Question

The interest rate is 1.6% per annum with discrete annual compounding. You want to create a principal protected note with a maturity of one year that is guaranteed to payout at least $2000, and also provide the potential for some upside if the stock market does well. You buy a certain number of call options with an exercise price of $2000 to achieve your objective. That number need not be a whole number. What is the maximum dollar value of the call options that you can buy? Your answer should be correct to two decimal places.

Answer 1

Annual Interest Rate is 1.6% and Guaranteed Payout is $2000.

Thertefore, such amount should be invested into Risk Free so that it will yield 2000 at the year end(AFTER Deducting the Prmium paid to Buy Call). And for the Balance amount, Calls should be purchased, so that, there is also a possibility of additional benefit.

Let the Premium of Call be x.

Therefore, Amount to be invested in Risk Free is 2000-x

Accordingly, FV of the Risk Free Investment LESS the Premium paid should be equal to 2000

[(2000-x)*1.016]-x = 2000

2032-1.016x-x = 2000

32 = 2.016x

Therefore, x = 32/2.016 = 15.87

Therefore, Maximum Dollar Value of Call Options that can be Bought is $15.87

Cross Verification: Return of Risk Free Investment will be (2000-15.87)*1.016 = $2015.87. And Even if, Call Option is Lapsed, Maximum Loss will be Premium Paid. Therefore, Net Gain will be 2015.87-15.87 = $2000