tailieunhanh - Lecture Financial modeling - Topic 10: Bond valuation, YTM, duration, convexity, and bond VaR
After completing this topic, you should be able to: Value bonds and compute yield to maturity; compute the sensitivity of bond prices with respect to changes in interest rates using duration and convexity and VaR; compute the VaR of a bond using duration and convexity; understand the duration and convexity of mortgages; use Excel’s built-in bond functions. | Financial Modeling Topic #10: Bond Valuation, YTM, Duration, Convexity, and Bond VaR L. Gattis 1 Learning Objectives Value bonds and compute yield to maturity Compute the sensitivity of bond prices with respect to changes in interest rates using duration and convexity and VaR Compute the VaR of a bond using duration and convexity Understand the duration and convexity of mortgages Use Excel’s built-in bond functions 2 3 Bond Fundamental Value (V) Where V = fundamental bond value (today) i = time period t = Maturity of bond in years f = Annual frequency of bond payments (2: 2 pmts per year) tf = Number of bond payments (.: 10yr bond, f=2; tf=20 pmts) CFi = cashflow at time i, usually consisting of coupon payments at each i (Par*CouponRate/f), and par at maturity r = discount rate for all cashflows (., YTM) Note: Many bonds make coupon payments 2 times per year, where each coupon payment is ½ the annual coupon and the annual discount rate is divided by 2 4 Bond Valuation 5 Bond Valuation Function Function bondval(cr, par, t, freq, r) n = t * freq 'number of pmts For i = 1 To n bondval = bondval + (cr * par / freq) / (1 + r / freq) ^ i Next i bondval = bondval + par / (1 + r / freq) ^ n End Function 6 Yield-to-Maturity YTM, or promised yield, is the discount rate that equates the market price of the bond with the present value of contractual “promised” cashflows. YTM is also the IRR of the bond investment (buying at market price and receiving promised cashflows) Calculate the YTM of bonds 1 and 2 if the are selling for 1,045 and 1,047? 7 YTM 8 Interest Rate Risk There is an inverse relationship between bond value and yields Long-term bonds are more sensitive to changes in yield Duration is a measure of the interest rate risk of bonds, however there are several duration measures that are used Macaulay Duration: “Weighted Avg. Maturity” Modified Duration: “Price Sensitivity” Effective Duration: Discussed Later 9 Macaulay Duration Macaulay duration is a measure . | Financial Modeling Topic #10: Bond Valuation, YTM, Duration, Convexity, and Bond VaR L. Gattis 1 Learning Objectives Value bonds and compute yield to maturity Compute the sensitivity of bond prices with respect to changes in interest rates using duration and convexity and VaR Compute the VaR of a bond using duration and convexity Understand the duration and convexity of mortgages Use Excel’s built-in bond functions 2 3 Bond Fundamental Value (V) Where V = fundamental bond value (today) i = time period t = Maturity of bond in years f = Annual frequency of bond payments (2: 2 pmts per year) tf = Number of bond payments (.: 10yr bond, f=2; tf=20 pmts) CFi = cashflow at time i, usually consisting of coupon payments at each i (Par*CouponRate/f), and par at maturity r = discount rate for all cashflows (., YTM) Note: Many bonds make coupon payments 2 times per year, where each coupon payment is ½ the annual coupon and the annual discount rate is divided by 2 4 Bond Valuation 5 Bond
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