You have just been promoted to head financial strategist in charge of new product development atthe First National Bank. Given current low levels of interest rates, you have decided to introduce anew deposit-based instrument that depositors will find attractive as it will offer them access tomarket equity returns.

Specifically, you would like to issue a 5-year CD in which the principal is indexed to the performance of the RM index. The product would pay no interest. Instead, on the day the depositor walks into the bank, the RM index number is recorded. Assume that the current value of the RM Index is 880. At maturity, the depositor receives a return on his/her deposit equal to the percentage increase in the RM index over the 5-year term. However, if the index falls over the 5-year term (i.e., to below 880), depositors are guaranteed the return of their exact deposited amount.

Assume that the RM Index has no dividend yield and the volatility (annualized std. dev.) is 25% / year. Also, assume that the 5-year risk free rate is 3.00%/ year.

Calculate the maximum fraction of the percentage increase in the index that you can promise investors? In other words, if the index increases by x%, what fraction of this increase (= x%) would you pay as interest.

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