You want to make a 6-month put-protected investment consisting of the stock market index, 6-month put options on the index, and a risk-free investment. Your objective is to achieve the maximum return when the index has positive return, and zero return when the index has negative return. The following table sets out the relevant information. Current index level 6,956 Current 6-month call price 636.43 Current 6-month put price 532.87 Annual risk free rate (continuously 3% compounded) The options have exercise price equal to the current index level, so the payoffs of the call and put options at maturity are max(0, index level in 6 months − 6,956) and max(0, 6,956 − index level in 6 months), respectively. Your total investment is $5m. Derive the breakdown of your investment into the three assets: the index, put options, and risk-free investment.
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