In order to provide in-depth discussion on the subject of bond interest structure, forwards rates and bonds spread it is firstly essential to select two different bond issuers. The document brief has asked to consider two bonds of sovereign nations or use two corporate bonds. However, with the objective of selecting two bonds issuer who shall have both the elements of corporates and two sovereign nations European Bank for Reconstruction and Development and Deutsche Bank AG have been selected. Detailed discussion on the bonds issued by the two different financial institutes from different countries have been made here with the objective of providing necessary information to the readers on different elements of bonds.
Firstly let’s have the brief details about the bonds issued by European Bank for Reconstruction and Development and Deutsche Bank AG. A clear understanding about the terms and conditions of the bonds issued by the European Bank for Reconstruction and Development, here in after to be referred to as EBRD only in this document and Deutsche Bank AG, here in after to be referred to as Deutsche only in this document shall helpful in estimating the interest structures, calculate forward rates and comment on the spread (Du, Tepper and Verdelhan, 2018).
The table below contains the information about the bonds issued by EBRD.
EBRD in order to finance the requirements of fund to the tune of 1,500,000,000 Russian Rouble (RUB) issued international bonds with nominal amount of 50,000 RUB per bond. As can be seen that the coupon rate of the bonds is 7.25% per annum with annual coupon frequency (Malkiel, 2015). The discounted rate to be used is the LIBOR +2% to calculate the present value of the bond and subsequently the forward rate. The interest structure of the above bond for EBRD is provided below.
|
Interest structure of bond |
Deutsche |
|
|
|
|
|
Years |
Bond amount (RUB) |
Coupon rate (7.25%) |
(A): Interest (RUB) |
(B): PV factors @5.25% |
Term structure (AxB) |
|
1 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.950119 |
103,325,415.68 |
|
2 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.902726 |
98,171,416.32 |
|
3 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.857697 |
93,274,504.82 |
|
4 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.814914 |
88,621,857.31 |
|
5 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.774265 |
84,201,289.60 |
|
6 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.735643 |
80,001,225.28 |
|
7 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.698949 |
76,010,665.35 |
|
8 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.664084 |
72,219,159.47 |
|
9 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.630959 |
68,616,778.60 |
|
10 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.599486 |
65,194,088.93 |
|
11 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.569583 |
61,942,127.25 |
|
12 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.541171 |
58,852,377.43 |
|
13 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.514177 |
55,916,748.16 |
|
14 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.488529 |
53,127,551.69 |
|
15 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.464161 |
50,477,483.79 |
|
16 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.441008 |
47,959,604.55 |
|
17 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.41901 |
45,567,320.24 |
|
18 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.398109 |
43,294,366.02 |
|
19 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.378251 |
41,134,789.57 |
|
20 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.359383 |
39,082,935.46 |
|
21 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.341457 |
37,133,430.37 |
|
22 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.324425 |
35,281,168.99 |
|
23 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.308242 |
33,521,300.71 |
|
24 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.292866 |
31,849,216.82 |
|
25 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.278258 |
30,260,538.55 |
|
26 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.264378 |
28,751,105.51 |
|
27 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.25119 |
27,316,964.86 |
|
28 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.238661 |
25,954,360.91 |
|
29 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.226756 |
24,659,725.33 |
|
30 |
1,500,000,000.00 |
7.25% |
108,750,000.00 |
0.215445 |
23,429,667.77 |
Deutsche has issued bonds denominated IDR (Indonesian Rupiah) to arrange 1,470,000,000 IDR from issue of bonds with 9% coupon rate (Schwarz, 2017). The details regarding the bonds issued by the Deutsche is provided in the table below:
As per the above terms and conditions of Deutsche the interest structure will be as following:
