5. Report

The left-hand side of the screen shows a text report with information about a stock. You select this stock by typing its ticker symbol into the list box or by clicking on the Scatterplot Chart. The chart then shows horizontal and vertical yellow lines through the graphic return and risk coordinates of the stock, along with its ticker symbol in blue.

Ticker Symbol

These stock ticker symbols consist of one to five alphabetic characters, with no numerals, spaces or punctuation. Type a valid ticker symbol into the Symbol? field described under Settings. Then press the Submit button or press the Enter key on your keyboard. The report and chart then should show the same uppercase ticker symbol.

We do not report data for all possible ticker symbols. We make no special effort to cover international stocks, penny stocks, funds, bonds and equities offered too recently for one year of price history. The result covers perhaps one third of the 8500-odd US stock quotations available.

Name

We use the stock name from Yahoo! Finance associated with the ticker symbol given by Wall Street Journal Online Markets Data Center for NYSE, AMEX and NASDAQ. The name provides no more detail than needed to confirm the identity of the stock in less than sixty-four characters.

If you you do not see your favorite ticker symbol or if you find errors in the stock name, please send an e-mail with your suggestions to Technical.Support at DiligentInvestor.com.

Return

As in Diagoran® 2006, the raw return is the linear least squares best fit to the logarithm base 10 of the closing price (split and dividend adjusted) as a function of date. Return, in units of deciBels per year (dB/y), represents continuously compounded interest as in a savings deposit. Three dB corresponds to doubling in price, six dB to quadrupling, and so on. Divide dB/y into 36 to get the number of months to double the value of the stock if positive, or the half-life in months if negative.

Risk

As in Diagoran, after subtracting the return trend found above (and significant cyclical behavior), we take the divided differences of the logarithm of price versus date. We do this for all adjacent dates in the dataset used above. The root mean square of these annualized daily slopes of the logarithm of price is then the raw Risk, also in dB/y. These two parameters, return and risk, appear to be the most robust, useful, efficient and powerful measurements that one can abstract from a normal price history. The method of ordinary least squares appears to provide the best linear unbiased estimators for common linear regression of these nearly normally distributed logarithmic data.

For example, the one-sigma bounds for a stock with a return of 3.0 and a risk of 1.0 are 3 +/-1. The upper bound, 4 dB/y, gives a doubling time of nine months. The lower bound, 2 dB/y, gives a doubling time of eighteen months. That is, we expect the stock to double in value in one year, and in two out of three identical trials, to do so in not less than nine months nor more than eighteen.

Recent market close

As shown for example in the arrow plot, Diagoran draws a hyperbolic envelope* around the return trend line. Its vertical width at each date is risk times the square root of time. If the most recent logarithm of price falls inside this envelope, we declare it on trend. Otherwise, there is some significant departure from expected behavior, which we declare as a recent market close of high or low.

A stock that has this characteristic may be acting in an unusual manner, and so might be worth your attention. The characteristic often appears to be persistent and so we report it even though possibly out of date.

Seasonal or cyclical behavior

Some stocks exhibit a pattern of rising and falling price depending upon the time of year. The classic example is a Christmas tree supplier, clearly seasonal. Some stocks seem to obey a pattern with a longer (but unpredictable) time between peaks or valleys. The market itself moving up or down for several consecutive quarters in this pattern is declared to exhibit a business cycle, so a stock moving with the market is cyclical.

In either case, we want to detect such a pattern over a fixed number of days in a cycle, and then attempt to extrapolate this behavior. The technique used in Diagoran and this screener depends upon the idea that the sum of some number of sine waves with carefully chosen cycle lengths, phases and amplitudes can fit any series of data. There is no implication that real seasonal or cyclic phenomena actually underlie the stock price.

As shown for example in the cycles in price plot, Diagoran draws the return trend line and its hyperbolic risk envelope modulated by significant cyclical or harmonic behavior. No such illustration appears in this screener, but it uses the same algorithm.

These calculations find a few most significant sine waves in the detrended price history and show where such behavior may exist, whether real or apparent. In Diagoran, they also find numerically correlated stocks by the fact that they share the same cycles. This reveals correlations not evident from the Pearson Product Moment method, in the case that stocks peak on the same cyclic interval but are out of phase, such as with natural gas and synthetic fertilizer.

The analysis is quite mechanical, having no more insight than a pocket calculator, but it produces a result you can test: the likely dates and ranges of closing prices at the next peak and valley of detected cyclic behavior.

Dates & Prices

As in Diagoran, if cyclical behavior appears to explain a significant part of price history, the report contains date and range of price associated with the next peak and the next valley. We find the center of the range from the return trend added to the sine waves as projected. The half-width of the reported range is the square root of time multiplied by the root mean square departure, the risk. That is, we assume that the underlying behavior is unchanging, see Warnings. We assume that the date exactly specifies the peak or valley of the combinations of sine waves we use. If you obtain the actual market close on the given date, it almost certainly will not be at the theoretical price, and the actual extreme will not occur on the theoretical high or low date.

Half-life or doubling time

In the case of no significant cyclic behavior, we report the return and risk, expressed in deciBels per year. The likely bounds of a normally distributed result are the return trend plus and minus one standard deviation in risk, similar to the root mean square departure used here. Each of these extremes is converted to a time in months by dividing into 36. If the extreme is positive, it is the doubling time; if negative, it is the half-life. In the case of zero extreme, we declare the result flat.

In either case, the numerical model assumes contrary to fact that the trend and behavior in recent past is a guide to the near future. The statistical model assumes that error bars describe a universe of stocks identical to the one reported, with only a Gaussian normal distribution in behavior. In about two-thirds of all cases, a sample from that universe should stay within a standard deviation of the mean. These are not verifiable statements, so please beware of the result. You should consider all available sources of information to invest in the market.

Rising or falling return

Version 2 of this screener adds a display of the return and risk measured at one and two months prior to the date of analysis shown at the bottom left corner of the Scatterplot Chart. The direction of this change in return is noted in the report as well. Stocks seem to show some momentum in this movement, providing an additional clue for your analysis.

*Technical note: the envelope marks the evolution of the root mean square departure, or risk, about the mean logarithmic return, from zero value at the extreme left of the chart to the annualized risk value at the right of a plot one year long. It is hyperbolic, open to the right, because the expected departure from the mean trend obeys the rules of a random walk described in stochastic calculus. These are not Bollinger Bands, which are a kind of moving window estimate of standard deviation. A good description of the idea can be found on page 111 of "Paul Wilmott Introduces Quantitative Finance", 2001, John Wiley & Sons. However, since Wilmott is working from theoretical data, his figure 6-7 has the zero risk point at the left coincident with the return at that point. The two plots noted above show that this is hardly ever the case for real data. The degree to which the actual returns fall outside the risk envelope at the left end of the plot give some indication of the degree to which the behavior of the stock does not fit the theoretical model.

© Copyright 2007-2008 DiligentInvestor