Several months ago, Buddy Inc. issued a unique fixed income security. As of today, the security is maturing in 11 months. The security pays semi-annual interest, which is equal to X% p.a minus the 6 month LIBOR, where X% is equal to the sum of 6% p.a. and the 3-month LIBOR rate. That is, in every six months, the interest is defined as: 6% 2 where, L6 (quoted on an annual basis, in %) is the 6-month LIBOR and L3 (also quoted on an annual basis, in %) is the 3-month LIBOR. Assume that the 6-month LIBOR will never exceed 6% p.a. At maturity, the company will pay $100 as the face value of the security. Also, assume all other bonds and floating rate notes have a face value of $100, respectively. 3-month LIBOR 6-month LIBOR + Table 1 shows the 3-month and 6-month LIBOR rates observed in the previous months as follows: Table 1 2 months ago L3% 4 1 month ago 3.1% p.a. 3.4% p.a. For example, two months ago, the 3-month LIBOR rate was observed at 3.4% p.a. 3-month LIBOR 6-month LIBOR Required: Table 2 shows the predicted 3-month and 6-month LIBOR rates over the next few months: Table 2 5 months from today 11 months from today L6% 2 3.4% p.a. 3.7% p.a. 2.6% p.a. 2.9% p.a. For example, five months from today, the 3-month LIBOR rate is predicted equal to 2.4% p.a. 2.4% p.a. 2.5% p.a. LIBOR 2.7% p.a. 2.8% p.a. 2.9% p.a. 3.0% p.a. Table 3 shows the current LIBOR rates (assume continuous compounding) with different maturities over the next 12 months: Table 3 Maturity 1 2 3 4 5 3.1% p.a. 6 3.2% p.a. For example, the current 3-month LIBOR rate is 2.9% p.a. compounded continuously. Maturity 7 8 9 10 11 12 LIBOR 3.25% p.a. 3.3% p.a. 3.35% p.a. Calculate the current price of the security. Show all working. 3.4% p.a. 3.45% p.a. 3.5% p.a.
Several months ago, Buddy Inc. issued a unique fixed income security. As of today, the security is maturing in 11 months. The security pays semi-annual interest, which is equal to X% p.a minus the 6 month LIBOR, where X% is equal to the sum of 6% p.a. and the 3-month LIBOR rate. That is, in every six months, the interest is defined as: 6% 2 where, L6 (quoted on an annual basis, in %) is the 6-month LIBOR and L3 (also quoted on an annual basis, in %) is the 3-month LIBOR. Assume that the 6-month LIBOR will never exceed 6% p.a. At maturity, the company will pay $100 as the face value of the security. Also, assume all other bonds and floating rate notes have a face value of $100, respectively. 3-month LIBOR 6-month LIBOR + Table 1 shows the 3-month and 6-month LIBOR rates observed in the previous months as follows: Table 1 2 months ago L3% 4 1 month ago 3.1% p.a. 3.4% p.a. For example, two months ago, the 3-month LIBOR rate was observed at 3.4% p.a. 3-month LIBOR 6-month LIBOR Required: Table 2 shows the predicted 3-month and 6-month LIBOR rates over the next few months: Table 2 5 months from today 11 months from today L6% 2 3.4% p.a. 3.7% p.a. 2.6% p.a. 2.9% p.a. For example, five months from today, the 3-month LIBOR rate is predicted equal to 2.4% p.a. 2.4% p.a. 2.5% p.a. LIBOR 2.7% p.a. 2.8% p.a. 2.9% p.a. 3.0% p.a. Table 3 shows the current LIBOR rates (assume continuous compounding) with different maturities over the next 12 months: Table 3 Maturity 1 2 3 4 5 3.1% p.a. 6 3.2% p.a. For example, the current 3-month LIBOR rate is 2.9% p.a. compounded continuously. Maturity 7 8 9 10 11 12 LIBOR 3.25% p.a. 3.3% p.a. 3.35% p.a. Calculate the current price of the security. Show all working. 3.4% p.a. 3.45% p.a. 3.5% p.a.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Transcribed Image Text:Several months ago, Buddy Inc. issued a unique fixed income security. As of today, the security is
maturing in 11 months.
The security pays semi-annual interest, which is equal to X% p.a minus the 6 month LIBOR, where
X% is equal to the sum of 6% p.a. and the 3-month LIBOR rate. That is, in every six months, the
interest is defined as:
L3%
+
2
6%
L6%
4
2
where, L6 (quoted on an annual basis, in %) is the 6-month LIBOR and L3 (also quoted on an annual
basis, in %) is the 3-month LIBOR. Assume that the 6-month LIBOR will never exceed 6% p.a. At
maturity, the company will pay $100 as the face value of the security. Also, assume all other bonds
and floating rate notes have a face value of $100, respectively.
Table 1 shows the 3-month and 6-month LIBOR rates observed in the previous months as follows:
Table 1
2 months ago
3.4% р.a.
1 month ago
3.1% р.а.
3-month LIBOR
6-month LIBOR
3.7% р.a.
For example, two months ago, the 3-month LIBOR rate was observed at 3.4% p.a.
3.4% р.a.
Table 2 shows the predicted 3-month and 6-month LIBOR rates over the next few months:
Table 2
5 months from today
2.4% p.a.
2.5% р.а.
For example, five months from today, the 3-month LIBOR rate is predicted equal to 2.4% p.a.
11 months from today
2.6% р.a.
3-month LIBOR
6-month LIBOR
2.9% р.a.
Table 3 shows the current LIBOR rates (assume continuous compounding) with different
maturities over the next 12 months:
Table 3
Maturity
LIBOR
Maturity
LIBOR
2.7% p.a.
3.25% p.a.
3.3% р.a.
3.35% p.a.
1
7
2.8% р.a.
2.9% р.a.
3.0% р.аa.
8
3
9
4
10
3.4% р.a.
3.45% p.a.
3.1% р.а.
11
6
3.2% р.a.
12
3.5% р.a.
For example, the current 3-month LIBOR rate is 2.9% p.a. compounded continuously.
Required:
Calculate the current price of the security. Show all working.
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