Reading a Profit-Loss Chart   1 comment


Figuring out your breakeven point and potential profit are important calculations. Options generally use what’s called a profit and loss chart/graph to visually represent the potential gains or losses, based on the closing price of the stock at expiry. Because a number of factors affect an option position’s breakeven, the profit-loss graph is only useful at a specific time for a specific underlying’s behavior and price.

We’ll start with a chart just showing stock ownership. Below is an example of a profit-loss chart when you are long XYZ stock.

long stock chart

P&L chart for Long Stock position

The red line above signifies your profit or loss (on a per-share basis) for your stock. The Y axis shows how much you would gain or lose if the stock is at the price designated by the X axis. In the chart above, the blue line shows your profit at $0 when the stock is at $50/share.

Notice that at $40/share, you would be in the red by $10/share, and at $60/share, you would be up by $10/share.

Now let’s look at a profit and loss chart for the buy-write discussed previously. (Long XYZ shares, purchased at $50, short June $45 calls sold for $7.50, net cost of shares $42.50 and max profit achieved at or above $45/share upon expiration).

P&L chart for buy-write

P&L chart for Buy-Write of XYZ Corp.

Notice the two blue lines above.

The one of the left shows that your breakeven on the stock you paid $50/share for on May 1st will only have cost you $42.50 at expiration in June. This is because you’ve deducted the option premiums you received from selling the $45 June calls.

The blue line on the right shows that at $50, your profit would be $2.50, just as it would be for any price of the stock above $45, since your maximum profit is limited to the maximum profit you could achieve at the strike price. Look back at the first chart – you would no longer be $10/share ahead at $60/share because you would be forced to sell your shares at $45. At the same time, you would only be down $2.50 if the stock closed at $40/share on expiration instead of down $10/share.

This is an important point – If you are not willing to sell your shares at the strike price of a call, don’t sell the call. Writing calls against your stock holdings will obligate you to sell your shares to the long owner of the calls if they want them. Normally, you would only be forced to sell if the stock went above the strike price on a buy-write position.

What happens at expiration?

If you have not already done so, you must read a document from the CBOE called “Characteristics and Risks of Standardized Options”, available at http://www.cboe.com/resources/intro.aspx . You will be required to acknowledge your understanding of this document when you apply for an options trading capability on your brokerage account. I cannot stress how important it is that you read and understand what you’re doing before you place a trade. All of the information I am presenting in these blog entries are basics and are a re-hash of what you should be reading elsewhere, with the hope that the way I put it together can reinforce your understanding of the topic or cause you to have that light-bulb moment where it all starts to make sense.

Unless you start making trade adjustments while your positions are open, the bulk of the “risks and obligations” happen at expiration.  In the scenario I’ve described, at expiration, if the stock:

Closes at or above $45.01:

  • You will be assigned and your stock will be called away.
  • In return for your shares, you will receive $45/share minus brokerage commissions.
  • You will get to keep the original $7.50 you received in options premiums for selling the calls.

Closes below $45:

  • You will (most likely) not be assigned and get to keep your shares of XYZ corp (read the CBOE document for the finer details)
  • You will get to keep the $7.50 you received from selling the calls

Why is everything regarding prices, breakeven, profits and so on qualified with “at expiration”?

Option contract prices are calculated using a number of factors, one of which is the time to expiration, expressed in days. Price calculations for options use input variables that are called “the Greeks” and “Theta” is the input that describes time.

When an option’s strike price is below the current price of the stock, the option is also said to be “in the money”, meaning that it has what’s called “intrinsic” value. In our example above, the $45 call had $5 worth of intrinsic value because the stock was trading at $50, which is $5 more than the strike price of the option.

The more intrinsic value the option has, the closer the option will be priced to par value. If an option is selling at par value, it means it is selling at exactly the difference between the strike and the current, higher, price of the underlying. Deep in-the-money options will frequently show bids at a discount to par, meaning that the call buyer will actually get a discount and be able to buy the stock for less than it’s currently trading for on the exchange. While this sounds odd, the important thing to remember about it is to always use “Limit” orders for your options trades so you don’t get caught out by having an option sell for a discount to what you expected it to go for.

What happens if a call buyer is able to buy a call at a discount to current prices? They can short-sell the stock and make a small profit by assigning the call writer (short selling a stock requires a margin account, which I don’t use and won’t be discussing). Normal retail investors have to pay fees, which would negate any small discount they might get turning into a profit. Big brokerages, on the other hand, don’t have the same fee overhead and would love to make a few cents at your expense – so be careful with “market” orders with options!

An interesting aspect of time value in options is that the value does not decay linearly with respect to days-to-expiration. In plain English: when an option has a lot of time to expiration, the amount of option’s time value decreases at a lower rate on a day-to-day basis. As the option approaches expiration, the rate of time decay of the option accelerates dramatically.

When you consider selling options (and when you consider making a trade adjustment) this is a factor to consider – you may notice that you’ll receive $5/day (in time value) if you sell an option with 20 days until expiry, but if you sell an option with 40 days left to expiration, you may only get $2.50/day.

You can compare the theta between potential short calls by doing some simple math. Extract the intrinsic value from the option and divide that remainder by the number of days until expiration. For our example above, we would divide the $2.50 we received in excess of the intrinsic value of the call by the number of days until expiration when we sold the calls. We could compare the June calls to August calls and it would show that the June calls decay faster (pay us more each day) than the August calls. I generally try to write calls on stocks for the nearest month available to leverage the time decay factor as much as possible.

Another interesting thing to consider is that as options go deeper and deeper in-the-money, the amount of premium above the intrinsic value of the option shrinks. We noted a $2.50 premium above intrinsic for a call that was $5 off the current share price. The $40 June calls might only have been trading at $10.50 – offering only $0.50 for the same amount of time, but offering a much higher level of protection from any potential pull back in the stock price in that time. It’s something to consider when you’re evaluating your expectations of the stock, the range the stock might trade in and the potential profits you find acceptable. As a general rule, once you get past about 10% of the stock’s value, the premiums aren’t as good on short calls and you might want to consider either a different strategy or a different underlying.

The intrinsic value of the call and time value of the call are not the only things that make up the $7.50 price we were able to get for the short calls we wrote. If it were that simple, everyone would be trading options and we would all be happy. The other major factor in options is Volatility, which is expressed for options as “Implied Volatility”, which should be compared to the stock’s actual historical volatility.  I’m not going to get into Volatility yet since it’s an advanced topic and requires some time to examine.

Anyway, as you can tell, there’s a lot to options pricing and the prices change from moment to moment. Doing manual calculations about the state of a position is not practical and if you want to dispense with the mathematical martyrdom, just get software that does it for you. I use Options Oracle (which is free and available at http://samoasky.com/ ) – all of the graphics you’ll see with the actual traded positions come from screenshots of Options Oracle. Otherwise I use OpenOffice spreadsheets setup to manage the breakeven and history management for my trades. OpenOffice is also freely available http://www.openoffice.org/ .

To be continued…

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One response to “Reading a Profit-Loss Chart

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  1. hi Jeff-

    Good information on covered call writing. I was looking to add a similar post but it looks like you beat me to it. Also looks like your RIMM trade turned out like mine when I write covered calls. On paper it works but in practice it seems like my broker makes more money than me.

    I’m adding you to my blog roll. please come visit:
    http:smallivy.wordpress.com

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