/1/16 0.47 0.65 0.92 1.23
9/1/16 0.53 0.85 1.24 1.55
12/1/16 0.77 1 1.32 1.69
3/1/17 0.98 1.15 1.42 1.8
6/1/17 1.22 1.3 1.45 1.74
9/1/17 1.23 1.33 1.51 1.78
12/1/17 1.56 1.69 1.84 2.11
3/1/18 1.88 2.31 2.45 2.66
6/1/18 2.09 2.34 2.5 2.76
9/1/18 2.26 2.4 2.6 2.92
12/1/18 2.52 2.8 2.87 3.01
3/1/19 2.5 2.6 2.66 2.71
6/1/19 2.4 2.32 2.2 2.18
9/1/19 2.02 2.09 2.06 2.03
12/1/19 1.76 1.91 1.91 2
Answer 1
5.1
Notional Amount $ 10,000,000
Type Plain Vanila Swap
Interest Floating rate 8.38% LIBOR-3M
Month Floating Rate LIBOR-3M Principal Days
March 8.38% $ 206,630.14 90
June 8.50% $ 211,917.81 91
Sep 8.38% $ 211,221.92 92
Dec 8.31% $ 209,457.53 92
$ 839,227.40
Fixed Interest 8.39%
The spread is Zero, So, Floating Rate of Interest and Fixed Rate of Interest are same.
Market Value of Swap
Month Fixed Rate of Interets Principal PVF @8% Present Value
March 8.38% $ 209,500.00 0.980 $ 205,392.16
June 8.38% $ 209,500.00 0.962 $ 201,442.31
Sep 8.38% $ 209,500.00 0.943 $ 197,641.51
Dec 8.38% $ 209,500.00 0.926 $ 193,981.48
$ 798,457.46
Market Value on 1/1/1990 $ 10,000,000
Add ; Interest $ 798,457.46
$ 10,798,457.46
Answer 2
5-2. Using the historical LIBOR, calculate the profit (or loss) of the fixed leg on each coupon payment date. Draw the graph.
Fixed Interest Rate to receive 8.39%
Floating Rate of Payment to make 8.38% at 3M LIBOR, Quaterly
Notional Amount $ 10,000,000
No of Days to considered 365
date Days FLOTING Rate %- 3M LIBOR Fixed Rate to Receive Difference Amount of Profit/(Loss)
3/1/90 90 8.38% 8.39% 0.01% $ 302.65
6/1/90 91 8.50% 8.39% -0.11% $ (2,685.77)
9/1/90 92 8.38% 8.39% 0.01% $ 309.37
12/1/90 92 8.31% 8.39% 0.08% $ 2,073.75
3/1/91 90 7.58% 8.39% 0.81% $ 20,028.67
6/1/91 91 6.38% 8.39% 2.01% $ 50,169.02
9/1/91 92 6.19% 8.39% 2.20% $ 55,509.37
12/1/91 92 5.63% 8.39% 2.76% $ 69,624.44
3/1/92 90 4.25% 8.39% 4.14% $ 102,138.26
6/1/92 91 4.37% 8.39% 4.02% $ 100,281.35
9/1/92 92 3.94% 8.39% 4.45% $ 112,221.70
12/1/92 92 3.27% 8.39% 5.12% $ 129,109.37
3/1/93 90 3.44% 8.39% 4.95% $ 122,110.87
6/1/93 91 3.25% 8.39% 5.14% $ 128,204.64
9/1/93 92 3.31% 8.39% 5.08% $ 128,101.15
12/1/93 92 3.38% 8.39% 5.01% $ 126,336.77
3/1/94 90 3.38% 8.39% 5.01% $ 123,590.32
6/1/94 91 3.94% 8.39% 4.45% $ 111,001.90
9/1/94 92 4.88% 8.39% 3.51% $ 88,528.55
12/1/94 92 5.50% 8.39% 2.89% $ 72,901.15
3/1/95 90 6.50% 8.39% 1.89% $ 46,658.81
6/1/95 91 6.25% 8.39% 2.14% $ 53,410.12
9/1/95 92 6.06% 8.39% 2.33% $ 58,786.08
12/1/95 92 5.95% 8.39% 2.44% $ 61,558.69
3/1/96 90 5.63% 8.39% 2.76% $ 68,110.87
6/1/96 91 5.47% 8.39% 2.92% $ 72,856.69
9/1/96 92 5.58% 8.39% 2.81% $ 70,884.71
12/1/96 92 5.63% 8.39% 2.76% $ 69,624.44
3/1/97 90 5.56% 8.39% 2.83% $ 69,836.89
6/1/97 91 5.77% 8.39% 2.62% $ 65,377.24
9/1/97 92 5.90% 8.39% 2.49% $ 62,818.96
12/1/97 92 5.77% 8.39% 2.62% $ 66,095.67
3/1/98 90 5.81% 8.39% 2.58% $ 63,672.51
6/1/98 91 5.71% 8.39% 2.68% $ 66,873.13
9/1/98 92 5.72% 8.39% 2.67% $ 67,355.95
12/1/98 92 5.31% 8.39% 3.08% $ 77,690.19
3/1/99 90 5.07% 8.39% 3.32% $ 81,919.08
6/1/99 91 5.00% 8.39% 3.39% $ 84,574.50
9/1/99 92 5.37% 8.39% 3.02% $ 76,177.86
12/1/99 92 6.08% 8.39% 2.31% $ 58,281.97
3/1/00 90 6.00% 8.39% 2.39% $ 58,987.58
6/1/00 91 6.29% 8.39% 2.10% $ 52,412.86
9/1/00 92 6.77% 8.39% 1.62% $ 40,890.19
12/1/00 92 6.81% 8.39% 1.58% $ 39,881.97
3/1/01 90 6.40% 8.39% 1.99% $ 49,124.56
6/1/01 91 4.88% 8.39% 3.51% $ ...