Q1 Consider a zero‐coupon bond with a face value of $110, a time‐to‐maturity of one year and a price of $105. What is its yield‐to‐maturity?

Q2 Consider a coupon bond with a face value of $100, a coupon rate of 20%, a time‐to‐maturity of two years and a price of $130. What is its yield‐to‐maturity?  Hint: Solve numerically using a scientific calculator or Excel.

Q3 (Essential to cover, a, b, and c only) Consider a coupon bond with a face value of $100, a coupon rate of 20%, a time‐to‐maturity of three years and a yield‐to‐maturity of 4% (implying a price of $144.40).

a. What would be the holding period return on buying the bond today and selling it in one year’s time if interest rates in one year’s time are such that the bond’s yield‐to‐maturity is still 4%?

b. What would be the holding period return on buying the bond today and selling it in one year’s time if interest rates in one year’s time are such that the bond’s yield‐to‐maturity is 5%?

c. What would be the holding period return on buying the bond today and selling it in one year’s time if interest rates in one year’s time are such that the bond’s yield‐to‐maturity is 3%?

d. Can you think of any reason why the change in holding period return is not symmetric even though the change in yield‐to‐maturity is, i.e. it is changing by one percent in both question b and c compared to question a (although in different directions)?

Q4 (Essential to cover) Suppose that there is a bank that is offering to lend and/or borrow money at an interest rate of 8% (risk free and regardless of the time‐to‐maturity of the loan). Further suppose that there is a two‐year risk‐free coupon bond trading with a face value of $100 and a coupon rate of 20% trading in the market.  Price the bond using an explicit no‐arbitrage argument.

Q5 (Essential to cover) Suppose that the bond in the previous question is actually trading for $120. Show how you could exploit the mispricing to make an arbitrage profit.

Q6 (Essential to cover) A 2‐year bond with par value of $1000 making annual coupon payments of $100 is priced at $1000. What is the yield to maturity of the bond (without any calculation, are you able to answer this question?)?  What will be the realized compound yield to maturity if the 1‐year interest rate next year turns out to be:

a) 8%

b) 10%

c) 12%

Q7 (Essential to cover) Suppose the pure yield curve is currently given by

A 3-year 6% annual coupon bond with a face value of $100 is currently trading in the market and is priced using the pure yield curve.

a. Without calculating the yield to maturity on the bond, will it be equal to, higher or lower than the 3-year spot rate y3?  Explain why?

b. Without calculating the price of the bond, will it be a par, premium or discount bond? Explain why?

c. If after the bond is purchased, the yield curve shifts down uniformly by 0.5%. Will the price of the bond stay the same, increase or decrease?

If the bond is held to maturity, will the realized compound yield be equal to, higher or lower than the yield to maturity on which the bond was purchased?  Will it be equal to, higher or   lower than the 3-year spot rate y3 when the bond was purchased? Explain why?

Q8 (Essential to cover) Suppose instead that the following bonds are trading in the market:

Infer the term structure of interest rates.