Question

The current yield curve for default-free zero-coupon bonds is as follows:

Maturity (years)	YTM
1	9.8	%
2	10.8
3	11.8

a. What are the implied one-year forward rates? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Maturity (years)	YTM		Forward Rate
1	9.8	%
2	10.8	%	%
3	11.8	%	%

b. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the pure yield curve (that is, the yields to maturity on one- and two-year zero-coupon bonds) be next year?

	There will be a shift upwards in next year's curve.
	There will be a shift downwards in next year's curve.
	There will be no change in next year's curve.

c-1. If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? (Hint: Compute the current and expected future prices.) Ignore taxes. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expected total rate of return             %

c-2. If you purchase a three-year zero-coupon bond now, what is the expected total rate of return over the next year? (Hint: Compute the current and expected future prices.) Ignore taxes. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expected total rate of return             %

Answer 1

a) when maturity = 2

YTM2 = 10.8% = 0.108

YTM1 = 9.8% = 0.098

1 + forward rate = [( 1+YTM2)²]/(1+YTM1) = [(1.108)²]/(1.098) = 1.118091

Forward rate , f2= 1.118091 - 1 = 0.118091 = 0.1181 or 11.81% ( rounding off to 2 decimal places)

when maturity = 3

YTM2 = 10.8% = 0.108

YTM3 = 11.8% = 0.118

1 + forward rate = [( 1+YTM3)³]/(1+YTM2)² = [(1.118)³]/(1.108)² = 1.138272

Forward rate, f3 = 1.138272 - 1 = 0.138272 = 0.1383 or 13.83% ( rounding off to 2 decimal places)

b) after 1 year

when maturity = 1

price of bond = par value/(1+f2) = 1000/(1.118091) = 894.381525

YTM of bond =f2 = 11.81%

when maturity = 2

price of bond = par value/[(1+f2)*(1+f3)] = 1000/[1.118091*1.138272] = 1000/1.2839961 = 785.7365027

YTM of bond = (f2+f3)/2 = (0.118091 + 0.138272)/2 = 0.1281813 or 12.81813% or 12.82%

we can see from above calculations

that YTM is increasing as maturity increases

hence , there will be a shift upwards in next year's curve

c-1)

Current price of bond of 2 year maturity , p0 = par value/(1+YTM2)² = 1000/(1.108)² = 814.55512

expected future price of bond , p1 = par value/(1+f2) = 1000/(1.118091) = 894.38152

expected total return= (p1-p0)/p0 = (894.38152-814.55512)/814.55512 = 0.098 = 9.8%

c-2)

Current price of bond of 3 year maturity , p0 = par value/(1+YTM3)³ = 1000/(1.118)³ = 715.60702

expected future price of bond , p1 = par value/[(1+f2)*(1+f3)] = 1000/[1.118091*1.138272] = 785.736503

expected total return= (p1-p0)/p0 = (785.736503-715.60702)/715.60702 = 0.098 = 9.8%