Theories Of The Term Structure Of Interest Rates

Question 1

Yield curve

Answer 1

The graphic representation of the relationship between the yield of bonds of the same credit quality (risk) but different maturity

(Different maturity since this topic of term structure looks at overtime!! So different maturities is relevant)

Question 2

What was the yield curve made of in the past?

Answer 2

Observations of prices and yields in the treasury market.

However this is unsatisfactory measure of relationship between yield and maturity.

Question 3

Why based of treasury market? (2)

Answer 3

Treasury securities are free of default risk, and differences in creditworthiness do not affect yield estimates

Treasury market is very liquid - easily converted into cash so can sell before maturity

Question 4

What is the price of a bond?

Answer 4

Present value of its cash flows.

Question 5

What is the appropriate interest rate on bonds

Answer 5

Treasury security yield (with same maturity as the bond) + risk premium

Question 6

Term structure of interest rates must explain … (3)

Answer 6

Interest rates on bonds of different maturities move together overtime. (E.g monetary policy can determine this; higher rate=higher bond rate)

When short-term interest rates are low, yield curves are more likely to have an upward slope (inflation risk more in long term, so higher yield demanded, also recall yield and liquidity relationship, short term bonds more liquid so longer bonds compensate with higher yields) ; and when short-term rates are high, yield curves are more likely to slope downward and be inverted.

Yield curves almost always slope upward.

Question 7

What 4 theories explain the shape of the term structure just mentioned

Answer 7

Expectations theory
Liquidity theory
Preferred habitat theory
Market segmentation theory

Question 8

Forward rates definition and example

Answer 8

Interest rate on bonds that will start in the future.

Investor with following two options:
Buy a one year Treasury bill
Buy a six-month Treasury bill, and when it matures in six months, buying another six-month Treasury bill.

The investor will be indifferent between the two alternatives if they produce the same return.

The investor knows the spot rate of the first six-month bill, but not the forward rate, i.e. the yield on the bill that will be purchased six months from now.

Question 9

Example pg 9

Question 10

Pure expectations theory, definition and formula

Answer 10

i = it +f₁ +f₂ +f₃ +…+ft+(n−₁)
/
n

Interest rate of a long term bond equals the average of short rates over the life of the bond.

Question 11

According to the pure expectations theory, what do the forward rates represent

Answer 11

Expected future (spot) rates

Question 12

Scenario: assume a flat term structure. News makes expected interest rates rise.

How would market participants respond?
How would speculators respond?
How would borrowers respond?
Overall effect?

Answer 12

Market participants avoid buying long term bonds since they expect price of bonds to fall. (r=B/Pb)

Speculators would anticipate this fall in price, and therefore sell long term bonds before they fall.

Borrowers are more incentised to borrow now before the rates rise.

Overall, these actions tilt the term structure upwards until it is consistent with expectations of higher future interest rates

Question 13

What does the pure expectations theory omit

Answer 13

Does not account for the risks of investing in bonds.

Question 14

Problem:

Answer 14

Pure expectation theory believes forward rates predict expected future rates:

If were perfect predictors of future interest rates, then future price of bonds and returns would be known with certainty

Question 15

2 uncertainty risks: what are we uncertain about

Answer 15

Uncertainty over price of bond at the end of investment horizon (as mentioned in previous FC)

Uncertainty about about rate at which proceeds from bond that matures during the horizon can be reinvested

Question 16

Uncertainty about about rate at which proceeds from bond that matures during the horizon can be reinvested. What is this called

Answer 16

Reinvestment risk

Question 17

Does the ‘Pure Expectations Theory explain the 3 observations we started with?

(Interest rates of different maturites move together

Low rates in SR, likely upward sloping. High rates in SR, likely downward sloping.

Yield curves almost always slope upwards)

Answer 17

1. Interest rates of different maturites move together - yes
2. Low rates in SR, likely upward sloping. High rates in SR, likely downward sloping.
   - yes
3. It does not explain why yield curves almost always slope upwards. It only answers why curve slopes upwards when interest rates are expected to rise (like scenario in FC 18, with news!)

Question 18

Liquidity premium theory

Firstly what risks do bondholders face (2)

Answer 18

Inflation and interest rate risk.

The longer the term of bond, the greater both risks.

Question 19

How does interest rate risk arise,

And 2 ways interest rate risk occurs

Answer 19

From the mismatch between the investor’s investment horizon and a bond’s maturity.

E.g if planning to sell before maturity, dependent on interest rate: (want lower interest/yield rates, so they can sell at a higher bond price)

The longer the term, the greater the price changes for a given change in interest rates: so larger potential capital losses if interest rate are high. (Longer=more volatility and amplified price reactions)

Question 20

So as there is more risk in longer term bonds, investors require compensation.

We can think about bond yields in 2 parts:

Answer 20

Risk free - expectations theory
Risk premium - inflation (uncertainty over real returns) & interest rate risk (long term - more volatility in price + selling before maturity want low interest!)

Together this makes the liquidity premium theory

Question 21

How do we show the liquidity premium theory equation

Answer 21

Use pure expectations equation (average of spot rate and forward rates/periods)

ADD lnt (risk premium)

Question 22

So basically liquidity premium explains upward sloping yield curve how?

Answer 22

Generally short term bonds are preferred as more liquid.

So, to invest in longer term bonds, they require a higher yield premium to compensate for less liquid, and inflation & interest rate risk.

Question 23

Preferred habitat theory

Answer 23

Investors have a preference for bonds of one maturity over another. (Their habitat)

Question 24

When will they deviate from their habitat (of a specific maturity?

Also do they prefer short/long term bonds in this theory?

Answer 24

Only buy bonds of different maturities if higher expected return.

Prefer short term bonds over long term bonds

Question 25

So what model explains why yield curves slide almost always upward?

Answer 25

Liquidity preference - cos of the interest and inflation risk associated with long term bonds, meaning they have to compensate with a higher yield so upwards sloping structure overtime!

Question 26

Segmented markets theory - main concept What are interest rates for each bond determined by? How does this explain why yield curves usually slope upwards?

Answer 26

Bonds of different maturities are not substitutes at all. Interest rates for each bond are determined by s&d, and investors have preferences for bonds with one maturity over another. If investors prefer bonds with shorter maturities with less interest-rate risk, this explains why yield curves usually slope upwards since S&D determines yield, demand lower for long term so need higher yield!