# Theory of the term structure

EIFM Seminar 4 – week commencing Nov 1st 2021

Question 1: “According to the expectations theory of the term structure, it is better to invest in one-year bonds, reinvested over two years, than to invest in a two-year bond if interest rates on one-year bonds are expected to be the same in both years.” Is this statement true, false, or uncertain?

According to the expectations theory the interest rate on a two-year bond should be equal to the average between the interest rate on a one-year bond now and the expected interest rate on a one-year bond next year. If interest rates on one-year bonds are expected to be the same in both years, then the interest rate on the two-year bond should be the same as that on the one-year bond and investors should be indifferent between investing in a one-year bond now and reinvest in another one-year bond next year and investing in a two-year bond.

Question 2: If bond investors decide that 30-year bonds are no longer as desirable an investment as they were previously, predict what will happen to the yield curve, assuming (a) the expectations theory of the term structure holds; and (b) the segmented markets theory of the term structure holds.

Answer: (a) Under the expectations theory of the term structure, if 30-year bonds become less desirable, this will increase the demand for bonds of other maturities, since they are viewed as perfect substitutes. The result is a higher price and a lower yield at all other maturities and an increase in yield at the end of the yield curve. In other words, the yield curve would steepen at the end, and flatten somewhat along the rest of the curve. (b) Under the segmented markets theory, the assumption is that each type of bond maturity is an independent market, and therefore not linked in any particular way. Thus changes in long rates won’t affect shorter- and medium-term bond yields. Thus, the yield curve under the segmented markets theory will result in a jump in the 30-year rate, with the remainder of the yield curve unchanged.

Question 3: Suppose the interest rates on one-, five-, and ten-year U.S. Treasury bonds are currently 3%, 6%, and 6%, respectively. Investor A chooses to hold only one-year bonds and Investor B is indifferent with regard to holding five- and ten-year bonds. How can you explain the behavior of Investors A and B?

Investor A, even though she receives a lower expected return, clearly prefers to hold short-term debt, perhaps because it is more liquid. Investor A’s preferences are consistent with the segmented markets theory. They could also be consistent with the liquidity premium theory if the liquidity premium five-year and ten-year bonds are greater than 3%. Investor B is apparently maximizing expected return, but since he is indifferent between the five- and ten-year bonds, Investor B doesn’t appear to favour any particular maturity, and so views the five- and ten-year bonds as essentially perfect substitutes, an assumption consistent with the expectations theory of the term structure.

Question 4: Read the first two pages of the article “Signals from Unconventional Monetary Policy” by Michael Bauer and Glenn Rudebusch and answer the questions below

Why did the Fed start LSAPs? What securities did the Fed buy in the first two phases of the LSAPs and in what quantity?

What is the estimated impact of LSAPs on long-term interest rates? Give an example.

What are the two components of long-term interest rates?

What does the portfolio balance channel assume for investors’ preference? Which component of long-term interest rates is the portfolio balance channel supposed to affect? How is LSAPs supposed to affect long-term interest rates through portfolio balance channel?

What does the signalling channel assume for investors’ preference? Which component of long-term interest rates is the signalling channel supposed to affect? How is LSAPs supposed to affect long-term interest rates through signalling channel?