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.

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

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

• Three year Treasury note which pays 5% coupon 5% annually, trades at ? = $101.90 3

1. (a) Compute YTM (yield-to-maturity, y) of all three bonds.

2. (b) Compute zero-coupon bond prices and zero-coupon yields (i.e. zero-rates) of all three maturities, T = 1, 2 and 3 years.

3. (c) 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.

4. (d) 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

Tenure	FV	MV	Coupon	Coupon	YTM	Zero Coupon Bond Price
1	100	97.100	0%	0	2.94%	97.141
2	100	100.602	4%	4	3.69%	93.013
3	100	101.903	5%	5	4.32%	88.073
YTM =	C + (F - P)/n		Zero Coupon Bond Value =			F
	(F + P)/2					(1 + r)^n
C = Coupon			F = Face Value
F = Face Value			r = returns
P = Price			n = Tenure
n = Tenure