**The Golden Ratio**

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is an irrational mathematical constant, approximately 1.6180339887.

At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.

The golden ratio is often denoted by the Greek letter Φ (phi). The figure of a golden section illustrates the geometric relationship that defines this constant.

**Fibonacci Projection and Retracement Ratios calculated by OLAPTrader****Projections:**

Often confused with Fibonacci Extensions, a Fibonacci Projection is a measurement from 2 points on a chart, and the range between those two price-points is then ‘projected’ into the future to be used to find support and resistance. The * Project* points can be used to determine possible areas of consolidation before continuing the advance or areas where the issue may reverse.

There is much conflicting information on the web with regard to projections vs extensions. As with retracements, we only need 2 price-points on the chart to define a Fibonacci projection, and we make sure to measure it in the same direction as the trend of the price-action.

We calculate the projected price corresponding to the Fibonacci ratios below.

**Fibonacci_Project_1.270Fibonacci_Project_1.414Fibonacci_Project_1.618Fibonacci_Project_2.000Fibonacci_Project_2.240Fibonacci_Project_2.618Fibonacci_Project_3.140Fibonacci_Project_3.618**

In the graphic below, a

**Fibonacci_Project_1.270**price projection would, in a downtrend, correspond to 127% reduction in price from the bottom of the current downtrend. In other words, 1.27 x the current trend height. * Image not to scale.

**Retracements:**

Fibonacci retracements are popular among technical traders. They are based on the key numbers identified by mathematician Leonardo Fibonacci in the 13th century. Fibonacci’s sequence of numbers is not as important as the mathematical relationships, expressed as ratios, between the numbers in the series.

In technical analysis, a Fibonacci retracement is created by taking two extreme points (usually a peak and a trough) on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%.

Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels.

The following charts illustrates how a Fibonacci retracement appears. In graphic #1, notice how the price changes direction as it approaches the support and resistance levels. In graphic #2, notice how a “Retracement” refers to retracing, or re-drawing the prior trend by a certain % of that trend.

For retracements, a technical analyst waits for the market to turn and then divides the previous trend movement, or wave, by the Fibonacci retracement ratios, starting from the previous high to the low in an uptrend and in the opposite direction in a down trend. Horizontal lines are then drawn at these levels and are used a possible support levels if the larger trend is an uptrend, or as possible resistance levels if the larger trend is a down trend. These thus become places at which the trader could buy in a larger uptrend or sell in a larger down trend. The most significant levels are usually the 61.8% level and the 38.2% level. The 23.6% level and the 78.6% (or 76.4%) levels are not as significant.

We calculate the projected price corresponding to the retracement ratios below:

**Fibonacci_Retrace_0.382Fibonacci_Retrace_0.447Fibonacci_Retrace_0.500Fibonacci_Retrace_0.618Fibonacci_Retrace_0.707Fibonacci_Retrace_0.786Fibonacci_Retrace_0.886**

As retracement and projection levels are analyzed in the context of identifying trend starts and stops, we feel it is prudent to look at multiple time cycles in which the trend may occur. As such, for each ratio, we calculate the retracement and projection prices for trends which exist within time cycles of 5, 20, 30, 50, 100, 200, 400, and 800 periods. The trend within the time cycle may only occupy a few periods of the cycle, so long as the Last High and Last Low values are not superseded. Some implementations may look at the high/low of the close, but, like many other vendors, we choose to look at the candle wicks to identify the trend start and trend stop.

See our graphics below for a better understanding.

**Last High**

The Last High function finds the highest high before the last downturn.

**Last Low**

The Last Low function finds the lowest low before the last upturn.

As an example, suppose we are looking at the 30 period cycle below, with dates between 11/06/2015 and 12/18/2015, we look for the “Last_High_Cycle_30” value and the Last_Low_Cycle_30 values.

Pretend that we are back in time and the current date is 12/18/2015 and a new Last_High for the cycle period is achieved. Because the Last_Low occurred before the Last_High, we identify Last_Low as *trendstart *and Last_High as *trendstop. *This indicates an *uptrend*.

On 12/18/2015, a trader sees the new Last_High indicating the continuation of an uptrend. However, he wants to short it. He waits for a downtick and, if he favors a 0.386 retracement ratio, he buys it (technically borrowing it as a short sale) and puts in a trailing stop order at 850.268 which is the predicted reversal price at the 0.386 retracement ratio. Three days later, the price falls below 850, invalidating the 0.386 retracement, but since he is shorting, he holds it and perhaps anticipates the 0.447 retracement price. If the price goes up, his trade executes.

The uptrend can also be seen in the chart below. Despite the stock falling off after the last high, it did not achieve a new low (below that of 11/30/2015) for the cycle period. The 0.386 retracement of the trend is therefore 850.268160 on 12/18/2015 which will remain unchanged until a new high or low is achieved – even if the close price goes below the retracement value as it did on 12/23/2015, thus invalidating the 0.386 retracement and forcing the trader to look to the next ratio – 0.447

An important consideration when looking a historical data is that, for most days there will be new retracement (and projection) prices calculated, as for each day that drops off the top of the grid, a new day appears at the bottom. Sometimes, there will be no change to Last_High or Last_Low for many days in a row (11/24/2015 – 12/04/2015), and thus, no change in the trend and no change in retracement price. Days pass and prices either obey certain Fibonacci ratios, or they don’t, in which case that ratio/price are invalidated for that particular occurrence. For our end-of-day offering, there will simply be one row per day per asset and will include all of our retracement and projection ratios and prices.

