Fixed Income Flashcards
Chapter 32: Term Structure and Interest rate dynamics
Spot rate
rate of interest on an option-free, default-free, zero-coupon bond (gov’t bond/bill)
forward rate
interest rate set today for some future period
Forward rates are read as f(when, what)
Forward rate model
[1+S(j+k)](j+k) = (1+Sj)j x [1 + f(j,k)]k
This model illustrates how forward rates and spot rates are interrelated.
For example, f(2,3) should make investors indifferent between buying a 5-yr zero-coupon bond versus buying a 2-yr zero-coupon bond and at maturity, reinvesting the principal for 3 additional years
Forward pricing model
When the spot curve is upward sloping, the forward curve lies
above the spot curve
When the spot curve is downward sloping, the forward curve lies…
below spot curve
YTM vs spot rate
YTM is simply the weighted-average of spot rates used in valuation
YTM is a poor proxy for expected return
YTM works as expected return only if:
- held to maturity
- no default
- coupon payments are reinvested at YTM
Par curve
YTM on coupon paying bonds (gov’t) priced at par
IF spot rates evolve as predicted by forward rates…
bonds of all maturities will realize a 1 period return = 1 period spot rate and the forward price would be the same
Active bond portfolio management is built on the assumption that..
current forward curve may not accurately predict future spot rates
IF implied forward rates are too high
buy bonds
if implied forward rates are too low
sell bonds
Riding the yield curve/rolling down the yield curve
buying bonds w/a maturity longer than the investment horizon would provide a total return > return on a maturity matching strategy.
The steeper the curve, longer the bond, greater the return
swap rates
price (in yield) that a fixed rate payer will pay for Libor
why use swap curve?
- some countries don’t have a liquid gov’t bond market
swap spread
swap spread = swap rate - Treasury bond yield
swap spread is the additional interest rate paid by the fixed rate payer of an interest rate swap over the rate of the “on-the-run” gov’t bond of the same maturity
on the run = most recently issued
Z-spread
constant bps spread added to spot rates so that risky bond’s DCF = PV
Z-spread assumes interest rate volatility = 0
Can’t use this to value bonds w/embedded options
TED spread
TED spread = 3mo Libor rate - 3mo Tbill rate
TED spread is used as an indication of the overall level of credit risk in the economy
LIBOR-OIS spread
Libor rate - overnight indexed swap
This is an indicator of risk and liquidity of money market securities
Pure expectations theory (also know as unbiased expectations theory)
Forward curve is an unbiased predictor of future spot rates
Curve reflects
Local expecatations theory
Bond maturity doesn’t influence returns for short-holding periods
Liquidity preference theory
Investors demand a liquidity premium that is positively related to a bond’s maturity
Segmented markets theory
The shape of the yield curve is the result of the interactions of supply and demand for funds in different markets
Market participants are unable or unwilling to invest in securities other than their segmented market
Preferred habitat theory
Similar to segmented markets theory. Borrowers/lenders will have a preference for a segment, but will move to other segments if returns are compelling
Effective duration
Measures the sensitivity of a bond’s price to parallel shifts in the benchmark yield curve
Key rate duration
Measures bond price sensitivity to a change in a specific spot rate keeping everything else constant
Chapter 33: Arbitrage-free valuation framework
Arbitrage
Arbitrage = riskless profit with 0 investment
2 types of arbitrage:
Value additivity
Dominance
Value additivity: value of the whole = value of the parts
Dominance:
A -> costing $100 and returning $105
B -> costing $200 and returning $220
Arbitrage free valuation
an approach to security valuation that arrives at a price that is arbitrage free
Lattice Model
Pathwise valuation approach
In the pathwise valuation approach, the value of the bond is simply the average of the values of the bond at each path.
For a n-period binomial tree, there are 2(n+1) possible paths
Chapter 34: Valuation and Analysis of Bonds w/Embedded option
Embedded option
contingency provision that can be exercised by the:
- holder - put option
- issuer - call option
European option - exercised on single date
American option - exercised anytime
Bermuda option - exercised on several selected dates
Value of option embedded in a callable or putable bond
Vcall = Vstraight bond - Vcallable bond
Vput = Vputable bond - Vstraight bond
When interest rates increase, value of call option
decreases
Therefore, the value of a callable bond decreases
When interest rate decreases, the value of the call option
increases
Therefore, the value of the callable bond increases
When the interest rate decreases, the value of the put option
decreases
Thus, the value of the putable bond increases
When the interest rate increases, the value of the put option
increases
Thus, the value of the putable bond decreases
Opition adjusted spread (OAS)
A constant spread added to each forward rate in a benchmark binomial interest rate tree, such that the sum of the PV of the credit risky bond’s cash flow = market price
Effective duration
Effective Duration = (BV-Δy - BV+Δy)/(2 x BV0 x Δy)
Δy = change in required yield, in decimal form
BV-Δy = estimated price if yield decreases by Δy
BV+Δy = estimated price if yield increases by Δy
BV0 = initial observed bond price
Effective Convexity
Effective convexity = (BV-Δy - BV+Δy)/(2 x BV0 x Δy)
Δy = change in required yield, in decimal form
BV-Δy = estimated price if yield decreases by Δy
BV+Δy = estimated price if yield increases by Δy
BV0 = initial observed bond price
effective duration of a callable bond is less than or equal to
effective duration of a straight bond
effective duration of a putable bond is less than or equal to
effective duration of a straight bond
One-sided duration
durations that apply only when interest rates rise
Key rate durations (also known as partial durations)
Key rate durations capture the interest rate sensitivity of a bond to changes in yields of specific benchmark maturities
Key rate duration is used to ID interest rate risk from changes in the shape of yield curve
Capped floater
Value of a capped floater = value of straight floater - value of the embedded cap
floored floater
Value of floored floater = value of a straight floater + value of the embedded floor
Conversion ratio
Conversion ratio is the # of common shares for which a convertible bond can be exchanged
conversion value
conversion value of a convertible bond is the value of the # of common stock into which the bond can be converted
conversion value = market price of stock x conversion ratio
market conversion price
market conversion price = market price of convertible bond / conversion ratio
market conversion premium per share
market conversion premium per share = market conversion price - market price
