Question

Bill purchases a 10-year T-note with 5 years to maturity, a 5.000% coupon rate, a market price of 97.000 and yield- to-maturity of 5.700%. Bill will hold the T-note for 3 years and then sell it in the secondary market to George who will hold the T-note to maturity. Bill's interest rates assumptions: Bill is a bank teller and is 100% certain that market returns (YTMs) for Treasures three years from now will be: 5.400% on T-notes with 1-year to maturity 5.600% on T-notes with 2-years to maturity 5.700% on T-notes with 3-years to maturity 5.800% on T-notes with 4-years to maturity 5.900% on T-notes with 5-years to maturity 6.000% on T-notes with 10-years to maturity Scenario 2: Bill, the bank teller, is wrong and interest rates are lower than expected. The market returns (YTMS) for Treasuries three years from now are: 2.800% on T-notes with 1-year to maturity 3.000% on T-notes with 2-years to maturity 3.200% on T-notes with 3-years to maturity 3.400% on T-notes with 4-years to maturity 3.600% on T-notes with 5-years to maturity 4.000% on T-notes with 10-years to maturity 6. 7. What is Bill's realized yield? What is George's yield-to-maturity? Scenario 3: Bill, the bank teller, is wrong and interest rates are higher than expected. The market retums (YTMS) for Treasuries three years from now are: 7.800% on T-notes with 1-year to maturity 8.000% on T-notes with 2-years to maturity 8.200% on T-notes with 3-years to maturity 8.400% on T-notes with 4-years to maturity 8.600% on T-notes with 5-years to maturity 8.800% on T-notes with 10-years to maturity 8. 9. What is Bill's realized yield? What is George's vield-to-maturity?

Answer 1

Ans and formula for both scenarios given below.Model remain same for scenario 2
Scenario 3 Bill realized yeild This will be Holding period return, let check at what price bill sells the bond Price of Bond Cashflow Interest Discount Y1Y2Y3 Y4Y5 5 105 Y4 will be year 1 to calculate the bond price at 3year end 8.60% 8.80% 0.92081 0.844777 1/((1+G8)^2) 0 0 4.604052 88.70161 G9*G10 (1+y)" 93.30566 1 (1+y) Present value will be price of bond in scen 2 - +- Present Value Holding period retun capital gain + coupon income/initial investment 93.30566 97 New price Init inv Capital gain Coupon incm HPR or Realized yeild Annualized yeild -3.69434 15 for 3 years to bill 11.7% 3.7% The formula for calculating YTM is as follows. YTM for George Annual Int Market price Par value Year to mat YTM 93.30566 100 Par Value - Market Price Annual Interest + Number of Years to Maturity Par Value + Market Price Yield to Maturity = 8.6%

Scenario 2) Bill realized yeild This will be Holding period return, let check at what price bill sells the bond Price of Bond Cashflow Interest Discount Y1Y2Y3Y4Y5 5 105 Y4 will be year 1 to calculate the bond price at 3year end 2.80% 3.00% 0.972763 0.942596 1/((1+G8)^2) 04.863813 98.97257 G9*G10 y). (1+y) 103.8364 Present value will be price of bond in scen 2 + Present Value Holding period retun capital gain + coupon income/initial investment New price Init inv Capital gain Coupon incm HPR or Realized yeild Annualized yeild 103.8364 97 6.836384 15 for 3 years to bill 22.5% 7.0% The formula for calculating YTM is as follows. YTM for George Annual Int Market price Par value Year to mat YTM 103.8364 100 Par Value - Market Price Annual Interest + Number of Years to Maturity Par Value + Market Price Yield to Maturity = 3.0%