## Volatility and price differentiation

In a rather surreal interview to the rather fantastically named Aurangzeb Naqshbandi and Hindustan Times editor Sukumar Ranganathan, Congress president Rahul Gandhi has made a stunning statement in the context of agricultural markets:

Markets are far more volatile in terms of rapid price differentiation, than they were before.

I find this sentence rather surreal, in that I don’t really know what Gandhi is talking about. As a markets guy and a quant, there is only one way in which I interpret this statement.

It is about how market volatility is calculated. While it might be standard to use standard deviation as a measure of market volatility, quants prefer to use a method called “quadratic variation” (when the market price movement follows a random walk, quadratic variation equals the variance).

To calculate quadratic variation, you take market returns at a succession of very small intervals, square these returns and then sum them up. And thinking about it mathematically, calculating returns at short time intervals is similar to taking the derivative of the price, and you can call it “price differentiation”.

So when Gandhi says “markets are far more volatile in terms of rapid price differentiation”, he is basically quoting the formula for quadratic variation – when the derivative of the price time series goes up, the market volatility increases by definition.

This is what you have, ladies and gentlemen – the president of the principal opposition party in India has quoted the formula that quants use for market volatility in an interview with a popular newspaper! Yet, some people continue to call him “pappu”.

## A culture of thinking and differentiated services

In a very interesting Op-Ed in Mint this morning, Anurag Behar argues against vocational training at the school level, arguing that the purpose of school education is to enable children to think, and that the ability to think is paramount in offering superior services.

He gives the example of a welder who understands basic geometry and the mechanics of metals, saying such a welder can offer superior services to one who has just been trained in welding. Thus, a welder who had been through school and thus understands the basics of geometry and mechanics can do a much better job as a welder than one that has just learnt how to weld.

Now, while this culture of thinking is important, another important pre-requisite is the culture of differentiated services. The question we need to ask is if the market here is mature enough to pay a premium for the welder who knows geometry and mechanics compared to an illiterate welder.

Intuitively it makes sense – an educated welder is likely to be more careful in his work and is likely to offer much superior quality. However, what I’m not so sure of is that the market in India is currently mature enough to recognize this increase in quality and thus pay a premium for such services. And unless the market matures to pay a premium for an educated welder, an educated person will choose a career other than being a welder and we will be only left with uneducated welders offering poor quality.