# Calculating opening and closing prices

• How the Australian sharemarket works

The same formula is used to calculate:

• Opening prices at the start of each trading day
• Closing prices at the end of each trading day
• Float prices (Initial Public Offerings "IPO")
• The price of a security after a price sensitive announcement has been received and/or a security's trading halt or suspension has been lifted
• The price of a security after a new listing.

How are opening and closing prices calculated?
The opening and closing price for a security is determined by a four step approach involving the use of conditional decision rules. If a clear result cannot be achieved when the first decision rule is applied, the model progresses to the second decision rule and so on. The decision rules are always applied in the same order. Schematically:

Principle 1 achieves a subset of potential auction prices from the list of overlapping buy and sell order prices.

If the subset consists of one price only, this becomes the official auction price and the process concludes.

Should the application of Principle 1 achieve more than one potential auction price, the algorithm moves to Principle 2 to narrow down the options. If Principle 2 eliminates all but one of the options, the remaining price becomes the official auction price and the process concludes. If however, the auction price is not determined by applying Principle 1 or Principle 2, the process moves to Principle 3 and then Principle 4 if required.

The following example illustrates this concept. While the example calculates opening prices, closing prices are established in exactly the same way.

There is a short period before Opening and Closing, called Pre-open. During Pre-open, new orders may be entered, but they do not trade against each other. Because of this, the market may overlap with buy prices being higher than sell prices.

The market for XYZ immediately before the market opens is:

SELL

Order

Qty

Price

Price

Qty

Order

A

4,500

825

818

6,600

K

B

25T

824

818

5T

L

C

3,200

824

819

3,600

M

D

1,900

822

820

17,500

N

E

49,700

820

823

1,900

O

F

8T

819

824

16,900

P

G

16,400

818

825

8,500

Q

H

5,400

815

826

21,650

R

I

900

814

828

11,420

S

J

4,575

812

831

290

T

Principle 1: Determining the Maximum Executable Volume

The principle establishes the price(s) at which maximum volume will be executed.

There are two steps involved in applying this principle. The first determines the Cumulative Buy and Sell quantities at each eligible price. The Cumulative Buy quantity increases as prices decrease - a buy price is the maximum that a buyer is willing to pay for their shares, however, it is accepted that the buyer is willing to pay a lower price. Conversely Cumulative Sell quantity increases as prices increase - a sell price is the minimum a seller will accept for their shares but the seller will accept a higher price. Using the example market above, the Cumulative Buy and Sell quantities at each price are as follows:

The second step establishes the total tradeable volume at each eligible price step. The total tradeable volume at a price is the minimum of the Cumulative Buy and Cumulative Sell quantities at that price. Using the same data, the Maximum Executable Volume (MEV) for each eligible price is shown as follows:

In this example, the maximum quantity of shares that may be traded is 32,700. Were there to be only one price at which this occurs that price would be the official auction price. In this example the maximum executable volume occurs at prices 820, 821, 822, 823 and 824. Therefore, at the completion of Principle 1, the potential auction price for XYZ may be any of these prices.

The algorithm has eliminated 825, 819 and 818 as opening prices. To further narrow the choices for an auction price we use Principle 2 to determine the Minimum Surplus level.

Principle 2: Establishing the Minimum Surplus

The second principle ascertains the eligible price levels at which the unfilled or unmatched quantity is a minimum. The quantity of shares left in the market at the auction price should always be the lowest possible.

The Minimum Surplus (MS) at each price level is equal to Cumulative Buy Quantity - Cumulative Sell Quantity.

The Minimum Surplus values at each potential opening price achieved after applying Principle 1 are:

Ignoring the positive and negative signs, the lowest number in the Minimum Surplus column is 1,900. Were there to be only one price at which this occurs that price would be the official auction price. In this example the minimum surplus occurs at prices 821, 822 and 823. Therefore, at the completion of Principle 2, the potential auction price for XYZ may be any of these prices.

The algorithm has further eliminated 824 and 820 as opening prices. To further narrow the choices for an auction price we use Principle 3 to determine Market Pressure.

Principle 3: Ascertaining where the Market Pressure exists

The third principle involves ascertaining where the market pressure of the potential auction prices exists: on the buy or the sell side. A positive sign (+) indicates a surplus will be left on the buy side, demonstrating buy side pressure at the conclusion of the auction. A negative sign (-) indicates a surplus will remain on the sell side, demonstrating sell side pressure at the conclusion of the auction.

If the market pressure is on the buy side, then the principle uses the highest of the potential auction prices. If the market pressure is on the sell side, then the algorithm chooses the lowest of the potential auction prices. If both positive and negative market pressure exists or if the Minimum Surplus is zero for each potential auction price, the algorithm continues to Principle 4: Consulting the Reference Price.

