Question

Consider three different US Treasury securities with maturities T = 1, 2 and 3 years, all with principal of $100. As usual convention, today is time t=0.

1. One year Treasury bill trades at price ? = $97. 1

2. Two year Treasury note which pays 4% coupon annually, trades at ? ₂= $100.60

3. Three year Treasury note which pays 5% coupon 5% annually, trades at ? ₃= $101.9

• Compute one period forward rates at times T=1, 2 and 3. Assume that the price of 4 year zero coupon bond price is $0.82.

• You are thinking of starting a business on year two (T=2) when you might need to borrow money. You believe interest rates are low today. What interest rate can you lock in today for borrowing on year two, assuming you want to borrow only for a period of 2 years?

Answer 1

• First, let's make a table of Cash inflows ( marked with -ve sign) and Cash outflows (marked with +ve sign) to calculate IRR (use the excel function IRR and select the Year 0-4 entries as input argument) for each type of bond :

Security type	Year 0	Year 1	Year 2	Year 3	Year 4	irr
One year treasury bill	-97.1	100				2.99%
Two-year treasury bill	-100.6	4	104			3.68%
Three-year treasury bill	-101.9	5	5	105		4.31%
Zero Coupon bond	-0.82	0	0	0	1	5.09%

Now, we calculate 1-yr forward rate as below:

Using the formula, we get

4.38%

= 5.58%

7.45%

Similarly, we can calculate 2-yr forward rate as below:

Putting the values for n=2, we get

6.51%

This 2-yr forward rate is the rate which market is expecting returns for 2-yr.

Thus, we can lock-in today for 6.51% rate for borrowing on year two, assuming a term period of 2 years.