Imagine you applied for a job at ZZBU8707 Asset Management firm, and you are being called for an interview with the CEO of the firm. This ZZBU8708-AM firm is in the business of structured products and offers their clients capital protection for their investments. During the job interview the CEO of the firm asked you to carry out the following analysis for the following case: 

"Suppose a client wants to invest $ 2 million and wishes to have his/her capital guaranteed after 1 year. Additionally, the client wishes to receive 40% of the increase in the S&P 500 index".

Answer each of the following questions:

1. How should the ZZBU8707 Asset Management firm allocate money to meet this client's demands if the volatility of the S&P 500 index is 25%. Assume that the S&P 500 index has zero dividend yield, and the risk-free interest rate (with continuous compounding) is 6%.
2. 
   
3. At present, is this product a "fair " deal to the client or is ZZBU8707 Asset Management firm attempting to make fees/profits from this product? 
4. 
   
5. Assume that you have now got the job at ZZBU8707 Asset Management firm. Working with this particular client, you realise that they actually want to achieve $2 million capital guaranteed and receive 50% of the increase in the S&P 500 index. You know under these terms ZZBU8707 would lose money, but to take the client into the firm you propose that they accept a new product with a cap on their gains if the S&P 500 rises by more than 30%. This means the client gets a fixed 15% if the S&P 500 index goes up 30% or more. Now answer:

• How can you add this extra feature to the product? 
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• Draw a graph with the payoff of this new product, calculate the allocations of money across the different securities and compute the profit for the ZZBU 8707 Asset Management firm.