## Saturday, May 26, 2012

### The costs in buying versus the costs in selling

All models are wrong, some models are useful. A model reduces complications that are true in return for tractability and insight. In finance, all too often, one complication which has been wished away is transactions costs. A great deal of what we see in the world around us is caused by the costs of transacting. Some of the most important finance is about analysing the causes and consequences of the costs of transacting.

### The bid offer spread as a measure of transactions costs

The first flush of the literature draws on markets with market makers, and treats the bid-offer spread as the measure of the cost of transacting. On the NYSE, the specialist posts a bid price and an offer price. If you do two transactions in quick succession -- buy 100 shares and then sell them back -- you will be poorer by the bid-offer spread. The spread is like a tax on a speculator doing a round-trip for a small transaction.

There is no doubt that in that environment, the spread measures something important about transacting. Large databases about the spread are available. A whole literature arose which is rooted in the spread as the measure of the cost of transacting.

### Limit order book markets are a whole new world in observability of liquidity

The world changed. Across countries and across asset classes, exchanges have been morphing into anonymous open limit order books. The market maker is not as important. On the open limit order book market, the full set of limit orders are observable, using which we can simulate a market order of any size, and calculate the exact cost that is paid. Suddenly, instead of just seeing a bid-offer spread, we see a whole new world which displays the full liquidity supply schedule' (LSS) that has the impact cost (in per cent) associated with a single market order of all possible sizes.

 An example of the Liquidity Supply Schedule': The impact cost associated with all possible transaction sizes

When the bid/offer stands at 98/102, and the midpoint quote is 100, if a single market order to buy 1000 shares gets executed at an average price of 105, the buy impact cost for 1000 shares is 5%. This calculation, repeated for all possible transaction sizes, paints the full Liquidity Supply Schedule (the LSS).

Once the LSS is visible, and we start thinking about the world in new ways, and the spread feels like a highly unsatisfactory measure of the cost of transacting. At the NYSE, the market lot is 100 shares for all firms. A share price of $5 means the spread refers to the cost of a transaction size of$500. If the share price is $200 instead, the spread pertains to a transaction of$20,000. Hence, the spread is itself not comparable across securities. In contrast, the LSS can be a standardised calculation that is comparable across all firms, with standardised units on the x axis either in rupees or basis points or market capitalisation.

For us in India who grew up with limit order book markets (NSE from 11/1994 onwards; BSE from 5/1995 onwards), the mainstream Western literature seems a little quaint, given their emphasis of the spread as the measure of transactions costs. We are seeing much more of the liquidity elephant through the LSS, while so many researchers are only seeing it's tail through the spread. In India, the construction of Nifty required the capture of multiple snapshots of the entire limit order book per day, and has generated information about the LSS going back to the mid 1990s.

Since exchanges worldwide have shifted over to an open electronic limit order book, the new focus of measuring liquidity in finance lies in understanding the LSS. What explains cross-sectional and time-series variation of the LSS? What are the consequences of various features of the LSS? These questions have only begun to be addressed in the literature. Rosu has a fascinating recent paper in the Review of Financial Studies, 2009, titled A Dynamic Model of the Limit Order Book that presents one of the first models which predicts the shape of the LSS in an open ELOB market.

### Does the impact cost in buying differ from that faced when selling?

One interesting dimension which the LSS makes possible is to think afresh about buying versus selling. The bid-offer spread tells us the round-trip transactions cost. It does not differentiate between buying and selling. When you see that the bid and offer are 100/102, there is no sense in which the transactions cost in buying differs from the transactions cost in selling.

But with the full LSS, we see the impact cost of buying at all transaction sizes separately from the impact cost of selling at all transaction sizes. A first question to ask is: Is there symmetry in liquidity? In the example of the LSS graphed above, it's quite obvious that the impact cost when buying is superior (i.e. lower) than that faced when selling. But this is just one anecdote.

In a recent paper Measuring and explaining the asymmetry of liquidity, Rajat Tayal and Susan Thomas explore this question. With equity spot trading on the NSE, they find strong evidence in favour of asymmetry: impact cost is higher for large sell market order compared to large buy market orders.

### Why might asymmetry arise?

What features about traders in the market generate differences between buying and selling? There is one candidate: how traders perceive sell market orders, particularly large sell orders that come despite constraints on borrowing shares, and restrictions on short-selling.

The speculator who makes a forecast that a share price will go down seldom owns the shares; selling requires borrowed shares. Particularly, in India, where formal mechanisms for borrowing shares are as yet quite small, a speculator who wants to sell physical shares has to mobilise borrowed shares on his own.

This may shape the thinking of the people placing limit orders. When I place limit buy orders (which will get hit by a speculative seller), the adverse selection runs against me. If the speculator was not confident about his forecast, he would not bother to borrow shares and sell short. Only when the speculator is really sure would he take the trouble of borrowing shares and doing a sell order. Hence, the person placing limit orders to buy would demand a bigger price of liquidity (i.e. the impact cost), since he runs a greater chance of losing money when giving liquidity to sellers.

The paper highlights a fascinating identification opportunity : at NSE, alongside the trading of the equity spot market, we also have trading in single stock futures. Everything about the two markets is identical: the same securities, the same trading system, the same participants, the same hours of day, etc. There are only two differences: stock futures trading is leveraged, and stock futures trading has cash settlement -- which removes the short-sales constraints. Cash settlement induces full symmetry between buying and selling.

If short sales were the reasons asymmetry in liquidity on the equity spot market, then the stock futures market should have no asymmetry between buy and sell orders. The paper uses the same measurement procedures and statistical tests to compare the asymmetry of liquidity on the spot market as well as for the stock futures market. They find that there is no asymmetry of liquidity on the stock futures market.

If their story is correct, it has many implications. In other market settings observed worldwide, cash settled derivatives should have symmetric liquidity. Physical settled derivatives should have asymmetry - which might get more accentuated as you come closer to expiry. Many natural experiments have taken place worldwide, where futures contracts have shifted from physical to cash settlement: these are all nice natural experiments where changes in asymmetry should become visible. On spot markets, asymmetry should vary with the ease of borrowing. Future research projects could explore these questions.

Financial economics benefits from the best datasets in all economics, and we are able to get sharp and clean papers which pretty decisively answer questions. In India, it has started becoming possible to do innovative work by drawing on data from the open ELOB equity exchanges, CMIE, etc.

Please note: LaTeX mathematics works. This means that if you want to say $10 you have to say \$10.