5. Know the two trends that define market limits

Sand Storm! 2010: Act I, Scene 5; Contoured Density Shows Two Trends.

The concept of number density, the count of stocks within the area of a grid cell in normal space, was introduced in the discussion about Scene 3 and amplified on the prior page. Unlike the idea of a trend as some behavior over time, here we talk about two trends in normal space as you might talk about the compass trend of a ridge seen on a map, a direction with East and North components. Since the use of contour lines along constant elevations on a map of the land or sea-floor is a very powerful way to illustrate shape, here we use contour lines along constant number densities to help you see the evolving shape of the market. This tells you where stocks are most concentrated in terms of return and risk, and where that concentration is going.

As you might expect from previous descriptions of the purple curve that marks the greatest stock density, we want to resolve details of the shape of the density along that curve. You have seen that the curve has a crescent shape, trending off toward high return and high risk at the upper right (northeast), and toward low return and high risk at the lower right (southeast). Starting from about middle height on the left side of the chart, draw two straight lines, each through one of these two ends-points on the right to mark the two trends. During the course of playback, you will see the market move from alignment on one trend line to alignment on the other, and back again. To remain a long-term buy-and-hold investor is to believe that the market eventually will move into alignment with the upper trend line (pointing toward the northeast). But there may be times when things go wrong, in the short term.

The contours and purple crescent curve appear in the Trends Snapshot taken from the animation. Just as you may have seen in the DiligentInvestor Screener or in the discussion of the first part of the animation, most stocks lie in a roughly triangular area, narrowing at the middle left, with a near-vertical and sometimes concave edge at the right. Especially evident in the preview on-line animation, link on the Purchase page, the upper and lower edges of that triangular area are where stocks stop moving. These upper and lower edges show you the two trend lines, and they represent the two places where forces on a stock are in equilibrium. The animation treats the market as surface which steadily changes in shape.

What does the equilibrium mean? The upper trend line has return increasing with risk, which corresponds to one of the fundamental ideas behind the Capital Asset Pricing Model: the riskier an equity, the more return must be offered. This is why long-term bonds pay a higher yield than short-term notes, because more can go wrong over a longer time interval. A stock lying on the upper edge of the triangle has a return proportional to its risk, so there is no reason for its return to change, and it stays where it is.

There is a paradox to CAPM, however. Many investors, especially those recently burned, become risk-averse (or need cash). They want to get rid of stocks perceived as being risky, driving down the price and hence the return. The lower trend line has return decreasing with risk, which is why it is so hard to gather evidence consistently supporting CAPM: sometimes the riskier an equity is, the less return will be offered for it. This is why perception of risk is so important, and may be why a market can collapse so much more rapidly than it can grow. All it takes is a change in perceptions to collapse, while it takes the accumulation of evidence in order to grow. A stock lying on the lower edge of the triangle has a negative return proportional to its risk, so there is no reason for its return to change and it stays where it is, until perceptions and hence expectations gradually improve. Here may be the location for bargain-basement opportunities.

What do we mean by the forces on a stock? The above changes in shape perhaps correspond to deformation or strain, under the influence of stress, force per unit area of normal space. This is a fascinating research question, and may be easier to answer in this normal space than in the raw return and risk coordinates. It is tempting to look into physics for an answer, as suggested by the analogy on the next page.

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