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Fixed Income - Bonds with Embedded Options
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Terms in this set (56)
Callable Bond
type of bond that benefits the issuer, as it can be called back as interest rates fall
Putable Bond
type of bond that benefits the holder, as it can be put back on the issuer as interest rates rise
Value of Callable Bond (General Formula, Relative to Straight Bond)
Value of Straight Bond - Value of Call Option
Value of Putable Bond (General Formula, Relative to Straight Bond)
Value of Straight Bond + Value of Put Option
Relationship Between Embedded Options and Interest Rate Volatility
the higher the interest rate volatility, the higher the value of the embedded option (both callable and putable)
Relationship Between Callable Bond Value and Interest Rate Volatility
the higher the interest rate volatility, the higher the value of the callable option, and thus the lower the value of the callable bond
Relationship Between Putable Bond Value and Interest Rate Volatility
the higher the interest rate volatility, the higher the value of the putable option, and thus the higher the value of the putable bond
General Backwards Induction Steps - Callable Bonds
begin at the right end of the tree with all values equaling Face Value + Final Coupon, then work backwards through the tree as normal to solve for value at each node, but if the value ever goes above the price the bond is callable at, replace the value with the callable price for the next value calculation
General Backwards Induction Steps - Putable Bonds
begin at the right end of the tree with all values equaling Face Value + Final Coupon, then work backwards through the tree as normal to solve for value at each node, but if the value ever goes below the price the bond is putable at, replace the value with the putable price for the next value calculation
Option-Adjusted Spread (OAS) (General Idea)
a fixed spread which is added to the one-year forward rates derived from default-free bonds normally used to calibrate a binomial interest rate tree to help price risky bonds, estimated from a pool of bonds with similar credit ratings
OAS Formula (Callable Bond)
Z-Spread - Option Cost
OAS Formula (Putable Bond)
Z-Spread + Option Cost
Relationship Between OAS and Interest Rate Volatility
since interest rate volatility doesn't affect a company at all, as interest rate volatility rises, the option cost increases, and since the z-spread remains constant, the OAS must fall for callable bonds and increase for putable bonds, meaning that the cost of the option explains more and more of the bond's z-spread
Effective Duration (Formula)
(Price of Bond if Benchmark Yield Curve Shifts Down - Price of Bond if Benchmark Yield Curve Shifts Up) / (2
Magnitude of Parallel Shift in Benchmark Yield Curve
Current Bond Price)
Relationship between Effective Duration of Callable/Putable Bonds and that of Straight Bonds
the effective duration of callable and putable bonds can never be more than the corresponding straight bond
One-Sided vs. Effective Duration for Callable Bonds
one-sided durations are larger than effective duration for rate increases, but smaller than effective duration for rate decreases
One-Sided vs. Effective Duration for Putable Bonds
one-sided durations are smaller than effective duration for rate increases, but larger than effective duration for rate decreases
Effective Convexity (Formula)
[Price of Bond if Benchmark Yield Curve Shifts Down + Price of Bond if Benchmark Yield Curve Shifts Up - (2
Current Bond Price)] / [(Magnitude of Parallel Shift in Benchmark Yield Curve)^2
Current Bond Price)]
Effective Convexity Trend for Option-Free Bonds
always low positive convexity, with the magnitude being relatively the same on both ends of the curve
Effective Convexity Trend for Putable Bonds
always positive convexity but approaches 0 as interest rates increase, as the convexity is floored by the put price
Effective Convexity Trend for Callable Bonds
positive convexity and growing for higher rates but decreases and can go negative for lower rates
Cap Provision
protects the coupon rate for a floating rate bond from increasing above a specified maximum rate, which protects the issuer against rising rates
Capped Floater
term for a floating rate bond with a cap provision
Value of a Capped Floater (Formula)
Value of Straight Floating Bond - Value of Embedded Cap
General Backwards Induction Steps - Capped Floater
