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Options & Put-Call Parity

So you want to start investing?  It seems like a great idea: the sooner you start making gains, the more they compound; and before you know it, you're sitting on some exotic beach. However, there is one major problem facing young investors: where to begin when there are millions of choices to allocate your money.  Like any analyst, do you simply march into a CEO's office and begin discussing how the slowdown in Chinese economic growth will affect future earnings growth of the firm?  Of course not, which shows the problem is that young investors don't have access to the kinds of information that Wall Street analysts do.  To compromise, most beginning investors turn to TV and magazines for a little advice, but many sound investments fly under the media's radar.  One such example is options.  Options can be used for either speculative purposes or to hedge against potential losses in the underlying asset.  Both are extremely practical, but for some reason, they never seem to get much attention.

Types of Options

Options are one type of derivatives, meaning they derive their price from the price of some underlying asset.  There are basically two types of options:  calls and puts.  When an investor buys a call, they are given the right, but not the obligation, to buy a particular quantity of the underlying asset at a predetermined price (called the exercise or strike price) at some date in the future.  On the other hand, a put gives an investor the right, but not the obligation, to sell a particular quantity of an asset.  Again, the price, quantity, and future date are determined when the put is purchased.  So you are probably thinking, why doesn't everyone just buy options and why haven't I heard of them before?  In exchange for the luxury of being able to buy or sell at a preset price in the future, investors must pay a fee for the option.  Also, if not used carefully, options can lead to big losses.

Using Options for Hedging Purposes

Because options allow investors to buy or sell an asset at a future date at a predetermined price, options can be used to hedge against possible losses from investing directly in the underlying asset.  Let's start by discussing the use of put options.  If an investor is long on the asset, he or she is worried that its price will fall in the future; however, by combining this long position with a put option, the investor can set a price floor on the asset.  This price floor is the exercise price of the option because if the price of the stock is below the exercise price, the investor simply exercises the put and sells the asset at the exercise price.  In this case, his or her gain from buying the put is equal to the exercise price (E) minus the current market price of the asset when the option is exercised (S) minus the fee paid for the put (P).  If the market price is greater than the exercise price, clearly the investor would simply sell the asset on the open market.  Now, the loss from buying the put is the fee paid for the put.  To review, just remember that any sensible investor always wants to see at the higher price:

E > S E < S
Investor exercises the put        Investor doesn't exercise the put
Gain:  E - S - P                      Gain:  - P   

A graphical representation of the relationship between E and S may help readers to further understand this situation.

Now, let's look at the use of put options.  If an investor is short on the asset, he or she is worried that its price will rise in the future, but by combining this short position with a call option, the investor can set a price-ceiling floor on the asset for when he or she needs to cover the short.  This price ceiling is the exercise price of the option. If the price of the stock is below the exercise price, the investor will not exercise the call because he or she can cover the short cheaper in the open market.  In this case, his or her loss from buying the call is equal to the fee paid for the call (C).  If the market price is greater than the exercise price, then the investor would exercise the call to get the cheaper price.  In this case, the gain from buying the call is the current market price of the asset when the option is exercised (S) minus the exercise price (E) minus the fee paid for the call (C).  To review, just remember that you always want to buy at the lower price:

E > S E > S
Investor doesn't exercise the call   Investor exercises the call
Gain:  -C                                         Gain:  S - E - C   

Again, a graph can be very helpful.

Pricing Options for Speculative Purposes

Options can not only be used to help investors reduce their risk, but they can also make investors a lot of money in their own right.  As stated before, the value of the option changes as the does the value of the underlying asset.  Thus, most options traded aren't even held till expiration; rather, they are used to solely for speculative purposes.  As we always do on this site (see Chris's article on intrinsic value or mine on CAPM), I need to stress the importance of finding the value of the option before trading them, and thanks to Nobel Prize winners Myron Scholes and Fischer Black, European options can easily be priced using the following Black-Scholes Option Pricing Model.

European Call:  C = S *N(d1) -Ee^(-dn) * N(d2)
European Put:  P = Ee^(-dn) * [1- N(d2)] - S[1-N(d1)]

Now it becomes clear why options fly under most of the media's radar.  Even as a math minor, I will admit that these formulas are so ugly that it practically requires a computer to use them.  Thankfully there is an easier way to price options.  If you can find a European put and a European call on the same underlying asset with the same expiration date, you can apply what is called put-call parity equation.  According to put-call parity:

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Discuss It!

senior living las vegas nevada said:

Well, I have been thinking about investing in mutual funds as my mom has recently started advising me about the same. But then, I am really confused about how it should be selected rightly and safe, as there is a million option out there.

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This makes things appear a lot more sophisticated, maybe I will need to consult a professional.

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