Question

Question 1: An investor buys a call and a put of apple at the same strike ($105) and same maturity (6 months from today). The prices for call and put are $3 and $2.5, respectively, and the current price for apple is $105.

Three month later, investor make money from selling the call and put at the same time. Assume that there is no transaction cost, what are all possible ranges of the price for the apple stock after 3 months?

Question 2: We purchase 10 shares of Amazon for $1960 a share on 50% initial margin. If the maintenance margin is 30%. What is the price for Amazon that will lead to a margin call from the broker? Assuming no interest rate for borrowing.

Answer 1

1) Buying a call and a put option of a stock at same strike price and same maturity is known as LONG STRADDLE.

Lets find out the total premium paid toward initiating the strategy

total premium or initial cost = Purchase price of Call    + Purchase price of Put

                                         =    3    +     2.5

                                         =   5.5

lets find out the break even price for the strategy to establish a range.

there are 2 BEP (Break even price) for a long straddle

the lower Break even   =    Strike - Initial Premium Cost

                                  =   105 -      5.5   = $ 99.5

the upper Break even   =    Strike + Initial Premium Cost

                                  =   105 +    5.5   = $ 110.5

so when apple price is within the range of $ 99.5 to $110.5, it wont be profitable.

BUT if the apple price goes above 110.5 we can sell both the call and PUT option

the call option will be in the money, and will have time value too since (3 months left for expiry) we can profit from the PUT option and this profit will offset the loss in the buy leg of put option.

similarly if the apple price goes below 99.5$ we can sell both our options.

the put option will be in the money, and will have time value too since (3 months left for expiry) we can profit from the PUT option and this profit will offset the loss in the buy leg of call option.

it is a strategy with limited loss( to the extent of premium paid) and unlimited profits- if there is a huge up or down movement

2)   a price below $ 1,400 will initiate a margin call

Given                   

Maintenance Margin       (MMR) = 30% or 0.30

Initial Margin    %     =    50%             or 0.50             

Original purchase price of Amazon =   $1,960      

Price at which margin call will occur                                                                         

                           =         original price X ( 1   - initial margin%)    /      (1 -   Maintenance margin %)                                                     

                            =                         1960             X   (   1     -     0.50    )    /       (   1     -     0.30    )                                                            

                             =                         1960             X        0.50        /              0.70                                                            

                               =                     $ 1400                                                          

a price below $ 1,400 will initiate a margin call