Question

In the Treasury market, what is the spot rate? What is the spot rate curve? Explain how the spot rate curve is constructed (please go beyond the term "bootstrapping" used for the process)? Why is the spot rate curve important?

Answer 1

Answer: A.Spot rate : It is the Discount rate at which the present value of the zero Coupon bond equals its price.

B.Spot rate Curve: The Curve Constructed using treasury Spot rates is known as the Spot rate Curve. In this We Plot the Spot rate for the Different Maturities of a bond.

It is used as a benchmark in Pricing Bonds, also known as Zero Curve.

C.Spot rate Curve Construction : Boot Strapping is the method used wildly in making Spot rate Curves. In this we have to calculate the Spot rate for different Maturities to Construct the Curve.

To give you an Example lets say we have this below given data for Different Securities.

Period	Year	Yield	Price
1	0.5	4%	100
2	1	4.30%	100
3	1.5	4.50%	100

Note,First two are zero Coupon Securities. So the Spot rate will remain Same as the yield of these Securities.

We will have to calculate the Spot rate for 3rd Security

Since 1.5 yr Security is selling at par, its coupon will be 4.5%

Cash Flow at 0,5 yr = 100* 0.045*0.5 = 2.25

Cash Flow at 1 yr = 100 * 0.045 * 0.5 = 2.25

Cash Flow at 1,5 yr = 100 + 100 * 0.045 * 0.5 =102.25

Now to calculate spot rate of 1.5 yr put the present value of cash flows to 100

100 = 2.25 / (1 + 4%/2)^1 + 2.25 / (1 + 4.3%/2)^2 + 102.25/(1+ Spot rate/2)^3

On Solving this you will get spot rate as 4.511 for the 1.5 yr

Similarly for any other Security as well you can calculate the spot rate, plot these rates against the maturity and you will get the Spot rate Curve

D. Spot rate curve are important as they use potentially better accurate discount factor for the Bonds present value calculation.