As of 09/22/2021
Indus: 34,258 +338.48 +1.0%
Trans: 14,001 67.19 0.5%
Utils: 898 0.44 0.0%
Nasdaq: 14,897 +150.45 +1.0%
S&P 500: 4,396 +41.45 +1.0%

YTD
+11.9%
+11.9%
+3.9%
+15.6%
+17.0%

35,600 or 33,800 by 10/01/2021
15,400 or 14,000 by 10/01/2021
930 or 890 by 10/01/2021
15,600 or 14,700 by 10/01/2021
4,650 or 4,350 by 10/01/2021

As of 09/22/2021
Indus: 34,258 +338.48 +1.0%
Trans: 14,001 67.19 0.5%
Utils: 898 0.44 0.0%
Nasdaq: 14,897 +150.45 +1.0%
S&P 500: 4,396 +41.45 +1.0%

YTD
+11.9%
+11.9%
+3.9%
+15.6%
+17.0%
 
35,600 or 33,800 by 10/01/2021
15,400 or 14,000 by 10/01/2021
930 or 890 by 10/01/2021
15,600 or 14,700 by 10/01/2021
4,650 or 4,350 by 10/01/2021
 
My book, Trading Basics, discusses both Fibonacci retracements (as a stop location, starting on page 50) and extensions (starting on page 84).
If you click on the above link and then buy the book (or anything) while at Amazon.com, the referral will help support this site. Thanks.
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This article discusses how to use Fibonacci retracements and extensions to determine price targets for securities.
Let's start with the daily chart of Boeing (BA). Notice the straightline run down in November, starting at point A and bottoming at point B. If Fibonacci retracements work, I would expect price to retrace or climb back up that steep decline between 38% and 62%. You can think of this as how far a ball would bounce after you drop it off a building.
I show the most common retrace values as three horizontal red lines. The lowest one is a 38% retrace of the AB move. The ball bounces about a third of the way up the building.
The middle line marks a 50% bounce and the top line shows a 62% retrace. I consider the 62% retrace value as most reliable of the three. Trading a stock expecting a reversal at the 38% or 50% retrace values is risky because price often continues moving through them. The chart shows an example of this. Price climbs to C, blowing right through the 38% and 50% retrace lines.
The downside to this argument is that if you wait for a 62% retrace, the stock may reverse at 38% or 50%, and you'll remain out of a promising trade.
Often you will want to look for nearby support or resistance to better determine where price is going to stop. And when it does approach a retrace value, think of it as an area and not a single price point. For example, the chart shows price approaching but not quite reaching the 62% retrace value, but it's still close. Notice on the far left a congestion area, circled in green. Price overlaps itself for three days before the downtrend resumes.
I would view this congestion or overhead resistance area as a weak one, but when coupled with a 62% Fibonacci retrace, it was strong enough to halt the rise and turn price down.
That is how Fibonacci retracements are supposed to work, but they apply to upward price trends as well. That is how I use them when buying a stock.
For example, consider the trade in Tesoro Corporation (TSO) I made starting on August 21, 2008.
Believing that the longterm downtrend that began in October 2007 was over, and as price neared the 62% Fibonacci retrace of the AB move, I jumped in and bought the stock.
Suspecting that I had made a mistake, I sold it on September 3 for a small profit.
The stock continued much lower after I sold.
The following tips may help you use Fibonacci retracements.

Now let's turn to Fibonacci extensions. You may not have heard of them which suggests it's not a popular technique. I don't use it, but that's just me.
Stock prices move in waves. After a strong move, the stock will pause and retrace part of the move followed by a resumption of its run. But how far will it travel? Answer: 38% of the prior move.
Look at the chart of Boeing again. The downhill run begins at A and ends at B. The height of the move is 54.65  36.17 or 18.48. Multiply the height by 38% to get the extension value and subtract it from the low price at B: 18.48 x 38% = 7.02, 36.17  7.02 = 29.14. The stock reaches a low of 29.07 at C.
Notice how deliciously close price comes to the target, missing it by just 7 cents.
Fibonacci extensions work for upward price moves too. You calculate it in the same manner, using a major swing high to swing low to determine the height, multiply it by 38%, and then add the result to the swing high price to get a target.
In the book, Candlesticks, Fibonacci, and Chart Pattern Trading Tools, by Robert Fischer and Jens Fischer  pictured on the right  they discuss using 0.618 and 1.618 as the multipliers instead of 0.38. In fact, I could find no mention of the 38% extension in the book (but I didn't look very hard).
You might consider using the 38% extension as a minimum price target and the 162% extension as the maximum.
Let me explain how they use the 0.618 and 1.618 extensions.
The chart on the left shows a five wave movement of price, following the basic motive wave progression of the Elliott Wave theory. That is a complicated way of saying price moves in waves.
The Fisher team indicates that if the price trend is just starting out (it's in wave two or three), then use the larger 1.618 extension.
If price has been trending upward and has formed several waves, the trend end may be closer. In that case, use the 0.618 extension.
In either case, measure the height of the swing move from the dotted line on the bottom to the associated peak and multiply the height by either 0.618 or 1.618, depending on whether the price trend is new (wave two or three) or old (wave four or five).
 Thomas Bulkowski
See Also

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Strategy: A comprehensive plan of inaction.