At the potential auction prices of 821 and 822 the surplus is positive (+1,900), indicating that Market Pressure is on the buy side. At 823 the surplus is negative, indicating that Market Pressure is on the sell side. If the market opens at 821 or 822 a surplus of +1,900 signifies that after the market opens 1,900 shares will remain unfilled on the buy side at 821 or 822, while if the market opens at 823 a surplus of -1,900 indicates that 1,900 shares will remain unfilled on the sell side at 823.

In this example it is not yet possible to calculate an auction price, since the surpluses at 821, 822 and 823 are identical in magnitude but different in sign.

In general, residual buy pressure is likely to cause the price to rise after the opening, therefore, if at this stage the surpluses are all positive, the algorithm chooses the highest of the potential prices and this becomes the official auction price. If at this stage the surpluses are all negative then the algorithm will opt for the lowest of the potential prices as the official auction price.

As the surpluses at 821, 822 and 823 are equal in size but opposite in direction, the algorithm continues to the fourth and final step to establish an auction price.

Principle 4: Consulting the Reference Price

The fourth and final principle determines an auction price from the range of prices established in Principle 3 on the basis of their proximity to a reference price.

Generally, the reference price is the last on-market traded price. Where on-market trades have occurred on the current trading day, the reference price will be the price of the latest on-market trade executed on that day. If, during the current trading day, an on-market trade has not occurred, the reference price will be the official closing price of the previous trading day i.e. the price of last trade executed on the previous trading day.

There are two steps to this Principle. The first step of is to narrow the options of potential auction prices to two within the entire range of possible auction prices as follows:

• If the result of Principle 3 is a combination of positive and negative Market Pressure, then the algorithm marks the two prices where the sign changes.

• If the Minimum Surplus for all possible auction prices is zero, then the algorithm marks the highest and lowest prices within that range as the potential auction prices to be applied in this principle.

In this example the sign at 821 and 822 is positive and changes to negative at 823. Therefore, the algorithm chooses 822 and 823 as the potential auction prices to be applied in this principle.

The second step is determining the relationship between the reference price and the final auction price as follows:

• If the reference price is equal to or greater than the higher of the two possible prices established in the first section of this principle, then the higher price becomes the auction price.

• If the reference price is equal to or less than the lower of the two possible prices established in the first section of this principle, then the lower price becomes the auction price.

• If the reference price lies between the two possible prices established in the first section of this principle, then the reference price itself becomes the auction price.

• If a reference price does not exist, for example, in the cases of an Initial Public Offering, new listing or the first day of trading a security on a reconstructed basis, the auction price becomes the lower of the two potential auction prices established in the first section of this principle.

In our example, if the algorithm was being used to determine the morning auction price for XYZ, and the previous trading day's closing price was \$8.22 or lower, then the official auction price for XYZ would be established at \$8.22. If the previous trading day's closing price was \$8.23 or higher, then the official auction price for XYZ would be \$8.23. For this example, we will assume the previous trading day's closing price was \$8.22, therefore, the official auction price is \$8.22.

All orders are filled at the same price regardless of the price actually stated when placing an order. Details of the trades executed during the opening are as follows:

• Buy Order A matches 4,500 securities at \$8.22 with Sell Order K
• Buy Order B matches 2,100 securities at \$8.22 with Sell Order K
• Buy Order B matches 5,000 securities at \$8.22 with Sell Order L
• Buy Order B matches 3,600 securities at \$8.22 with Sell Order M
• Buy Order B matches 14,300 securities at \$8.22 with Sell Order N
• Buy Order C matches 3,200 securities at \$8.22 with Sell Order N

The market in XYZ immediately after the opening will be:

SELL

Order

Qty

Price

Price

Qty

Order

Qty

Price

Sell

Order

Order

D

1,900

822

823

1,900

O

3,200

822

C

N

E

49,700

820

824

16,900

P

14,300

822

B

N

F

8T

819

825

8,500

Q

3,600

822

B

M

G

16,400

818

826

21,650

R

5,000

822

B

L

H

5,400

815

828

11,420

S

2,100

822

B

K

I

900

814

831

290

T

4,500

822

A

K

J

4,575

812

When there is no overlap
The algorithm will only be applied when an even or overlapping market exists. If the market is not even or overlapping before opening, the opening price is the price of the first trade executed when the market opens.

If the market does not overlap before the Closing Single Price Auction, the closing price is the price of the last trade executed before the market closed.

### How float prices are calculated

Float prices are calculated using exactly the same method used for calculating opening and closing prices. The exact opening time for a new float (Initial Public Offering) varies. ASX announces the time to the market.