A Guide toBasic Positions inOptions
Ombretta Pettinato and William L. Silber
Table 1: Basic position: Long a Call
The Set-Up and Some Insights:
1)A Call option is a financial instrument whose owner has the right (not the obligation)to purchase the underlying asset at a specified fixed strike (exercise) price.
2)Table 1 reports the payoff diagram (the red line) and the profit line (the green line) for a long Call position at expirationwith an exercise price (E) equal to $ 100 (Cell B4) and a premium (p) equal to $10 (Cell B5). The lines are obtained assuming different values of stock prices (S) at expiration (Column B, lines 8 through 18)
3)The payoff table for long a Callat expiration is reported in Column C (lines 8 through 18) and it is given by:
Payoff (Long a Call)= Max (0, S-E)
Where :
S= Stock price at expiration (underlying asset)
E=Exercise price (or strike price)
It means that, at expiration, the call will be worth either zero or (S-E).
4)The profit of the Call is reported in Column E (lines 8 through 18) and it is given by:
Profit (Long Call)= Max (0, S-E) – premium (p)
To better understand the difference between the payoff and the profit table, let’s go through an example.
Let’s assume (at expiration) that S is higher than E, namely S= $ 110 (see Cell B14). Therefore, the value of the call will be S-E = 110-100=10 (Cell C14). However, because of the price of the option (paid by the buyer to the seller for the rights conferred in the option), the profit of the call will turn out to be zero (Cell E14).
As a result, profit and payoff are perfectly related by a fixed amount: the premium. That’s why the profit is always $10 lower than the payoff (the profit line is a vertical displacement of the payoff line)
Lessons from Table 1:
5)Long a call has asymmetric payoffs: it allows you unlimited upside when the stock price goes up and limits losses when the stock price goes down.6)Because of asymmetric payoffs, options look very different from the underlying assets.
7)At expiration the only factor that influences the value of the call is the stock price.
8)If the stock price is less than or equal to the exercise price (Cell B8 through Cell B13) the option would expire worthless (Cell C8 through Cell C13) and the maximum that you would lose is the premium that you paid (Cell E8 through Cell E13) .
Extensions:
9)You can change the strike price (Cell B4) and/or the stock prices at the expiration (Column B, lines 8 through 18) to see the effect on the payoff/profit dyagrams.
10)See the payoff/profit table forShort a Call assuming an exercise price (E) of $100 and a premium of $10. Remember that the profit of the short Call in that case is given by:
Profit (short Call) = - Max (0, S-E) + premium (p)
You should notice that if the stock price goes below the exercice price the difference between the stock price and the exercise price (S-E) is negative, therefore the value of the call is zero. However, becauseof the premium,the green line (profit line) will always be above the red line (payoff line). Also notice thatwhen the stock price is higher than the exercise price(S-E is positive) so you start losing money on the position.
Table 2:Basic position: Long a Put
The Set-Up and Some Insights:
1)A Put option is a financial instrument whose owner has the right(not the obligation) to sellthe underlying asset at a specified fixed strike (exercise) price.
2)Table 2 reports the payoff diagram (the red line) and the profit line (the green line) at expiration for a long Put position assuming an exercise price (E) of$ 100 (Cell B3) and a premium (p) equal to $10 (Cell B4). Both lines are obtained assuming different values of stock prices at expiration (Column B, lines 7 through 17).
3)The payoff table(is reported in Column C (lines 7 through 17) and is given by:
Payoff (Long a Put) = Max (0, E-S)
Where :
S= Stock price (underlying asset)
E=Exercise price (or strike price)
4)The profit of the Putis reported in Column E (lines 7 through 17) and is given by the following:
Profit (Long Put)= Max (0, E-S) – premium (p)
Lessons from Table 2:
5)Long a Put has asymmetric payoffs: it allows you upside when the stock price is lower than the strike price and at the same time it limits losses when the stock price is higher than the strike price.
6)If the stock price is greater than or equal to the exercise price (Column B, lines B12 through 17) the option would expire worthless (Column C, lines 12 through 17) and the maximum that you would lose is the premium that you paid (Column E, lines 12 through 17).
Extensions:
7)You can change the strike price (Cell B3) and/or the possible stock prices at expiration (Column B, lines 7 through 17) to see the effect on the payoff/profit diagram.
8)See the payoff/profit table forShort a Putwith an exercise price (E) of $100 and a premium of $10. Remember that the profit of the Put in that case is given by:
Profit (Short Put) = - Max (0, E-S) + premium (p)
You should notice that if the stock price goes above the exercice price, the difference between the exercise price and the stock price (E-S) is negative so the value of the Put is zero but becauseyou received the premium the green line (profit line) is always above the red line (payoff line). However, if the stock price is lower than the exercise price youstart losing money on the position.
