A buy and sell return occurs when an investment 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.

A buy and sell return results in a percent return that is a profit, loss or break-even.

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

Note: The buy and sell return calculations no not include trading volumes. So the percent return is an unweighted measure.

Assume a price pattern defined by a period of rising prices (upside that ends with the peak price) and a period of declining prices (downside that begins with the first price after the peak price). For such a pattern there are three trade or return types:

• Buy on the upside and sell on the upside returns
• Buy on the upside and sell on the downside returns
• Buy on the downside and sell on the downside returns

The number of buy and sell returns for a series of N upside and downside prices is N*(N-1)/2.

The number of buy and sell returns for the upside and downside trade types are:

NU*(NU-1)/2 for buy on the upside and sell on the upside where NU is the number of prices on the upside.

NU*ND for buy on the upside and sell on the downside where NU is the number of prices on the upside and ND is the number of prices on the downside.

ND*(ND-1)/2 for buy on the downside and sell on the downside where ND is the number of prices on the downside.

## Example

Below is an example of a sequence of ten prices, six of which are the upside and four are on the downside.  There are:

• 45 returns for all prices
• 15 buy upside and sell upside returns
• 24 buy upside and sell downside returns
• 6 buyupside and sell upside returns

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