Read the article below:

1. How many shares does Bankers Trust need to buy or sell to delta-hedge its net exposure for each share purchased by the employees of the firm under the terms of the program?

Wimps to wizards The Economist (US) v331.n7861 (April 30, 1994): pp. S3(2).

WHAT does the thoroughly modern banker think about these days? Sometimes this: how to persuade a cautious French worker employed by an about-to-be privatised industrial company to borrow money so that he can buy some of the company's stock. This is a tricky task, but by no means an impossible one. Welcome to the exotic world of financial derivatives.

In the summer of 1993 France was preparing for the first instalment of a colossal sale of state assets. Edouard Balladur's newly elected conservative government intended to privatise a score of state-owned companies. Bankers from all over the world swooped on the chosen firms and on the French Treasury, eager to grab a slice of the action.

One such bank was Bankers Trust, on the face of it an unlikely contender. Bankers Trust is a relatively small bank measured by assets, with a reputation for trading in flashy new financial instruments. More to the point, it is an American bank, and the French privatisation was taking place during one of France's periodic fits of anti-Americanism, sharpened by a quarrel, then still unresolved, over the Uruguay round of world trade talks. Bankers Trust knew that it would be difficult to do well out of the French privatisation programme unless it could offer something more than a traditional underwriting service.

In discussions with French companies, however, Bankers Trust began to sense an opportunity. One aspect of the privatisation programme was causing particular worry to French managers. The government wanted to make sure that shares in the privatised companies would be distributed as widely as possible. In particular, it wanted a sizeable proportion of shares to be purchased by workers in the relevant companies. But this was easier said than done in a country with no tradition of individual share ownership. Workers do not typically have a lot of spare cash to invest, and they are understandably reluctant to risk what they do have in the stockmarket.

A commonly used half-solution to this problem is to allow employees to buy shares at a big discount. But this has some obvious drawbacks. It is expensive to the seller and it tends to mean that employees sell their shares and take their profit early on, instead of holding on to the shares and therefore, in theory, retaining a long-term interest in the progress of the company. In the late summer of 1993 Thibaut de Gaudemar, a member of what Bankers Trust calls its Transaction Development Group, therefore began to work on a different concept. What if a way could be found to let employees buy shares, and to benefit from any rise in their value, but at the same time to protect themselves from the consequences of any fall in the price?

By June 1993 Bankers Trust had devised a mechanism about which it felt sufficiently confident to present it to the French Treasury and to the management of Rhone-Poulenc, a large chemicals company and an early candidate for wholesale privatisation. It worked as follows. Bankers Trust would obtain finance for workers who wanted to buy shares in the company: for every share an employee purchased, a French bank would lend enough money for him to buy a further nine. If after five years the share price had fallen below the offer price, Bankers Trust would guarantee that workers recovered their principal. But if the share price rose, the workers would be entitled to only about two-thirds of the profit. The remaining third of any gain would belong to Bankers Trust.

The easy part of this exercise was to persuade French banks to stump up the necessary loans to workerbuyers, using the Rhone- Poulenc shares the workers were buying as collateral. Bankers Trust enjoys an AA rating from the independent agencies such as Standard & Poor's that assess a financial institution's creditworthiness. In other words, once Bankers Trust had undertaken to make up any shortfall in the value of the shares after five years, the French banks were in effect taking no risk: they could be sure of Bankers Trust paying up. As for the workers, they were also being offered protection against risk, plus a chance to use highly leveraged loans to make a handsome profit if the share price rose. Unsurprisingly, they applied for even more shares than were available.

What, though, if the price after five years was lower than the offer price? In that case, Bankers Trust would, naturally, have to pay the French banks for the "floor" it had put under the share price. So the hard part of the scheme was finding a way for Bankers Trust to protect itself. It did so by using the technique the bank had over many years made into its speciality. It "hedged" the risk.

