How do you decide if you're an advanced investor? Here's our definition: There are two parts. The first is skill. You should be fluent reading financial statements, which means you should be comfortable making adjustments to GAAP (generally accepted accounting principles) earnings to better understand business profitability and risks.  

You should have a working sense of market history -- not only its 11% average annual climb over the last 80-plus years -- but its prolonged periods of weakness. British economist John Maynard Keynes once said, "Simply because events have been observed repeatedly in the past is a poor excuse for believing that they will probably occur in the future." For investors, this means we need a healthy sense of skepticism. (By the way, a great introduction to Keynes and economic history is Todd Buchholz's New Ideas From Dead Economists, and for market history, Jeremy Siegel's Stocks for the Long Run.)

You should understand the trade-off between risk and reward. Investing isn't just about returns. A high return at any cost doesn't count as a sound investment strategy. And you should understand how profits, interest rates, and inflation affect stock prices.

This is an inside-outside definition. You need the skills to pull apart an individual business, and you also need to understand how the market works and how larger forces in the economy impact stocks.  

The second part is your personal interest. Even if your skills are still developing, if you're willing to knuckle down and learn the nuts and bolts, if you're reaching for more than you can really understand at this point, you're well on your way. 

(One way we're helping investors pick apart companies this fall is through our Succeeding With Small Caps Online Seminar. Small caps present more risk than large cap companies, and allow you to use your analytical skills in new ways.) 

Compounding and discounting formulas -- Richard McCaffery (TMF Gibson)
These are two key formulas that an advanced investor needs:

a. FV = PV(1 + i)^n  (This is compounding)
b. PV = FV/(1 + i)^n (This is discounting)
FV = future value
PV = present value
i = interest rate
n = time period
^ the caret symbol represents an exponent (Or the "power" to which the previous number is raised. Your calculator does this easily for you. It's usually the "yx" function, where y is the number you want to raise to the xth power.)

These formulas look frightening, but they aren't too hard to understand, and you can perform them easily on your calculator. For starters, they're really not two different equations, but one succinct equation in two different forms. You multiply to compound and divide to discount -- discounting is just the reverse of compounding.

If you can get even a basic grasp of how it works, you're on your way to understanding perhaps the two most important concepts in finance: risk, and the time value of money.

Let's start with the time value of money. I would rather have $1,000 in cash today than $1,000 a year from now, in part because inflation reduces the value of a dollar. This statement is quite obvious, but its implications aren't. Say I decide to delay spending $1,000. I could let the money sit in my wallet until I need more food or a new toy. In one sense, this is exactly what money is: A way to store value. I don't need $10,000 worth of food in my house. I need $300 or $400. The rest I'd rather have in cash to spend or save. People know this instinctively.

But there are options besides letting your money sit around getting eaten by inflation. You can invest it. The reward for delaying consumption and, if you choose, taking additional risk, is called interest. If I invest $1,000 at 10% for five years the compounding formula takes that $1,000 and turns it into $1,610.51. I've not only earned interest, but I've earned interest on my interest. From this equation: FV = PV(1+i)^n, we can see that this part of it, (1 + i)^n, is the compounding engine.

The reverse of this process is discounting, which is just a financial way of saying that money in hand a year from now is worth less than money in hand today. This follows logically from the compounding concept, but is less intuitive. Think of it this way: Say I tell you I'm going to give you $1,000 in one year if you give me $1,000 today. What's in it for you? Nothing.

To make it worth your while, you'd have to give me less than $1,000. That way your money would be earning interest and, perhaps, include a kicker for the risk of loaning to a guy like me, who offered you such a lousy deal in the first place. Risk is a big part of the investing equation, and we can account for it by embedding compensation in the interest rate we choose. Let's say you settle on the same 10% interest rate. In that case, $1,000 in five years is worth $620.92 today. You can see that the discounting engine is the same as the compounding engine, only we activate it by dividing rather than multiplying. Compounding and discounting are the two sides of the "time value of money" coin.

I'm not a math whiz, to say the least, but I can appreciate a formula that allows us to account for time and risk so easily, that is symmetrical forward and backward, and that accomplishes all of this with just a few variables.

Rich McCaffery's (TMF Gibson)  profile  reveals him to be an international man of mystery.

Shorting -- Rick Aristotle Munarriz (TMF Edible)
Feeling naughty? Want to cash in on a stock's decline? While inherently riskier than buying stocks outright, selling short might be right for you. After all, once you feel comfortable enough to choose stocks that will appreciate, it's almost second nature to pick the ones that won't. By placing a short sale, you are actually borrowing shares from your broker. When you're ready to close out your pessimistic position you simply cover your short. In a nutshell, it's like selling first and buying later. Sell high, buy low.

For instance, say you felt that the semiconductor market was stumbling last summer and decided to short industry bellwether Intel(Nasdaq: INTC). You could have shorted the company at $60 back then. With the stock falling below $30 now, you could close out your position making that $30 difference for each share sold short -- or a 50% return on your initial position.

The risk here is that while owning a stock has a limited downside -- 100% of your investment -- being short means you are responsible for the seemingly infinite upside, or more than 100% of your initial position. You also have history as a speed bump, knowing that stocks typically rise in value. That is why short positions need constant supervision. However, done properly, it provides some welcome balance when the stock market sputters and even better performance when the market does well but your short position languishes. In
short, it's not for everyone but it clearly has its advantages. In short, it's shorting.

For extra credit, you can consult our Motley Fool shorting extravaganza, Is Shorting Stocks Foolish? And for an inside look at the life of an investor who makes his living in the land of shorts, Manuel Asensio's Sold Shortmakes exciting reading.

Rick Aristotle Munarriz (TMF Edible) owns no shares of Intel, and his co-Fools think he has an inexplicable affinity for amusement parks. For fun, check out his profile.

Buying on margin -- Jeff Fischer (TMF Jeff)
Advanced investors can benefit by using a margin loan from their broker to buy more stock than they otherwise could. The stock that you hold is collateral for your loan. Therefore, if your stocks decline, and you hold too much margin, the broker could demand extra money from you, or will sell enough of your stock to cover the loan. They can sell at-will.

On the other hand, if your stocks rise and you own stock on margin, you'll earn more money than you otherwise would. We recommend that you never use more than 10% to 20% margin, tops. This means that if you have a $50,000 account, don't borrow more than $5,000 to $10,000, at most. And don't buy extremely risky, volatile stocks on margin, such as Amazon(Nasdaq: AMZN), or upstart biotechs like Human Genome Sciences(Nasdaq: HGSI). Margin has wiped out more than a few "advanced" investors. Even large accounts are easily laid to waste when using too much margin.

You do pay interest on margin loans – interest typically ranging from 6% to 9% annually. Unless you can earn more than that with your investments, there's no reason to take the extra risk. The Fool has a Margin FAQ.

Jeff Fischer (TMF Jeff) once ignored orders to evacuate as a hurricane approached. He drove away at the last minute, savoring the danger. He doesn't own shares of Amazon or Human Genome Sciences, which you will see in his profile.

As always, The Motley Fool reminds you to do your homework before you invest. You can review our complete  disclosure policy  online.