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Unformatted text preview: Understanding Profit and Loss Graphs The axis defined…
The “Y” axis, or the vertical, up/down axis, represents the profit or loss for the strategy
being analyzed. Anything on the “Y” axis above the “X” axis represents a gain.
Anything on the “Y” axis below the “X” axis represents a loss.
The “X” axis represents the price of the underlying (stock, index or whatever other
investment we are analyzing). As we know, the prices of stocks and indices cannot go
negative, thus the “X” axis (theoretically) ends at zero on the “Y” axis. One way to
differentiate between what axis is the X axis or Y axis is that the letter Y has an up/down
line where as the letter X does not, thus the Y axis it the up/down axis and the X axis is
the left/right axis. Why are profit/loss graphs useful?
Profit and loss graphs help us visualize how a certain options strategy may perform over
a variety of prices. These graphs help us understand our gain or loss potential for a given
strategy. Profit/loss graphs also assist us in trying to replicate various positions with
options. For example, how to replicate the gain/loss profile for a long stock position with
a particular option strategy (long call coupled with a short put). Ironically, these graphs
also have proven helpful in naming certain strategies as a result of the way the graph
appears. For example, one complex option strategy, the butterfly spread, is so named
because the shape of the profit/loss graph resembles that of a butterfly. Profit and Loss diagram for a long stock position of 100
shares. Reviewing the above graph for a the gain/loss potential for a long stock position we can
identify a few features that will assist us in furthering our understanding of these graphs
for various option strategies. Using an example of buying 100 shares of stock for $30 or
a total out of pocket cost of $3,000. This corresponds to point “B” on the graph. We
have not made or lost anything yet so this corresponds to zero on the “Y” axis.
If the stock price increased to $50 a share, this translates to a profit of $2,000 or point
“A” on the red line. If the stock price declined by $20 a share, to $10, we would have a
loss of $2,000. This corresponds to point “C”. As the stock price can only go to zero,
our downside loss is limited to $3,000 (the amount of our initial investment), which
explains why the red line ends on the Yaxis at –3,000.
In theory, there is no upper limit on a stock’s price. That is why the red arrow increases
to the upper right of the graph indefinitely because a stock’s price can, in theory, rise
infinitely. Please note we have not factored in any commissions or other brokerage fees
and these could potentially have a significant impact on any profit or loss. We can now simplify our graph to show the gain/loss potential for a single long stock
position as follows: . Long option positions
Looking at a profit/loss diagram for a long option position, we get a picture of how the
strategy may perform under various stock prices. Take a look at the long call graph below
for a call option with a $50 strike price and a cost of $200. Our downside risk is limited
to the premium paid plus commissions. Our maximum loss is the $200 premium and that
is why the red line intersects the Yaxis at $200.
If the underlying stock price was $50 at expiration, our option would be worthless and we
would have lost $200 (point “C”). The breakeven stock price at expiration for the long
call option is $52 (point “B”). At $52, our gain or loss is zero – remember we are not
referring to the option’s intrinsic value, only our gain or loss for overall the position. As
the stock price increases beyond $52, at expiration, we make $1 for every $1 increase in
stock price. At point “A”, we have a profit of $200. Once again, we can now remove all the numbers and simplify the graph for a long call
option position as seen below. Now take a look at the graph below representing a long put option with a strike price of
50 and for which we paid $2.00. As with other long option strategies, our maximum loss
is the premium paid to establish the position (point “C”). At a stock price of $48, we
have not made or lost anything, this is our breakeven price (point “B”). Should the stock
price decline to $46 per share at expiration, our gain would be $200 (point “A”). Our
maximum gain is not seen on this graph (we would have to expand it). Our maximum
gain would be to the upper left with the stock price at zero and would be equal to the
strike price times 100, less our premium. As with our other graphs, we again can simplify the long put graph as seen below. In summary, profit and loss diagrams have proven useful for a visual representation
regarding the gain and loss potential for various option strategies. Furthermore, when
using these diagrams, we get a better understanding of how to replicate the gain/loss
profile of different investment strategies using options. This can be useful to further
understand and visualize many investment strategies.
These simple graphs represent the profit and loss potential, at expiration, assuming the
positions are closed at their intrinsic value, if any. As with any investment strategy, you
should consider and understand all of the risks associated with that particular strategy and
how it fits into your objectives, risk profile and portfolio prior to making an ivestment
decision. Now that we have an understanding of diagrams, the possibilities are nearly endless.
Here are a few common option strategies and their gain/loss potential explained by the
profit and loss diagrams. ...
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This note was uploaded on 07/30/2011 for the course ECONOMICS 101 taught by Professor Xxxxx during the Spring '11 term at HKU.
 Spring '11
 xxxxx

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