|
Interest structure of Deutsche |
|
|
|
||
|
Years |
Bond amount (IDR) |
Coupon rate (9%) |
Interest (RUB) |
(B): PV factors @5.25% |
Term structure (A x B) |
|
1 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.950119 |
125,700,712.59 |
|
2 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.902726 |
119,430,605.79 |
|
3 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.857697 |
113,473,259.65 |
|
4 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.814914 |
107,813,073.31 |
|
5 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.774265 |
102,435,224.04 |
|
6 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.735643 |
97,325,628.54 |
|
7 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.698949 |
92,470,905.98 |
|
8 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.664084 |
87,858,342.97 |
|
9 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.630959 |
83,475,860.31 |
|
10 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.599486 |
79,311,981.29 |
|
11 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.569583 |
75,355,801.70 |
|
12 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.541171 |
71,596,961.24 |
|
13 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.514177 |
68,025,616.38 |
|
14 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.488529 |
64,632,414.61 |
|
15 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.464161 |
61,408,469.94 |
|
16 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.441008 |
58,345,339.61 |
|
17 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.41901 |
55,435,002.00 |
|
18 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.398109 |
52,669,835.63 |
|
19 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.378251 |
50,042,599.18 |
|
20 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.359383 |
47,546,412.52 |
|
21 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.341457 |
45,174,738.73 |
|
22 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.324425 |
42,921,366.97 |
|
23 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.308242 |
40,780,396.17 |
|
24 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.292866 |
38,746,219.64 |
|
25 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.278258 |
36,813,510.35 |
|
26 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.264378 |
34,977,206.98 |
|
27 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.25119 |
33,232,500.69 |
|
28 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.238661 |
31,574,822.51 |
|
29 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.226756 |
29,999,831.36 |
|
30 |
1,470,000,000.00 |
9.00% |
132,300,000.00 |
0.215445 |
28,503,402.72 |
There are different types of bonds which are issued by the corporations, governments and financial institutions. Such bonds include zero coupon bond, bonds carrying fixed interests and flexible bonds. Also bonds can be classified on the basis of characteristics of issuers, i.e. Government bonds and corporate bonds (Wu and Xia, 2017).
Forward rates of zero coupon bonds are calculated by using the following formula:
The cash flows in zero coupon bonds are takes place twice only, once at the time of issue of bonds and at the time of repayment of bonds. The present value factor, generally the market interest rates, used to calculate the present value of cash flow to calculate forward rate of zero coupon bonds. Following table indicates use of present value factor to discount the cash flows to calculate the forward rate of zero coupon bond.
To calculate the forward rate of fixed coupon bond the following formula is used:
The interest rate can be locked with the (rn) for investing money for n number of years. Algebraically the equation can be rearranged as following to calculate the forward rate of fixed interest bond (Kung, 2015).
The above has to be applied repeatedly to find the value to the following equation:
Taking into consideration the discussion above the forward rate of EBRD bond shall be calculated by using fixed coupon rate formula. It is important to note that the coupon rate in case of EBRD bond is 7.25% as can be seen and it is fixed as per the terms and conditions provided in the bond issue template provided at the beginning of the document (Borio, McCauley, McGuire and Sushko, 2016). Accordingly, the following formula has been used to calculate forward rate of fixed coupon EBRD bond:
Using the above formula the forward rate of EBRD bond is 1.0455.
Again the bond denominated in IDR to collect necessary funds by Deutsche a 9% fixed coupon bond has been issued. Using the fixed coupon formula the forward rate for the bond is calculated below.
The forward rate of Deutsche bond is 1.055.
The difference between the forward rates is (1.055- 1.0455) = 0.0095.
