R.36 Valuation and Analysis: Bonds with Embedded Options Flashcards
LEARNING OUTCOMES The candidate should be able to: describe fixed-income securities with embedded options; explain the relationships between the values of a callable or putable bond, the underlying option-free (straight) bond, and the embedded option; describe how the arbitrage-free framework can be used to value a bond with embedded options; explain how interest rate volatility affects the value of a callable or putable bond; explain how changes in the level and shape of the yield curve af
1
Q
Convertible Bonds (know terminology)
- Conversion ratio
- Market conversion price
- Conversion value
- Straight value
- Minimum value of convertible bond
- Market conversion premium
- Market conversion premium ratio
- Premium over straight value
A
- Conversion ratio: #shares per bond
- Market conversion (effective) price
Market Price Bond / Conversion ratio
-
Conversion value: (Post-conv share price)(conv ratio)
- CV = P0 x CR
- Straight value: PV of CFs if not converted (usually given)
-
Min value of convertible bond: Greater of conversion value or straight value
- most likely to show up on exam
-
Mkt conversion premium: (Mkt conv price) - (mkt stock price)
- MCP/sh = (PV0 / CR) - P0
-
Market conversion premium ratio:
- (Mkt conv premium) / (mkt price)
-
Premium over straight value:
- (MV of bond / straight value) -1
Mkt conv price is effective price per share when converting.
2
Q
Convexity
A
Positive convexity - price impact or rate decrease greater than price impact of rate increase
- putable bond
- straight bond
Negative convexity
- Callable bonds - price appreciation of callables is limited due to the short call (price compression).
3
Q
Effective Duration
- (relationships in call/putable, zero, fixed, floater)
- formula
A
Effective durations:
- durationcallable/putable ≤ effective durationstraight
- duration(zero) ≈ bond maturity
- durationfixed rate < bond maturity
- effective duration of floater ≈ time in years to next reset
4
Q
Volatility impact on Embedded Options
- Straight bond value impact if volatility increases?
- Embedded bond value impact if volatility increase?
- OAS impact?
A
Straight bond impact from volatility?
- None! Straights are impacted by rate changes!
Embedded impact of increased volatility?
- Vcall option ↑, V<span>put option</span> ↑, Vcallable bond ↓, V<span>putable bond</span> ↑
Volatility (σ) is an assumption!
↑ σ = ↓ lower OAS for callable bonds
↑ σ = ↑ higher OAS for puttable bonds
Assumed σ impacts calculated OAS (which isn’t observable so different data providers can have very different OAS). If σ is wrong, then OAS will be wrong.
