Valuation & Analysis: Bonds With Embedded Options Flashcards
What’s the difference in valuing fixed rate option free bonds vs valuing bonds with embedded options?
- Valuation of fixed-rate option-free bonds simply requires discounting the future cash flows.
- Valuing bonds with embedded options, such as callable and putable bonds, is more complicated because the cash flows vary with interest rates.
What is a callable bond, and what rights does the issuer have, additionally when will issuers exercise their right on callable bonds?
- callable bond: bond with an embedded call option
- gives the issuer the right to redeem the bond prior to maturity.
- Issuers will exercise this right when they can refinance the debt at a lower rate, which typically occurs because interest rates have fallen or the issuer’s credit quality has improved.
What is a protection period in bonds?
- prevents the issuer from calling the bond or exercising their bond during certain period of time.
What’s the difference between European style call option, American style, and Bermudan style call option?
European-style call options can only be called on the date the protection period expires.
American-style call options can be called any time after the protection period has expired.
Bermudan-style call options can be exercised on scheduled dates after the protection period has expired.
What is a putable bond and what rights are there?
- putable bond: bond with an embedded put option, which investors (lenders) have the right to sell back to the issuer prior to maturity, usually at par. (vast majority are European style bonds, no American style bonds.)
What is an extendable bond?
- holder of an extendible bond has the right to keep the bond past the maturity date, potentially at a different coupon rate. ( 3-year bond with the option to extend to Year 5 is similar to a 5-year bond with a put option that can be exercised after Year 3.)
What is the difference between convertible bond, estate put, sinking fund bonds?
- Convertible bonds: allow the investor to convert the bond to common shares of the issuing company.
- estate put: bond can be sold back to the issuer in the aftermath of the holder’s death.
- Sinking fund bonds: require the issuer to set aside funds to retire the bond, thus reducing credit risk.
What’s the formula for value of callable bond vs value of putable bond?
value of callable bond = value of straight bond (bond without option) - value of issuer call option
value of putable bond = value of straight bond + value of investor put option
What’s formula for valuing a bond that’s option free and default free?
bond value = coupon / (1+ spot rate) + coupon / (1+ spot rate ^2) + coupon + selling price/par value + coupon / (1+ sport rate ^3)
What are the steps involved for Valuing a 3 year Callable Bond with Zero Volatility?
- calculate one year forward rate (1+ spot rate in 2 years ^2) / (1+ spot rate in 1 year) = f1,1
- calculate one year forward rate in 2 years (1+ spot rate in 3 years ^3) / (1+ spot rate in 2 years^2) = f2,1
- discount cash flows backwards (bond price/value + coupon payment / 1+ forward rate)
- If bond price is less than par value (eg. 100) issuer will not exercise, will exercise only if higher than par value
When will a putable bond holder exercise their option?
- when value of putable bond trades below 100 of par value.
What’s the relationship between value of callable bond and the yield curve, specifically a flattening/inverted curve vs an upward sloping curve?
- Flattening/inverted curve (lower interest rates): value of call option goes up (due to issuer more likely to call).
- Upward sloping curve (higher interest rates): value of call option goes down (less likely for issuer to call).
What’s the relationship between value of putable bond and the yield curve, specifically a flattening/inverted curve vs an upward sloping curve?
- Flattening/inverted curve (lower interest rates): value of put option goes down (due to lower chance bondholder will exercise bond)
- Upward sloping curve (higher interest rates): value of put option goes up (higher rates higher chance bondholder will exercise bond).
When would an issuer exercise a bond when valuing a Callable Bond with Interest Rate Volatility?
- will exercise if value at each node is higher than call price
- determine value using the binomial tree method
0.5 [(VH + coupon payment / 1+ spot rate) + VL + coupon payment / 1+ spot rate)]
When would an issuer exercise a bond when valuing a Putable Bond with Interest Rate Volatility?
- will exercise if value at each node is less than than put price
- determine value using the binomial tree method
0.5 [(VH + coupon payment / 1+ spot rate) + VL + coupon payment / 1+ spot rate)]
What is Option Adjusted Spread (OAS) in the Valuation of Risky Callable and Putable Bonds?
OAS: Like Z-spread but adjusts for embedded options; used to value risky bonds with options. (Trial and error process to adjust the spread until bond price matches market price.)
Z spread: Fixed spread added to forward rates for option-free risky bonds when issuer-specific yield curves are unavailable.
How does OAS work in valuing bonds using binomial tree?
- option-adjusted spread (OAS): constant spread that is added to all the one-period forward rates in order to make the arbitrage-free valuation match a bond’s current market price.
What does high vs low OAS mean for callable bonds?
