The math of banning short sales

Good article on why banning short sales is just not a good idea;

In response to the market turmoil of the last several weeks, several countries, including ours, have tightened restrictions on short-selling or eliminated shorting entirely in some classes of stocks. These restrictions have come with the expressly stated intent of reducing market turbulence. In the U.S., the entire sector of financial stocks (including, curiously, General Electric and General Motors) has been temporarily placed off-limits to short-sellers. Our research, which is strongly supported by market data, shows that rather than calming the markets, these types of restrictions produce heightened volatility and asset bubbles punctuated by sudden crashes.

While our work is mathematical in nature, the essential features are very easy to grasp. Any restriction in shorting is equivalent to a market cost. This cost disseminates itself into the price of options (puts and calls) and into the equity price as well. Normally all sellers--both those who hold shares and those who sell short--provide the liquidity necessary to pair off buyers.

By using regulation to remove one group of sellers, this equilibrium is disturbed. Generally the stock is forced to a higher price, but this higher price comes with greater instability and occasional crashes. The measured volatility is higher in this elevated price regime, not lower.

It may seem that elevated stock prices are an unalloyed good thing, but they may not be. Workers buying into a retirement fund tomorrow may be purchasing artificially pumped up stocks and thus will be tying up more of their assets. (How many people who bought EBay at $700 have recovered their money?)

The same holds for the economy as a whole, which must allocate resources among expensive alternatives. Furthermore, the regulation-induced short-squeeze will lift up suspect companies as well as good ones, making it very hard to recognize those companies most likely to fail and magnifying losses when they do fail.

A perfect laboratory for our work exists in China. Stocks listed in Shanghai are virtually impossible to short, whereas those in Hong Kong are less difficult. Frequently, the same stock is listed on both exchanges. Despite being absolutely identical except for short-sale restrictions, the Shanghai stocks have traded at up to twice the price of their Hong Kong doppelgangers with extreme volatility and sharp down-spikes. Those who wish to see examples of these stocks can find them here.

The reality of the stock market is that excess volatility is the mathematical equivalent of speeding up the trading clock. Market turmoil needs to be regulated by methods that slow down the process, not by those which unbalance the entry of participants. The natural way to do this is by restricting financial leverage, for example, by increasing margin requirements in times of high volatility. This is the approach taken by the futures markets with consistent success.

Restrictions on short-selling may sometimes come with an erroneous assumption. The idea is that perhaps colluders are driving down a stock price that would by itself be much higher. In fact, all sales require a counterparty buyer. It is the balance of buyers and sellers that sets the stock price. In essence, short-restrictions create a "collusion of buyers." The sharp up-spikes in financial stocks after the SEC's emergency ruling last week were the illustration of this singular effect.

There is a political point to be made here. Recently, short-sellers have been targets of invective, and even legal, threats. The attorney general of New York has determined to investigate short-sellers, while a television commentator has described short-selling as financial terrorism. The same rhetoric is echoed across the Atlantic.

Such McCarthy-esque witch hunting is horrible--and horribly misplaced. The health of the stock market depends both on those willing to invest, and on those willing to put their money at risk by selling short. Often, the same investor is long on one stock and shorts another. Both longs and shorts are playing an essential part in a well-functioning economy and, at the very least, they do not deserve to be labeled unpatriotic.

Michael D. Lipkin is an adjunct professor of finance at Columbia and managing member of Katama Trading, LLC. Marco Avellaneda heads the division of financial mathematics at the Courant Institute, New York University, and is a partner at Finance Concepts, LLC.