Fixed income

Question 1

List key characteristics of T-bills

Answer 1

1) Mature in one year or less
2) Do not pay coupons - traded at a discount of the par
3) Typical maturities: 28d, 91d, 182d, 364d
4) Quoted on an annualized discount basis:
(FV - Spot)/FV * 360/(days till maturity) * 100%

Question 2

List key characteristics of T-notes and T-bonds

Answer 2

1) T-notes - 2 to 10 years, T-bonds - 30 years
2) Pay coupons twice a year
3) Quoted at percentage of par (XX:n reads XX% + n/32%)

Question 3

List key characteristics of TIPS

Answer 3

1) The principal is adjusted to the US CPI
2) Coupon is fixed
3) Maturities: 5y, 10y, 30y

Question 4

Key issues with LIBOR

Answer 4

1) Annualized based on 360-day year

2) Add-on rate: interest = LIBOR x (Mat / 360)

Question 5

Who publish LIBOR and Euribor?

Answer 5

LIBOR - British Banker’s Association

Euribor - ECB

Question 6

Formula for calculation of a continuously compounded rate

Answer 6

ln(1 + discrete_rate)

Question 7

Pricing of a floating-rate band

Answer 7

Floating-rate bond price is equal to par at each settlement date. This is because if the coupon rate of a bond is equal to the market rate, the bond is traded at par

Question 8

Riding the field curve / rolling down the yield curve strategy

Answer 8

Buying bonds longer than the investment horizon and selling them pre-matured (works only if the curve is upward slopping and if there is no downward shifts)

Question 9

Advantages of swap curve

Answer 9

1) Reflects credit risk of commercial banks instead of government
2) The swap market is not regulated which makes it more comparable across countries
3) The swap curve has more points

Question 10

Return over a one-year holding period

Answer 10

Will be the same for bonds of different maturities if the spot rates will evolve exactly as forward rates predict

Question 11

Popular interest rate spreads

Answer 11

1) Swap spread (LIBOR Swap vs. T-sec of some t) - reflects level of risk of banks
2) I-spread (YTM vs. Swap rate of some t) - reflects individual bond risk
3) Z-spread (add-on to swap curve making NPV of bond equal to its market price) - reflects individual bond risk
4) TED-spread (3-month LIBOR vs. 3-month T-bill) - better than 10-year swap spread
5) LIBOR-OIS - reflect gener well-being of banking system

Question 12

Term structure of interest rates theories

Answer 12

1) Unbiased expectations theory (yield curve reflects expectations on change in interest rates)
2) Local expectations theory (as UET, but risk-neutrality holds only in the short run)
3) Liquidity preferences theory
4) Segmented markets theory (rates for different tenors are not inter-connected and rather depend on preferences of players on different markets)
5) Preferred habitat theory (markets for different tenors are not completely separated, but preferences do exist)

Question 13

Term structure models

Answer 13

Equilibrium-based models imply mean-reversion:
1) Cox-Ingersoll-Ross - r > 0, volatility ~ r
2) Vasicek - volatility does not depend on r, however r may become negative
Arbitrage-free-models:
3) Ho-Lee - takes yield curve as given (can be calibrated to current market conditions)

Question 14

What are relative weights of yield curve movements in changing returns of a bond portfolio

Answer 14

1) Level change (parallel shifts) - 75%
2) Steepness change - 24%
3) Curvature shape change - 1%

Question 15

What is the dynamics of interest-rate volatility?

Answer 15

Short rates are relatively more volatile

Question 16

Types of durations

Answer 16

1) Effective duration - sensitivity to small parallel shifts
2) Key rate duration - sensitivity to shift in one particular rate
3) Level / steepness / curvature durations

Question 17

Getting spot rate curve from the par curve

Answer 17

Bootstrapping spot rates from S_1 to S_T:
S1 = P1
Par = Par_rate/(1 + S1) + (Par = Par_rate)/(1 + S2)^2

Question 18

Core things about binomial interest rate trees

Answer 18

1) Distance between adjunct nodes is exp(2*std)
2) Average node = Forward rate
3) Binomial trees does not allow for path-dependence

Question 19

Effective duration

Answer 19

[V(-dy) - V(+dy)]/[2V0dy]
Embebed options create insurance against rate movements so average effective durations are lower. For this reasons one-side duration are more applicable for them.

Question 20

Effective convexity

Answer 20

[V(-dy) + V(+dy) - 2V0]/[V0dy^2]
For normal bonds convexity is positive
For callable bonds convexity is negative for low rates

Question 21

Key rate durations - difference between different tenors

Answer 21

1) In most cases the most important duration is the maturity one
2) For bonds with embedded options option-maturity duration might be the most important one
- If dividends are low for putable bonds
- if dividends are high for callable bonds
3) For bonds with low coupon payments duration could be negative for horizons other than maturity

Question 22

Ratchet bond

Answer 22

Floating-rate bond with progressively decreasing cap

Question 23

Convertible bonds

Answer 23

1) Usually have embedded put options on specific events (e.g. mergers)
2) Value = min(straight value, value of converted shares)
3) Market conversion price = Price of bond / conversion factor
4) Conversion premium ratio = Conversion premium / share price
5) Premium over straight vale = (Market value of bond / Straight value of bond) - 1

Question 24

Put-call parity for bonds with embedded options

Answer 24

C - P = PV(Forward price on exercise date) - PV(Exercise price)

Question 25

Estate bond

Answer 25

Bond with put option for heirs of the investor when she dies

Question 26

Relation between put bonds and extension bond

Answer 26

3y bond with put option after 2 years has the same value as 2y bond with option for 1y extension