# BMW Glossary

Average CAGR
The "best fit" CAGR of a sequence of historical stock prices
Average CAGR is the annual growth rate of an exponential curve that is the best fit to a sequence of historical stock prices. "Best fit" means that the total error of actual stock prices to the Average CAGR curve is minimized. The Average CAGR, if taken over a long enough price history, indicates the annual return of the stock over a very wide range of market and business and economic conditions.
If you are buying to open then you are going long and you would have to sell to close.
CAGR
Compounded Annual Growth Rate
The annualized growth rate of a compounding investment such as a share of stock. All investments that compound (prior years' gains are added to the amount invested, not taken out) exhibit an exponential growth, and that growth is best characterized by CAGR. Exponential growth usually catches people by surprise by how rapidly it grows after a few years, which is why compounding is sometimes called the 8th Wonder of the World. An investment that starts at price S and ends at price E over a period of N years can be considered to have grown by a constant percentage each year even if its actual price movement was far more erratic; this constant percentage is its CAGR. Example: 16% gain one year followed by 25% the next year does not provide a 41% gain (the sum of the two gains) but a 45% gain (1.16 * 1.25 - 1) due to compounding; this example's CAGR is 20.4%. This investment would look identical in its end result if it had had two consecutive years of 20.4% gain. CAGR is calculated by finding the Nth root of the fraction E / S, then subtracting 1 from the result. In the example, CAGR = square root (1.16 * 1.25) - 1 = 1.204 - 1 = 0.204, or 20.4%.
Call
An option contract giving the owner the right, but not the obligation, to buy a specified amount of an underlying stock at a set price within a specified time. The buyer of a call option estimates that the underlying stock will raise above the exercise price before the expiration date.
Current CAGR
The CAGR of a stock from the beginning of the sequence of historical stock prices to its current price
Current CAGR is the CAGR of a stock starting at its price at the beginning of the price history and ending at its actual price today. In the BMW charts, the starting price is actually the price where the Average CAGR line intersects the left edge, not the actual price on that date, so that Current CAGR is less dependent on the start date chosen.
Expiration Date
The day on which an option is no longer valid and, therefore, ceases to exist. Expiration date is always the Saturday after the third Friday of the month. The last trading day is the Friday. For example, an expiration date of Jan 08, the option will expire on Jan 20, 2008 with the last trading day on Jan 19, 2008. Options are considered "wasting assets." In other words, they have a limited life because each expires on a certain day, although it may be weeks, months, or years away. The expiration date is the last day the option can be exercised, otherwise it is worthless and useless after it expires.
LEAPS
Long-term Equity Anticipation Securities
An options contract that's expiration date is more than nine months in the future, and can be two years in the future. Short-term options tend to last no longer than nine months.
Linear Chart
BMW chart with the price (Y) axis linear, showing compounded growth as an exponential curve
A linear chart shows the price (Y) axis in linear units, which shows compounded (exponential) growth as an exponential curve. A certain dollar amount is the same height anywhere on the chart (but percentage change is not, being greatly compressed on the left). Some prefer linear charts for BMW, and some prefer logarithmic charts.
Logarithmic Chart
BMW chart with the price (Y) axis logarithmic, showing compounded (exponential) growth as a straight line
A logarithmic chart shows the price (Y) axis logarithmic, which shows compounded (exponential) growth as a straight line. A certain percentage change in price is the same height anywhere on the chart. Some people prefer logarithmic charts for BMW work, and some prefer linear charts.
Long (position)
The buyer is considered to have a long position, and the seller a short position. This is important when dealing with taxable vs. non-taxable accounts because most non-taxable accounts will not let you go short except covered calls.
Option Assignment
Assignment is what a writer receives when an owner exercises an option. If you have written a put (you have the obligation to take the stock at the strike price) then you might get the stocks assigned to you. If you have written a call then you may be required to deliver shares of the stock (if they are covered you own them and if naked you must buy the shares on the open market).
Option Contract
A privilege, sold by one party to another, that gives the buyer the right, but not the obligation, to buy (call) or sell (put) a stock at an agreed-upon price within a certain time period until a specific date. Each Option Contract is the right to buy or sell 100 shares of the underlining stock. For example, 10 options contracts control 1000 shares of the underling stock. Understand that if you buy 1 contract then the price is equal to 100*the strike price.
Option Exercise
The owner of an option contract may exercise it and the contract itself is terminated. When exercising a call, the owner of the option purchases the stock at the strike price from the option seller, while for a put, the owner of the option sells the stock at the strike price to the option seller.
This is the price of an option that controls one share of the stock, Since the option contract gives the buyer a right and the writer an obligation, the buyer pays the option premium to the writer. The premium is expressed in terms of one share, and the option's contract is to control 100 shares. Therefore if the premium is \$1.50 then one contract will cause \$150 to change hands.
Option Pricing
An option is a derivative of the stock, so there are many factors that go into the price of an option. There are a number of factors which contribute value to an option contract and thereby influence the premium or price at which it is traded. The most important of these factors are the price of the underlying stock, time remaining until expiration, the volatility of the underlying stock price, cash dividends, and interest rates. Two other factors that are not described in most of the texts are the psychology of the outlook of the stock, and the forces of supply and demand. Some can be used to our advantage by putting the odds in our favor. We will talk about some of these as we move through the discussion.
Put
An option contract giving the owner the right, but not the obligation, to sell a specified amount of an underlying stock at a set price within a specified time. The buyer of a put option estimates that the underlying stock will drop below the exercise price before the expiration date.
RF
Return Factor, the return on a stock investment if it were to move immediately to its Average CAGR curve.
Return Factor is the ratio between the stock's current value on the Average CAGR curve and its current price. In contrast with RMS, which expresses a relative deviation from Average CAGR (relative to its own history), RF expresses the absolute deviation from Average CAGR. For example, a stock with an RF of 2.5 means that the stock is significantly below its Average CAGR curve, and if the stock were to move immediately to its current value on the Average CAGR curve, it would return 2.5x the original investment, or 150%.
RMS
Root Mean Square. A statistical measure of how far from Average CAGR the current price is, relative to the price's historical deviations
When fitting a CAGR curve to historical stock prices, one of the measures of "fit" is RMS. The higher the RMS, the wider the deviations the price has taken from the "best fit" Average CAGR curve over its history. RMS for a curve fit is comparable to Standard Deviation of a static data sample. Roughly, about 68% of all historical prices should be within 1 RMS (above and below) of the value on the Average CAGR curve, and 95% should be within 2 RMS. When referring to the current price of a stock, RMS means how many RMS units from the current point on the Average CAGR the price is. A price outside the 2 RMS band around the Average CAGR curve should only occur rarely, 2.5% of the time above and 2.5% below the band, and is normally cause for taking interest in the stock as it may be substantially undervalued if 2 RMS below Average CAGR, or substantially overvalued if 2 RMS above Average CAGR.
Sell to Open/Close a Position