calibrate the tree with floating coupons rather than interest rates, then start at the right side of the tree with Value = Face Value + Last Floating Coupon, and work backwards through the tree calculating values with the same formula, but with coupon rates used in discounting; and whenever a value appears above Face Value + Embedded Cap, replace it with that value for the next value calculation
Floor Provision
protects the coupon rate for a floating rate bond from decreasing below a specified minimum rate, which protects the investors against falling rates
Floored Floater
term for a floating rate bond with a floor provision
Value of a Floored Floater (Formula)
Value of Straight Floating Bond + Value of Embedded Floor
General Backwards Induction Steps - Floored Floater
calibrate the tree with floating coupons rather than interest rates, then start at the right side of the tree with Value = Face Value + Last Floating Coupon, and work backwards through the tree calculating values with the same formula, but with coupon rates used in discounting; and whenever a value appears below Face Value + Embedded Floor, replace it with that value for the next value calculation
Effective Duration of Floating Rate Bond - General Trend
the effective duration is close to equivalent to the time until the next coupon reset
Threshold Dividend
a cap amount for which if the dividend of a convertible bond exceeds, the company will lower the conversion price accordingly
Change of Control Conversion Price
the new conversion price of a convertible bond if there's a takeover or merger
Issuer Call Price
the call option on the stock of the company for its convertible bonds, which allows the company to force you to convert your shares into stock with an incentive of guaranteed extra return
Interpretation: Issuer Call Price of 110%
means you would be forced to convert your convertible shares into stock with a 10% extra return
Hard Put
provision in a convertible bond that allows the holder to put the bond back on the company for cash
Soft Put
provision in a convertible bond that allows the company to decide whether to pay the holder back in cash, stock, or subordinated notes when they put the bond back on the company
Conversion Value (aka Parity Value) (Formula)
Share Price * Conversion Ratio
Conversion Ratio (Formula)
Par Value / Conversion Price
Conversion Ratio (General Idea)
represents the number of shares you get when you convert your convertible bond into stock
Conversion Value (General Idea)
represents the dollar amount you'd make by converting all your shares and then selling at the current market price
Minimum Value of Convertible Bond
Max(Conversion Value, Underlying Straight Bond Value Using Arb-Free Valuation)
Market Conversion Premium (MCP) Per Share (Formula)
(Current Bond Price / Conversion Ratio) - Current Share Price
Market Conversion Premium (MCP) Per Share (General Idea)
represents the difference in value between selling the convertible bond itself and converting the bond to shares
MCP Per Share Minimum Value
can never be less than 0, or else there would be an arbitrage opportunity of buying the convertible bond and immediately converting it
Market Conversion Price (Formula)
Current Bond Price / Conversion Ratio
Market Conversion Price (General Idea)
represents what you could sell the convertible bond for in the market instead of converting it
MCP Ratio (Formula)
MCP Per Share / Current Share Price
MCP Ratio (General Idea)
represents how much of a percentage premium you get from trading the the convertible bonds rather than the actual shares
Advantage of MCP Ratio Over MCP Per Share
MCP Ratio allows for better comparability across different convertible bonds, as everything is scaled by its share price
Premium Over Straight Value (Formula)
(Convertible Bond Price / Straight Bond Value) - 1
Premium Over Straight Value (General Idea)
represents the downside risk of a convertible bond and demonstrates the amount extra we pay for the benefit of conversion
Value of Convertible Bond (Simplest Formula)
Value of Straight Bond + Call Option on Issuer's Stock
Value of Convertible Bond (with Issuer Call Option)
Value of Straight Bond + Call Option on Issuer's Stock - Issuer Call Option
Value of Convertible Bond (with Issuer Call Option and Holder Put Option)
Value of Straight Bond + Call Option on Issuer's Stock - Issuer Call Option + Holder Put Option
Busted Convertible
term for a convertible bond when the stock price is below the conversion price
Convertible Bond Risk-Return Characteristics Based on Share Price
as share price increases past the conversion price, the convertible bond behaves more like a stock, and as the share price decreases below the conversion price, the convertible bond behaves more like a bond
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