Chapter 15 Practice Question 15.1

[George Philip]

A building society issues a one-year bond that entitles the holder to the return on a weighted-average share index (ABC500) up to a maximum level of 30% growth over the year. The bond has a guaranteed minimum level of return so that investors will receive at least x% of their initial investment back. Investors cannot redeem their bonds prior to the end of the year.

(i) Explain how the building society can use a combination of call and put options to prevent
making a loss on these bonds.

The question asks us to find the right combination of call and put options to prevent making a loss.
The solution asks us to draw a graph of the payoff of the bond and compare with the graphs of each short and long position of calls and put options.

Is there a process to follow in connecting the graphs to achieve the correct combination or are the graphs drawn simply to give us more clarity of the question?

 

[Steve Hales]

If you can find the correct combination without drawing the graph then that's fine. However, the graph will probably make things a lot easier. Once the graph is drawn you then need to replicate it using the payoffs from European call and puts options, ie shapes like _/ and \_ respectively.
Every time you see a bend or discontinuity in your graph it indicates that you'll need another derivative to start paying out at that location.