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

Question

The current yield curve for default-free zero-coupon bonds is as follows: What are the implied 1-year forward rates? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.) Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the pure yield curve (that is, the yields to maturity on 1- and 2-year zero coupon bonds) next year? If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a 3-year zero-coupon bond? Ignore taxes. (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.) What should be the current price of a 3-year maturity bond with a 8% coupon rate paid annually? If you purchased it at that price, what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes. (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.)

Explanation / Answer

Implied 1year forward rate =

( 1 + forward rate) = [(1 + 2nd year YTM)*2] / (1+ first year ytm)

forward rate = {[(1 + 2nd year YTM)*2] / (1+ first year ytm) } - 1

={ [(1+ 0.065)*2] / (1+0.055) } - 1

= [1.134225/ 1.055]-1

= 1.07509 - 1

= .0751 or 7.51%

Implied 1year forward rate(3rd year) =

( 1 + forward rate) = [(1 + 3rd year YTM)*3] / (1+ 2nd year ytm)*2

forward rate = [(1 + 3rd year YTM)*3] / (1+ 2nd year ytm)*2 - 1

={ [(1+ 0.085)*3] / (1+0.065) } - 1

= [1.2773/ 1.134225]-1

= 1.1261- 1

= 0.1261 or 12.61%

Assuming the pure expectation hypothesis of term structure is correct, the pure yeild curve will shift upward

If we purchase 2 year zero coupon bond now, the expected rate of return will be 5.5%

and If we purchase 3 year bond now, the expected rate of return will be 5.5%

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