The present value of interest spread over the maturity period of bond is calculated by using the simple excel format for the benefit of the readers. The present value of maturity amount of each bond has been calculated and added with the total present value of coupon interest to calculate the value of the bond at the date of issue of the bond (Campbell, Sunderam and Viceira, 2017).
|
|
EBRD |
|
|
|
|
|
Years |
Bond amount (RUB) |
Coupon rate (7.25%) |
(A): Interest (RUB) |
(B): PV factors @5.25% |
Term structure (AxB) |
|
1 |
50,000.00 |
7.25% |
3,625.00 |
0.950119 |
3,444.18 |
|
2 |
50,000.00 |
7.25% |
3,625.00 |
0.902726 |
3,272.38 |
|
3 |
50,000.00 |
7.25% |
3,625.00 |
0.857697 |
3,109.15 |
|
4 |
50,000.00 |
7.25% |
3,625.00 |
0.814914 |
2,954.06 |
|
5 |
50,000.00 |
7.25% |
3,625.00 |
0.774265 |
2,806.71 |
|
6 |
50,000.00 |
7.25% |
3,625.00 |
0.735643 |
2,666.71 |
|
7 |
50,000.00 |
7.25% |
3,625.00 |
0.698949 |
2,533.69 |
|
8 |
50,000.00 |
7.25% |
3,625.00 |
0.664084 |
2,407.31 |
|
9 |
50,000.00 |
7.25% |
3,625.00 |
0.630959 |
2,287.23 |
|
10 |
50,000.00 |
7.25% |
3,625.00 |
0.599486 |
2,173.14 |
|
11 |
50,000.00 |
7.25% |
3,625.00 |
0.569583 |
2,064.74 |
|
12 |
50,000.00 |
7.25% |
3,625.00 |
0.541171 |
1,961.75 |
|
13 |
50,000.00 |
7.25% |
3,625.00 |
0.514177 |
1,863.89 |
|
14 |
50,000.00 |
7.25% |
3,625.00 |
0.488529 |
1,770.92 |
|
15 |
50,000.00 |
7.25% |
3,625.00 |
0.464161 |
1,682.58 |
|
16 |
50,000.00 |
7.25% |
3,625.00 |
0.441008 |
1,598.65 |
|
17 |
50,000.00 |
7.25% |
3,625.00 |
0.41901 |
1,518.91 |
|
18 |
50,000.00 |
7.25% |
3,625.00 |
0.398109 |
1,443.15 |
|
19 |
50,000.00 |
7.25% |
3,625.00 |
0.378251 |
1,371.16 |
|
20 |
50,000.00 |
7.25% |
3,625.00 |
0.359383 |
1,302.76 |
|
21 |
50,000.00 |
7.25% |
3,625.00 |
0.341457 |
1,237.78 |
|
22 |
50,000.00 |
7.25% |
3,625.00 |
0.324425 |
1,176.04 |
|
23 |
50,000.00 |
7.25% |
3,625.00 |
0.308242 |
1,117.38 |
|
24 |
50,000.00 |
7.25% |
3,625.00 |
0.292866 |
1,061.64 |
|
25 |
50,000.00 |
7.25% |
3,625.00 |
0.278258 |
1,008.68 |
|
26 |
50,000.00 |
7.25% |
3,625.00 |
0.264378 |
958.37 |
|
27 |
50,000.00 |
7.25% |
3,625.00 |
0.25119 |
910.57 |
|
28 |
50,000.00 |
7.25% |
3,625.00 |
0.238661 |
865.15 |
|
29 |
50,000.00 |
7.25% |
3,625.00 |
0.226756 |
821.99 |
|
30 |
50,000.00 |
7.25% |
3,625.00 |
0.215445 |
780.99 |
|
Present value interest |
|
|
|
54,171.64 |
|
|
Add: Present value of repayment (50000 x 0.215445) |
|
10,772.26 |
|||
|
Present value of EBRD bond |
64,943.90 |
Thus, present value of EBRD Bond is 64,943.90 RBU for the investors. Thus investing in the bond is a profitable option from the point view of the investors (Miyajima, Mohanty and Chan, 2015).
