What Are Fibonacci Retracement Levels?

Fibonacci retracement levels—stemming from the Fibonacci sequence—are horizontal lines that indicate where support and resistance are likely to occur.

Each level is associated with a percentage. The percentage is how much of a prior move the price has retraced. The Fibonacci retracement levels are 23.6%, 38.2%, 61.8%, and 78.6%. While not officially a Fibonacci ratio, 50% is also used.

The indicator is useful because it can be drawn between any two significant price points, such as a high and a low. The indicator will then create the levels between those two points.

Suppose the price of a stock rises $10 and then drops $2.36. In that case, it has retraced 23.6%, which is a Fibonacci number. Fibonacci numbers are found throughout nature. Therefore, many traders believe that these numbers also have relevance in financial markets.

Fibonacci retracement levels were named after Italian mathematician Leonardo Pisano Bigollo, who was famously known as Leonardo Fibonacci.  However, Fibonacci did not create the Fibonacci sequence. Instead, Fibonacci introduced these numbers to western Europe after learning about them from Indian merchants. Fibonacci retracement levels were formulated in ancient India between 450 and 200 BCE.

Numbers First Formulated in Ancient India

Despite its name, the Fibonacci sequence was not developed by its namesake. Instead, centuries before Leonardo Fibonacci shared it with western Europe, it was developed and used by Indian mathematicians.

Most notably, Indian mathematician Acarya Virahanka is known to have developed Fibonacci numbers and the method of their sequencing around 600 A.D. Following Virahanka’s discovery, other subsequent generations of Indian mathematicians—Gopala, Hemacandra, and Narayana Pandita—referenced the numbers and method. Pandita expanded its use by drawing a correlation between the Fibonacci numbers and multinomial co-efficients.

It is estimated that Fibonacci numbers existed in Indian society as early as 200 B.C.

The Formula for Fibonacci Retracement Levels

Fibonacci retracement levels do not have formulas. When these indicators are applied to a chart, the user chooses two points. Once those two points are chosen, the lines are drawn at percentages of that move.

Suppose the price rises from $10 to $15, and these two price levels are the points used to draw the retracement indicator. Then, the 23.6% level will be at $13.82 ($15 – ($5 × 0.236) = $13.82). The 50% level will be at $12.50 ($15 – ($5 × 0.5) = $12.50).

How to Calculate Fibonacci Retracement Levels

As discussed above, there is nothing to calculate when it comes to Fibonacci retracement levels. They are simply percentages of whatever price range is chosen.

However, the origin of the Fibonacci numbers is fascinating. They are based on something called the Golden Ratio. Start a sequence of numbers with zero and one. Then, keep adding the prior two numbers to get a number string like this:

• 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…with the string continuing indefinitely.

The Fibonacci retracement levels are all derived from this number string. After the sequence gets going, dividing one number by the next number yields 0.618, or 61.8%. Divide a number by the second number to its right, and the result is 0.382 or 38.2%. All the ratios, except for 50% (since it is not an official Fibonacci number), are based on some mathematical calculation involving this number string.

Interestingly, the Golden Ratio of 0.618 or 1.618 is found in sunflowers, galaxy formations, shells, historical artifacts, and architecture.

What Do Fibonacci Retracement Levels Tell You?

Fibonacci retracements can be used to place entry orders, determine stop-loss levels, or set price targets. For example, a trader may see a stock moving higher. After a move up, it retraces to the 61.8% level. Then, it starts to go up again. Since the bounce occurred at a Fibonacci level during an uptrend, the trader decides to buy. The trader might set a stop loss at the 61.8% level, as a return below that level could indicate that the rally has failed.

Fibonacci levels also arise in other ways within technical analysis. For example, they are prevalent in Gartley patterns and Elliott Wave theory. After a significant price movement up or down, these forms of technical analysis find that reversals tend to occur close to certain Fibonacci levels.

Fibonacci retracement levels are static, unlike moving averages. The static nature of the price levels allows for quick and easy identification. That helps traders and investors to anticipate and react prudently when the price levels are tested. These levels are inflection points where some type of price action is expected, either a reversal or a break.

Fibonacci Retracements vs. Fibonacci Extensions

While Fibonacci retracements apply percentages to a pullback, Fibonacci extensions apply percentages to a move in the trending direction. For example, a stock goes from $5 to $10, then back to $7.50. The move from $10 to $7.50 is a retracement. If the price starts rallying again and goes to $16, that is an extension.

