Annotations for an Options Slide Show

Fin 640 Web

Use with Optionsweb.ppt

Steven C. Isberg, Instructor

Slide Number 1

Options are contracts for which the value depends upon the outcome of another transaction or event. For example, we will be discussing options on equity securities (stocks). The value of an option contract will depend upon the outcome of a stock price at a particular point in time. Therefore it is contingent upon that other outcome.

An option is simply a contract that gives the owner certain rights to either buy or sell an asset at a predetermined price either at or within a predetermined time period. All it takes is two agents to agree on the terms and an option can be written against any asset. For example, I might sell you an option to buy my car in two years for $10,000.

Options are “zero sum games” in the sense that for every trading agent who makes $1, there is a trading agent who loses $1. The long (owner) and short (seller) positions in an option transaction always offset in the end. You’ll understand this a bit better as we move through the unit.

The earliest options in the US were written on agricultural and other commodities. Some trading agents used options as a means to reduce risk, while others use them to speculate on price changes.

Options are widely believed to make today’s markets more efficient by increasing the liquidity, or the amount of capital traded within those markets. Option markets also allow for more efficient links between different markets, such as the stock and interest rate markets. You’ll see more about this later.

Slide Number 2

It is important to understand some of the basic option terminology before we move forward. If a trading agent occupies the long position, it means that s/he owns (has purchased) the option contract, and hence, has the right to exercise the option if it is beneficial to do so. Someone occupying the short position has sold the option and is liable in the event that the option is exercised. If the option is exercised, the short position will pay the long position. For every dollar gained by the long position, a dollar is lost by the short position, and vice versa.

Slide Number 3

A call option gives the owner the right to buy an asset at a predetermined price. The price is referred to as the strike or exercise price. If the option is an American option, it can be exercised at any time up to its expiration date. If it is a European option, it can only be exercised at its expiration date.

A call option will be exercised if the value of the asset itself exceeds the exercise price at the time the owner decides to exercise or at maturity. For example, if I own an option to purchase 100 shares of Microsoft at an exercise price of $70 per share, and the market price of Microsoft is $80 on the day the option expires, I will exercise the option and make $10 per share on the transaction. If the value of Microsoft is only $65 per share on the day the option expires, I will not exercise the option, and it will be worth nothing. I lose what I paid for it.

The following hold for relationships between the value of the option contract and its different features:

· The higher the exercise (strike) price, the lower the value of the option. This is so because it is less likely that an option with a higher strike price will be exercised at all.

· The longer the term, the greater the value of the option. The longer the term, the greater the probability that I will be able to exercise the option at a profit.

· The greater the market rate of interest (risk free rate) the greater the value of an option. Imagine the exercise price as being the future price to be paid for an asset. The higher are market interest rates, the lower the present value of that purchase price. The lower the discounted price, the greater the value of the option.

· The greater the risk of the underlying asset, the greater the value of the option. This is because in cases of greater volatility, it is more likely that the option will be exercised at a profit. As you will see for call options, the potential “upside” profit is unlimited, while the loss in an option transaction is limited to what you paid for the option contract itself.

Slide Number 4

An option has value at the point that it expires as well as a market price at any time prior to the expiration date. The value at the expiration date is determined by the relationship between the underlying asset price and the option’s exercise price. For example, if I own a call option to purchase Northrup-Grumman stock at $80 per share, and the market price of N-G stock is $65 per share on the day the option expires, the option is worth $15 per share (or the stock price S less the exercise price X). If the stock value is less than the exercise price on the expiration date, the option is worth nothing because it won’t be exercised.

The market price at any point in time is primarily based on the likelihood that the option will be exercised at a profit some time in the future. The net position (loss or gain) for the owner of an option (i.e. the long position) will be equal to the profit less the price paid. The profit is unlimited, but the loss will be limited to the price paid.

Slide Number 5

It is very helpful to understand options graphically. This graph shows the value of the long and short positions in a call option at the expiration date of the option. The horizontal axis shows the price of the underlying asset (in this case a stock, S). The exercise price is shown as X. Starting with the long position (the green line), if the stock price is less than the exercise price at expiration, the owner loses the price paid for the option. If the stock price (S) exceeds the exercise price (X), the value of the option contract rises. For every dollar increase in the stock price, the profit to the long position increases by that same dollar. The long position breaks even when (S-X) is equal to the price paid for the option.

The long position (red line) is the mirror image of the long position. If the option is unexercised (i.e. S <X) the seller (short position) keeps the price paid for the option when s/he sold it. If the option is exercised, the occupant of the short position is liable for the settlement, and can lose an unlimited amount of money. The vertical sum of the red and green lines is always zero.

Slide Number 6

A put option is a contract that allows the owner (long position) the right to sell an asset at a predetermined price either at (in the case of a European option) or up to (in the case of an American option) an expiration date. In all other respects, it is similar to a call option. It will be exercised, however, if the underlying asset value falls below the exercise price (i.e. it is profitable to exercise the right to sell if your selling price exceeds the going market value).

Slide Number 7

If the exercise price of a put option is greater than the underlying asset value at expiration, the put option will be exercised and will have a value of X-S. If the asset value is greater than the exercise price at expiration, the option will not be exercised (why would I sell something for $25 when I can sell it on the open market for $35?), and it will have a zero value. As with the call option, the most that the long position can lose on a put option is the price paid for the contract itself.