Similarly the present value of Deutsche bond issued by the bank with 9% coupon rate is calculated below.
|
Years |
Bond amount (IDR) |
Coupon rate (9%) |
Interest (RUB) |
(B): PV factors @5.25% |
Term structure (AxB) |
|
1 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.950119 |
8,551,068.88 |
|
2 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.902726 |
8,124,531.01 |
|
3 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.857697 |
7,719,269.36 |
|
4 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.814914 |
7,334,222.67 |
|
5 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.774265 |
6,968,382.59 |
|
6 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.735643 |
6,620,791.06 |
|
7 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.698949 |
6,290,537.82 |
|
8 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.664084 |
5,976,758.03 |
|
9 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.630959 |
5,678,629.95 |
|
10 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.599486 |
5,395,372.88 |
|
11 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.569583 |
5,126,245.01 |
|
12 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.541171 |
4,870,541.58 |
|
13 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.514177 |
4,627,592.95 |
|
14 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.488529 |
4,396,762.90 |
|
15 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.464161 |
4,177,446.93 |
|
16 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.441008 |
3,969,070.72 |
|
17 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.41901 |
3,771,088.57 |
|
18 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.398109 |
3,582,982.02 |
|
19 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.378251 |
3,404,258.45 |
|
20 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.359383 |
3,234,449.83 |
|
21 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.341457 |
3,073,111.48 |
|
22 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.324425 |
2,919,820.88 |
|
23 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.308242 |
2,774,176.61 |
|
24 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.292866 |
2,635,797.25 |
|
25 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.278258 |
2,504,320.43 |
|
26 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.264378 |
2,379,401.84 |
|
27 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.25119 |
2,260,714.33 |
|
28 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.238661 |
2,147,947.11 |
|
29 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.226756 |
2,040,804.85 |
|
30 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.215445 |
1,939,006.99 |
|
Present value total interest |
|
|
|
134,495,104.99 |
|
|
Add: Present value of principal(100,000,000 x 0.215445) |
|
21,544,522.09 |
|||
|
Present value of Deutsche Bond |
156,039,627.08 |
As can be seen from the above that the investors by investing 100,000,000 IDR in Deutsche bond expected to receive a present value of 156,039,627.08 IDR over the life time of the bond. Hence, from the point of view of investors the proposal of investing in the bonds issued by Deutsche is a profitable investment proposal (Hanson and Stein, 2015).
The spread is calculated to show the yield expected to be earned over the life time of a bond. In this case the present value of bond from the point of view of investors, in both case, show that the investors are expected to earn significant amount of return by investing in the bond of EBRD and Deutsche. The method used here is relatively simple to find out the present value of interest to be earned by the investors on the bond over the useful life of the bond (Rachel and Smith, 2015). The coupon rate of bonds, i.e. 7.25% for EBRD RBU bond and 9% for Deutsche IDR bond are fixed. Hence, there is no question fluctuation in the actual spread and yield of bonds throughout the life time of the bond. Thus, there is no confusion regarding the periodic coupon to be received from the bond (Du, Tepper and Verdelhan, 2018). However, in order to calculate the present value of coupon as well as the principal to be rapid at the end of the maturity period of the respective bonds it is important to use an appropriate rate of interest. 5.25% has been used, i.e. LIBOR plus 2% to calculate the present value of interest and the principal amount to calculate the present value of respective bonds (Liao, 2016).
