Fixed Income

Question 1

What is the first main assumption of the Cox-Ingersoll-Ross (CIR) model.

Answer 1

1. Assumes the short-term rate (r) converges to the natural long-run interest rate (b) .

Question 2

Name two types of Equilibrium term structure models

Answer 2

1. Cox-Ingersoll-Ross (CIR)

2. Vasicek model

Question 3

What is the main assumption of the Vasicek model

Answer 3

1. Vasicek model:Similar to the CIR model
2. Assumes that interest rate volatility level is independent of the level of short-term interest rates.

dr= a(b − r)dt+ σdz

Question 4

Name one arbitrage free term structure model.

Answer 4

1. Ho-Lee

Question 5

Describe Ho-Lee model.
What class of model?
What is its main assumption?
What is the formula?

Answer 5

1. Arbitrage free term structure model
2. Uses market prices to find time-dependent drift term θt
3. This model defines thecurrentterm structure as
   drt= θtdt+ σdzt

Question 6

Give three reasons Market participants prefer the swap rate curve as a benchmark interest rate curve rather than a government bond yield curve.

Answer 6

1 . Swap yield rates reflect the credit risk of commercial banks not governments.

2 .The swap market is not regulated by any government.

3. The swap curve has quotes at many maturities.

Question 7

What does the swap rate curve show

Answer 7

The rates used represent the interest rates or yield of the fixed-rate leg in an interest rate swap.

Question 8

Describe the Swap spread

Answer 8

1. The additional interest rate paid by the fixed-rate payer of an interest rate swap over the rate of the “on-the-run” government bond of same maturity.
2. Swap spread = (swap rate) − (Treasury bond yield)

Question 9

What is the presumption underlyimg Active bond portfolio management.

Answer 9

The current forward curve may not accurately predict future spot rates.

Question 10

Explain what interest rates managers forecast or model for active bond management

Answer 10

Managers forecast how spot rates will evolve relative to the rates from forward rate curves.

Question 10

Explain active bond management decisions

Answer 10

If the manager believes future spot rates will be lower than suggested by current forward rates the manager will buy a straight bond.

This is because a fall in spot rates in the future means the bond will be discounted by a lower rate in the in the future and the value of the bond will increase.

Question 11

Explain “riding the yield curve” in 3 points.

Answer 11

1. When the yield curve is upward sloping.
2. Hold long-maturity bonds (relative to their investment horizon).
3. Excess returns can be earned as the bond “rolls down the yield curve” (i.e., approaches maturity and increases in price).

Question 12

Explain What the Z-spread is

Answer 12

1. The spread that, when added to the spot rate makes the present value of all a bond’s cash flows equal to the bond’s market price.
2. TheZrefers to zero volatility—a reference to the fact that theZ-spread assumes interest rate volatility is zero.
3. The Z-spread is not appropriate to use to value bonds with embedded options.

Question 13

What is the Ted-Spread

Answer 13

The difference between rates of Private Banks and Government rates

Question 14

What does the Ted spread indicate

Answer 14

The overall level of credit risk in the economy.

Question 15

Explain the LIBOR OIS spread

Answer 15

1. The amount by which the LIBOR rate (which includes credit risk) exceeds the overnight indexed swap (OIS) rate (which includes only minimal credit risk).
2. LIBOR - OIS

Question 16

Explain Unbiased (Pure) expectations theory

Answer 16

Forward rates are an unbiased predictor of future spot rates.

Forward rate = future spot rate

Question 17

Local expectations theory

Answer 17

1. Preserves the risk-neutrality assumption only for short holding periods.
2. Over longer periods, risk premiums should exist.
3. This implies that over short time periods, every bond (even long-maturity risky bonds) should earn the risk-free rate.

Question 18

What is the driver of volatility in the CIR model

What does CIR stand for

Answer 18

1. The volatility of interest rates depends on short rate, r.

dr= a(b − r)dt+ σ sqrt(r) dz

dr= a(b − r)dt+ σdz

Cox Ingersoll Rosd

Question 19

How is TED spread calculated

Answer 19

TED spread (bank - gov)=
(three-month LIBOR rate)
− (three-month T-bill rate)

Question 20

What is the name of the spread that compares Treasury with Eurodollar?

Answer 20

TED spread