# 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?

Answer: False.

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?

Answer:

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?

Answer:

The Fed started LSAPs after the short-term interest rates reached the zero-lower bound. While the short-term interest rates were virtually zero, long-term interest rates were still high, discouraging borrowing of consumers and firms and decreasing aggregating demand. The objective of the LSAPs is to lower long-term interest rates which are more relevant to the borrowing decision of consumers and firms.

The first phase of LSAPs started in Nov 2008 when the Fed announced that it will purchase \$100 billion of GSE agency debt and \$500 billion of MBS. The Fed bought GSE agency debt worth \$175 billion, MBS worth \$1,250 billion and Treasury bonds worth \$300 billion in the first phase of LSAPs. It bought Treasury bonds worth \$600 billion in the second phase of LSAPs.

Using different methodologies, researchers generally agree that the Fed was successful in lowering long-term interest rates. For example, Gagnon et al. (2011) estimated that QE1 announcement lowered the yield on the ten-year Treasury note about 0.50 to 1.0 percentage point.

The interest rate on a long-term bond can be decomposed into an average of future expected short-term interest rates and a term premium that investors require for bearing the risk of a long-term bond investment.

The portfolio balance channel assumes investors are heterogeneous: different investors prefer different kinds of assets. They have preferred habitat on a yield curve: the markets for bonds with different maturities are at least partly separated. The portfolio balance channel is supposed to affect the term premium component. Through LSAPs, the Fed decreases the supply of long-term bonds available to private investors, leading to lower interest rates because of a decrease in term premium. LSAPs probably removed the investors who are less willing to hold long-term bonds and left only those investors who are most willing to bear interest rate risk to hold them. And they require less compensation, or term premium for holding these bonds.

The signalling channel assumes investors treat bonds with different maturities as substitutes. When short-term interest rates are expected to stay low for longer, long-term bonds’ interest rates will be brought down too. It is supposed to affect the average of expected future short rates. Through LSAPs, the Fed could send out the signals to make the market believe that the economic conditions are worse than previously thought and that it would leave the policy rate near zero for longer than previously expected.