You have just been promoted to head financial strategist in charge of new product development at the First National Bank. Given current low levels of interest rates, you have decided to introduce a new security that depositors will find attractive as it will offer them access to market equity returns. Specifically, you would like to issue a 5-year CD (certificate of deposit) in which the final amount received is linked to the performance of the RM index.

The CD would pay no interest. Instead, on the day the depositor walks into the bank, the RM index number is recorded. Assume that this value of the RM Index is 880. At maturity, the depositor receives a return on his/her deposit proportional 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 to receive their exact deposited amount.

Assume that the RM Index has no dividend yield and the annualized std. dev. is 25% / year. Also, assume that the 5-year risk free rate is 3.00%/ year and 5-year call options on the RM Index are available.

(i) If the RM Index increases after 5 years, can you give investors the entire percentage increase in the RM

Index? Briefly (<=2 lines) explain, Yes or No.

(ii) If No, then 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 (y%) can you pass on to the investors.