Limitations of Using Fibonacci Retracement Levels

While the retracement levels indicate where the price might find support or resistance, there are no assurances that the price will actually stop there. This is why other confirmation signals are often used, such as the price starting to bounce off the level.

The other argument against Fibonacci retracement levels is that there are so many of them that the price is likely to reverse near one of them quite often. The problem is that traders struggle to know which one will be useful at any particular time. When it doesn’t work out, it can always be claimed that the trader should have been looking at another Fibonacci retracement level instead.

The Bottom Line

Fibonacci retracements are useful tools that help traders identify support and resistance levels. With the information gathered, traders can place orders, identify stop-loss levels, and set price targets. Although Fibonacci retracements are useful, traders often use other indicators to make more accurate assessments of trends and make better trading decisions.

What Is an Exponential Moving Average (EMA)?

An exponential moving average (EMA) is a type of moving average (MA) that places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average simple moving average (SMA), which applies an equal weight to all observations in the period.

Formula for Exponential Moving Average (EMA)


$\begin{aligned} &\begin{aligned} EMA_{\text{Today}}=&\left(\text{Value}_{\text{Today}}\ast\left(\frac{\text{Smoothing}}{1+\text{Days}}\right)\right)\\ &+EMA_{\text{Yesterday}}\ast\left(1-\left(\frac{\text{Smoothing}}{1+\text{Days}}\right)\right)\end{aligned}\\ &\textbf{where:}\\ &EMA=\text{Exponential moving average} \end{aligned}$​EMAToday​=​(ValueToday​∗(1+DaysSmoothing​))​where:​

While there are many possible choices for the smoothing factor, the most common choice is:

That gives the most recent observation more weight. If the smoothing factor is increased, more recent observations have more influence on the EMA.

Calculating the EMA

Calculating the EMA requires one more observation than the SMA. Suppose that you want to use 20 days as the number of observations for the EMA. Then, you must wait until the 20th day to obtain the SMA. On the 21st day, you can then use the SMA from the previous day as the first EMA for yesterday.

The calculation for the SMA is straightforward. It is simply the sum of the stock’s closing prices during a time period, divided by the number of observations for that period. For example, a 20-day SMA is just the sum of the closing prices for the past 20 trading days, divided by 20.

Next, you must calculate the multiplier for smoothing (weighting) the EMA, which typically follows the formula: [2 ÷ (number of observations + 1)]. For a 20-day moving average, the multiplier would be [2/(20+1)]= 0.0952.

Finally, the following formula is used to calculate the current EMA:

• EMA = Closing price x multiplier + EMA (previous day) x (1-multiplier)

The EMA gives a higher weight to recent prices, while the SMA assigns equal weight to all values. The weighting given to the most recent price is greater for a shorter-period EMA than for a longer-period EMA. For example, an 18.18% multiplier is applied to the most recent price data for a 10-period EMA, while the weight is only 9.52% for a 20-period EMA.

There are also slight variations of the EMA arrived at by using the open, high, low, or median price instead of using the closing price.

What Does the EMA Tell You?

The 12- and 26-day exponential moving averages (EMAs) are often the most quoted and analyzed short-term averages. The 12- and 26-day are used to create indicators like the moving average convergence divergence (MACD) and the percentage price oscillato (PPO). In general, the 50- and 200-day EMAs are used as indicators for long-term trends. When a stock price crosses its 200-day moving average, it is a technical signal that a reversal has occurred.

Traders who employ technical analysis find moving averages very useful and insightful when applied correctly. However, they also realize that these signals can create havoc when used improperly or misinterpreted. All the moving averages commonly used in technical analysis are lagging indicators.

Consequently, the conclusions drawn from applying a moving average to a particular market chart should be to confirm a market move or to indicate its strength. The optimal time to enter the market often passes before a moving average shows that the trend has changed.

An EMA does serve to alleviate the negative impact of lags to some extent. Because the EMA calculation places more weight on the latest data, it “hugs” the price action a bit more tightly and reacts more quickly. This is desirable when an EMA is used to derive a trading entry signal.