Tables 3: Protective Put (portfolio insurance)
The Set-Up and Some Insights:
1)Table 3 shows how to arrange a portfolio that allows an investorwho owns stock to make money if the stock price goes up but to limit losses if the stock declines.
2)Suppose you own a stock at $100 (Cell B7) and that you buy a Put with an exercise price (E) of $100 (Cell B8) that has a premium (p) of $10 (Cell B9). The profit on this position comes from adding the outcomes for long stock (item 3 below) and long a Put (item 4 below).
3)The profit table for long a stock for any given stock price reported in Column B (lines 13 through 23) is reported in Column F (lines 13 through 23). For example, if the stock price turns out to be $120 (Cell B20) you will gain $20 on the stock (Cell F20). Conversely, if the stock price turns out to be $60 (Cell B14) you will loose $40 (Cell F14). The green line (long a stock) displays the possible outcomes for any given stock price reported in Column F (lines 13 through 23).
4)The profit table forlong a Put (for any given stock price reported in Column B, lines 13 through 23) is reported in Column E (lines 13 through 23). As we have seen in Table 2 above, the profit is computed as follows:
Profit (Long Put)= Max (0, E-S) – premium (p)
The red line (Long a Put)shows the possible outcomes (Column F, lines 13 through 23)for any given stock price at expiration.
5)By combiningthe two positions --the green line (long a Stock) and the red line (long a Put) -- you get the purple line (which looks like long a call).This position (Column G, lines 13 through 23) is also called a protective put and provides portfolio insurance.
Lessons from Table 3:
6)When the stock price goes down, the red line and the green line offset eachother except for the premium (Column G, lines 13 through 18).7)The protective put gives you the upside benefit but protects you against downside losses.
8)Portfolio insurance shows that options are useful risk management tools (you get upside potential and downside protection).
Extensions:
9)You can change the strike price (Cell B8), the stock price (Cell B7) and/or the premium (Cell B9) to see the effect on the payoff/profit diagrams.
Table 4: COLLAR
The Set-Up and Some Insights:
1)Table 4 shows you how to create a COLLAR by adding to a “ long stock, longput position ” a short (out-of-the-money) call (same expiration). In that case, an investor who owns stock buys a put option (to protect the downside) and alsosells a call option(with a higher strike price) to partially offset the cost of the put -- which also gives away some of the upside.2)Suppose you own a stock at $100 (Cell B4) and you buy a Put with and exercise price (E) of $100 (Cell B5) and a premium of $10 (Cell B6). As we have seen in Table 3 above, by combining the two positions - long a stock (Column F, lines G15 through G25) pluslong a Put (Column E,lines 15 through 25) you get the green line, namely the Protective Put payoff reported in Column G (lines 15 through 25).
3)Assume now that you sell an out-of-the-money call with a strike price of $120 (Cell B7, higher than the Put exercise price) and you receive a premium of $5 (Cell B8). The profit of short a call (the red line) for any given stock price listed in Column B (lines 15 through 25) is reported in Column J (lines 15 through 25) and is given by the following formula:
Profit (Short a call) = -Max (0, S-E) + premium
4)If you add the two positions-- the green line (the protective put) and the red line (short a call) you will get the blue line (the Collar) as shown in Column K, lines 15 through 25).
Lessons from Table 4:
5)Looking at the blue line, you can easily see that the collar produces a smaller loss if the stock price goes downbut you no longer benefit when the stock price goes up above 120 (the strike price of the OTM Call).
6)Investors may enter into a Collar position if they believe the stock will not appreciate greatly in the near future and they want to be protected against losses.
Table 5: Long a Straddle
The Set-Up and Some Insights:
1)A long straddle involves purchasing both a call option and a put optionwith the same strike price and expiration.
2)Suppose you buy a Call and a Put option with an exercise price of $100 (CellsB5 and B7)with each costng a premium of $10 (Cells B6 and B8). If you combine these two positions(already explored in Tables 1 and 2 above) for any given stock price at expiration (Column B, lines 15 though 25) you get the final payoff reported in Column I (lines 15 through 25).
3)The blue line in the graph shows the v-shapedpayoff you get by combining the two positions.
Lessons from Table 5:
4)The long straddle makes a profit if the underlying price moves far from the strike price, either above or below. Thus, an investor may take a long straddle position if she thinks the market is highly volatile but does not know in which direction it is going to move.
Extensions:
5)Using Table 5, try to change the premiumof both options (Cells B6 and B8) to see what happen if the cost is higher (or lower).
6)See the next tab for the payoff diagram for Short a Straddle, that is when an investor sellsboth a call and a put option on a stock with the same strike price (E=$100) and expiration date.
7)Notice that in the short straddle the risk is virtually unlimited but you make a lot of money if nothing happensbecause you get two premiums.