## How markets work

A long time back, there was this picture that was making the rounds on Twitter and (more prominently) LinkedIn. It featured three boys of varying heights trying to look over a fence to see a ball game.

Here is what it looked like:

These pictures were used to illustrate that equality of outcomes is not the equality of opportunity, or some such things, and to make a case for “justice”.

As it must be very clear, the allocation of blocks on the right is more efficient than the allocation of the blocks on the left – the tallest guy simply doesn’t need any blocks, while the shortest guy needs two.

And if you think about it, you don’t need any top-down “justice” to allocate the blocks in the right manner. All it takes is a bit of logical thinking and markets – and not even efficiently.

Think about how this scenario might play out at the ball park. The three boys go to see the ball game, and see three blocks at the fence. Each of them climbs a block, and we get the situation on the left.

Shortest boy realises he can’t see and starts crying. There are many ways in which this story can play out from here onward:

1. Tallest boy realises that he doesn’t really need that extra block, and steps down and gives it to the shortest guy, giving the picture on the right.
2. Tallest boy continues to stand on his block. Shortest boy realises that the tallest boy doesn’t need it, and requests him for the block. Assuming tallest boy likes him, he will give him the block.
3. Tallest boy continues on the block. Shortest boy requests for it, but tallest boy refuses saying “this is my block why should I give it to you?”. Shortest boy negotiates. Tells tallest boy he’ll give him a chocolate or some such in return for the block. And gets the block.
4. Tallest boy doesn’t want chocolate or anything else the shortest boy offers. In fact he might want to settle a score with the shortest boy and refuses to give the block. In this case, the shortest boy realises there is no point being there and not watching the ball game, and makes an exit. In some cases, the middle boy might negotiate with the tallest boy on his behalf, leading to the transfer of the block. In other situations, the shortest boy simply goes away.

Notice that in none of these situations (all of them reasonably “spontaneous”) does the picture on the left happen. In other words, it’s simply unrealistic. And you don’t need any top down notion of “justice” to enable the blocks to be distributed in a “fair” manner.

## USD/INR Volatility

The stated objective of the Reserve Bank of India when it comes to foreign exchange rates is that they want to maintain a “stable” exchange rate, and will step in only to curb volatility. There is no stated level at which the bank seeks to hold the rupee, and so it will intervene only when the rupee is volatile.

In this post, we will look at how the volatility in the USD/INR exchange rate has varied over the last seven years. For purpose of this analysis, we will use a 30-day Quadratic Variation as a measure of volatility (this is a lagging indicator, so the volatility number for today is the QV of the last 30 days).

The following graph shows both the level of USD/INR (black line, left axis) and the quadratic variation (red line, right axis).

Notice that for most time periods, irrespective of the exchange rate, the RBI’s stated objectives have been met – the volatility in the exchange rate has been low for large period of time. Volatility of the exchange rate spiked once following the financial meltdown of late 2008 and again towards the end of 2011 (when Europe got into trouble).

It is interesting to note that for all the footage that the sliding rupee has received in the last month or so, the volatility of the rupee has been quite low (compared to the peaks). It will probably take a significantly higher volatility in the rate for the RBI to step in.

It is also interesting to note that in the second half of 2010, even though the rate level was fairly stable, volatility was significant!