It is important to keep in mind that LIBOR is not going to stay at 3.25% throughout the useful life of the bonds thus, the calculation of present value of interest spreads and bonds will not be completely correct (Borio et. al. 2016). Taking into consideration this constraint the present value of interests spreads is calculated in the table below by using simple formula in the table below:
|
Years |
Bond amount (RUB) |
Coupon rate (7.25%) |
(A): Interest (RUB) |
(B): PV factors @5.25% |
Term structure (A x B) |
|
1 |
50,000.00 |
7.25% |
3,625.00 |
0.950119 |
3,444.18 |
|
2 |
50,000.00 |
7.25% |
3,625.00 |
0.902726 |
3,272.38 |
|
3 |
50,000.00 |
7.25% |
3,625.00 |
0.857697 |
3,109.15 |
|
4 |
50,000.00 |
7.25% |
3,625.00 |
0.814914 |
2,954.06 |
|
5 |
50,000.00 |
7.25% |
3,625.00 |
0.774265 |
2,806.71 |
|
6 |
50,000.00 |
7.25% |
3,625.00 |
0.735643 |
2,666.71 |
|
7 |
50,000.00 |
7.25% |
3,625.00 |
0.698949 |
2,533.69 |
|
8 |
50,000.00 |
7.25% |
3,625.00 |
0.664084 |
2,407.31 |
|
9 |
50,000.00 |
7.25% |
3,625.00 |
0.630959 |
2,287.23 |
|
10 |
50,000.00 |
7.25% |
3,625.00 |
0.599486 |
2,173.14 |
|
11 |
50,000.00 |
7.25% |
3,625.00 |
0.569583 |
2,064.74 |
|
12 |
50,000.00 |
7.25% |
3,625.00 |
0.541171 |
1,961.75 |
|
13 |
50,000.00 |
7.25% |
3,625.00 |
0.514177 |
1,863.89 |
|
14 |
50,000.00 |
7.25% |
3,625.00 |
0.488529 |
1,770.92 |
|
15 |
50,000.00 |
7.25% |
3,625.00 |
0.464161 |
1,682.58 |
|
16 |
50,000.00 |
7.25% |
3,625.00 |
0.441008 |
1,598.65 |
|
17 |
50,000.00 |
7.25% |
3,625.00 |
0.41901 |
1,518.91 |
|
18 |
50,000.00 |
7.25% |
3,625.00 |
0.398109 |
1,443.15 |
|
19 |
50,000.00 |
7.25% |
3,625.00 |
0.378251 |
1,371.16 |
|
20 |
50,000.00 |
7.25% |
3,625.00 |
0.359383 |
1,302.76 |
|
21 |
50,000.00 |
7.25% |
3,625.00 |
0.341457 |
1,237.78 |
|
22 |
50,000.00 |
7.25% |
3,625.00 |
0.324425 |
1,176.04 |
|
23 |
50,000.00 |
7.25% |
3,625.00 |
0.308242 |
1,117.38 |
|
24 |
50,000.00 |
7.25% |
3,625.00 |
0.292866 |
1,061.64 |
|
25 |
50,000.00 |
7.25% |
3,625.00 |
0.278258 |
1,008.68 |
|
26 |
50,000.00 |
7.25% |
3,625.00 |
0.264378 |
958.37 |
|
27 |
50,000.00 |
7.25% |
3,625.00 |
0.25119 |
910.57 |
|
28 |
50,000.00 |
7.25% |
3,625.00 |
0.238661 |
865.15 |
|
29 |
50,000.00 |
7.25% |
3,625.00 |
0.226756 |
821.99 |
|
30 |
50,000.00 |
7.25% |
3,625.00 |
0.215445 |
780.99 |
Present value of interest spread for the Deutsche bond is calculated below:
|
Years |
Bond amount (IDR) |
Coupon rate (9%) |
Interest (RUB) |
(B): PV factors @5.25% |
Term structure (AxB) |
|
1 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.950119 |
8,551,068.88 |
|
2 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.902726 |
8,124,531.01 |
|
3 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.857697 |
7,719,269.36 |
|
4 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.814914 |
7,334,222.67 |
|
5 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.774265 |
6,968,382.59 |
|
6 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.735643 |
6,620,791.06 |
|
7 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.698949 |
6,290,537.82 |
|
8 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.664084 |
5,976,758.03 |
|
9 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.630959 |
5,678,629.95 |
|
10 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.599486 |
5,395,372.88 |
|
11 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.569583 |
5,126,245.01 |
|
12 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.541171 |
4,870,541.58 |
|
13 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.514177 |
4,627,592.95 |
|
14 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.488529 |
4,396,762.90 |
|
15 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.464161 |
4,177,446.93 |
|
16 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.441008 |
3,969,070.72 |
|
17 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.41901 |
3,771,088.57 |
|
18 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.398109 |
3,582,982.02 |
|
19 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.378251 |
3,404,258.45 |
|
20 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.359383 |
3,234,449.83 |
|
21 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.341457 |
3,073,111.48 |
|
22 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.324425 |
2,919,820.88 |
|
23 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.308242 |
2,774,176.61 |
|
24 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.292866 |
2,635,797.25 |
|
25 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.278258 |
2,504,320.43 |
|
26 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.264378 |
2,379,401.84 |
|
27 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.25119 |
2,260,714.33 |
|
28 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.238661 |
2,147,947.11 |
|
29 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.226756 |
2,040,804.85 |
|
30 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.215445 |
1,939,006.99 |
However, as already mentioned that the reliability of the above data is questionable because to expect that LIBOR would remain at 3.25% over the course of 30 years, i.e. time after which the respective bonds shall be matured will be extremely naïve from financial view point. Thus, in order to address the concern of the investors it would be beneficial to calculate the present value of spreads by using different LIBOR rates. This will enable the investors to understand the expected outcome of investing in the bond even if the market rate of interest changes in the future (Ismailov and Rossi, 2018).
