This is a great post! Its key to understand the stock market at its most basic level. I'll try to answer a few of the questions; please forgive me if what I say is redundant with a number of great posts made by other contributors
We've established that a share, is literally a part of ownership of a company. If you buy a share of a company directly (not through a mutual fund/ETF) you will start receiving mail from them. For example, I own a few B shares of Berkshire Hathaway (Warren Buffet's Company). I have the opportunity to vote on major decisions of the company as well as see a copy of their annual report showing their performance/balance sheet. I will note here that businesses can have several different kinds of shares. Berkshire has A shares and B shares. A's are approximately worth 1500 x B shares.
To actually purchase more shares of BRK.B I have a brokerage account (Optionhouse, TD Ameritrade, Chase, eTrade, etc etc). There are several different type of trades available to use. I'll use the 2 most common here: the "market Trade" and the "limit trade". If you were are watching the market for a stock you'll see two important numbers. The "Bid", and the "Ask". A seller may have an asking price of $100.01, and the bid might be $99.99. If you were to put in a buy "market" order, you would pay $100.01 to the seller asking $100.01 (the difference is called the "spread"). If your order was for more shares than were on offer at $100.01, you would purchase whatever the next lowest price a bidder was willing to sell at.
In instead of a market buy, you used a limit buy, you would specify that you would only purchase stock at a certain price, say $99.99. Then, you wait. If a seller decides, he really has to sell, he can put in a market sell, and sell to the highest price purchaser (the first in line at $99.99). If however, there is more demand, then the price might keep going up as the sellers might put limit orders higher ($101). In that case, no one ever sells you stock.
In addition to the bid/ask prices, the third (and arguably more important) number is the price of the last transaction. This is whats reported in the graphs you see. The numbers you see in the newspaper are the price of the last transaction of the previous day. Some orders are specifically timed to occur at the end of day. It should be noted that there are sales after hours as well.
OK, I'm going to try and define a few more terms so as you see them, you have an idea. (I'm by no means and an expert, so please someone jump in if I botch this)
Index: An index is a metric thats create/used to give an understanding/part of the market as a whole. One of the most commonly used one is the S&P 500. Standard and Poors (S&P) creates a list of 500 large cap (large capital) companies that it believes adequately express the opinion of the entire market. In this case the sum (?) of 500 companies share prices.
http://www.investopedia.com/ask/answers/05/sp500calculation.asp. Then during trading this numbers as Shares of AT&T go up, and shares of Johnson and Johnson & Johnson go down. Theres nothing particularly special about indexes, and you could actually could create one if you so desired; for example: the ampersand index, the summation of all companies that include an ampersand in their name (AT&T, Johnson&Johnson, Etc). You cannot buy indexes directly, only mutual funds that closely follow the stated index.
Mutual Fund: A group of money controlled by a company to follow a certain goal. There are several common "types".
There are "index" mutual funds. Their goal is to follow a stated index. They generally just buy and sell the same stocks that are in the index that they follow at the correct percentages. Because the stocks change very rarily, they can do this at a relatively low cost and without significant effort. Many of the vanguard funds fall under this designation.
"Active Mutual Funds are run by managers who think that they can beat the market through analysis/skill/luck. Because they are trading more frequently they also incur higher costs/taxation, and expect more money for their efforts that result in higher fees. There are precious few mutual funds that can consistently perform over the costs of the big indexes.
Mutual funds generally only give share prices at the end of the day.
"Target Date Funds"
Mutual funds are not restricted to just stocks. Target fund dates present themselves as the easy way for novices to not worry about asset allocations. The funds directors determine what they believe to be the ideal allocations of stocks/bonds for a given date. Essentially this means that as the funds go closer to their end date, they become more conservative, and become more reliant on bonds. aka a 2060 fund is mostly stocks right now. A 2020 fund will have a significant portion of bonds to preserve itself against a market downturn.
Exchange Traded Fund (ETF). These are very similar to mutual funds in that they contain a number of different stock/bond/other sources. The main difference, is they trade in real time during the day. So instead of all the math happening at the end of the day, it happens in realtime throughout the day. SPY is a ETF that has shares that mimics the S&P 500. You can find an ETF for about anything now: Gold, indexes, REIT's.
Real Estate Investment Trusts (REITS): These deal in real estate. They are treated specially in the tax code in that they can pass along their profits directly to their share holders without tax, but cannot keep anymore than a very small percentage of it for internal use.
Intrinsic value: To go back to the mention of George's Mustache Company, if his business is going to make $100k every year for forever it has an intrinsic value attached to it.
OK; I think that covers a few of the terms you're going to see as you start to explore the subject. I want to bring up two different competing theories of the market. The "Efficient Market Hypothesis" states that the market is always correcting itself so that the price is always exactly what the underlying securities (Properties/stocks/bonds) are worth. Basically, the market always has it figured out and is pricing things according to what they are actually worth.
A lot of people thing this is bogus (including me). It is extremely difficult to determine the "intrinsic value" of a company at any given time. If you knew their exact sales values, and had a crystal ball about future sales numbers, sure, but in reality.... its tough. Therefor, a lot of people are making educated guesses, or even worse buying without really understanding. (AKA. if I bought shares of Verizon wireless now, I don't know anything about their balance sheet/ market positions/patents etc). Because of the lack of knowledge, many people think that at any given time, certain stocks are over/under priced.
Value investors specifically look for undervalued stocks, purchase them, and then hope that enough people come around to seeing the value in those companies to return the value to a reasonable level. A common example is Warren Buffet buying up American Express when they were having a PR fiasco. Eventually the share prices returned to a reasonable level, and he made out like a bandit.
You also mentioned dividends. When a company is making a lot of money and its stacking up in its bank acount as cash they have 3 real options. They can A. Reinvest the money into equipment, processes, infastructure (AKA, buy a new mustache making factory to produce more mustaches). B. They can return that cash to shareholders through dividends. or C. They can issue share buy backs.
It is then up to the management on how they think they can make the most money. If they think they can make a better return on the money than the market they will use the money for investment. If they think their business wont benefit more than the general market they choose between dividends and buybacks. Everyone likes a dividend, but they have to pay taxes on that money. If the share price is at a lower value though, the company can opt to buy back shares and destroy them. AKA if their are a 120 shares available and the company purchases 20 shares and "destroys" them, the other holders shares effectively become more important. If the had 20 shares before (1/6 ownership), they now have 1/5 ownership and don't have to pay taxes on the increase in value until they sell their shares.
If on other hand the other hand the company needed cash, they can sell shares and dilute everyone's ownership. This is why its important to read up on company management to determine their trustworthiness before buy shares of an individual company.
Ok... enough of me babbling. I'll attempt to answer direct questions as they come up. In the mean time. I'd suggest reading "The Warren Buffett Way" by robert hagstrom. The motley fool (
www.fool.com) has good articles on companies and their share value. Their mutual funds also have the clearest/best prospectus available in the industry. (If only other mutual funds would take the time to write such a clear/precise definition).
Best of luck in the learning curve. You're asking the right questions. I regret deeply that the american school systems don't teach this.