Last week, we began a discussion about risk and diversification in stock investing, and how they relate to your portfolio's performance. Today we'll try to apply what we learned to some real-world situations.

The issue of risk and diversification goes well beyond individual companies listed on U.S. stock exchanges. One can consider international diversification, for instance, or diversification across different asset classes such as bonds and real estate. For this column, however, let's once more concentrate on stocks.

One of the benefits of diversification is that it smoothes out your portfolio's returns. In the example from last week (courtesy of Burton Malkiel in A Random Walk Down Wall Street), an investor in both the umbrella company and the vacation resort achieved a 12 1/2% average annual return -- the same return achieved by an undiversified investor who chose only one company and either gained 50% or lost 25% in any given year. Depending on the weather, the latter investor could suffer many years of negative returns, while the former would never have a losing year, always gaining exactly 12 1/2%.

This situation works only because the stocks of the umbrella maker and resort company move in a precisely opposite manner, while each have the same expected return. In statistician-speak, these stocks have a negative covariance, and their correlation coefficient is -1.0. Stocks with a correlation coefficient of +1.0 move in precisely the same manner. Of course, virtually every pairing of stocks (or industries or markets) will produce something in between.

Why should we care about smoothing our returns if it all winds up the same in the end? Good question!

Heads you lose
I used a virtual coin-flipper at to simulate what an investor in either the umbrella or the resort stock might experience over a 10-year period (remember, rainy and sunny seasons on the island occur with equal frequency in the long run). Let's say heads represents a sunny season, and tails a rainy season. Here are the results of my first 10 coin flips:

  1. Heads -- Sunny
  2. Heads -- Sunny
  3. Heads -- Sunny
  4. Heads -- Sunny
  5. Heads -- Sunny
  6. Tails -- Rainy
  7. Tails -- Rainy
  8. Tails -- Rainy
  9. Heads -- Sunny
  10. Heads -- Sunny

With these results (and yes, they're truly random), it's very easy to see two reasons for smoothing your returns: ulcers and emergencies. If you own just the umbrella stock, you're probably going to develop a few ulcers as you lose 25% of your money during each of the first five sunny years. Sure, you know that in the long run you're supposed to average a 12 1/2% annual return. But it's hard to remember that when your spouse is asking you where the retirement money has gone after five straight losing years.

You also have to consider the possibility of unforeseen events that might require you to take money out of the market before you had planned. As an umbrella investor, the last thing you want to do is cash out after five down years.

Thus, we can condense current thinking about risk and return into a proverb. As long as the expected return is the same, a smooth road is better than one with many bumps.

Real life
Now we move from the theoretical world of umbrellas and resorts to the real world of our own portfolios. These days, I always try to consider how each potential new purchase relates to the rest of my stock portfolio. Ideally, I'll buy a stock that has a negative covariance with another company or with my portfolio as a whole.

That brings up the question of how to find correlation coefficients and the like. Unfortunately, they are not publicly available and they are difficult to calculate. The entire process involves the kind of work many of us don't have the time or inclination for. However, it's not necessary to have these exact figures in order to help our portfolios; we can look at past performances and use a little common sense.

We'll take some of my stock holdings as an example, but first, a disclaimer. I currently have eight stocks in my portfolio, though I also contribute regularly to a large-cap index fund and have money in cash and real estate. The eight-stock portfolio, therefore, only represents a portion of my net worth.

Two of my holdings are Anheuser-Busch (NYSE:BUD) and Constellation Brands (NYSE:STZ). Though they're involved in somewhat different aspects of the industry, both make, distribute, and sell alcoholic beverages. A glance at their five-year charts shows that although they don't move in lockstep, they have similar movements. It doesn't take a lot of common sense to realize my next purchase probably should not come from the alcoholic beverage industry. In fact, I sold off some of my Anheuser-Busch holdings when I bought Constellation Brands. If I found another company in the same industry that I thought had the potential for fabulous returns, though, I'd sell off some more A-B or some Constellation Brands to keep my total exposure to that sector at a reasonable level.

Now compare the five-year chart of Anheuser-Busch and another stock I own, Microsoft (NASDAQ:MSFT). Even without calculating the correlation coefficient between these two, it's easy to see they quite often move in opposite directions, and thus provide me with a significant amount of risk reduction. It makes some sense that Microsoft might not do very well in a faltering economy, while A-B is fairly recession-proof. Indeed, while Mr. Softie and the tech sector were crashing in 2000, A-B was performing quite well.

As you can see, you needn't fret over finding stocks that move in precisely opposite directions. Harry Markowitz, who invented modern portfolio theory in the 1950s, showed it's not even necessary to achieve negative correlation in order to derive some risk reduction. "Markowitz's great contribution to investors' wallets," said Malkiel, "was his demonstration that anything less than perfect positive correlation can potentially reduce risk."

My advice, then, is to use common sense and do the best you can. Don't diversify just for diversity's sake. If you're a do-it-yourselfer, continue to seek out excellent companies for your stock portfolio that you feel are primed for excellent long-term performance. If you subscribe to Motley Fool Stock Advisor or Hidden Gems, surely you've already identified one or two or three that you really like.

Of those, consider how each would fit with the rest of your portfolio, and go with the ones that will make your investing road a little bit smoother.

Rex Moore's second-favorite proverb is, "All things in moderation, including all things in moderation." He owns shares of every company mentioned in this column, and then some. The Motley Fool has a smooth disclosure policy.