As already mentioned that the benefit of calculating the present value of spreads of bonds as well as present value of bond is that the periodical coupon amount does not change. In this case the annual interest on Deutsche and EBRD bond will remain at 9% and 7.25% of the nominal amount of bond. Thus, to compensate the future uncertainty in market rate of interest little adjustments to the LIBOR will be helpful in calculating the present value of spreads. Accordingly, the present value of spread is calculated for both bonds by using different LIBOR (Sushko et. al. 2017).
In case the LIBOR changes in the future to 3.75% instead of 3.25%. As the discount rate has been taken at LIBOR plus 2% thus, the present value of interests spreads for EBRD bond is shown in the table below:
|
Years |
Bond amount (RUB) |
Coupon rate (7.25%) |
(A): Interest (RUB) |
(B): PV factors @5.75% |
Term structure (AxB) |
|
1 |
50,000.00 |
7.25% |
3,625.00 |
0.945626 |
3,427.90 |
|
2 |
50,000.00 |
7.25% |
3,625.00 |
0.894209 |
3,241.51 |
|
3 |
50,000.00 |
7.25% |
3,625.00 |
0.845588 |
3,065.26 |
|
4 |
50,000.00 |
7.25% |
3,625.00 |
0.799611 |
2,898.59 |
|
5 |
50,000.00 |
7.25% |
3,625.00 |
0.756133 |
2,740.98 |
|
6 |
50,000.00 |
7.25% |
3,625.00 |
0.715019 |
2,591.94 |
|
7 |
50,000.00 |
7.25% |
3,625.00 |
0.676141 |
2,451.01 |
|
8 |
50,000.00 |
7.25% |
3,625.00 |
0.639377 |
2,317.74 |
|
9 |
50,000.00 |
7.25% |
3,625.00 |
0.604612 |
2,191.72 |
|
10 |
50,000.00 |
7.25% |
3,625.00 |
0.571737 |
2,072.55 |
|
11 |
50,000.00 |
7.25% |
3,625.00 |
0.54065 |
1,959.85 |
|
12 |
50,000.00 |
7.25% |
3,625.00 |
0.511253 |
1,853.29 |
|
13 |
50,000.00 |
7.25% |
3,625.00 |
0.483454 |
1,752.52 |
|
14 |
50,000.00 |
7.25% |
3,625.00 |
0.457167 |
1,657.23 |
|
15 |
50,000.00 |
7.25% |
3,625.00 |
0.432309 |
1,567.12 |
|
16 |
50,000.00 |
7.25% |
3,625.00 |
0.408803 |
1,481.91 |
|
17 |
50,000.00 |
7.25% |
3,625.00 |
0.386575 |
1,401.33 |
|
18 |
50,000.00 |
7.25% |
3,625.00 |
0.365555 |
1,325.14 |
|
19 |
50,000.00 |
7.25% |
3,625.00 |
0.345679 |
1,253.09 |
|
20 |
50,000.00 |
7.25% |
3,625.00 |
0.326883 |
1,184.95 |
|
21 |
50,000.00 |
7.25% |
3,625.00 |
0.309109 |
1,120.52 |
|
22 |
50,000.00 |
7.25% |
3,625.00 |
0.292302 |
1,059.59 |
|
23 |
50,000.00 |
7.25% |
3,625.00 |
0.276408 |
1,001.98 |
|
24 |
50,000.00 |
7.25% |
3,625.00 |
0.261379 |
947.50 |
|
25 |
50,000.00 |
7.25% |
3,625.00 |
0.247167 |
895.98 |
|
26 |
50,000.00 |
7.25% |
3,625.00 |
0.233728 |
847.26 |
|
27 |
50,000.00 |
7.25% |
3,625.00 |
0.221019 |
801.19 |
|
28 |
50,000.00 |
7.25% |
3,625.00 |
0.209002 |
757.63 |
|
29 |
50,000.00 |
7.25% |
3,625.00 |
0.197637 |
716.44 |
|
30 |
50,000.00 |
7.25% |
3,625.00 |
0.186891 |
677.48 |
Similarly with LIBOR rate of 3.75% instead of 3.25% the present value of interests spreads for bond issued Deutsche is calculated in the table below:
|
Years |
Bond amount (IDR) |
Coupon rate (9%) |
Interest (RUB) |
(B): PV factors @5.75% |
Term structure (AxB) |
|
1 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.945626 |
8,510,638.30 |
|
2 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.894209 |
8,047,884.92 |
|
3 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.845588 |
7,610,293.06 |
|
4 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.799611 |
7,196,494.62 |
|
5 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.756133 |
6,805,195.86 |
|
