Buy and Sell Combinations - An Explanation

A buy and sell combination occurs when an investment (e.g. stock, bond, index fund, exchange-traded fund, commodity, real estate) is purchased on a given date and time and then sold on another date and time. The interval between the purchase and sale can be any unit (e.g. minute, hour, day, week, month, year). When the time interval between a purchase and sale is brief, a buy and sell combination is synonymous with a "trade".

A buy and sell combination results in in a profit, loss or break even.

For any given price series the total number of buy and sell combinations is a function of the number of prices in the series. The formula used to compute the number of buy and sell combinations for a series of N prices is:

Number of buy and sell combination = N*(N-1)/2

The formula assume that a purchase and sale can not occur at the same time. For example, if the time interval were one day, a buy would occur at the closing price of the day and the first sale opportunity would be the closing price of the next day. You could not buy and sell at the same closing price on the same day.

Trade Table

To illustrate all of the buy and sell combinations for a price series consider a series of ten monthly closing prices. Here a buy and a sell occurs at a closing monthly price. The total number of buy and sell combinations is 45. The return of each buy and sell combination is shown in the following trade table.

Locate the Sell Date and Sell Price columns on the left side of the trade table. The next column to the right includes the gains and losses for the buy and sell combinations for the first buy price, which is $10.10 and occurs on Jan-02. The buy prices and dates are located in two rows at the bottom of the table.

For the first buy price, the first sell price is $12.50 on Feb-02. So the gain for the first buy and sell combination is 23.8%. The second sell price is $11.20 for a 10.9% gain. The third trade results in a 44.6% gain for the $14.60 sell price. The last trade for the first buy price occurs on Oct-02 at the $12 sell price. The gain is 18.8%. There are nine trades for the first buy price.

The second buy price is $12.50 and occurs on Feb-02. The first trade for this buy price occurs on Mar-02 at the $11.20 sell price for a 10.4% loss. The second trade occurs on Apr-02 at the $14.60 sell price for a 16.8% gain. The last trade for the $12.50 buy price occurs on Oct-02 at $12 for a 4.0% loss. There are eight trades for the second buy price.

The third buy price of $11.20 has seven trades and the fourth buy price of $14.60 has six trades.

The last buy and sell combination, which occurs on the Sep-02 buy date and the Oct-02 sell date, results in a 20% loss. There is no trade for the last price in the series on Oct-02 because a buy and sell transaction on the same date is not allowed.

You can download a free program that computes percent winners and losers for any price series.

Posted September 22, 2006.