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# 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 of time (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 percentage return that is a profit, loss or break-even.

Return = ((buy price - sell price) / buy price) * 100.

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 combinations (returns) = 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.

Returns 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 results table.

Locate the Sell Date and Sell Price columns on the left side of the returns 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 top 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 return is a 44.6% gain for the \$14.60 sell price. The last return for the first buy price occurs on Oct-02 at the \$12 sell price. The gain is 18.8%. There are nine returns for the first buy price.

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

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

The last buy and sell combination, which occurs on the Sep-02 buy date and the Oct-02 sell date, results in a 7.7% loss. There is no return for the last price in the series on Oct-02 because a buy and sell transaction on the same date is not allowed.

The average percent return for all possible buy and sell combinations is the sum of the individual returns for all buy and sell combinations divided by the total number of buy and sell combinations.

See Returns Table - Three Price Upside and Price Downside Return Types for more discussion about the trade types.

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