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You have just been promoted to Chief Financial Strategist in charge of new product development at the central Bank. Given the current low levels of interest rates, you have decided to introduce a new security that will be attractive to depositors 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 paid to the depositor is linked to the performance of the "SPY Index".
The CD would pay no interest (So, it's like a zero coupon bond). Instead, on the day the depositor walks into the bank, the SPY Index number is recorded. Assume that this value of the SPY Index is 500.
At maturity, the depositor receives a return on his/her deposit proportional to the percentage increase in the SPY Index over the 5-year term. However, if the index falls over the 5-year term (i.e., to below 500), depositors are guaranteed to receive their exact deposited amount. Assume that the SPY Index has no dividend yield and the annualized std. dev. of the SPY Index is 15% / year. Also, assume that the 5-year risk free rate is 3.00%/ year and your bank must at least break even on the transaction.
Calculate the maximum fraction of the percentage increase in the index that you can promise investors? Show all your work clearly.
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Organisations' behaviour is guided by financial data. In the short term, such data will help determine operational expenditures; in the long term, historical data may help generate forecasts aimed at determining strategic plans. In both instances.
How much will you have left over each half year if you adopt the latter course of action?
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