Question

ABC stock is trading at 40. The trader has already sold one put with the strike price of 40 at 4 with expiry date 1 month from now. The trader reviews the market and short sells one share. You are required to analyse the trader's strategy at the time T = 1 month. Assume the interest rate is flat at 0% pa for all periods. Also assume that 1 put is on one share

a. Compute the net profit at S = 0,20,30,40, 50, 100 where T = 1 month

b. What is the break even point

c. Draw the profit graph. Mark the points where the graph intersects the X axis and Y axis

d. What was the traders view when he sold the puts

e. what was the trader's opinion when he later short sold the stock

Answer 1

Positions of the trader are,
Sold put (P^-) with a strike price of 40 for a premium of 4
Short Sold the share (S^-) with the price of the share at 40.

A trader or investor sells a put option, when he has a bullish or to be more precise a non bearish view of the market, and he expects that the price of the stock is not going to fall to a greater extent than what premium he has recieved for selling the put option, as any fall in the stock price above what premium he has recieved would result in a loss for him, as the put option would be exercised by tghe buyer of the option when the stock price is below the stock price. If the price of the stock rises, the option would not be exercise and he would make a profit of the whole of the premium recieved.

However, after review of the market, he also short sells one share, and short selling a share means that a person is bearish on the market, and his expectations is that the market price of the shares are going to fall. Here, he has decided to short sell the stock because he wants to hedge himself against the risk of a fall in the share price, and has now opened a position wherein if the share price rises above 40, he would have to make a payment or suffer a loss on his positions. In a nutshell, he enters this new short selling position on the stock as he is expecting that the share price will either stay at 40 or go below that, and selling the put option gives him a cushion of 4, i.e. if the stock price rises upto the point of 44, he would still not make losses and not have a negative cash outflow till 44. If the prices fall below 40, the put option would be exercised resulting in a negative cashflow, but the stock he has short sold would lead to a positive cash flow of the same amount, and net he would be profiting the amount of premium he has recieved, i.e. 4.

Answer A)

Expected Payoff when Price = 0,
Put Option exercised , i.e a negative cash flow of ( Expiry Price - Strike Price )
= 0-40
= - 40
Inflow from Short Selling the stock, as the price has fallen, ( Short Selling Price - Expiry Price )
= 40 - 0
= 40
Inflow from the Put Premium,
= 4

Therefore, Net Cashflow = -40+40+4 = 4.

Expected Payoff when Price = 20,
Put Option exercised , i.e a negative cash flow of ( Expiry Price - Strike Price )
= 20-40
= - 20
Inflow from Short Selling the stock, as the price has fallen, ( Short Selling Price - Expiry Price )
= 40 - 20
= 20
Inflow from the Put Premium,
= 4

Therefore, Net Cashflow = -20+20+4 = 4.

Expected Payoff when Price = 30,
Put Option exercised , i.e a negative cash flow of ( Expiry Price - Strike Price )
= 30-40
= - 10
Inflow from Short Selling the stock, as the price has fallen, ( Short Selling Price - Expiry Price )
= 40 - 30
= 10
Inflow from the Put Premium,
= 4

Therefore, Net Cashflow = -10+10+4 = 4.

Expected Payoff when Price = 40,
Put Option exercised , i.e a negative cash flow of ( Expiry Price - Strike Price )
= 40-40
= 0
Inflow from Short Selling the stock, as the price has fallen, ( Short Selling Price - Expiry Price )
= 40 - 40
= 0
Inflow from the Put Premium,
= 4

Therefore, Net Cashflow = -40+40+4 = 4.

Expected Payoff when Price = 50,
Put Option not exercised , i.e no cash flow
Outflow from Short Selling the stock, as the price has risen, ( Short Selling Price - Expiry Price )
= 40 - 50
= -10
Inflow from the Put Premium,
= 4

Therefore, Net Cashflow = -10+4 = -6.

Expected Payoff when Price = 100,
Put Option not exercised , i.e no cash flow
Outflow from Short Selling the stock, as the price has risen, ( Short Selling Price - Expiry Price )
= 40 - 100
= -60
Inflow from the Put Premium,
= 4

Therefore, Net Cashflow = -60+4 = -56.

Answer B,

Break Even point is the point where the cashflows are equal to 0.
Any point wherein the price is below 40, would be a positive cash flow, and hence the break even point is above that.

Break Even Point for the positions entered by the trader = Strike Price + Premium recieved for put
= 40 + 4

= 44.
Any price above this would lead to a negative payoff.

Answer C

Attached as PDF.

Answer D & E

A trader or investor sells a put option, when he has a bullish or to be more precise a non bearish view of the market, and he expects that the price of the stock is not going to fall to a greater extent than what premium he has recieved for selling the put option, as any fall in the stock price above what premium he has recieved would result in a loss for him, as the put option would be exercised by tghe buyer of the option when the stock price is below the stock price. If the price of the stock rises, the option would not be exercise and he would make a profit of the whole of the premium recieved.

However, after review of the market, he also short sells one share, and short selling a share means that a person is bearish on the market, and his expectations is that the market price of the shares are going to fall. Here, he has decided to short sell the stock because he wants to hedge himself against the risk of a fall in the share price, and has now opened a position wherein if the share price rises above 40, he would have to make a payment or suffer a loss on his positions. In a nutshell, he enters this new short selling position on the stock as he is expecting that the share price will either stay at 40 or go below that, and selling the put option gives him a cushion of 4, i.e. if the stock price rises upto the point of 44, he would still not make losses and not have a negative cash outflow till 44. If the prices fall below 40, the put option would be exercised resulting in a negative cashflow, but the stock he has short sold would lead to a positive cash flow of the same amount, and net he would be profiting the amount of premium he has recieved, i.e. 4.