In summary, for 8 different time cycles, we look back at the previous trend and calculate the relevant future price targets for the various projection/retracement ratios. For our Historical data offerings, we also include the closing price of the asset 5, 20, 30, 50, 100, 200, 400, and 800 periods later, perfectly matching our time cycles and facilitating back testing of the various ratios.

Click HERE to Purchase Historical Data

Click HERE for a sample:

Our offerings include Historical or end-of-day OHLCV as well as the metadata shown below.

**Data will be presented in csv format. You will receive the following for each Exchange, Global Index, or Fund:**

Ticker

Company Name

Country

Exchange

Currency

Type

ISIN

Date

Open

High

Low

Close

Volume

Split

Retrace_Lvl_1_Ratio_382_Cycle_5

Retrace_Lvl_1_Ratio_382_Cycle_20

Retrace_Lvl_1_Ratio_382_Cycle_30

Retrace_Lvl_1_Ratio_382_Cycle_50

Retrace_Lvl_1_Ratio_382_Cycle_100

Retrace_Lvl_1_Ratio_382_Cycle_200

Retrace_Lvl_1_Ratio_382_Cycle_400

Retrace_Lvl_1_Ratio_382_Cycle_800

Retrace_Lvl_2_Ratio_447_Cycle_5

Retrace_Lvl_2_Ratio_447_Cycle_20

Retrace_Lvl_2_Ratio_447_Cycle_30

Retrace_Lvl_2_Ratio_447_Cycle_50

Retrace_Lvl_2_Ratio_447_Cycle_100

Retrace_Lvl_2_Ratio_447_Cycle_200

Retrace_Lvl_2_Ratio_447_Cycle_400

Retrace_Lvl_2_Ratio_447_Cycle_800

Retrace_Lvl_3_Ratio_500_Cycle_5

Retrace_Lvl_3_Ratio_500_Cycle_20

Retrace_Lvl_3_Ratio_500_Cycle_30

Retrace_Lvl_3_Ratio_500_Cycle_50

Retrace_Lvl_3_Ratio_500_Cycle_100

Retrace_Lvl_3_Ratio_500_Cycle_200

Retrace_Lvl_3_Ratio_500_Cycle_400

Retrace_Lvl_3_Ratio_500_Cycle_800

Retrace_Lvl_4_Ratio_618_Cycle_5

Retrace_Lvl_4_Ratio_618_Cycle_20

Retrace_Lvl_4_Ratio_618_Cycle_30

Retrace_Lvl_4_Ratio_618_Cycle_50

Retrace_Lvl_4_Ratio_618_Cycle_100

Retrace_Lvl_4_Ratio_618_Cycle_200

Retrace_Lvl_4_Ratio_618_Cycle_400

Retrace_Lvl_4_Ratio_618_Cycle_800

Retrace_Lvl_5_Ratio_707_Cycle_5

Retrace_Lvl_5_Ratio_707_Cycle_20

Retrace_Lvl_5_Ratio_707_Cycle_30

Retrace_Lvl_5_Ratio_707_Cycle_50

Retrace_Lvl_5_Ratio_707_Cycle_100

Retrace_Lvl_5_Ratio_707_Cycle_200

Retrace_Lvl_5_Ratio_707_Cycle_400

Retrace_Lvl_5_Ratio_707_Cycle_800

Retrace_Lvl_6_Ratio_786_Cycle_5

Retrace_Lvl_6_Ratio_786_Cycle_20

Retrace_Lvl_6_Ratio_786_Cycle_30

Retrace_Lvl_6_Ratio_786_Cycle_50

Retrace_Lvl_6_Ratio_786_Cycle_100

Retrace_Lvl_6_Ratio_786_Cycle_200

Retrace_Lvl_6_Ratio_786_Cycle_400

Retrace_Lvl_6_Ratio_786_Cycle_800

Retrace_Lvl_7_Ratio_886_Cycle_5

Retrace_Lvl_7_Ratio_886_Cycle_20

Retrace_Lvl_7_Ratio_886_Cycle_30

Retrace_Lvl_7_Ratio_886_Cycle_50

Retrace_Lvl_7_Ratio_886_Cycle_100

Retrace_Lvl_7_Ratio_886_Cycle_200

Retrace_Lvl_7_Ratio_886_Cycle_400

Retrace_Lvl_7_Ratio_886_Cycle_800

Projection_Lvl_1_Ratio_1_270_Cycle_5

Projection_Lvl_1_Ratio_1_270_Cycle_20

Projection_Lvl_1_Ratio_1_270_Cycle_30

Projection_Lvl_1_Ratio_1_270_Cycle_50

Projection_Lvl_1_Ratio_1_270_Cycle_100

Projection_Lvl_1_Ratio_1_270_Cycle_200

Projection_Lvl_1_Ratio_1_270_Cycle_400

Projection_Lvl_1_Ratio_1_270_Cycle_800

Projection_Lvl_2_Ratio_1_414_Cycle_5