Since Bankers Trust could not know whether, after five years, Rhone-Poulenc shares would be worth more or less than their initial price, it decided, following the conventional rules of portfolio theory, to assume that there was a 50:50 probability in either direction. The obvious way to offset this risk was to sell half (about $80m-worth) of the Rhone-Poulenc shares that workers had purchased immediately after the company was privatised in November. Since then, as the share price has waxed or waned, Bankers Trust has continued to revise its assessment of the probable price of the share at the end of five years, and to trade accordingly. If the price goes down, the bank sells more shares; if it rises, the bank buys.

Selling low and buying high in this way is a neat hedging strategy but not, you might think, an obvious way to make a killing. However, Bankers Trust does not need to make a killing. The money it uses for this trading is in effect the premium--the forgone one- third of their potential capital gain--that RhonePoulenc's workers agreed to pay in return for protection when they entered the scheme. Provided that Bankers Trust does not spend this whole premium by the time five years is up, it will have made a profit on the transaction. Naturally, its hedging strategy might go wrong. But the bank is confident of its risk-management skills. And the risk associated with the Rhone-Poulenc transaction does not stand alone. It is diluted within the pool of exposures and hedging strategies which make up Bankers Trust's portfolio.

Though simple enough in concept, this scheme was of course fiendishly difficult to manufacture and to sell. Consider only one potential wrinkle. It is all very well for Bankers Trust to hedge its risk by buying and selling Rhone-Poulenc shares. The wrinkle is that the bank did not really buy, and therefore does not in fact own, any of the shares in question. They remain the property of the French firm's employees. And the French Treasury would not have agreed to a plan that allowed Bankers Trust to offload $80m of Rhone-Poulenc's shares immediately after the company was privatised. That sort of massive selling might easily have undermined the newly created market in the shares.

A fatal flaw? Not in the elegant world of derivatives. The bank manoeuvred past this impediment by identifying institutional investors who had wanted to buy into the Rhone-Poulenc share offering but, for one reason or another, had not been able to. To these investors it offered what bankers call a "synthetic" product, namely an agreement under which the investors could exchange payments with Bankers Trust in a way that would exactly mimic the gains and losses that they would have made if they had really bought Rhone-Poulenc shares. If the share price rises, Bankers Trust "sells" these nonexistent shares to the investors. If it falls, Bankers Trust "buys" shares from them.

Ultimate deriving machine

A derivative is a financial instrument whose value is derived from some underlying asset--in this case, the price of shares in Rhone- Poulenc. Creating them, and trading in them, are among the fastestgrowing parts of the finance industry. The majority of derivatives are used for far simpler purposes than in this case. They consist of futures, options and other ways to hedge the various risks--of price and currency fluctuations, for example--that companies face in the course of doing business. Most big banks should be able to devise them.

To invent a designer derivative like the one used in the Rhone- Poulenc privatisation is a good deal harder. It does not simply require a lot of mathematical skill (and sometimes a lot of capital to pay for the hedge). Banks competing at this end of the market also need complex risk-management skills, the flair to apply new forms of financial technology to novel problems, and considerable political nous. Even after this derivative had been designed, teams of lawyers were required to hoop together the three main parties to the transaction: Rhone-Poulenc, Bankers Trust and the French banks that were advancing the loans to the workers. Initially, the participation of the American bank was not disclosed.

Although Bankers Trust will not say how much it expects to earn from its Rhone-Poulenc transaction, the rewards for being first with a new idea in this field are clearly high. After its success with RhonePoulenc, Bankers Trust performed a similar service in the privatisation of Elf Aquitaine, a French oil company, and it hopes to win more business from the rest of the French privatisation programme soon. But the life-cycle of such a product can also be alarmingly short. Bankers Trust's privatisation idea is already being copied by other derivatives houses. To stay ahead, such banks have to live by their wits.

What Bankers Trust did with Rhone-Poulenc might seem a world away from the traditional business of commercial banking. It is. And that is the point not only of the story but also of the rest of this survey. Twenty years ago Bankers Trust was not known, as it is now, for its sharp young mathematicians. It was an ordinary commercial bank, doing rather less well than most of its rivals in a business which, clever pundits were beginning to say, was slowly being killed by new technology. Bankers Trust saved itself by becoming a completely new kind of business, albeit one that is still called a bank. In that sense it has become a symbol of the industry as whole.