- higher OAS than other bonds with similar characteristics and credit quality is relatively undervalued and should be purchased.
- low OAS is an indication that a bond is overvalued.
How does increased volatility affect OAS?
- Increased volatility reduces OAS because increased volatility makes call option more valuable, lowering the callable bond price.
- OAS calculation compensates increased value of embedded call option due to higher interest rate volatility, by lowering the required spread to match bond prices.
What does duration measure?
- Duration: measures the sensitivity of a bond’s price to changes in its yield to maturity
What is effective duration formula and what does it measure?
- measures the percentage change of a bond’s price for a 100 bps parallel shift of the benchmark yield curve
Effective Duration: (PV -) - (PV+)/ 2 * change in curve * PV0
PV- = bond price after downward change in yield curve
PV+ = bond price after upward change in yield curve
PV0 = initial bond price
How doe callable, putable, and float adjusted bonds duration affected by increase and decrease of in interest rates?
- Callable bond: duration drops in a falling rate environment.
- Putable bond: duration drops in a rising rate environment.
- Floaters have low duration due to periodic rate resets. (floaters: bonds that reset periodically and tied to reference rate)
Are callable bonds more sensitive to increase or decrease of interest rates, are putable bonds more sensitive to increase or decrease of interest rates?
- Callable bonds are typically more sensitive to rate increases than decreases
- putable bonds tend to be more sensitive to rate decreases than increases
Why use one sided duration vs 2 sided duration (effective duration)?
- Effective durations are normally calculated by averaging the changes from shifting the yield curve up and down.
- One-sided durations often better capture the interest rate sensitivity of callable or putable bonds since their more sensitive to one or the either, sensitivity is symmetrical
What’s formula for one sided duration?
One Sided Duration: (PV0) - (PV+)/ change in curve * PV0
What’s the difference between effective duration and key rate duration?
- Effective duration: calculations assume a parallel/proportionate shift in the yield curve.
- Key rate (aka partial durations: address problem of effective duration
What is effective convexity and formula?
- measures the sensitivity of a bond’s duration to changes in interest rates (used for larger movements and changes, increases accuracy)
effective convexity ={(PV-) + (PV+) - [2*(PV0)]} / change in curve ^2 * PV0
When is convexity positive or negative for callable bonds and putable bonds?
- Callable bond convexity depends on rates:
1. negative convexity at low rates since price gains are limited due to the likelihood of being called.
2. At high rates, the bond is unlikely to be called and behaves like an option-free bond with positive convexity. - Putable bonds always have positive convexity, with the highest convexity when rates are high.
What is formula for valuation of a capped floater vs valuation for a floored floater?
value of capped floater = value of straight bond - value of embedded cap
value of floored floater = value of straight bond + value of embedded floor
Capped: upper limit on coupon rate, regardless of how high reference rate goes.
Floored: lower limit on coupon rate, regardless of how low reference rate goes.
What are conversion terms, and what is conversion ratio?
- conversion terms: pre-determined conversion price and conversion period.
- conversion ratio: # of shares received when bondholder converts
What’s the difference between hard puts and soft put options?
- Hard puts: Issuer must redeem in cash.
- Soft puts: Issuer can redeem in cash, stock, or subordinated notes.
What are 2 features of call options on bonds?
- Issuers can call the bond (call bond means usually with a premium and lockout period).
- Can force conversion if stock price exceeds the conversion price, stopping coupon payments.
What’s conversion value formula?
conversion value = underlying share price * conversion ratio
What is Market Conversion Price, Market Conversion Premium per Share, and Market Conversion Premium Ratio formulas?
- Market conversion premium ratio = market conversion premium per share/ underlying share price after downward
- market conversion premium per share = market conversion price - underlying share price
- market conversion price = convertible bond price /conversion ratio
What is formula for premium over straight value?
premium over straight value = (convertible bond price / straight value) -1
- overvalued if it is priced at a higher premium over straight value.
What is formula for convertible bond value? How can formula be adjusted to account for issuers call option and investors put option?
convertible bond value = straight bond value + call option on the issuers stock value
convertible bond value = straight bond value + call option on the issuers stock value - issuer call option + investors put option value
How do convertible bonds behave like stock prices at low stock prices vs high stock prices?
Acts Like a Bond at Low Stock Prices:
- Conversion is unlikely, so it trades based on its straight bond value.
- If the stock price approaches zero, the straight bond value also declines, reflecting bankruptcy risk.
Acts Like a Stock at High Stock Prices:
- Conversion is likely, so the bond’s value moves with the stock price.
- However, it still holds a small premium over the conversion value due to downside protection.
