guidelines You are NOT to discuss any of these problems with your tutor or other

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guidelines You are NOT to discuss any of these problems with your tutor or other instructors . You need to clearly show all necessary formulae and calculations Question 1. Term Structure (3 points total) The current yield curve for default-free zero-coupon bonds is as follows: Maturity (Years) /YTM (% 10% 12 a. What are the implied 1-year forward rates? b. 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? e! If you purchase a 2-year zero-coupon bond now, what is the expected total rate of rettrm over the next year? What if you purchase a 3-year zero-coupon bond? Ignore taxes. What should be the current price of a 3-year maturity bond with a 12% 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. Question 2. Duration and Convexity (3 points total) aking annual coupon payments with a coupon rate of 10% and a par valu d m

Explanation / Answer

1.

1 year forward rate 1 year from now=(1+11%)^2/(1+10%)-1=12.01%

1 year forward rate 2 years from now=(1+12%)^3/(1+11%)^2-1=14.03%

2.

ytm on 1 year bond next year=(1+11%)^2/(1+10%)-1=12.01%

ytm on 2 year bond next year=((1+12%)^3/(1+10%))^(1/2)-1=13.01%

3.

2 year bond :

Price today=1000/1.11^2

Price 1 year later=1000/1.1201

Retunrs=(1000/1.1201)/(1000/1.11^2)-1=10%

3 year bond:

Price today=1000/1.12^2

Price 1 year later=1000/1.1301^2

Returns=(1000/1.1301^2)/(1000/1.12^3)-1=10.01%

4.

3 year bond 12% coupon:

price today=1000*12%/0.12*(1-1/1.12^3)+1000/1.12^3=1000

price 1 year later=1000*12%/0.1301*(1-1/1.1301^2)+1000/1.1301^2=983.1543561

Returns=(983.1543561+1000*12%)/1000-1=10.3154%

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