# P1.T3.22.31. Term structure theories

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Learning objectives: Derive forward interest rates from a set of spot rates. Derive the value of the cash flows from a forward rate agreement (FRA). Calculate zero-coupon rates using the bootstrap method. Compare and contrast the major theories of the term structure of interest rates.

Questions:

22.31.1. Assume the following six-month forward rates that are quoted per annum with semi-annual compounding:
• F(0.5, 1.0) = 2.0%; i.e., the six-month forward rate starting in six months
• F(1.0, 1.5) = 4.0%
• F(1.5, 2.0) = 6.0%
If the price of a 7.0% semi-annual coupon bond is $103.20, which is nearest to the 2-year spot rate? a. 4.30% b. 5.40% c. 6.60% d. 7.90% 22.31.2. Suppose six months ago Acme Global entered into a forward rate agreement (FRA) applied to notional of USD$20,000,000; aka, $20.0 million. At the time (aka, inception), the FRA paid a fixed rate of 3.00% in exchange for receiving the three-month floating rate starting in one year, S(1.0, 1.25). Acme is the borrower who pays a fixed rate (i.e., 3.00%) and receives the floating rate. Today the six-month spot rate is 2.80% and the nine-month spot rate is 3.10%. From Acme's perspective, which of the following is nearest to the present value of the FRA? a. -$115,000
b. -68,700
c. $34,200 d.$1.490 million

22.31.3. There are various theories of the term structure of interest rates, and they include the following:
• Liquidity preference (proposed by John Maynard Keynes) says that investors prefer to hold liquid assets
• Preferred habitat says that borrowers and lenders have preferences for their particular maturities
• Pure expectation theory says a 5-year (or X-year) bond has the same expected return as a series of 5 (or X) one-year bonds
• Segmented markets theory says that yield is only a function of supply/demand for each particular maturity
About these four theories, each of the following statements is true EXCEPT which is false?

a. Market segmentation theory is unrealistic
b. The observation of a persistently upward-sloping yield curve can justify all four of these theories (such that none can be excluded by it)
c. In pure expectations, the forward rate is an unbiased predictor of the future spot rate, but in liquidity preference theory, it is a biased predictor
d. Preferred habitat theory is among the more realistic of the set because it accepts elements of both pure expectations and market segmentation