1 / 23

Chapter Three

Chapter Three. Interest Rates and Security Valuation. Chapter Outline. Bond Valuation Review Interest Rate Risk and Factors Affecting Interest Rate Risk Duration. Bond Valuation Example. V b = 1,000(.1) (PVIFA 8%/2, 12(2) ) + 1,000(PVIF 8%/2, 12(2) ) 2

miyo
Télécharger la présentation

Chapter Three

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter Three Interest Rates and Security Valuation

  2. Chapter Outline • Bond Valuation Review • Interest Rate Risk and Factors Affecting Interest Rate Risk • Duration

  3. Bond Valuation Example Vb = 1,000(.1) (PVIFA8%/2, 12(2)) + 1,000(PVIF8%/2, 12(2)) 2 Where: Vb = $1,152.47 (solution) M = $1,000 INT = $100 per year (10% of $1,000) N = 12 years id = 8% (rrr) PVIF = Present value interest factor of a lump sum payment PVIFA = present value interest factor of an annuity stream

  4. Premium, Discount, and Par Bond • Premium bond—when the coupon rate, INT, is greater than the required rate of return, rrr, the fair present value of the bond (Vb) is greater than its face value (M) • Discount bond—when INT<rrr, then Vb <M; bond in which the present value of the bond is less than its face value • Par bond—when INT=rrr, then Vb =M; bond in which the present value of the bond is equal to its face value

  5. 2. Interest Rate Risk • There is a negative relation between interest rate changes and present value changes • As interest rate increases, security price decrease at a decreasing rate • The higher the interest rate level, the less sensitive of bond price to the change of interest rate, that is the lower the interest rate risk

  6. Impact of Interest Rate Changes on Security Values Interest Rate Bond Value 12% 10% 8% 874.50 1,000 1,152.47

  7. Impact of Interest Rate Changes on Security Values Bond Value 1,152.47 1,000 874.50 Interest Rate 12% 8% 10%

  8. Factors Affecting Interest Rate Risk • Time Remaining to Maturity • The shorter the time to maturity, the closer the price is to the face value of the security • The longer time to maturity, the larger the price change of the securities for a given interest rate change • which increases at a decreasing rate • Coupon Rate • The higher the coupon rate, the smaller the price change for a given change in interest rates

  9. Summary of Factors that Affect Security Prices and Price Volatility when Interest Rates Change • Interest Rate • negative relation between interest rate changes and present value changes • increasing interest rates correspond to security price decrease (at a decreasing rate) • Time Remaining to Maturity • shorter the time to maturity, the closer the price is to the face value of the security • longer time to maturity corresponds to larger price change for a given interest rate change (at a decreasing rate) • Coupon Rate • the higher the coupon rate, the smaller the price change for a given change in interest rates (and for a given maturity)

  10. 3. Macauley’s Duration: A Measure of Interest Rate Sensitivity The weighted-average time to maturity on an investment N N  CFt  tPVt  t t = 1(1 + R)tt = 1 D = N = N CFt PVt t = 1 (1 + R)t t = 1

  11. Macauley’s Duration (p.76) PV=981.41 FV=1000, PMT=40, I/Y=5, N=2 CPT PV=981.41 CF1= 1040 CF0.5= 40

  12. Macauley’s Duration PV1=943.31 PV0.5=38.1 PV=981.41 40/(1+.05)=38.1 1040/(1+.05)2=943.31 CF1= 1040 CF0.5= 40

  13. Macauley’s Duration PV1=943.31 PV0.5=38.1 PV=981.41 40/(1+.05)=38.1 1040/(1+.05)2=943.31 CF1= 1040 CF0.5= 40

  14. Macauley’s Duration PV1=943.31 PV0.5=38.1 PV=981.41 40/(1+.05)=38.1 38.1/981.41=3.88% 1040/(1+.05)2=943.31 943.31/981.41=96.12% CF1= 1040 CF0.5= 40

  15. Macauley’s Duration PV1=943.31 PV0.5=38.1 PV=981.41 40/(1+.05)=38.1 38.1/981.41=3.88% 1040/(1+.05)2=943.31 943.31/981.41=96.12% So 3.88% of the initial investment will be paid back in 0.5 year, 96.12% of the initial investment will be paid back in 1 year. CF1= 1040 CF0.5= 40

