Homework 5 Due on April 8 Name: ID:

1. The table below presents the spot rates an investor faces.

Assume that, for each maturity, there is a zero-coupon bond traded in the market. These zeros pay $1,000 at their respective maturity.

a. Is the term structure positive, inverted, or flat?

b. What is the forward rate from t=1 to t=2?

c. Suppose that the investor is expecting to receive $1 million at t=1. This is a future cash inflow. He is planning to do the following investment strategy for this future cash inflow. He will borrow $990,099.01 (this is $1 million / (1+1%)) now, and use this borrowing to buy a two-year zero. At t=1, the one-year zero matures, and he will make the payment to the one-year zero lenders. At t=2, the two-year zero matures, and he will receive the payment from the two-year zero. Fill the below cash flow table (the unit is $1 million).

Year	Spot rates
1	2%
2	3%
3	4%
4	5%

	t=0	t=1	t=2
One-year zero	1 1+1%
Two-year zero	11+1%
Others (the $1 million that the investor is expecting to receive at t=1)	0	1	0
Total	0

d. What is the net return that this investor will get from his $1 million future cash flow from t=1 to t=2? Compare it with the forward and comment on what you find.

2. Suppose that we have two Treasury securities traded in the market, and we need to use them to calculate the theoretical spot rates. The first Treasury is a one-year zero, which pays $1,000 at t=1, and the current price is $950. The second Treasury is a two-year maturity, 5% coupon bond, and its current price is $900. The par value of the second Treasury is $1,000. Calculate the one-year spot rate and two-year spot rate, assuming that coupon payments are annual.

3. The table below presents the spot rates an investor faces.

a. What is the price of a two-year maturity 5% annual coupon bond? Par value is $1,000. What is its YTM?

b. What is the price of a two-year maturity 10% annual coupon bond? Par value is $1,000. What is its YTM?

Year	Spot rates
1	2%
2	3%
3	4%
4	5%