Projection_Lvl_2_Ratio_1_414_Cycle_20

Projection_Lvl_2_Ratio_1_414_Cycle_30

Projection_Lvl_2_Ratio_1_414_Cycle_50

Projection_Lvl_2_Ratio_1_414_Cycle_100

Projection_Lvl_2_Ratio_1_414_Cycle_200

Projection_Lvl_2_Ratio_1_414_Cycle_400

Projection_Lvl_2_Ratio_1_414_Cycle_800

Projection_Lvl_3_Ratio_1_618_Cycle_5

Projection_Lvl_3_Ratio_1_618_Cycle_10

Projection_Lvl_3_Ratio_1_618_Cycle_20

Projection_Lvl_3_Ratio_1_618_Cycle_50

Projection_Lvl_3_Ratio_1_618_Cycle_100

Projection_Lvl_3_Ratio_1_618_Cycle_200

Projection_Lvl_3_Ratio_1_618_Cycle_400

Projection_Lvl_3_Ratio_1_618_Cycle_800

Projection_Lvl_4_Ratio_2_000_Cycle_5

Projection_Lvl_4_Ratio_2_000_Cycle_20

Projection_Lvl_4_Ratio_2_000_Cycle_30

Projection_Lvl_4_Ratio_2_000_Cycle_50

Projection_Lvl_4_Ratio_2_000_Cycle_100

Projection_Lvl_4_Ratio_2_000_Cycle_200

Projection_Lvl_4_Ratio_2_000_Cycle_400

Projection_Lvl_4_Ratio_2_000_Cycle_800

Projection_Lvl_5_Ratio_2_240_Cycle_5

Projection_Lvl_5_Ratio_2_240_Cycle_20

Projection_Lvl_5_Ratio_2_240_Cycle_30

Projection_Lvl_5_Ratio_2_240_Cycle_50

Projection_Lvl_5_Ratio_2_240_Cycle_100

Projection_Lvl_5_Ratio_2_240_Cycle_200

Projection_Lvl_5_Ratio_2_240_Cycle_400

Projection_Lvl_5_Ratio_2_240_Cycle_800

Projection_Lvl_6_Ratio_2_618_Cycle_5

Projection_Lvl_6_Ratio_2_618_Cycle_20

Projection_Lvl_6_Ratio_2_618_Cycle_30

Projection_Lvl_6_Ratio_2_618_Cycle_50

Projection_Lvl_6_Ratio_2_618_Cycle_100

Projection_Lvl_6_Ratio_2_618_Cycle_200

Projection_Lvl_6_Ratio_2_618_Cycle_400

Projection_Lvl_6_Ratio_2_618_Cycle_800

Projection_Lvl_7_Ratio_3_140_Cycle_5

Projection_Lvl_7_Ratio_3_140_Cycle_20

Projection_Lvl_7_Ratio_3_140_Cycle_30

Projection_Lvl_7_Ratio_3_140_Cycle_50

Projection_Lvl_7_Ratio_3_140_Cycle_100

Projection_Lvl_7_Ratio_3_140_Cycle_200

Projection_Lvl_7_Ratio_3_140_Cycle_400

Projection_Lvl_7_Ratio_3_140_Cycle_800

Projection_Lvl_8_Ratio_3_618_Cycle_5

Projection_Lvl_8_Ratio_3_618_Cycle_20

Projection_Lvl_8_Ratio_3_618_Cycle_30

Projection_Lvl_8_Ratio_3_618_Cycle_50

Projection_Lvl_8_Ratio_3_618_Cycle_100

Projection_Lvl_8_Ratio_3_618_Cycle_200

Projection_Lvl_8_Ratio_3_618_Cycle_400

Projection_Lvl_8_Ratio_3_618_Cycle_800

Last_High_Cycle_5

Last_High_Cycle_20

Last_High_Cycle_30

Last_High_Cycle_50

Last_High_Cycle_100

Last_High_Cycle_200

Last_High_Cycle_400

Last_High_Cycle_800

Last_Low_Cycle_5

Last_Low_Cycle_20

Last_Low_Cycle_30

Last_Low_Cycle_50

Last_Low_Cycle_100

Last_Low_Cycle_200

Last_Low_Cycle_400

Last_Low_Cycle_800

Trend_Direction_Cycle_5

Trend_Direction_Cycle_20

Trend_Direction_Cycle_30

Trend_Direction_Cycle_50

Trend_Direction_Cycle_100

Trend_Direction_Cycle_200

Trend_Direction_Cycle_400

Trend_Direction_Cycle_800

* Cycle refers to the # of periods in the trend – 5, 20, 30, 50, 100, 200, 400, and 800

In addition, for our historical product, we have calculated and are providing the following columns to aid you in back testing:

Close_Plus_5_days

Close_Plus_20_days

Close_Plus_30_days

Close_Plus_50_days

Close_Plus_100_days

Close_Plus_200_days

Close_Plus_400_days

Close_Plus_800_days