Stripping, Reconstitution

Stripping
If a dealer finds Treasury coupon bonds trading at a lower price than Treasury strips, he can make a riskless (arbitrage) profit by buying coupon bond and selling strips.

Reconstitution
If a dealer finds Treasury coupon bonds trading at a higher price than Treasury strips, he can make an arbitrage profit by buying strips and selling coupon bonds.

Appropriate discount rate

· The minimum interest rate that an investor should accept is the yield that is available in the market place for a risk-free bond.
· The on-the-run Treasury security is most often used as they reflect the latest yields and are the most liquid securities.
· For corporate bonds, a risk premium can be added to the risk free rate.

Ideally, each cash flow should be valued using the spot rate corresponding to its maturity. Bond price is inversely related to discount rate. Can add risk premium to the risk free rate or series of risk free sport rates

Computation of Bond Price

Bond prices can be expressed as a percentage of par value or as a yield.

Yield to Maturity (YTM)
· A single discount rate that makes the present value of a bond’s cash flows equal to the market price.
· YTM for a semiannual-pay bond is twice the semiannual discount rate and so called as bond equivalent yield.

YTM_annual-pay = (1+YTM _{semianual-pay}/2)²-1
YTM_{semiannual-pay} = [(1+YTM_annual-pay)^1/2-1]x2 = BEY

Bond price of a bond with semi-annual coupon payment:

P = CPN1 / (1-YTM/2) + CPN2 / (1-YTM/2)² +.+ (CPN2N + PAR) / (1-YTM/2)^2N

Where: YTM is BEY

Bond price for a zero-coupon bond
P = Par / (1 + YTM/2)^{2 N}

Where: YTM is BEY


Full price of a bond between coupon payments

P= Σ[Cash flow in period t/(1 + Discount rate)^(t-1+w)]

Where:
w is the no. of days remaining until next coupon (i.e. between settlement date (exclusive) and next copon date(inclusive)/ Total days in coupon period)

Accrued interest = Coupon x (1 - w)

Clean price = Full price - Accrued coupon.

Day count conventions:
· Actual/Actual (US governmentt bond);
· Actual/365 (Bristish government bond),
· 30E/360 (German government bond, Eurobond, most corporate bond, most munis)

Price-Yield Relationship
Inversely related, convex ( bond prices go up faster than they go down)

Pull to par
As time passes, the price of a bond trading at a premium will fall back to par and the price of a bond trading at a discount will rise to par.

Deficiency of traditional approach to valuation:
Each cash flow is unique. Valuing all cash flows of a security using a single discount rate is incorrect unless for a flat term structure. YTM is only a an approximate or weighted average of a set of spot rates.

Arbitrage-free valuation
Each individual cash flow is valued by discounting it at a spot rate corresponding to its maturity.

P = CPN1 / (1-S1) + CPN2 / (1-S2)² +.+ (CPNN + PAR) / (1-SN)^N

Where Si is the corresponding spot rate.
Arbitrage: If the sum of the PVs of cash flows is more than the price of the security, then buy the security and sell the cash flows individually, and vice versa.
Cash flows are valued using the spot rate corresponding to their maturity. It is more accurate than the traditional approach.

Difficulty in estimating expected cash flow

· Bonds with embedded option - uncertain timing of principal repayment
· Bonds with variable coupon - uncertain coupon payment rate as it will be reset occasionally
· Bonds with conversion or exchange privilege

Bond Valuation Process

1. Estimate the expected cash flows
2. Determine the appropriate discount rates.(either the bond’s yield to maturity or a series of spot rates
3. Calculate sum of present values {= ΣCash Flow_t/(1 +Discount rate)^t}