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C - P = S -X + i - d
Where:
C = Call option price
P = Put option Price
S = Stock price
X = exercise price
i = cost of carry
d = present value of dividends
This relationship between the Put, Call and stock prices originally
appeared in a paper by Hans Stoll entitled "The Relationship Between
Put and Call Prices" in 1969. The formula was developed for European
options (those are the ones that can't be exercised early) but it also
applies pretty well to American options. The reason is because unless
one of the options is really deep in the money or the dividend is
extremely large, the value of the early exercise component in the
American style options is generally small and doesn't have much impact
on the formula.
In my opinion, it is very important that you understand this basic
relationship between Puts, Calls and Stock. I am constantly amazed
when I talk to people who have been trading options for any
significant length of time and I realize that they don't know there is
a connection between the prices. I guess on one level that's okay, it
helps me pay my son's college tuition!
Let's see how to calculate the i and d terms, and then we will apply
the formula to some examples. The cost of carry, i, is calculated by
multiplying the risk free rate of return by the exercise price times
the number of days to expiration divided by 365. For our purposes,
this risk free rate is what you can get on an investment with only a
minute possibility of default, such as short term CD's. Traders, I
know have recently been using about 5%, although after the last 2 rate
cuts, perhaps a lower rate like 4.5% may be more appropriate.
To calculate the d, we must take into account any dividends that are
being paid prior to expiration and calculate their present value. All
that means is we must divide the dividend amount by (1 + risk free
interest rate) raised to a power. That power is the time to expiration
divided by 365. By the way, since the dividend amount is usually small
relative to the stock price and with interest rates being as low as
they currently are, most traders just use the actual dividend amount
instead of the present value of the dividend, in the formula. It has a
minimal effect on the prices. Let's say we know the following about
XYZ stock and options:
It's trading @ $52, and doesn't pay a dividend
There are 37 days to Jan expiration
The Jan 50 Call is trading @ 5.50
My risk free rate of return is 5%
The question is, how much should the Jan 50 Put be trading for?
First, calculate i as .05 x 50 x (37/365) = .25 We also know that d =
0, so our equation becomes;
C - P = S - X + i - d
Or 5.50 - P = 52 - 50 + .25 - 0
5.50 - P = 2.25
Finally, we get P = 3.25
Just for fun, let's assume that XYZ did have a 40¢ dividend that was
payable in 25 days. I would calculate the present value of the
dividend as .40/(1.05)^(25/365) = .399, i.e. .40 (Now it should be
apparent why traders would just use the value of the dividend.)
Substituting .40 for d in the above equation and solving, we get P =
3.65. In a like manner, we could calculate the Call if we knew the Put
price, or for that matter the Stock price, if we knew where the Put
and Call were trading.
Okay, this is all very nice, but now that I know it, how do I use it
in my trading? That's the $497,097 question ($64,000 increased for
inflation.) First, you should feel good knowing that you know and
understand something that probably 80% of non-professional options
traders don't know. Second, if the prices are out of line, then
something may be going on. You may not be able to short the stock, or
it may be hard to borrow, or some corporate action such as a merger or
takeover may be pending. Finally, if none of these things apply, and
the prices are out of line, there is a way to capture the difference.
If the Put is trading for less than the equation says it should be,
relative to the Call, we can buy the Put, sell the Call and then lock
up our profit by buying stock. Similarly, if the Call is undervalued
relative to where the Put is trading, we can buy the Call, sell the
Put, and again, lock in the profit by shorting the stock. These
positions are called Conversions and Reverse Conversions (or
Reversals), respectively. A future article will describe in detail how
these positions lock in the profit, but for now it would be
educational for you to think about it. Oh, before you get too excited
about finding these pricings and making lots of money, you should
realize that they don't come along all that often anymore. Also, when
they do appear, it's only for a short time, so you have to react
quickly, since selling the overpriced options and buying the under
priced options brings the prices back into line rather quickly.
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What System is Your Trading Style |
The Novice Trader
1. They tend to follow the crowd.
• Watch what others are doing
• Comfort in numbers
2. They avoid taking risk unless others are sharing the risk as well.
3. They feel that if others are buying then it is "ok" for them to
buy, too.
4. They act on the advice of so called "experts", i.e. the advice of
market gurus, CNBC, analysts, and their brokers.
5. As humans, they tend to complicate the trading process and ignore
the important simplicity of markets.
6. They always make the same two mistakes: They buy and sell after a
move in price is well underway (late and high risk) and they buy into
resistance and sell into support (low probability).
The Consistently Profitable Trader
1. They lead the herd.
2. They tune out all the subjective noise that can get in the way of
making proper trading decisions. They don't care what others are doing
and make decisions based on a very mechanical and unemotional set of
criteria based solely on the laws and principles of supply and demand.
3. They learn to identify the proper entry that most people never see.
4. They buy after a period of selling and into support. They buy fear.
5. They sell after a period of buying and into resistance. They sell
greed.
6. Successful traders:
• Can identify opportunity before others.
• Execute trading plans mechanically.
Successful Trading
1) Having the ability to find two sets of ill-informed individuals in
the markets in any time frame.
• Those willing to sell their stock or futures to you at a price you
know is too cheap. You know by objectively assessing supply and
demand.
• Those willing to buy your stock or futures at a price that you know
is too expensive. You know by objectively assessing supply and demand.
2) Having the tools, knowledge, and ability to take the proper action
when these two groups appear.
3) Play the bandwagon correctly...
• Proper trading is knowing how other market participants think and
react when they are correct and, more importantly, when they are
wrong. Price patterns are thought patterns. |
