CFA® Preparation FIXED INCOME www.dbf-finance.com Reading Reading Title Study Session Number 32 The Term Structure and Interest Rate Dynamics 12 33 The Arbitrage-Free Valuation Framework Valuation and Analysis of Bonds with Embedded 34 Options 35 Credit Analysis Models 13 36 Credit Default Swaps Luis M. de Alfonso CFA® Preparation FIXED INCOME www.dbf-finance.com Valuation and Analysis of Bonds with Embedded Options Study Session 13 Reading Number 34 Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.a: Describe fixed-income securities withembedded options Ø Embedded options in a bond allow an issuer to (1) manage interest rate risk and/or (2) issue the bonds at an attractive coupon rate Ø Embedded options can be (a) Simple options or (b) Complex options a) Simple options a.1) Callable bonds • Gives the issuer the option to call back the bond • Investor is short the call option a.2) Putable bonds • Allow the investor to put (sell) the bond back to the issuer prior to maturity • Investor is long the put option b) Complex options b.1) Estate put • Allows the heirs of an investor to sell the bond upon the death of the investor b.2) Sinking Fund bonds • Require the issuerto set aside funds periodically to retire the bond • This provision reduces the credit risk Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.b: Explain the relationships between the values of a callable or putable bond, the underlying option-free (straight) bond, and the embedded option V = value of the callable bond "#$$#%$& Price of a callable bond is lower V"#$$#%$& = V'()#*+,( - V"#$$ than the price of a comparable V = value of a straight (option-free) bond '()#*+,( straight bond because callable bond V"#$$ = V'()#*+,( - V"#$$#%$& incorporates a right for the issuer V"#$$ = value of the embedded call option V = value of the putable bond -.(#%$& Price of a putable bond is higher V-.(#%$& = V'()#*+,( + V-.( than the price of a comparable V = value of a straight (option-free) bond '()#*+,( straight bond because putable bond V-.( = V-.(#%$& - V'()#*+,( incorporates a right for the investor V-.( = value of the embedded put option Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.c: Describe how the arbitrage-free framework can be used to value a bond withembedded options LOS 34.f: Calculate the value of a callable or putable bond from an interest rate tree To value a callable or putable bond Use backward induction process and a binomial interest rate framework Note 1 When using a callable bond, the valueat any nodewhere the bond is callable, must be either the price at which the issuer will call the bond (call price) or the computed value, whichever is lower Note 2 When using a putablebond, the valueused at any nodewhere the bond is putable, must be either the price at which the investor will put the bond (put price) or the computed value, whichever is higher Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.c: Describe how the arbitrage-free framework can be used to value a bond withembedded options LOS 34.f: Calculate the value of a callable or putable bond from an interest rate tree Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.c: Describe how the arbitrage-free framework can be used to value a bond withembedded options LOS 34.f: Calculate the value of a callable or putable bond from an interest rate tree Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.c: Describe how the arbitrage-free framework can be used to value a bond withembedded options LOS 34.f: Calculate the value of a callable or putable bond from an interest rate tree $100.000 CALL RULE When using a callable bond, the value at any node where the bond is callable, must be either the price at which the issuer will call the bond (call price) or the computed value, whichever is lower Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.c: Describe how the arbitrage-free framework can be used to value a bond withembedded options LOS 34.f: Calculate the value of a callable or putable bond from an interest rate tree $100.000 PUT RULE $103.081 When using a putable bond, the value used at any node where the bond is putable, must be either the price at which the investor will put the bond (put price) or the computed value, whichever is higher Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.d: Explain how interest rate volatility affects the value of a callable or putable bond Ø Option values are positively relatedto the volatility of their underlying Ø Value of a straightbond isaffected by changesin the level of interest ratesbut is unaffected by changesin the volatility of interest rates Value of calloption Value of callable bond Interest rate volatility Value of put option Value of putable bond V"#$$#%$& = V'()#*+,( - V"#$$ Remember V-.(#%$& = V'()#*+,( + V-.( Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.e: Explain how changes in the level and shape of the yield curve affect the value of a callable or putable bond 1) LEVEL OF INTEREST RATE Value of a callable bond rises less than an Interest rate (because the maximum value of a callable bond is equivalent straight bond limitedby the exercise value of the call option) Interest rate Value of a putable bond falls less than (because the minimum value of a putable bond is an equivalent straight bond limitedby the exercise value of the put option) 2) SHAPE OF THE YIELD CURVE The value of a call option will be lower, as the probability Higher future interest rates of the option going in the money is low. Call option value increases as anupward sloping yield flattens Upwardsloping yield curve Value of a call option The value of a put option will be higher, as the probability of the option going in the money is higher. Put option Value of a put option value declines as an upward sloping yield flattens Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.g: Explain the calculation and use of option-adjusted spreads OAS (option adjusted spread) Is the constant spread added to each forward rate in a bechmarrk binomial interes rate tree, such that the sum of the present values of a credit risky bond´s cash flows equals its market price Backward induction process is based on risk-free binomial interest rate tree (the valuation assumes that the underlying bond is risk-free) If we are valuing a credit risky bond, it is necessary to add an increment for everyforward rate to adjust the price. This increment is called OAS § Bonds with similar credit risk should have same OAS § If a bond has an OAS higher than OAS of its peers, it is considered to be undervalued good investment § Conversely, bonds with low OAS (relative to peers) are considered to be overvalued Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.g: Explain the calculation and use of option-adjusted spreads Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.g: Explain the calculation and use of option-adjusted spreads The estimation of OAS is a largelyiterative process (beyond the scope of the exam) Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.h: Explain how interest rate volatility affects option-adjusted spreads “Assumed” Value OAS OAS Levelof (CALL) (PUT) volatility Calls Puts Callable Putable High High High Low High Low High Low Low Low High Low High Low Ø When analyst uses a higher/lower than actual level of volatility (when generating his benchmark interest rate tree), computed OAS for a callable bond will be too low/high and the bond will be erroneously classified as overpriced/underpriced Ø When analyst uses a higher/lower than actual level of volatility (when generating his benchmark interest rate tree), computed OAS for a putable bond will be too high/low and the bond will be erroneously classified as underpriced/overpriced Luis M. de Alfonso CFA® Preparation FI – Valuation and Analysis of Bonds with Embedded Options www.dbf-finance.com LOS 34.i: Calculate and interpret effective duration of a callable or putable bond Modified duration Measures a bond´s price sensitivity to interest rate changes(assuming that cash flows do not change) Convexity Curvature of the relation price-returnof a bond Comparison of convexity of two bonds with similar duration § Modified duration consider the variation of price withchanges in yield to be constant, so it is only useful forsmall changes in yield. Bond price § Bond A and Bond B have similar duration but different convexities § When changes on interest rate are high, we can observe that change in price differs due to different convexity in bonds Bond´s modified Bond A § duration When changes in yield are high, convexity has to be taken into account Bond B ∆0 3 4 § = - D x ∆ r + x C x (∆ r) 0 2 4 yield duration convexity Luis M.