Question

Suppose that you observe the following prices of three zero-coupon bonds issued by the government: YTM (spot rate) Price 985.22 1-year zero-coupon bond X 2-year zero-coupon bond Y 3-year zero-coupon bond Z Face value 1,000 1,000 1,000 P2 4% 901.94 Questions: A. (4 pts) Draw a yield curve based on the above three zero-coupon bonds. Comment on the shape. B. (6 pts) Calculate the implied 1-year forward interest rate, two years from now (i.e. f2.a)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

DE F Years until maturity 1-year zero coupon bond X 2-year zero coupon bond Y 3-year zero coupon bond Z Face value $1,000.00 $1,000.00 $1,000.00 Price $985.22 $924.56 $901.94 YTM(spot rate) 1.50% 4.00% 3.50% Yield Curve 4.50% 4.00% 3.50% 3.00% YTM (spot rate) 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% 0.5 3.5 1.5 2 Years until maturity Shape of yield curve in upward sloping (Normal Yield curve) 25 26 27 B. Forward rate (F2,3] 2.51% 28 29

Cell reference -

C D E F Years until maturity | 1-year zero coupon bond X 1 2-year zero coupon bond Y 2 3-year zero coupon bond z 3 Face value 1000 1000 1000 Price | YTM(spot rate) 985.22 =D3/E3-1 =D4/(1+F4)^2 0.04 901.94 =(D5/E5)^(1/3)-1 Yield Curve 4.50% 4.00% 3.50% 3.00% 2.50% YTM (spot rate) 2.00% 1.50% 1.00% 0.50% 0.00% 0.5 1.5 2.5 3 3.5 2 Years until maturity Shape of yield curve in upward sloping (Normal Yield curve) Forward rate [F2,3] = (1+F5)^3/(1+F4)^2-1 27 B. 28 29 30

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.