Zuana Cossa is working in the team that manages the bond portfolio investments in Jomaro Bank. Arbitrage trading can be used to profit from incorrectly priced bonds. Zuana is asked to estimate the price of 20 government bonds using zero coupon bond yields (ZCYs), calculate what their yield to maturity (YTM) p.a. will be, and then identify an arbitrage opportunity.

i) Estimate the prices of the 20 Treasury bonds listed in the table below. All the bonds have a face value of $100.

ii) Calculate the YTM (semi-annually compounded) for each of the 20 Treasury bonds using the prices that you estimated in (i). - Plot the YTMs calculated and the ZCYs on the same graph. The yield can be on the vertical axis and term on the horizontal axis. Explain why the plots of YTMs and ZCYs are different.

iii) A two year zero-coupon bond (ZCB) with a face value of $100 is currently being traded at $98. Construct an arbitrage portfolio by trading the ZCB and also the first four Treasury bonds. - Summarise the weights and dollar amounts of the five bonds in your arbitrage portfolio in a table. - Explain how this arbitrage portfolio is profitable.