Investor sentiment, a powerful driver of financial markets, often toggles between the twin poles of greed and fear. During the bull market of 1995 to 2000, for example, when U.S. equity prices returned more than 20 percent per year, the standard question from investors was, “How much can I make?”

Times have changed and so did investor concerns. The S&P 500 fell 42 percent from January 2000 through the first quarter of 2003. As markets endured their “perfect storm” of economic uncertainty and negative corporate announcements, “How much can I lose?” became the more common investor query. Fear, or its cousin, risk, has taken center stage.

Yet despite the current market, investors generally share the view that over the long term, a diversified portfolio of stocks will provide a return superior to cash or bonds. Thus, the dilemma for investors is how to achieve equity-like returns in a more predictable, less risky manner. Simply stated, how can they invest for the long term while keeping the short term clearly in view?

Predictably, financial-services firms are eager to answer this question. They spend considerable effort researching investor sentiment and creating products to meet identified preferences. In the past decade, Wall Street has generated a wide spectrum of investments designed to resonate with investor psychology — in the process, patenting an astounding array of acronyms, such as LYONs, MMAPs, PERCs and KIKOs.

So, in this golden age of financial engineering, what if Wall Street could create a product that addressed both greed and fear? What if it were able to combine the return potential of equities with insurance against loss? That would be a terrific idea. And in fact, such a product exists: It's commonly known as an equity-linked note or a principal-protected investment. Not surprisingly, these products have recently become very popular with investors.

BUYER BEWARE

Before rushing to purchase, remember there is no free lunch. These wonderful-sounding products often contain hidden complexities that can cause surprises for investors. The following analysis of a recent offering provides a case in point.

A few firms have introduced an equity-linked note with a minimum return plus a simple formula for equity-market participation. An initial $1,000 grows to at least $1,100 in five years (with a minimum return of 2 percent) or to a return calculated by adding the monthly returns of the S&P 500 during the investment's lifetime. The investor receives the higher of the two. If the S&P 500 is up 1 percent each month for 60 months (five years), the return is 60 percent: a final value of $1,600. The only slight adjustment is that monthly returns are capped at a maximum of 3 percent. Seems like a good investment, right?

Well, yes and no. This kind of investment has a path-dependent structure. In simple English, this means what matters isn't just where it goes but also how it gets there.

Here's how it works: If, for example, the S&P gradually goes up 1 percent each month, the return is 60 percent. In reality, though, the stock market usually follows a much bumpier path. What if the market rallied 12 percent each January and did nothing for the rest of the year? The 3 percent cap would change the return in this case to 3 percent each January, for a five-year total of 15 percent. The S&P still ends at the same level, but now the equity-linked note returns 15 percent — a big difference from 60 percent.

Essentially, this investment is a bet against market volatility. The bumpier the ride, the less likely an investor will receive a return above the minimum 2 percent. To be fair, we should analyze the investment against current market conditions. We can do this with a statistical metric known as standard deviation, which effectively describes how returns vary from their average over time. (See “Historic Stock Market Volatility,” this page.) After determining the pattern of market volatility, we use statistical-modeling techniques to analyze the probability of achieving returns above the minimum, using different assumptions for volatility. (See “What Are the Odds?,” page 71.) Finally, we arrive at the cumulative probability of earning a return.

As the worst case is a simple return of 2 percent, providing $1,100 at maturity, we see a vertical line at 2 percent (technically 1.92 percent annualized) up to the point at which there's a probability of earning a higher return. Thus, if the market has annual volatility of 10 percent, there is roughly a 34 percent chance of earning the minimum and a 66 percent chance of earning more. As market volatility rises, this likelihood declines. If we continue at the current volatility level of roughly 20 percent, the chance of earning the minimum return is roughly 95 percent.

Unless the market becomes less volatile than it has been recently, there's only a 5 percent statistical probability of earning more than the minimum 2 percent return. That's not so hot.

While statistical projections are useful for illustrative purposes, it may be even more helpful to conduct a test using real returns to demonstrate how this investment would have performed historically. (See “Historic Return,” this page.) What do we find? As expected, such an investment produced attractive returns during periods when the stock market had calm moves upward, but performed less well in other environments. The mid-1990s was the most attractive period to own such an investment. The past few years have not been as favorable.

THE PATH MATTERS

People usually describe assets in terms of their long-term expected returns. But these returns are usually generated unevenly, not in a smooth annual progression. (See, “Monthly Stock Returns,” this page.) In fact, it's very common for the stock market to have moves of 3 percent up or down in any given month.

It's true that structured products have served investors well over time. They provide access to a range of assets, creative risk/reward patterns and efficient tax structures. But the financial engineering behind these products is often complex, and that can affect final returns in unexpected ways.

For investors, understanding the factors that influence returns is critical. The performance of the equity-linked note we've analyzed, for example, will be largely determined by market volatility in the next five years. If markets calm down and move quietly higher, the note might prove a prescient investment. But in a path-dependent structure, it's not just where you're going that matters.