L10 - The Term Structure of Interest Rates

Question 1

What are yield curves?

Answer 1

• The yield curve (term structure of interest rates) is a plot of yields to maturity (YTMs) across different contract lengths
• There are 4 main types:
  
  • Flat –> yield is pretty much the same no matter what the maturity of the bond is
  • Rising –> normal shape
  • Inverted
  • Hump-Shaped
• Yields in the Yield curve table are the spot rates

Question 2

What is a Pure Yield Curve?

Answer 2

• It uses the YTMs of pure discount Treasuries (i.e., zero-coupon bonds, or STRIPS) to generate the yield curve plot
• Pure yield curve can be used to price coupon bonds.

Question 3

What determines the spot rates?

Answer 3

• The short rates
• The short rate for a given time interval (e.g. 1 year) is the interest rate available during that period.
  
  • We are usually look at historical data to predict the future short rates (albeit not precisely)

Question 4

Differences between the spot and short rates?

Answer 4

Question 5

How do you calculate the spot rate from the short rates?

Answer 5

• the n year spot rate is the geometric average of all the short rates till year t

Question 6

What is the Forward Rate?

Answer 6

Question 7

What determines the term structure?

Answer 7

• Expectations Hypothesis
  
  • Forward rates that are the market’s expected future short rates.
  • That is, f_t = E(r_t)
  • By construction, we use the yield curve to derive the forward rate
  • Implication of this hypothesis: the yield curve provides information on the market’s expectations about the future
• Liquidity Preference Hypothesis
  
  • Different investors have different liquidity preferences.
  • Forward rates and yield curves may or may not reflect the market’s expectations about the future.
  • Suppose most of the investors prefer short-term bonds because they are safer (lower interest rate risk, default risk, ……) and have better liquidity.
  • In this case, investors demand a liquidity premium for holding long-term bonds. f_t > E(r_t)
  • However, if most of the investors prefer long-term bonds e.g. penion funds, we may see f_t < E(r_t)

Question 8

How can we interpret a upward-sloping yield curve?

Answer 8

Question 9

How can we interpret inverted yield curves?

Answer 9

Question 10

Does an inverted yield curve guarantee a market melt-down?

Answer 10

• Since March 2019, multiple news articles have viewed this as a sign of financial crisis.
• The Treasury yield curve inverted multiple times from 2019 to 2020. Crisis?
• Their argument:
  
  • It happened in the ‘80s, so it will happen again.
  • Investors are flooding to the long-term credit market because they are worried about the current environment.
  • Not enough liquidity in the short-term credit market. Firms cannot borrow so they bankrupt.
• We still haven’t seen any credit market crisis because:
  
  • Interest rate is very low. There is plenty of capital in the market.
  • In 2019, short-term rates were high partially because the market was worried about the inflation risk and political uncertainty.
  • The market did not expect inflation or political risk to plague the economy in the long-run. Thus, long-term rates did not increase that much.