Term Structure of Interest Rates

Question 1

What is the typical (unconditional) shape of the yield curve?

Answer 1

It typically slopes a bit upwards. Rarely flat

Question 2

What are the 3 key theories of the term structure?

Answer 2

1) Expectation hypothesis
2) Liquidity preference explanation
3) Market segmentation & preferred habitat explanations

Question 3

What are the assumptions for the Expectation Hypothesis?

Answer 3

Long-term and short-term securities are perfect substitutes
Securities are free of default-risk
Individuals are risk neutral

Question 4

What is the Expectations hypothesis (EH)?

Answer 4

Observed long-term rates are a function of today’s short term rates and expected future short term rates. Implied forward rate is equal to the market’s consensus expectation of future short-term spot interest rates

Question 5

Under the EH, what does an upward sloping yield curve predict?

Answer 5

Investors anticipate an increase in short-term interest rates

Question 6

Under the EH, what does an downwards sloping yield curve predict?

Answer 6

Future short term rates are expected to be lower than current short-term rates

Question 7

What is the effect of uncertainty on the Expectation Hypothesis?

Answer 7

It does not hold. Rolling over one-uear zero coupon gives a higher expected return than holding a two-year zero coupon bond.
This follows from the general property that for a positive sequence, the harmonic mean is weakly smaller than the arithmetic mean

Question 8

What is the Liquidity Preference theory?

Answer 8

Yield curve slopes upwards because of a preference for more liquid securities. Market participants are assumed to be risk-averse. There is a liquidity premium on longer term securities.
Long term rates are determined by market expectations of future short term interest rates plus a liquidity premium

Question 9

What is the explanation of Market Segmentation theory?

Answer 9

Market participants prefer to stay in distinct maturity segments of the market. Trading in distinct maturity segments determines rates by forces of supply and demand. Short and long term rates may move independently.

Question 10

What is the Preferred Habitat Model?

Answer 10

A modification of the Market Segmentation hypothesis, incorporating both expectations and maturity preferences.
Market participants are not unwilling to shift from their preferred habitat, but reluctant to do so
Securities of different maturities are imperfect substitutes

Question 11

Why do you use trinomial trees to model interest rate options?

Answer 11

Because interest rates cannot go up indefinitely, unlike stocks

Question 12

What is the ‘put-call parity’ relationship of interest rate options?

Answer 12

CAP - FLOOR = SWAP

Question 13

Which are smooth functions R(t,T) for a fixed t or T?

Answer 13

For a fixed t R(t,T) is a smooth function of T
This is the yield curve
For a fixed T R(t,T) is a non-smooth function of T
This is the path of the yield on a bond maturing at T

Question 14

What are the puzzles of the term-structure

Answer 14

1) The term structure is upwards sloping although spot interest rates have been historically stable
2) The term structure has been flattening in recent years

Question 15

What are the explanations for the upwards term structure puzzle?

Answer 15

Risk-premium
Liquidity
Preferred habitat
Rep. agent w. Transaction Technology

Question 16

What are the explanations for the recent flattening of the yield curve?

Answer 16

More stable inflation
Reduced volatility in real economy
Increased demand (changed regulation of pension funds and increased demand from growing countries)
Lower supply long-term bonds (US Treasury’s temporary decision to issue 30 year bonds)

Question 17

What is Espinoza’s explanation for the upwards sloping yield curve?

Answer 17

State prices are a function of default and Central bank liquidity supply. States of the world with higher interest rates are also states of nature with higher risk-neutral probabilities. The risk-premium in the model comes from monetary costs. This can generate an upwards sloping term structure

Question 18

What is the yield curve?

Answer 18

The yield on a zero coupon bond as a funciton of the time to maturity

Question 19

What is the general procedure for calculating forward rates?

Answer 19

Important idea is, you only buy something in t=0. That is what it means to ‘lock’ in the forward rate.
Set up a system of equation for weight in each asset. Impose restriction to achieve the desired payout (i.e. 0 today, buy a million tomorrow)