Slide Number 8

This slide shows the same graphical representation as slide number 5, but for the put option contract. As can be seen, put options are exercised and the long position makes money if the stock price (S) falls below the exercise price (X) at expiration. If the stock price remains above the exercise price, the option remains unexercised and the long position loses the price paid for the option. The long position (green line) and the short position (red line) offset each other (they vertically sum to zero).

Slide Number 9

It was mentioned earlier that presence of options trading improves the efficiency of financial markets. To see this, we will build an example of how options may be combined with each other and with other securities to form “synthetic securities.” We will create a “synthetic bond.” This is done by combining a long position in a stock (i.e. buy the stock, +S), a long position in a put option on that stock (+P, and a short position in a call option on that stock (-C). As you can see, the + sign is used to denote a long position and the – sign denotes a short position. The only restriction is that the exercise price and expiration dates of the put and call options are the same.

Slide Number 10

If you map these out graphically, you can see the long position in the put option (green line) the short position in the call option (red line) and long position in the stock (violet line). The stock position earns money if the price goes up and loses money if the price goes down. If you take the vertical sum of those three lines at any place along the line, you will end up with a straight line (the white line). This shows that regardless of what the stock price is when the options expire, the position will always provide a constant net cash flow.

Slide Number 11

By purchasing a stock at any given price, and simultaneously buying a put option and selling a call option on that same stock, I can guarantee a risk free cash flow to be earned at the time that the options expire. This will be true as long as the call and put options each have the same exercise price (X) and term to maturity (t). Because the cash flow is risk free, this synthetic security resembles a risk free treasury-bond, in which you would pay a price and collect a cash flow at the end of the term. The cash flow is guaranteed.

Slide Number 12

Let’s try a numerical example. Microsoft stock is selling for $76 per-share today. Additionally, there is a call option available selling for $4 with an exercise price of $80 per share and term of one year. There is also a call option selling at $6 with an exercise price of $80 and a term of one year. To set up the synthetic bond (i.e. buy the synthetic bond you would buy the stock, spending $76, buy the put option, spending $6, and sell the call option, receiving $4. Your net cost is $78 ($76 + $6 - $4). At the end of the year, you will close out the position by selling the stock and closing on the option contracts. If the stock price is above the exercise price of the options, $80, the call option will be exercised (but remember, since you sold the call, you are short, and it will be exercised against you). If the price of the stock ends up below $80, you will exercise the put option (you are long in the put), but the call will not be exercised against you.

Slide Number 13

Regardless of the where the price of the stock ends up at the end of the year, you will end up with a total of $80 when you close out the position. First, suppose the stock price rises to $86 per share. You will make money on the stock transaction, the put option will not be exercised (because S>X), but the call option will be exercised against you (since S>X). Your cash flow from closing out the position will include $86 from selling the stock, zero from the put option position, since it goes unexercised, and a loss of $6 on the call option position, since it is exercised against you (i.e. –(S-X) or –(86-80)). Your net cash flow is $86 +$0 -$6 or $80.

If the price of the stock ends up being below $80, you will sell the stock for that price, exercise the put option, earning (X-S), and the call option will be unexercised because S<X. Suppose the stock price falls to $72. You sell the stock for $72, earn $8 on the put option position (X-S = $80 - $72 = $8), and the call goes unexercised for $0. The net position is $80 ($72 + $8 - $0).

Therefore, regardless of where the stock ends up, the cash flow earned at closeout at the end of the year is always $80. This corresponds to the $80 exercise price of the options. By simultaneously taking the long position in the put option and short position in the call option, you lock in the closeout price of $80 guaranteed. Your rate of return, therefore, depends upon what you paid for the synthetic bond when you set the position up i.e., the net cost of $78)

Slide Number 14

The above can be seen in this slide. The cash flow from the synthetic bond is risk free. The price paid for the synthetic bond is composed of the purchase prices of the stock and put option, less the selling price of the call. This nets out to be $78. The rate of return is equal to the net cash flow provided ($80 - $78 = $2) divided by the initial outlay of $78. The rate of return is therefore 2.56%.

The rate of return on this risk free synthetic bond should be compared to the treasury-bill rate of return. Investors will prefer the higher rate of return. An arbitrage opportunity exists therefore, by selling the bond with the lower return and using the proceeds to buy the bond with the higher return. The sale of one bond takes the form of a short sale, which involves borrowing the security (stock or bond), selling it, and then buying it back at a certain point in the future.

Slide Number 15

In this case the synthetic bond earns 2.56%, and the Treasury bill earns 5.5%. The arbitrage opportunity is to short sell the synthetic and use the funds to buy the Treasury bill. To short sell the synthetic bond, you take the opposite of the long position by short selling the stock (-S, i.e. borrow someone else’s share and promise to return it in one year), selling the put option (-P) and buying the call option (+C). If the current stock price is $76, and the put option price is $6, you will receive $82 from the sales. Buying the call option at $4 reduces your cash flow to $78. You will take this $78 and buy a Treasury bill that will earn 5.5% over the next year.