Like all moving average indicators, EMAs are much better suited for trending markets. When the market is in a strong and sustained uptrend, the EMA indicator line will also show an uptrend and vice-versa for a downtrend. A vigilant trader will pay attention to both the direction of the EMA line and the relation of the rate of change from one bar to the next. For example, suppose the price action of a strong uptrend begins to flatten and reverse. From an opportunity cost point of view, it might be time to switch to a more bullish investment.

Examples of How to Use the EMA

EMAs are commonly used in conjunction with other indicators to confirm significant market moves and to gauge their validity. For traders who trade intraday and fast-moving markets, the EMA is more applicable. Quite often, traders use EMAs to determine a trading bias. If an EMA on a daily chart shows a strong upward trend, an intraday trader’s strategy may be to trade only on the long side.

The Difference Between EMA and SMA

The major difference between an EMA and an SMA is the sensitivity each one shows to changes in the data used in its calculation.

More specifically, the EMA gives higher weights to recent prices, while the SMA assigns equal weights to all values. The two averages are similar because they are interpreted in the same manner and are both commonly used by technical traders to smooth out price fluctuations.

Since EMAs place a higher weighting on recent data than on older data, they are more responsive to the latest price changes than SMAs. That makes the results from EMAs more timely and explains why they are preferred by many traders.

Limitations of the EMA

It is unclear whether or not more emphasis should be placed on the most recent days in the time period. Many traders believe that new data better reflects the current trend of the security. At the same time, others feel that overweighting recent dates creates a bias that leads to more false alarms.

Similarly, the EMA relies wholly on historical data. Many economists believe that markets are efficient, which means that current market prices already reflect all available information. If markets are indeed efficient, using historical data should tell us nothing about the future direction of asset prices.

What Is A Candlestick?

A candlestick is a type of price chart used in technical analysis that displays the high, low, open, and closing prices of a security for a specific period. It originated from Japanese rice merchants and traders to track market prices and daily momentum hundreds of years before becoming popularized in the United States. The wide part of the candlestick is called the “real body” and tells investors whether the closing price was higher or lower than the opening price (black/red if the stock closed lower, white/green if the stock closed higher).

The Basics Of A Candlestick

The candlestick’s shadows show the day’s high and low and how they compare to the open and close. A candlestick’s shape varies based on the relationship between the day’s high, low, opening and closing prices.

Candlesticks reflect the impact of investor sentiment on security prices and are used by technical analysts to determine when to enter and exit trades. Candlestick charting is based on a technique developed in Japan in the 1700s for tracking the price of rice. Candlesticks are a suitable technique for trading any liquid financial asset such as stocks, foreign exchange and futures.

Long white/green candlesticks indicate there is strong buying pressure; this typically indicates price is bullish. However, they should be looked at in the context of the market structure as opposed to individually. For example, a long white candle is likely to have more significance if it forms at a major price support level. Long black/red candlesticks indicate there is significant selling pressure. This suggests the price is bearish. A common bullish candlestick reversal pattern, referred to as a hammer, forms when price moves substantially lower after the open, then rallies to close near the high. The equivalent bearish candlestick is known as a hanging man. These candlesticks have a similar appearance to a square lollipop, and are often used by traders attempting to pick a top or bottom in a market.

Two-Day Candlestick Trading Patterns

There are many short-term trading strategies based upon candlestick patterns. The engulfing pattern suggests a potential trend reversal; the first candlestick has a small body that is completely engulfed by the second candlestick. It is referred to as a bullish engulfing pattern when it appears at the end of a downtrend, and a bearish engulfing pattern at the conclusion of an uptrend. The harami is a reversal pattern where the second candlestick is entirely contained within the first candlestick and is opposite in color. A related pattern, the harami cross has a second candlestick that is a doji; when the open and close are effectively equal.

Three-Day Candlestick Trading Patterns

An evening star is a bearish reversal pattern where the first candlestick continues the uptrend. The second candlestick gaps up and has a narrow body. The third candlestick closes below the midpoint of the first candlestick. A morning star is a bullish reversal pattern where the first candlestick is long and black/red-bodied, followed by short candlestick that has gapped lower; it is completed by a long-bodied white/green candlestick that closes above the midpoint of the first candlestick.

What Is a Bullish Engulfing Pattern?

