Fixed Income Security
Chapter 1: Bond Prices, Discount Factors and Arbitrage
1. Use this list of Treasury bond prices as of January 15, 2013 (which should be taken as the current date for all the questions below except for question 7) to derive the discount factors for cash flows to be received in 0.5, 1, 1.5 and 2 years.
Bond
Price
6.0s of 7/15/13
102-15+
5.0s of 1/15/14
103-7 3/4
8.0s of 7/15/14
107-24
4.0s of 1/15/15
100-23 1/2
Answer:
(a) To find d(0.5)
The equation from the 6.0s of 15 July 2013, is
(b) To find d(1.0)
The equation from the 5.0s of 15 January 2014, is
From part (a), the d(0.5) = 0.99499
(c) To find d(1.5)
The equation from the 8.0s of 15 July 2014, is
From part (a), the d(0.5) = 0.99499, and part (b), the d(1.0) = 0.98297.
(d) To find d(2.0)
The equation from the 4.0s of 15 January 2015, is
From part (a), the d(0.5) = 0.99499, part (b), the d(1.0) = 0.98297, and part (c), the d(1.5) = 0.95998
2. Use the discount factors determined above to calculate the fair price of a Treasury issue with a 3.5% coupon maturing on 1/15/15.
Answer:
The fair price of a Treasury bond issue with a 3.5% coupon bond maturing on 15 January 2015:
By discount factor,
From part (a), the d(0.5) = 0.99499, part (b), the d(1.0) = 0.98297, part (c), the d(1.5) = 0.95998 and part (d), the d(2.0) = 0.92998
Therefore, the fair price of a Treasury Bond issue with a 3.5% coupon bond maturing on 15 January 2015 is $99.77
3. If the market price of the above bond is $1 (per face of $100) less than the fair price, determine an arbitrage strategy that you could use to profit from this mispricing.
Answer:
In order to determine an arbitrage strategy that we could use to profit from this mispricing, we will construct a replicating portfolio as follow:
By using the table in question 1, and the cash flow of the above bond, we obtain the following equation:
103x1 + 2.5x2 +
1. Use this list of Treasury bond prices as of January 15, 2013 (which should be taken as the current date for all the questions below except for question 7) to derive the discount factors for cash flows to be received in 0.5, 1, 1.5 and 2 years.
Bond
Price
6.0s of 7/15/13
102-15+
5.0s of 1/15/14
103-7 3/4
8.0s of 7/15/14
107-24
4.0s of 1/15/15
100-23 1/2
Answer:
(a) To find d(0.5)
The equation from the 6.0s of 15 July 2013, is
(b) To find d(1.0)
The equation from the 5.0s of 15 January 2014, is
From part (a), the d(0.5) = 0.99499
(c) To find d(1.5)
The equation from the 8.0s of 15 July 2014, is
From part (a), the d(0.5) = 0.99499, and part (b), the d(1.0) = 0.98297.
(d) To find d(2.0)
The equation from the 4.0s of 15 January 2015, is
From part (a), the d(0.5) = 0.99499, part (b), the d(1.0) = 0.98297, and part (c), the d(1.5) = 0.95998
2. Use the discount factors determined above to calculate the fair price of a Treasury issue with a 3.5% coupon maturing on 1/15/15.
Answer:
The fair price of a Treasury bond issue with a 3.5% coupon bond maturing on 15 January 2015:
By discount factor,
From part (a), the d(0.5) = 0.99499, part (b), the d(1.0) = 0.98297, part (c), the d(1.5) = 0.95998 and part (d), the d(2.0) = 0.92998
Therefore, the fair price of a Treasury Bond issue with a 3.5% coupon bond maturing on 15 January 2015 is $99.77
3. If the market price of the above bond is $1 (per face of $100) less than the fair price, determine an arbitrage strategy that you could use to profit from this mispricing.
Answer:
In order to determine an arbitrage strategy that we could use to profit from this mispricing, we will construct a replicating portfolio as follow:
By using the table in question 1, and the cash flow of the above bond, we obtain the following equation:
103x1 + 2.5x2 +