6 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.715019 |
6,435,173.39 |
|
7 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.676141 |
6,085,270.35 |
|
8 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.639377 |
5,754,392.76 |
|
9 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.604612 |
5,441,506.16 |
|
10 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.571737 |
5,145,632.30 |
|
11 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.54065 |
4,865,846.15 |
|
12 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.511253 |
4,601,272.95 |
|
13 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.483454 |
4,351,085.53 |
|
14 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.457167 |
4,114,501.69 |
|
15 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.432309 |
3,890,781.74 |
|
16 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.408803 |
3,679,226.23 |
|
17 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.386575 |
3,479,173.74 |
|
18 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.365555 |
3,289,998.81 |
|
19 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.345679 |
3,111,109.98 |
|
20 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.326883 |
2,941,947.98 |
|
21 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.309109 |
2,781,983.90 |
|
22 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.292302 |
2,630,717.64 |
|
23 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.276408 |
2,487,676.25 |
|
24 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.261379 |
2,352,412.53 |
|
25 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.247167 |
2,224,503.58 |
|
26 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.233728 |
2,103,549.48 |
|
27 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.221019 |
1,989,172.09 |
|
28 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.209002 |
1,881,013.79 |
|
29 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.197637 |
1,778,736.45 |
|
30 |
100,000,000.00 |
9.00% |
9,000,000.00 |
0.186891 |
1,682,020.28 |
The above steps can be repeated by as many times as required by using different discount rates to increase the reliability of the calculations made using the above method (Kaufman and Hopewell, 2017).
The spread above does reflect the way that the short term spread between the two issuers is likely to move.
The trading strategy can be very effectively designed and generated by using the above method. It is because the above method would give the investors and traders complete analysis about the expected returns in different years along with the present value of cash inflows from the investment over the life period of respective bonds (Hawawini, 2017). In addition the investors and traders would be able to calculate the expected present value of different investment options to determine whether to invest in a particular investment option or not. Also sensitivity analysis can be conducted by using different underlying variables to compensate for the uncertain future (Hawawini, 2017).
Trading strategy and design for the investors:
With LIBOR 3.25%:
The present value of EBRD bond is 64,943.90 RUB with nominal value of the bond is 50,000 RUB hence, investors should certainly invest in the bond in case the above circumstances persist in the future (Schlarbaum, Racette and Boquist, 2017).
