portfolio calculations

You are a portfolio manager, and you want to invest in an asset having σ = 40%. You want to create a put on the investment so that at the end of the year you have losses no greater than 5%. Since there is no put on this specific asset, you plan to create a synthetic put by engaging in a dynamic investment strategy—purchasing a portfolio composed of dynami- cally changing proportions of the risky asset and riskless bonds. If the interest rate is 6%, how much should your initial investment be in the portfolio and in the riskless bond?