The Hindu Business Line : Applying laws of physics to study Sensex behaviour

Hero Honda, Cipla and ACC. These are the three companies that stood out among the Sensex constituents, with high acceleration but low deceleration, during the period from February 1 to June 30.

To explain how, we have to draw upon physics lessons. So, brace up. First, what is acceleration? It is `the rate at which an object changes its velocity', defines www.physicsclassroom.com. And velocity is `the rate at which an object changes its position'.

Formula to compute velocity is given as `v = u + at'. In this expression, `v' is the final velocity or velocity after an object accelerates for a time; `u' is the initial velocity; `a' is acceleration; and `t' is time.

Well, the `object' in our study is not a racecar or a space shuttle, but each of the 30 scrips that constitute the Sensex. And this is how we went about relating the formula's variables to the market data.

For each share we identified two phases in the 5-month period under study: the ascent and the descent. The divide happens at the peak or the maximum value achieved by the share. This is `v' or the final velocity for the ascent phase. Between February 1 and the day of the peak, we identified the lowest value, and named it `u', the initial velocity. And `t' is the number of days that `u' took to become `v'.

With these variables known, we computed `a', the acceleration. But not before removing the effects of scale, by dividing `v' and `u' by `u'; and `t' by 250, the approximate number of trading days.

A similar exercise was performed for the descent phase. Here, the peak became the initial velocity, and the minimum value from the date of peak to the end of June was the final velocity. The formula, though, is the same, with the only difference that the final answer is a negative, indicating deceleration.

The graph shows a scatter of 30 pairs of values, with acceleration on Y-axis and deceleration on X-axis. Bisecting both the axes, we find that the `high acceleration low deceleration' quadrant has but three companies, mentioned at the beginning of the story.

The opposite is visible in the `low acceleration high deceleration' quadrant, bottom left, where you can identify four dots at the far end. These are ONGC, Bajaj Auto, L&T and Maruti.

(With software support from A. Karthik)