# Opinion Oscillator

Muranaka, Ken, Futures (Cedar Falls, IA)

How can you forecast a market turn? Try taking the participants' psychological temperature.

Sentiment indicators are a measure of the emotions and expectations of investors. In Japan, technical analysts use the psychological index (psychological line or PI), a stochastic oscillator, to predict market direction. It's a simple measure to compute. Yet, if viewed as a statistical model, the PI can be a powerful tool to analyze swings in speculative markets.

The P1 formula is simply:

(X/12] * 100 = PI%

where x is the number of days that the market closed higher compared to the previous day in the past 12 consecutive observations. The PI always ranges between 0% and 100%. The PI usually is plotted like the stochastic oscillator and the relative strength index (RSI). If the PI at or above 75%, the market is considered overbought, generating a sell signal. A PI reading at or below 25%, depicts an oversold market and generates a buy signal.

The PI is not a primary analytical method used by Japanese traders, but rather is one more tool that a trader can add to his current approach. Used in conjunction with other oscillators such as the RSI and moving averages, the PI can capture short-term moves that may not be detected by moving averages and thus can improve the overall predictive power of the trader's analysis.

PI as a statistical model The PI as a random variable will follow a binomial distribution. The 75% line means that the market closed higher nine out of 12 times, whereas the 25% line means that the market closed higher only three out of 12 times.

It is easy to compute the PI values with a spreadsheet such as Excel. Here, the Excel's IF function is used to assign a value of 1 if the closing price is higher than that of the previous day. Otherwise, a value of 0 is assigned. Next, the sum of the 12 consecutive observations is divided by 12. The PI can be expressed by the binomial distribution:

([n above x])[P.sup.x][(1 - P).sup.n-x] for x=0 1, 2,[ldots], or, n,

where n = 12. The PI is defined by the probability of "X ups in n observations."

If p = 0.5, then the market goes up or goes down by the same chance. For the PI with n = 12 and p = 0.5, the index reaches 75% or above with the probability of 7.3%, which is the sum of the probabilities for x = 9, x = 10, x = 11 and x = 12. The index falls to 25% or below with this same probability, which is the sum of the probabilities for x = 3, x 2, x = 1 and x = 0. These probabilities can be computed directly from the binomial formula or a table found in any statistical textbook.

Can the 25% and 75% psychological lines really determine a turning point in the market? Because the PI is associated more often with stock markets than with commodities, we chose the Nikkei 225's data to test the predictive power of this indicator along with the short-term five- and 12-day moving averages.

Testing the model Swings in the cash values of the Nikkei 225 were modeled by the PI as a binomial random variable. Two cases were considered -- bull and bear markets. The prices were obtained from the newspaper Nihon Keizai Shimbun. For a bear market, 201 PIs were computed using the closing prices between Aug. 26, 1997, and June 23, 1998. All the calculations were done with Excel 97.

"Probabilities" (above) is the observed probability distribution showing a fairly good fit with the theoretical binomial distribution having the parameters p = 0.5 and n = 12, but the observed probability distribution is slightly skewed. By trial and error, the value of the probability p to minimize the sum of squares [(observed - theoretical).sup.2] was found to be about 0.48, suggesting that the Nikkei 225 index may not appreciate or depreciate with equal probability, and that the market is more likely to decline by 2% as compared to the previous day. However, the theoretical probabilities for the PI [leq] 25% and PI [geq] 75% are 6. …

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