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# Cumulative Returns

Cumulative return are used to determine if prices have moved from the downside to the upside or from the upside to the downside.

For each sell date of a price series the cumulative returns are computed using the following procedure:

1. Computes the cumulative sum of gains and losses. The gains and losses for all buy and sell combinations are stored in the CTM Trade Table.

2. Computes the cumulative number of all trades (winning plus losing trades).

3. Divides the cumulative sum of gains and loses by the cumulative number of all trades.

This ratio is called the cumulative return.

For example, suppose the first buy and sell combination lost 10%. After one trade the cumulative sum of returns is -10%, the total number of trades is one so the cumulative return is -10%. Suppose trade 2 was a 15% gain. After two trades the running sum of returns is 5%, the total number of trades is two and the cumulative return is 2.5%. Continuing on suppose after 20 trades the running sum of the returns is -10% so the cumulative return is -0.5%.

## Why Use Cumulative Returns?

Suppose you are watching a upside price series unfold in real time and then you see prices start to decrease. But you're not sure if the price drop signals a new downside or just a temporary blip on the upside. Therefore, you need a measure to confirm if the drop in prices is for real and a new downside is forming. The cumulative returns serves that purpose.

As prices move up, the cumulative returns move up because more and more trades are winners. Eventually prices peak and then turn down so more and more trades become losers. Therefore, the cumulative returns peak and then begin to turn down thus confirming the down move in prices. The cumulative returns peak soon after cumulative percent winners peak.

Similarly, you use cumulative returns to detect when prices move from the downside to the upside. As prices bottom and begin to move to the upside, the cumulative returns bottom and then move up. The cumulative returns bottom after the cumulative percent winners bottom.

Example for An Upside to Downside Move

Kulicke & Soffa (KLIC), a semiconductor equipment maker whose prices follow a cyclical price pattern, serves to show how the cumulative percent winners behave. The first upside started on August 1, 1996 at \$4.56 and peaked at \$28.62 on September 11, 1997. The downside began on September 12 and ended on October 8, 1998 at a low of \$5.19 and the next upside began.

The chart of cumulative returns for the upside to downside analysis of the Kulicke & Soffa price series shows that the cumulative returns peaked at 95.17% on October 3, 1997 approximately three weeks after prices peaked. The fact that cumulative returns have peaked helps to confirm that prices have moved to the downside.

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