Fibonacci retracement: Golden ratio

This function calculates the Fibonacci retracement 61.8% level, also referred to as 'the golden mean' or 'the golden ratio'. It uses simple vector-based functions to do this. The function accepts one parameter which is the lookback period to use to define the highest and lowest close prices.
Fibonacci retracement is a very popular tool used by many traders. It is based on the key numbers identified by mathematician Leonardo Fibonacci to calculate the Fibonacci ratios. These ratios levels are then used to identify critical points that could cause an asset's price to reverse.

As I said earlier, the calculation is rather simple. First of all we need to determine the difference between the highest and lowest close prices for the defined lookback period. We store this data into a variable whose name is (dif). The second step is to try to determine which of the highest or lowest close price occurred first; this is done using the (BarsSince) formula. Depending on the last result, we calculate the 61.8% level. In case the highest close price happened before the lowest close price, the variable 'dif' (calculated previously) is multiplied by 0.618. In the other case, the same variable 'dif' is multiplied by (1 - 0.618). We finally add the lowest close price value to the 61.8% level value and plot the resulting time-series.

We can create a bar chart that displays the difference between the current price and the 61.8% Fibonacci level by subtracting this level to the close price.

In order to create a time-series that plots other Fibonacci ratio levels like the 23.6% ratio or the 38.2% ratio, you just need to change the "level" variable. For the 23.6% level, just replace the value (0.618) by (0.236). You can also easily tweak the code and offer the possibility to define the Fibonacci ratio level by adding another parameter to this function.

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