Consider a bull spread strategy on two European put options on a given stock “XYZ”. One put option has a price of $30 and costs $2. The other put option has a strike price of $35 and costs $3.5.

a) Write down and comment on the payoff and profit tables of a bull spread on these two put options.

[5 marks]

b) Determine the maximum profit from the strategy and the future price(s) of stock “XYZ” at which this maximum profit is obtained.

Lower Put Strike Price = $30

Lower Put Premium = $2

Higher Put Strike Price = $35

Higher Put Strike Price = $3.5

For creating a bull spread using put options, an investor needs to sell the higher strike put options and buy the lower strike put options of the same underlying assets and time to expiry. Here underlying asset is same for both the options i.a. Stock of XYZ and time to expiry is also assumed to be the same. So, to create a bull put spread,

1. Sell the Put Options with a strike price of $35 and collect the premium on it @$3.5

2. Buy the Put Options with a strike price of $30 and pay the premium on it @$2.

Now, as we know that following formula is used to find out the payoff and profits of a put option:

Payoff of a Long Put Option = Max(Strike Price - Spot Price at Expiration, 0)

Profit / Loss of a Long Put Option = Payoff of the long Put option - Premium Paid

Payoff of a Short Put Option = - Max(Strike Price - Spot Price at Expiration, 0)

Profit / Loss of a Short Put Option = - Payoff of the long Put option + Premium Collected.

These formulas are used to fill up the following table:

Comments on the Strategy:

1. As the name suggests, this strategy is a spread which will generate returns in a bull market i.e. rising markets. So, we can see that as the stock price of XYZ is equal to or higher than 35, it is attaining the maximum profit of $1.5. At the same time if it is lower than or at the $30, this strategy is incurring a maximum loss of $3.5. Thus, we are getting profits on rising market while losses on falling market which is essentially a bull spread.

2. The Profit would be linear between these 2 points i.e. $30 and $35, i.e. linear transition from a loss of $3.5 towards the profit of $1.5. Thus, breakeven price would be $33.5.

3. Maximum Profit is the credit i.e. net premium received while creating the spread.

Maximum Profit = Premium Received - Premium Paid

Maximum Profit = $3.5 - $2

Maximum Profit = $1.5

4. Maximum Loss would be the difference between the 2 strikes less the net premium received.

Maximum Loss = (Higher Strike Price - Lower Strike Price) - Net Premium Received

Maximum Loss = (35 - 30) - 1.5

Maximum Loss = $3.5

5. Breakeven price for this strategy would be the higher strike price less the net premium received. If the stock price remains above this breakeven price, we would be in a profitable position and if it is less than that, we would be in a loss making position while at this price net profit or loss would be 0.

Breakeven Price = Higher Strike Price - Net Premium Received

Breakeven Price = 35 - 1.5

Breakeven Price = $33.5

b)

As written above, maximum profit from this strategy would be $1.5 and any price of Stock XYZ above or at $35 in future would give us that maximum profit.