You are given the following data about the market of options on the CAC 40 index:

Also, consider that the cost of a ZCB with expiry in 5 years is 97 Euros. You want to structure a certificate with full capital protection that allows the investor to participate only to the positive performance of CAC 40, that is, at maturity (5 years from now), the certificate will pay Eur100(1+Pmax[0,(CAC

Final

CAC

Initial

)/CAC

Initial

])

100(1+Pmax[0,(CACFinalCACInitial)/CACInitial]). Considering an initial selling price of Eur 100, what is the maximum participation rateP

Pthat the certificate can offer to the investors?

(Note: do not use the % symbol, e.g., write 0.55 for 55%).