So, what's on your mind these days, financially speaking? Some of you may be wondering whether the three-year bear market that turned 401(k)s into 201(k)s is finally over. Others are pondering just how that $13.27 balance in the 529 plan will ever put junior through college. But according to the independent financial advisors at The Ayco Company L.P., the No. 1 reason TMF Money Advisor subscribers call the Financial Helpline is to get help with asset allocation.

We have always been careful when talking about asset allocation at The Motley Fool. Be leery of those in the business who would have you reallocate your portfolio every quarter according to some blanket recommendation for percentage holdings of stocks, bonds, and cash. Those kinds of transactions can cost you more in taxes, sales commissions, and trading fees than they are worth. And everyone's life situation and risk tolerance are different.

One Foolish way to allocate your assets is to simply put your long-term savings -- those you won't need for at least the next five years -- in a broad stock market index fund. That solution would be cost-effective and would frustrate most Wise guys (after all, where's their cut?). It might also prove unsatisfactory for Fools who feel more comfortable keeping some portion of their portfolios in bonds or other fixed-income securities. We addressed the subject of asset allocation in a recent online seminar, and I'll follow up over my next few columns as well.

Simply put, asset allocation deals with the best ways to divide your money between various asset classes (stocks, bonds, real estate, precious metals, hole in the backyard, etc.). It can also refer to ways to divide your money within an asset class, and that's what I'm going to talk about today.

Specifically, we'll look at stock investing and the kinds of risk that can and cannot be diversified away, and we'll explore whether there's such a thing as a "free lunch" in stock portfolio allocation -- a way to both reduce risk and boost returns.

Risk and diversification
When you see the term "risk" in connection with investing, it usually refers to the chance that a particular security will decline in value. A stock that carries higher risk, therefore, is more likely to show a negative return at any point in time than a lower-risk stock. But, as you've no doubt heard, higher risk securities also carry the potential of higher returns -- a risk premium, if you will. If not, no one would invest in them.

It's hard to get everyone to agree on a precise definition of risk, but it's widely accepted that risk is tied to volatility. The greater a stock's volatility, the greater chance it will be way down or way up when you need to sell it. Volatility is commonly measured by beta . A beta of 1 means a stock moves in perfect concert with "the market," which is usually defined as the S&P 500. Disney (NYSE: DIS) is a current example.

A beta above 1 means the stock is more volatile than the market, while a beta below 1 means the stock is less volatile than the market. If a stock has a beta of 2, then, it tends to go up 20% when the market rises 10%, and fall 20% when the market drops 10%. Intel (Nasdaq: INTC) , Nokia (NYSE: NOK) , and Cisco (Nasdaq: CSCO) all have betas around 2. Conversely, a stock such as ChevronTexaco (NYSE: CVX) with a beta of 0.5 swings less than the market.

I can almost hear you now: "Wouldn't it be great to lower the risk, and still keep the higher returns?" Why, yes... yes, it would. And you'll be happy to know that you can do that, though to what extent is open to debate.

Umbrellas and resorts
The solution is to own a combination of stocks that tends to balance a portfolio's volatility as a whole. Princeton professor Burton Malkiel provides a great example in his classic A Random Walk Down Wall Street .

Imagine a tropical island with just two businesses: a large beach resort and an umbrella manufacturer. When the weather is good, the resort does a booming business and provides a 50% rate of return to its owners. But since no one is buying umbrellas when the sun is shining, that business loses 25%. During the rainy season, however, umbrella sales skyrocket and the resort all but shuts down, so the returns are reversed.

Umbrella Co. Resort Co.
Rainy season 50% -25%
Sunny season -25% 50%

Assuming there are as many rainy seasons as sunny seasons, the average return for each company is 12.5%. Over a period of many years, investors can expect about the same return from either company. But imagine owning shares of the resort's stock during an unexpected run of rainy seasons. As the losing seasons pile up, so do the ulcers.

Though you saw it coming from a mile away, I'll tell you anyway: The solution to eliminating the ulcers while still achieving the 12.5% return is to own equal amounts of both stocks. Each year, no matter which weather pattern inflicts itself on the island, an investor could sleep easy, pulling in a steady 12.5% return. Put simply, this investor reduced risk without reducing return.

This scenario works because the umbrella and resort stocks have a negative covariance -- in this case, a covariance of -1, meaning they move in a precisely opposite manner. If the umbrella manufacturer moves to Bermuda to avoid the island's tax laws and is replaced by a maker of suntan lotion, our diversification game ceases to work.

This example is extremely simplified, of course. In the real world, it's very difficult to find perfect negative relationships, because other factors will intervene. Still, it's possible to build your portfolio in such a way as to reduce risk.

Two kinds of risk
"But wait," I hear you saying. (I hear a lot of voices, if you haven't figured it out by now.) "I'm sure I've read that I can boost returns by taking on morerisk. Why should I try to reduce it?"

This is true, but we're talking about a different thing here. When academics developed the controversial capital-asset pricing model , they defined two kinds of risk. The first -- unsystematic risk -- is the kind that can be reduced by diversification. It is company-specific and causes a stock to move independently of the market. Malkiel offers as examples the receipt of a large, new contract, the discovery of gold or oil on a company's property, labor problems, or news of fraud by the chief financial officer. Investors who own both umbrella and resort stocks are reducing their portfolio's unsystematic risk.

The second kind is, you guessed it, systematic risk (also called market risk). And, as you no doubt guessed again, systematic risk can't be eliminated or reduced by stock diversification. This is the type of risk that affects all stocks. Examples include changes in national income, interest rates, or inflation.

To repeat, systematic risk affects all stocks; unsystematic risk is company-specific.

Drum roll...
As we get back to the idea of boosting returns by taking on more risk, keep in mind that academics believe that investors receive no premium for bearing risk that can be diversified away . Though many aspects of the capital-asset pricing model are disputed, Malkiel says this one is not. "Only systematic risk will command a risk premium in the market."

In other words, when investors strive to take on more risk in order to generate higher long-term returns, it is systematic risk they want to increase, not unsystematic.

What do I think? I do not believe one should diversify away all unsystematic risk while ignoring the quality of the stocks. Those who do are "random walkers" who subscribe to the theory that stock prices are so efficient that there's no use trying to pick individual winners. At the other extreme are those who pick a very small number of stocks they think will achieve the highest returns on an absolute basis, ignoring other factors (such as risk and diversification).

I believe there's a happy medium, where investors can do well choosing individual stocks -- while still considering the benefits of diversification. And that's where we'll pick up next Wednesday.

Rex Moore makes it sound easy, but everyone could use a little individual attention now and then. If you haven't yet, you'll want to check out TMF Money Advisor . It may not be a free lunch, but it is a 30-day free trial.

Rex Moore also regrets to inform you that due to insurance reasons, he can no longer perform at birthday parties. He owns no companies mentioned in this column, but you can check his profile to see what he does own. The Motley Fool is investors writing for investors.