Suppose you are asked to assist in the design of an equity-linked security. The instrument is a five-year zero coupon bond with a guaranteed return of 1 percent, compounded annually. At the end of five years the bond will pay an additional return based on any appreciation of the Nikkei 300 stock index, a measure of the performance of 300 Japanese stocks. The risk-free rate is 5.5 percent, compounded annually, and the volatility of the index is 15 percent.
In addition the index pays a dividend of 1.7 percent continuously compounded. Presently the index is at 315.55 and the additional return is based on appreciation above the current level of the index. You expect to sell these bonds in minimum increments of $100. Overall you expect to sell $10 million of these securities. Your firm has determined that it needs a margin of $175,000 in cash today to cover costs and earn a reasonable profit.
Determine the percentage of the Nikkei return that your firm should offer to cover its costs.
Your firm would then set the percentage offered at less than this. If your firm sells this security, comment on the risk it creates for itself and suggest how it might deal with that risk.