You have $1mn invested in the market and wish to use 3-month puts to protect it from any falls in the market, whilst retaining any upside potential. The current index level is 4,000 and three-month at-the-money calls and puts are priced at 179.307 and 139.703 respectively. The market rate of interest for a three-month period is 1%. Derive the breakdown of your investment into three assets: the index, put options, and risk-free investment.