Market maker Anna makes four trades in the following example. As three successive 20-contract buy orders enter the market followed by a 60-contract sell order, Anna sells to the buy orders and then buys from the sell order.
For the sake of simplicity, the example assumes that the stock price does not change. The issue of changing stock prices will be discussed in later exercises.The stock has a bid price of 80.40 and an ask price of 80.42.

The 80 Call has a bid price of 4.50, an ask price of 4.60, and a delta of 0.60. It is assumed that the necessary number of shares and options can be traded at the prices indicated.In step 1 in Table 9-3, Anna sells 20 of the 80 Calls at the ask price of 4.60 and purchases 1,200 shares of stock at 80.42 to hedge the option position. Given the call delta of 0.60, Anna calculates the number of shares as follows: The underlying for 20 short calls is 2,000 short shares, but given the delta, the market exposure is equivalent to short 1,200 shares (2,000  0.60  1,200).

To be delta-neutral and offset this short market exposure, Anna immediately buys 1,200 shares at the ask price of 80.42. Since Anna’s position now has 20 short calls, she must adjust the bid and ask prices in compliance with her predetermined rule to manage risk.In step 3, Anna sells 20 more of the 80 Calls at the new ask price of 4.62 and purchases 1,200 more shares of stock at 80.42 to hedge the newly sold calls.After step 3 in Table 9-3, Anna’s position has increased to 40 short calls, the next 20-contract increment.

The bid and ask prices therefore have to be raised again in step 4, when she raises the bid and ask prices by another 2 cents each, this time to 4.54 bid and 4.64 ask. In step 5, Anna sells 20 more of the 80 Calls at the new ask price of 4.64 and again buys 1,200 more shares of stock at 80.42 to hedge the newly sold options.With Anna’s position now at the next 20-contract increment of 60, Anna again raises the bid and ask prices to 4.56 bid and 4.66 ask, another 2-cent increase shown in step 6.

Finally, in step 7, a sell order of 60 contracts enters the market. As a market maker, Anna buys all 60 of the 80 Calls at the bid price of 4.56 and simultaneously sells all 3,600 shares at the bid price of 80.40.Calculating Profit and Loss:Step 8 in Table 9-3 calculates Anna’s profit and loss. In this example,Anna bought all 3,600 shares of stock at 80.42 and sold them all at 80.40. This loss of 2 cents per share amounts to a total loss of \$72, not including transaction costs.

Turning to the option profit/loss calculation, Anna purchased all options at the same price of 4.56 but sold them at three different prices, 4.60, 4.62, and 4.64. As indicated under option trade 1, option trade 2, and option trade 3, the profits on these trades were \$80, \$120,and \$160, respectively. Combining the loss on the stock trades with the profits on the option trades yields Anna a net profit of \$288.

The eight steps in Table 9-3 show that scaling into positions is a technique that market makers can use to avoid taking on a large position all at one price. Also, by adjusting the bid and ask prices, the profitability of a position can be maintained. The exercise, however, raisestwo questions.First, how many times can the bid and ask be raised before a profitable trade becomes a losing one, and second, how are bid and ask prices monitored and adjusted in the face of fluctuating stock prices?These questions will be addressed with some examples.

The Limit on Adjusting Bid and Ask Prices Table 9-4 calculates the maximum number of times that a bid-ask spread can be adjusted (raised or lowered) so that a break-even result still can be achieved on the last adjustment. It is assumed that the same number of contracts are purchased or sold at each price.Table 9-4 contains six columns. Column 1 indicates the number of times that the bid-ask spread is raised. The bid and ask prices are in columns 2 and 3, respectively, and column 4 describes each trade and its price.

Each row of column 5 indicates the average sale price of all the contracts sold up to that point. Column 6 keeps a running total after each trade of contracts sold up to that point.In the first row of Table 9-4, for example, column 1 is blank because 1.75 in column 2 and 1.80 in column 3 are the initial bid and ask prices. Column 4 contains the trade description, “Sell 1 at 1.80,” and column 5 contains the average sale price of 1.80. Since only one contract has been sold at 1.80 at this point, this is the average price. Column 6 indicates that up to this point there is one short contract in the total position.