to guarantee shares going to the highest bidder.

Twice recently, the Shell Company of Bermuda Ltd. has put in bids to buy shares in different firms and has failed to receive any.

Yet, on both occasions, stock in the companies it bid for traded at a price less than Shell had offered to pay.

Mr. Bob Stewart, general manager of Shell in Bermuda, said: "It says absolutely nothing for the efficiency of the Exchange when you put in the highest bid but don't get any stock. It's something which in this day and age shouldn't happen.'' The method of operating the local stock exchange has not changed since it was set up in 1970.

The Exchange currently meets every Tuesday at 10 a.m., its location rotating on a monthly basis between Bermuda's three banks, whose traders are the only ones allowed to put in bids and offers.

On average, about eight people are present during trading, including a Recording Referee, part of whose job is to ensure fair play.

Before trading commences, dealers draw numbers -- it used to be table tennis balls -- to determine whose business takes priority during that day's trading.

The bank which has been luckiest in the draw will then announce what price it is offering to sell shares for in a single company.

Then, it is a race between the other two banks to shout "bid'', with the trader who is quickest off the mark securing the sale. Volume of stock is then discussed.

It is the job of the Recording Referee to determine who shouted first. The first bank then goes through the same procedure for every company whose stock it has instructions to sell, going down the list in alphabetical order.

Once the first bank has finished its offerings, the second bank and then the third go through the same process.

Mr. Stewart called the system unfair and outdated and said it urgently needed to be changed.

"Whether a sale or purchase goes ahead should depend on prices, not on who holds a table tennis ball or who can shout the loudest,'' he said.

"There should be only one determinate of the sale or purchase and that's the price, otherwise both the buyer and the seller are losing out.

"Stock markets are supposed to be the most efficient markets of all, not the least efficient.'' The current trading system could leave the Exchange open to allegations of favouritism or "wrong-doing'', said Mr. Stewart.

Mr. Monty Nearon, a portfolio manager with Shell, referred to two recent occasions when Shell was "shortchanged'' on the local stock market.

On August 12, Shell placed an order via its agent to buy 1,500 shares in Bermuda Electric Light Company for $15.50.

During the next trading on Tuesday, August 18, the order was not filled, yet 8,752 Belco shares did trade that day for $15.00 -- 50 cents per share less than Shell's offer.

If Shell's offer had been accepted, the seller of the shares would have received $750 more than he or she actually got.

On Tuesday, November 17, a similar thing happened, this time involving Bank of Bermuda stock, whose shares Shell had wanted for its local pension fund.

Through its agent, the Bank of Butterfield, Shell bid $35 for 2,000 shares in the Bank of Bermuda and did not get any. On the same day, though, 1,007 of the Bank's shares were sold for $34.75 -- 25 cents per share less than Shell's offer.

Mr. Nearon said: "Given our bid price of $35, we were surprised that we weren't able to pick up any stock.

"We feel the manner of trading on the Exchange does not benefit the seller or the purchaser.'' He added: "Here at Shell, we manage quite a large pension fund and we institutionally invest in the global equity market and, occasionally, we do purchase shares for local pension funds.

"It makes you wonder when we can trade easily in all the global markets and, yet, have problems trying to pick up local stock.'' As an alternative, Mr. Nearon suggested an "auction'' type system whereby shares would simply go to the highest bidder "rather than the person with the right ping pong ball''.

Bermuda Exchange chairman Mr. Bill Dolan defended the Exchange and said it had "served the public of Bermuda well for over 20 years''.

But he agreed that there was a need for change, which, he said, he first suggested during a previous spell as Exchange chairman in the late 1980s.

Mr. Dolan said the Exchange would be modernised within a few months, although he would not go into details.

"The method of trading is presently under review and a more modern way of trading is planned for early in 1993,'' he said. "I can't say more than that.'' MR. BOB STEWART -- `Stock markets are supposed to be the most efficient markets of all.'