Question

Consider the file named yield curves. If the current yield curve is the one represented by Yield Curve 1 (Normal), then we can guess that the bond market participants expect the one-year interest rates one year hence and two years hence to be percent and percent, respectively. On the other hand, if the yield curve was the inverted one, we could conclude that the bond market participants expect the one-year interest rates one year hence and two years hence to be percent and percent, respectively. Note: 1. Use the approximate formula. 2. Assume risk neutrality.

Answer 1

Part 1: Normal Yield curve The approximate formula to calculate the one year forward rate, one year in the future is as shown below: 52 +f12 = 2x 52 Here, The annual 1-year spot interest rate is denoted by sz. The annual 2-year spot interest rate is denoted by sa The annual forward rate from year 1 to year 2 is denoted as f12- Now, in the given yield curve, the 1-year spot rate, s, is 2%. And the 2-year spot rate is 4%. Substitute these values in the formula above to calculate the 1-year forward rate, one year from now as follows: 2%+f12 = 2x 4% f12 = 8%-2% = 6% Similarly, the 1-year forward rate, 2 years hence can be calculated by extending the above formula to 3 years as shown below: 2xs + f23 = 3x 5 2x4%+f23 = 3 x 5% f23 = 7% Therefore, in this case the approximate value of 1-year forward, one in the future is 6%, and that two years into the future is 7%). Part 2: Inverted yield curve Calculate the 1-year forward rate, one year hence as follows: 8%+f12 =2x7% fiz =14%-8% = 6% Calculate the 1-year forward rate, two years hence as follows: 2x52 + f23 = 3x 52 2x7%+ f23 = 3x5% f23 =1% Therefore, in this case the 1-year forward, one in the future is 6%, and that two years into the future is 1%