RATE OF CHANGE

Rate of change is the simplest way to understand time
Speculations in stock markets are about a price change. A change in price can increase or decrease profits. How do we measure this change? If the Sensex rose from 14,000 to 15,000, you could say either that it rose by 1,000 points or, alternatively, that it increased by 7 per cent. Stating the increase as 1,000 points (an absolute measure) is simple and straightforward. Yet to interpret the figure it must be judged against another figure, such as the starting level. A rise of 1,000 points in an index standing at 2,000 is much more dramatic than an increase of 1,000 points in an index which started at 14,000. The percentage change (a relative measure) is easy to interpret. It indicates the size of a change when the starting level is 100. Percentages therefore provide a consistent yardstick for interpreting changes.
This is a similar perspective what technicians use when they study long term data. An arithmetic scale for a multi-year stock history (that has been part of a bull market looks like a propelled rocket) could be tougher to judge compared to a log scale which illustrates similar percentage changes. Most oscillators built around a price illustrate this price change in one way or the other. The simplest of them is called rate of change. Aka ROC, the indicator is a very simple yet effective momentum oscillator that measures the percent change in price from one period to the next. The ROC calculation compares the current price with the price some time ago.
Concept and application
The concept is also widely used for other time series. The differential calculus is the study of the slope (or derivative) of a function or the rate of change of a function. The rate of change of a function (called a derivative) is an extremely useful concept in economics. For example, a cost function tells us the total cost associated with each quantity level of production of a firm. The rate of change of the cost function is called the marginal cost of the firm and it tells us how much it will cost the firm to produce one additional unit. Similarly, the revenue function of a firm tells us the total revenue generated by the sales at each quantity level and the rate of change of the revenue function, the marginal revenue, tells us how much additional revenue is generated by an additional sale. If the cost of producing one additional unit is less than the additional revenues generated by that unit, then the firm can earn more profits by producing and selling that extra unit. In other words, if the rate of change of the cost function is less than the rate of change of the revenue function, then a profit-seeking firm should produce and sell more units of the good.
Markets, interest rates and prices
In the book, Stock Market Cycles: A Practical Explanation, Steven E Bolton explains various stages of stock market cycles using the dynamics of earnings and interest rate. Expected earnings, on average, fluctuate with the economic cycle and create cyclical patterns. In the first stage, common stock prices hit their lows shortly before the trough in economic activity when the rate of change in expected earnings equals the rate of change in interest rates. In the second stage, rising common stock prices continue as long as the rate of increase in the expected earnings exceeds the rate of increase in interest rates. Stage three is when the common stock bear market starts when the rate of increase in expected earnings is less than the rate of increase in interest rates. In the final stage, expected earnings continue to decrease but at a slower rate. That rate of decrease in expected earnings is greater than the rate of decrease in interest rates.
Common stock prices continue to fall but not as rapidly. The low in common stock prices is reached when the rates of decrease in expected earnings and interest rates are equal. The common stock price cycle reenters its upward phase when the rate of decrease in the expected earnings is less than the rate of decrease in interest rates.
The book illustrates rate of change to explain the stable expected earnings of traditional electric utilities and how their common stock prices is sensitive to the rate of change in interest rates. Common stocks with stable expected earnings, such as traditional electrical utilities, behave more like bonds than stocks because the rate of change in their expected earnings is less than the rate of change in interest rates.
The author makes a good attempt explaining stock market cycles using dynamics between economic parameters. However, not even once does the author wonder why rate of change illustrates the market cycle so well. There are a host of traders who use conventional oscillators buying at oversold levels and selling at overbought levels without crediting the basic idea of time cyclicality. ROC models is time cyclicality made easy.
Rate of change and indices
To demonstrate the simplicity we can take Sensex and start tabulating the default 14-period ROC results with above zero ROC as a buy and below ROC zero values as sell. Monthly ROC data gave a buy on May 31, and sell on September 3, 2008. The signal captured a large part of the bull market with returns at 358 per cent. We went a time frame lower to weekly period ROC. The buy signal came at March 29, 2009 and sell signal is yet to come. The signal captured most of the upside since March lows and is still a buy after 56 per cent per cent registered gains. We can go to daily ROC and so on till the last 1 min. It was this ROC cycle we illustrated in “A Dow theory” that was published here on March 27, 2009 where we explained how even Dow Jones industrials has an average fixed time cyclicality historically. We also talked about a multi month move in 2009 that happened.
ROC and cyclicality
So if it is so easy, why don’t we ROC more? There are a few reasons. First: just like everything we look for equality in ROC lows while ROC as an expression of time is more proportional than equal. Second: Majority does not relate to sideways action as a down cycle in time. This is why till we have a crash which washes trillions of dollars we don’t understand or relate to cyclicality. Martin Pring has long called retracement in time equivalent to retracement in price. What he is indirectly explaining is that retracement in time is more important than retracement in price. This is why if a bear market that does not show real down price moves but still sees a long time of sideways action qualifies as bear markets in time. Pring made an attempt to reconcile cyclicality using three time frames ROC together and also in an indicator he calls as KST (Know Sure Thing). KST indicator is the idea of time fractals on three degrees. One can extend the same to all time frames and we reach the same idea again, the idea of cyclicality existing at all degrees and all time frames. ROC is the simplest tool to see time fractals. The large monthly ROC cycle has weekly ROC cycles in it, which in turn has daily ROC cycles nested in it, a classic fractal solution.
But, where we fail is to be able to synchronise various time frames and understand them together and not just individually. In the articles ahead we will explain how ROC can create time triads. Till then try out ROC today take the first few steps into time cyclicality.
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ORPHEUS RESEARCH AT REUTERS – UNITED KINGDOM
ORPHEUS RESEARCH AT REUTERS – USA
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