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Chapter 6

This

**preview**shows half of the first page. to view the full**2 pages of the document.**Chapter 6A: The Term Structure of Interest Rates

Spot Rates and Yield to Maturity

So far we have assumed that interest rates are constant over the all future periods

o They actually vary over time because inflation rates differ over time

The spot rate is the interest rate over one period of the investment

PV =

If we want to calculate a single rate for the bond:

o PV(known) =

solve for r

Graphing the Term Structure

The term structure describes the relationship of the spot rate with different maturities

Explanations of the Term Structure

We will begin by defining the term forward rate and relate it to future interest rates

Definition of the Forward Rate

If an individual can earn a 10% spot rate over two years, it is equivalent if he were to earn

8% in the first year and 12.04% (

) during the second year

o This hypothetical rate over the second year is the forward rate

So: (1+r2)2 = (1+r1) x (1+f2) f2 =

General Formula:

Estimating the Price of a Bond at a Future Rate

The spot rate from date 0 to date 1 will differ from the spot rate going from dates 1 to 2

The second rate will not be known to us until the first period has passed

o Should the rate of inflation rise between date 0 and 1, the spot rate for the year 2

would likely be high the opposite is also true

Amount that a two year bond is expected to sell at date 1 =

o Expected value differs across individuals; this is a forecasted selling price

The Expectations Hypothesis

It seems reasonable that investors would set interest rates in such a way that the forward

rate = the spot rate expected by the marketplace one year from now

o Therefore f2=Spot rate expected over year 2 (assuming investors are risk-neutral)

Why would you buy a two year bond if you expect the value at date 1 to be less than that

of a one year bond at date 1

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