The present value of Deutsche bond is 156,039,627.08 with discount rate of 5.25% (LIBOR 3.25% + 2%) is significantly higher than the Nominal value of the bond hence, the option provides significant opportunity to earn substantial return on the amount of investment in the bond. Hence, the investor should invest in the bond (Schlarbaum, Racette and Boquist, 2017).
Borio, C.E., McCauley, R.N., McGuire, P. and Sushko, V., 2016. Covered interest parity lost: understanding the cross-currency basis.
Borio, C.E., McCauley, R.N., McGuire, P. and Sushko, V., 2016. Covered interest parity lost: understanding the cross-currency basis.
Campbell, J.Y., Sunderam, A. and Viceira, L.M., 2017. Inflation bets or deflation hedges? the changing risks of nominal bonds. Critical Finance Review, 6(2), pp.263-301.
Du, W., Tepper, A. and Verdelhan, A., 2018. Deviations from covered interest rate parity. The Journal of Finance, 73(3), pp.915-957.
Du, W., Tepper, A. and Verdelhan, A., 2018. Deviations from covered interest rate parity. The Journal of Finance, 73(3), pp.915-957.
Hanson, S.G. and Stein, J.C., 2015. Monetary policy and long-term real rates. Journal of Financial Economics, 115(3), pp.429-448. Hanson, S.G. and Stein, J.C., 2015. Monetary policy and long-term real rates. Journal of Financial Economics, 115(3), pp.429-448.
Hawawini, G., 2017. Bond Duration and Immunization: Early Developments and Recent Contributions. Routledge. Available at: https://www.taylorfrancis.com/books/e/9781351381116/chapters/10.4324%2F9781315145976-1 [Accessed on 15 November 2018]
Hawawini, G., 2017. The Mathematics of Macaulay’s Duration. In Bond Duration and Immunization (pp. 47-55). Routledge.
Ismailov, A. and Rossi, B., 2018.Uncertainty and deviations from uncovered interest rate parity. Journal of International Money and Finance, 88, pp.242-259.
Kaufman, G.G. and Hopewell, M.H., 2017. Bond price volatility and term to maturity: A generalized respecification. In Bond Duration and Immunization (pp. 64-68). Routledge. Available at: https://www.taylorfrancis.com/books/e/9781351381116/chapters/10.4324%2F9781315145976-5 [Accessed on 15 November 2018]
Kung, H., 2015. Macroeconomic linkages between monetary policy and the term structure of interest rates. Journal of Financial Economics, 115(1), pp.42-57.
Liao, G.Y., 2016. Credit migration and covered interest rate parity. Project on Behavioral Finance and Financial Stability Working Paper Series,(2016-07).
Malkiel, B.G., 2015. Term structure of interest rates: expectations and behavior patterns. Princeton University Press.
Miyajima, K., Mohanty, M.S. and Chan, T., 2015. Emerging market local currency bonds: diversification and stability. Emerging Markets Review, 22, pp.126-139.
Rachel, L. and Smith, T., 2015. Secular drivers of the global real interest rate.
Schlarbaum, G.G., Racette, G.A. and Boquist, J.A., 2017. Duration and Risk Assessment for Bonds and Common Stocks. In Bond Duration and Immunization (pp. 102-107). Routledge. Available at: https://content.taylorfrancis.com/books/e/download?dac=C2017-0-55182-X&isbn=9781315145976&doi=10.4324/9781315145976-8&format=pdf [Accessed on 15 November 2018]
Schwarz, K., 2017. Mind the gap: Disentangling credit and liquidity in risk spreads.
Sushko, V., Borio, C.E., McCauley, R.N. and McGuire, P., 2017. The failure of covered interest parity: FX hedging demand and costly balance sheets.
Wu, J.C. and Xia, F.D., 2017. Time-varying lower bound of interest rates in Europe.
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