<u>Solution and Explanation:</u>
a) Let us calculate the value of call using Put-Call Parity,
i.e. Put + Stock = Call + Present Value of Exercise Price (note that it is 6 - months time period)
Therefore, Call = $ 14.31
b1) The option strategy best suited in the given condition is - Short or Sell Straddle.
In shorting a straddle, you simultaneously sell a call and a put, thereby earning premium in both the legs of the strategy. It is a neutral options strategy wherein profits can be made when stock price is expected to remain stagnant. However it is to be noted that the profits are limited to the option premium earned on call and put but the risk is unlimited. i.e. only when you are reasonably sure as to the stock price remaining more or less constant, go for short straddle.
b2) Assuming that we went for short straddle, we earn $ 8.19 premium on put and $ 14.31 premium on call i.e. we earn maximum of $ 22.50 on this stock due to our position in options.
b3) WITHOUT CONSIDERING TIME VALUE -
Now, CONSIDERING TIME VALUE - the stock price would need to swing in either direction by ( $ 23.49 for us to start incurring losses.
c) Buy the call, sell the put and lend $ 138.8848
Let 'Price' in the table below denote the stock price at the end of 6 months.
If we take a long position in call, the immediate CF is $ 14.31 (premium outflow).
If we take a short position in put, the immediate CF is $ 8.19 (premium inflow)
Position Immediate CF CF in 6 months CF in 6 months
(if price < X) (if price > X)
Call (Long) -14.31 0 Price - 145
Put (Short) 8.19 - (145 - price) 0
Lending Position 145 145
Total Price Price
NOTE- FIGURES ARE SUBJECT TO ROUNDING OFF.