by Ajay Shah.

### Liquidity matters

One of the most important features of a financial market is liquidity. In a well functioning market, a trader faces low costs of transacting and can confidently expect that at future dates, across many states of nature, the cost of transacting will prove to be low.

The immediate impact of a low cost of transacting is that it imposes a lower `tax' upon the speculator, who brings new information into prices, and the arbitrageur, who removes obvious mistakes in prices. The long-term impacts that are obtained when the trader can confidently expect that transactions will be inexpensive are in two parts. When investors expect to waste money in buying and then selling a certain security, they demand higher rates of return from it: i.e., the cost of capital for the issuer goes up. And, when traders are confident that high liquidity will persist into the future into a diverse array of states of nature, they will more confidently embark upon dynamic trading strategies which are required for producing useful securities such as options.

### Measurement of liquidity

In an electronic limit order book market, a static concept of liquidity is eminently visible: you look at the order book and work out what is the impact cost faced when doing transactions of a desired size. E.g. it is easy to take order book data from NSE and work out the impact cost seen for doing a transaction of Rs.10,000 for all companies.

Impact cost accurately measures the instantaneous cost faced when placing an order of the stated size. It is a observed precisely in a modern exchange setting. There are two weaknesses. No large order is going to be placed as one single market order into the order book. Hence, the analysis of the NSE order books does not guide us in understanding liquidity when doing large sized transactions, e.g. Rs.1,000,000. The moment we think of orders that are spaced over a short time (e.g. I break up an order for Rs.1 million into 100 orders of Rs.10,000 each) or over a long time (e.g. dynamic hedging of an option book) I have to worry about the fluctuations of impact cost, or my liquidity risk.

The biggest problem lies in the fact that in numerous market situations, order book information is not observed. Two key areas are: the deep past, before order book data existed, and the OTC market, where there is no order book. E.g. the CMIE daily returns data for BSE starts from 1/1/1990. NSE equity trading began in 11/1994. But NSE's order book snapshots (thrice a day) only exist from 4/1996 onwards. For the period prior to 1996, there is no data on liquidity.

### The power of range

The first flush of the financial economics focused on

*returns*. It was amazing, the amount of interesting work that could be done once you had assembled a dataset with daily returns. This was first done at the Centre for Research on Security Prices (CRSP) at the University of Chicago, and it made possible an entire generation of financial economics.

As an example, the ARCH model is a very clever way to utilise pure returns information and construct a time-varying notion of volatility. Models of the ARCH family assumes that volatility is

*deterministic*, and that it responds to realisations of returns.

A remarkably important fact looks beyond returns to the

*range*between the day's high and the day's low price. When volatility is high, the range is higher. Range is a volatility proxy. This has been known for a while -- e.g.

*On the estimation of security price volatilities from historical data*, M. B. Garman and M. J. Klass, page 67--78,

*Journal of Business*, 1980.

In the late 1990s, people got back to looking at this in a new way. We understood that range is an enormously informative volatility proxy. There is much more information in the range of the day than is found in the squared returns of the day.

Another new volatility proxy is `realised volatility', where you difference intra-day returns to construct a time-series of returns

*within*the day. As an example, in an 8-hour trading day, there are 480 minutes. So you could difference returns into 5-minute intervals, and you have 96 readings of returns on each day. The standard deviation of this is a good measure of the volatility of the day. As an example, the recent paper by Grover and Thomas,

*Journal of Futures Markets*, August 2012, does performance evaluation for a VIX estimator by asking for better predictions of future realised volatility.

In the ARCH world, volatility

*of the day*was not observed, and squared daily returns was a poor proxy for this. Realised volatility is a highly precise estimator of the volatility of the day, and range is also remarkably good.

### Constructing a deep history of stock volatility

Using intra-day data, it is possible to construct a realised volatility for every security for every day. This is obviously infeasible for the period when intra-day data is not observed - e.g. in India before electronic trading came along, i.e. before November 1994.

But as long as the day's high and the day's low are observed, one can construct a range-based measure, and thus push deeper into history.

### Constructing a deep history of stock liquidity

When trading is electronic, it is possible for the exchange to produce `snapshots' of the limit order book, as has been done by NSE from April 1996 onwards. Using these, it is easy to get precise estimates of the spread for all stocks. But what about the period before that?

I just read a fascinating paper:

*A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices*by Shane A. Corwin and Paul Schultz,

*Journal of Finance*, April 2012. Their key insight is that the day's high is almost always at the ask and the day's low is almost always at the bid. When the high/low is computed over two days, the variance is doubled but the spread component is intact. This generates a mechanism for extracting a spread estimator using only high-low data.

I liked the paper a lot. At its best, finance is close to data, the data has low measurement error, the work is careful and grounded in a detailed institutional understanding of reality, and the results open up new lines of inquiry.

Using these new ideas, it becomes possible to dig into history, using the CMIE data for BSE which goes back to 1/1/1990, and construct liquidity measures for that deep period.

The authors do precisely this:

They show a big and dramatic drop in the spread at the time when electronic trading came in. There are three key dates here: NSE started electronic trading on 3 November 1994, BSE started electronic trading on 14 March 1995 and in November 1995, NSE became the dominant exchange [link]. This is a valuable addition to our understanding of these events. I do worry about mistakes in measurement of the day's high and day's low, however, prior to the onset of electronic trading at NSE in November 1994.

I found it fascinating, how a 2012 paper has produced a better understanding of our history of the mid-1990s.

###
Understanding the *badla* episode

What is equally interesting, and what is not mentioned by the authors, is the dog that did not bark prior to the launch of NSE. This is the event where SEBI forced BSE to stop

*badla*trading.

I had worked on this question at the time (in 1996). I had rigged up a matching scheme where each A group company (where

*badla*trading used to take place) was matched against a partner from the B group (where there had never been

*badla*trading). This allowed you to construct a hedged portfolio: long the A group companies and short the B group companies. The performance of this portfolio is:

This hedged portfolio has a most satisfying zero return in the days before SEBI's decision. This gives us confidence that the matching is done well. The two big dates of SEBI decisions -- 12 December 1993 and 12 March 1994 -- show big negative returns for A group companies. And from 4 November 1994, when trading at NSE began, we start seeing a recovery.

At the time, this was interpreted at the time as a liquidity premium. See

*Short-term traders and liquidity: A test using Bombay Stock Exchange data*by Berkman and Eleswarapu,

*Journal of Financial Economics*, 1998, who worked this out nicely.

But the new evidence for the deep history of spreads on the BSE, by Corwin and Schultz, suggests that

*there was no big change in liquidity in 1993 or 1994*. This raises new questions about why such large price reactions were observed. I used to think this was a great liquidity premium story; now I'm not so sure. I'm pretty certain that A group companies had sharp negative returns in early 1994, but I am now less sure that we know why.

Joel Hasbrouck's related work will be of interest: "Trading costs and returns for US equities: estimating effective costs from daily data"

ReplyDeletehttp://pages.stern.nyu.edu/~jhasbrou/Research/GibbsCurrent/gibbsCurrentIndex.html

Nice post.

- Vishal Belsare