Question 15.1?

Hi, I'm struggling with the charts in the answers to question 1 on chapter 15.

Question states "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 30% growth over the next year. The bond has a guaranteed minimum level of return so that investors 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 answers then shows charts to recreate the payoff of the bond which supposedly should be a long put and a short call but I can't see how that recreates the payoff as I think it looks more like a long call and a short put...??

 

Good question. Consider the following from the investor's point of view:

1. the bond provides a guaranteed minimum level of return (i.e. the investor's loss is capped, irrespective of how badly the index performed over the year). The investor would need to be long a put as this would give them the right to sell the bond at the strike (x% of initial investment).

If they were short a put option (as you suggest), the investor would be obligated to buy (and not sell) the index at the put option's strike price.

2. the investor earns a return up to a maximum of 30% growth over the year. They would therefore need to purchase / be long the index between the put option's strike price and the strike that correspondents to the maximum 30% index growth rate. This would be achieved by investing the initial investment into the index directly.

3. the investor does not participate in growth in excess of 30% over the year. A short call option obligates the call writer to sell stock at the strike price.

If they were long a call (as you suggest), the investor would have the option to buy (and not sell) the index. This is a bullish position.

Combining a long put (at stike K1) with the underlying (index) and a short call (at strike K2) is called a collar.

The building society eliminates its risk of loss by replicating its exposure / payoff profile of the investor. It makes money via the spread (i.e. the difference between the cost it charges investors to participate in the issue and the cost it pays to replicate its exposure)


Hope that helps.

 

Sorry for the late reply but this was super helpful and my brain much preferred that way of thinking, thank you!!!