Question

Finance

Suppose that the prevailing Treasury spot rate curve is the one shown in the following table.

Period	Year	Cash Flow	Spot Rate	Discount Factor	Buy for
1	0.5		0.03
2	1		0.033
3	1.5		0.035053
4	2		0.039164
5	2.5		0.044376
6	3		0.04752
7	3.5		0.049622
8	4		0.05065
9	4.5		0.051701
10	5		0.052772

a)What is the (arbitrage-free) value of a 4.5% 5-year Treasury issue?

b)Suppose that the 4.5% 5-year Treasury issue is priced in the market based on the on-the-run 5-year Treasury yield. Assume further that yield is 4.8%, so that each cash flow is discounted at 4.8% divided by 2. What is the price of the 4.8% 5-year Treasury issue based on a 4.8% discount rate?

c)

Given the arbitrage-free value found in part a and the price in part b, what action would a dealer take to earn an would the arbitrage profit? (Hint: the arbitrage profit is $1.77). Select one:

a. reconstitute the bond

b. Strip the bond

Answer 1

Assume Face Value of Bond $1000

a)

Period	Year	Cash Flow	Spot Rate	Discount Factor	Buy for
1	0.5	45	0.03	0.985329278	44.34
2	1	45	0.033	0.968054211	43.56
3	1.5	45	0.035053	0.949633698	42.73
4	2	45	0.039164	0.926044409	41.67
5	2.5	45	0.044376	0.897134984	40.37
6	3	45	0.04752	0.869987533	39.15
7	3.5	45	0.049622	0.844082241	37.98
8	4	45	0.05065	0.820668456	36.93
9	4.5	45	0.051701	0.797048427	35.87
10	5	1045	0.052772	0.773265032	808.06
Price of bond					1170.67

b)

Period	Year	Cash Flow	Spot Rate	Discount Factor	Buy for
1	0.5	48	0.024	0.988211769	47.43
2	1	48	0.024	0.9765625	46.88
3	1.5	48	0.024	0.965050555	46.32
4	2	48	0.024	0.953674316	45.78
5	2.5	48	0.024	0.942432183	45.24
6	3	48	0.024	0.931322575	44.70
7	3.5	48	0.024	0.920343929	44.18
8	4	48	0.024	0.909494702	43.66
9	4.5	48	0.024	0.898773368	43.14
10	5	1048	0.024	0.88817842	930.81
Price of bond					1338.13

c) b- Strip the bond