  16. Macauley’s Duration PV1=943.31 PV0.5=38.1 PV=981.41 D = (38.1/981.41)×(0.5)+(943.31/981.41) ×(1) = .0388×(0.5)+.9612×(1)=.9806 years CF1= 1040 CF0.5= 40

  17. Features of the Duration Measure • Duration and Coupon Interest • the higher the coupon payment, the lower its duration • Duration and Maturity • The longer the maturity, the higher the duration • Duration and Yield to Maturity • The higher the yield to maturity, the lower the duration

  18. Example of Duration Calculation (10% Semiannual Coupon & 8% YTM) 1 CFt CFt x t Weighted t CFt (1 + 4%)2t (1 + 4%)2t (1 + 4%)2t Time-to-maturity .5 1 1.5 2 2.5 3 3.5 4 50 50 50 50 50 50 50 1,050 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 24.04 46.23 66.67 85.48 102.75 118.56 133.00 3,068.88 3,645.61 48.08 46.23 44.45 42.74 41.10 39.52 38.00 767.22 1067.34 .5(48.08/1067.34) = 0.02 1(46.23/1,067.34) = 0.04 1.5(44.45/1,067.34) = 0.06 2(42.74/1,067.34) = 0.08 2.5(41.10/1,067.34) = 0.10 3(39.52/1,067.34) = 0.11 3.5(38.00/1,067.34) = 0.13 4(767.22/1,067.34) = 2.88 3.42 3,645.61 1,067.34 D = = 3.42 years

  19. Base case: D = 3.42 yearsCoupon rate changes from 10% to 6% 1 CFt CFt×t Weighted t CFt (1 + 4%)2t (1 + 4%)2t (1 + 4%)2t Time-to-maturity .5 1 1.5 2 2.5 3 3.5 4 30 30 30 30 30 30 30 1,030 0.9615 …….. …….. …….. …….. …….. …….. 0.7307 28.84 …….. …….. …….. …….. …….. …….. 752.62 932.68 14.42 …….. …….. …….. …….. …….. …….. 3,010.48 3,356.5 .5(28.84/932.68)=0.01 …….. …….. …….. …….. …….. …….. 4(752.62/932.68)=3.32 3.6 3,356.5 932.68 D = = 3.6 years

  20. Base case: D = 3.42 yearsYTM change from 8% to 10% 1 CFt CFt X t Weighted t CFt (1 + 4%)2t (1 + 4%)2t (1 + 4%)2t Time-to-maturity .5 1 1.5 2 2.5 3 3.5 4 50 50 50 50 50 50 50 1,050 0.9524 …….. …….. …….. …….. …….. …….. 0.6768 47.62 …….. …….. …….. …….. …….. …….. 710.68 1000.00 23.81 …….. …….. …….. …….. …….. …….. 2,842.72 3,393.18 .5(47.62/1000)=0.02 …….. …….. …….. …….. …….. …….. 4(710.68/1000)=2.84 3.39 3,393.18 1000 D = = 3.39 years

  21. Base case: D = 3.42 yearsTime to maturity changes from 4 years to 3 years 1 CFt CFt X t Weighted t CFt (1 + 4%)2t (1 + 4%)2t (1 + 4%)2t Time-to-Maturity 0.9615 …….. …….. …….. …….. 0.7903 48.08 …….. …….. …….. …….. 829.82 1052.42 24.04 …….. …….. …….. …….. 2,489.46 2,814.63 .5(48.08/1052.42)=0.02 …….. …….. …….. …….. 4(829.82/1052.42)=2.37 2.67 50 50 50 50 50 1050 .5 1 1.5 2 2.5 3 2814.63 1052.42 D = = 2.67 years

  22. Economic Meaning of Duration • Measure of a bond’s interest rate sensitivity (elasticity)

  23. Errors in Duration Estimation Bond Value Yield For large interest rate increases, duration overestimates the fall in security prices; for large interest rate decreases, duration underestimates the rise in security.

More Related