A bullish engulfing pattern is a white candlestick that closes higher than the previous day’s opening after opening lower than the previous day’s close. It can be identified when a small black candlestick, showing a bearish trend, is followed the next day by a large white candlestick, showing a bullish trend, the body of which completely overlaps or engulfs the body of the previous day’s candlestick.

A bullish engulfing pattern may be contrasted with a bearish engulfing pattern.

Understanding a Bullish Engulfing Pattern

The bullish engulfing pattern is a two-candle reversal pattern. The second candle completely ‘engulfs’ the real body of the first one, without regard to the length of the tail shadows.

This pattern appears in a downtrend and is a combination of one dark candle followed by a larger hollow candle. On the second day of the pattern, the price opens lower than the previous low, yet buying pressure pushes the price up to a higher level than the previous high, culminating in an obvious win for the buyers.

What Does a Bullish Engulfing Pattern Tell You?

A bullish engulfing pattern is not to be interpreted as simply a white candlestick, representing upward price movement, following a black candlestick, representing downward price movement. For a bullish engulfing pattern to form, the stock must open at a lower price on Day 2 than it closed at on Day 1. If the price did not gap down, the body of the white candlestick would not have a chance to engulf the body of the previous day’s black candlestick.

Because the stock both opens lower than it closed on Day 1 and closes higher than it opened on Day 1, the white candlestick in a bullish engulfing pattern represents a day in which bears controlled the price of the stock in the morning only to have bulls decisively take over by the end of the day.

The white candlestick of a bullish engulfing pattern typically has a small upper wick, if any. That means the stock closed at or near its highest price, suggesting that the day ended while the price was still surging upward.

This lack of an upper wick makes it more likely that the next day will produce another white candlestick that will close higher than the bullish engulfing pattern closed, though it’s also possible that the next day will produce a black candlestick after gapping up at the opening. Because bullish engulfing patterns tend to signify trend reversals, analysts pay particular attention to them.

Bullish Engulfing Pattern vs. Bearish Engulfing Pattern

These two patterns are opposites of one another. A bearish engulfing pattern occurs after a price moves higher and indicates lower prices to come. Here, the first candle, in the two-candle pattern, is an up candle. The second candle is a larger down candle, with a real body that fully engulfs the smaller up candle.

Example of a Bullish Engulfing Pattern

As a historical example, let’s consider Philip Morris (PM) stock. The company’s shares were a great long in 2011 and remained in an uptrend. In 2012, though, the stock was retreating.

On January 13, 2012, a bullish engulfing pattern occurred; the price jumped from an open of $76.22 to close out the day at $77.32. This bullish day dwarfed the prior day’s intraday range where the stock finished down marginally. The move showed that the bulls were still alive and another wave in the uptrend could occur.

Bullish Engulfing Candle Reversals

Investors should look not only to the two candlesticks which form the bullish engulfing pattern but also to the preceding candlesticks. This larger context will give a clearer picture of whether the bullish engulfing pattern marks a true trend reversal.

Bullish engulfing patterns are more likely to signal reversals when they are preceded by four or more black candlesticks. The more preceding black candlesticks the bullish engulfing candle engulfs, the greater the chance a trend reversal is forming, confirmed by a second white candlestick closing higher than the bullish engulfing candle.

Acting on a Bullish Engulfing Pattern

Ultimately, traders want to know whether a bullish engulfing pattern represents a change of sentiment, which means it may be a good time to buy. If volume increases along with price, aggressive traders may choose to buy near the end of the day of the bullish engulfing candle, anticipating continuing upward movement the following day. More conservative traders may wait until the following day, trading potential gains for greater certainty that a trend reversal has begun.

Limitations of Using Engulfing Patterns

A bullish engulfing pattern can be a powerful signal, especially when combined with the current trend; however, they are not bullet-proof. Engulfing patterns are most useful following a clean downward price move as the pattern clearly shows the shift in momentum to the upside. If the price action is choppy, even if the price is rising overall, the significance of the engulfing pattern is diminished since it is a fairly common signal.

The engulfing or second candle may also be huge. This can leave a trader with a very large stop loss if they opt to trade the pattern. The potential reward from the trade may not justify the risk.

Establishing the potential reward can also be difficult with engulfing patterns, as candlesticks don’t provide a price target. Instead, traders will need to use other methods, such as indicators or trend analysis, for selecting a price target or determining when to get out of a profitable trade.