Evaluation and SensitivityAnalysis of Bond Securities By VISHAL KUMAR SINHA IIT KHARAGPUR
Types of bonds• Sovereign bonds,• Semi-government bonds,• Municipal or province securities,• Corporate debt securities,• Mortgage-backed securities,• Asset-backed securities,• Collateralized debt obligations
General principles of valuation• Estimate the expected cash flow.• Determine the appropriate discount rate/rates for discounting cash flows.• Calculate the present value of expected cash flows using discount rate/rates.
Change in a Bond’s Value as it Moves Toward Maturity: .• Decreases over time if the bond is selling at a premium.• Increases over time if the bond is selling at a discount.• Is unchanged if the bond is selling at par value.
Valuation Using Multiple Discount RatesThat is to value the cash flows of a bond to use a different discount rate that is unique to the time period in which a cash flow will be received.
Valuing a Zero-Coupon BondThat is only one cash flow-the maturity value.The value of a zero-coupon bond that matures N years from now is = maturity value (1 + i)N 2i = is the semi-annual discount rate.
Valuing a Bond Between Coupon PaymentsThat is to price a bond between coupon payments.Full price when a bond is purchased between coupon periods.present valuet = expected cash flow (1 + i)t−1+ww = days between settlement date and next coupon payment date days in coupon periodi = discounting rate.t = time for which cash flow is calculated.
Valuing a Bond Between Coupon Payments(contd.)Full price includes the accrued interest(interest that is earned but not distributed to the bondholder) that the buyer is paying the seller.Accrued interest = semi-annual coupon payment (1 − w)Hence clean price is =Full price − Accrued interestwhere clean price is price without accrued interest.
THE ARBITRAGE-FREE VALUATION APPROACHHere various zero-coupon bonds are valued individually and added together to determine value.The value of the bond based on the spot rates is the arbitrage-free value.Present value = Cash flow (1 + Spot rate/2)period
Yield is income return on Investment. .Types of Yield in bond:Coupon - The bond interest rate fixed at issuance,Current - The bond interest rate as a percentage of the current price of the bond,Yield to maturity - An estimate of what an investor will receive if the bond is held to its maturity date.
Traditional yield measures• Current yield =coupon Price of bond• YTM• Yield Call / Put• Yield to worst• Cash flow yield (Bond equivalence Yield) =2((1-rmonthly)6-1)
Forward rate from Spot rate(1+rm+n)(m + n) = (1+rm)m(1+mfn)nm= number of years from todayn= number of years after m yearsrm + n = spot rate for (m + n) yearsrm = present rate of interestmfn = forward rate of interest
Valuation approach• Full valuation approach: % P= P P 0• Duration / Convexity approach: % P= P = -D r + C r2 P 0 Convexity Duration
Estimating the New Price for a Large Change for Bonds with DifferentConvexities.
- +Duration = P - P . 2P Y 0 - +Convexity = P + P - 2P 0 2P0 Y2 Y = change in interest ratewhere Duration / Convexity is sensitivity of bond price in response to change in interest rate.