मूविंग एवरेज

13.1 औसत 'मूविंग' को समझना 

स्कूल के दिनों में, संभव है कि हम औसत के बारे में नहीं सीखते हैं और मूविंग एवरेज केवल एक कदम आगे हैं. मूविंग एवरेज टेक्निकल एनालिसिस में ट्रेंड इंडिकेटर हैं, और इनका इस्तेमाल अक्सर किया जाता है क्योंकि वे सरल और प्रभावी हैं.

मूविंग एवरेज ट्रेंड इंडिकेटर हैं जो किसी निर्धारित समय अवधि में आउट प्राइस डेटा को आसान बनाकर अंतर्निहित ट्रेंड को निर्धारित करने में मदद करते हैं. आइडिया सरल है: पूर्वनिर्धारित अवधि में औसत क्लोजिंग प्राइस का पता लगाएं.

"मूविंग" शब्द का अर्थ है नए दिन के क्लोजिंग प्राइस को जोड़ने के कारण औसत करंट बनाए रखने के लिए सबसे पुराने डेटा पॉइंट को कम करने की प्रक्रिया.

सिंपल मूविंग एवरेज: साधारण मूविंग औसत गणना में प्रत्येक डेटा बिंदु को एक समान भार देता है.

एक्सपेंशियल मूविंग एवरेज (EMA): 

साधारण मूविंग एवरेज की तुलना में, एक्सपोनेन्शियल मूविंग एवरेज नई जानकारी के प्रति अधिक संवेदनशील होता है और कीमतों में बदलाव के प्रति तेज़ी से प्रतिक्रिया देता है क्योंकि यह हाल ही की कीमतों पर अधिक भार डालता है. इस कारण से, ट्रेडर अक्सर SMA पर EMA का पक्ष लेते हैं.

मूविंग एवरेज में जाने से पहले, आइए बेसिक एवरेज की गणना करने के बारे में तुरंत जानकारी देते हैं.

मासिक औसत रेस्टोरेंट खर्च

मान लें कि रमेश इस बात पर नज़र रखता है कि हर सप्ताह औसतन खाने पर वह कितना खर्च करता है:

सप्ताह में खर्च की गई राशि (₹)

सप्ताह 1 ₹800

सप्ताह 2 ₹1,200

सप्ताह 3 ₹600

सप्ताह 4 ₹1,400

औसत मासिक खर्च जानने के लिए, वह हर साप्ताहिक राशि जोड़ता है, और उसे सप्ताह की संख्या से विभाजित करता है:

औसत = (₹800 + ₹1,200 + ₹600 + ₹1,400) ÷ 4 = ₹4,000 ÷ 4 = ₹1,000

इस प्रकार, रमेश ने एक सप्ताह में रेस्टोरेंट पर औसतन ₹1,000 खर्च किए हैं.

यहां, हमें औसत से एक सामान्य विचार मिलता है कि रमेश आमतौर पर खाने पर हर सप्ताह कितना खर्च करता है. जाहिर है, ऐसे सप्ताह थे जब उन्होंने औसत से अधिक और सप्ताह बिताये थे जब उन्होंने कम खर्च किया था. उदाहरण के लिए सप्ताह 4 में उन्होंने ₹1,400 खर्च किया था, जो ₹1,000 के औसत से काफी अधिक था और सप्ताह 3 में उन्होंने केवल ₹600 खर्च किया था जो औसत से बहुत कम था. यह दर्शाता है कि औसत केवल एक अनुमान है जो डेटा का सारांश देने में मदद करता है लेकिन खर्च की पूरी रेंज को पूरी तरह से ध्यान में नहीं रखता है. इसलिए, रमेश ने हर सप्ताह ₹1,000 खर्च नहीं किया, हालांकि यह औसत साप्ताहिक खर्च है.

अब, आइए इसे स्टॉक मार्केट से कनेक्ट करें. ट्रेडिंग में, हम कीमतों या वॉल्यूम पर समान तर्क लागू करते हैं. रमेश द्वारा कितना खर्च किया जाता है, इसकी गणना करने के बजाय, हम निर्धारित दिनों में स्टॉक के औसत क्लोजिंग प्राइस की गणना करते हैं. इसे मूविंग एवरेज कहा जाता है, और यह ट्रेडर को ट्रेंड को अधिक स्पष्ट रूप से पहचानने के लिए शॉर्ट-टर्म उतार-चढ़ाव को आसान बनाने में मदद करता है.

कॉन्सेप्ट को स्टॉक की कीमतों तक बढ़ाना

आइए स्टॉक मार्केट में औसत के विचार को लागू करें. मान लीजिए कि हम पिछले 5 ट्रेडिंग सेशन में Larsen & Toubro (L&T) की क्लोजिंग कीमतों पर विचार कर रहे हैं. जैसे हमने हर सप्ताह रमेश द्वारा खर्च की गई औसत संख्या की गणना की, अब हम एक स्टॉक की औसत क्लोजिंग कीमत की गणना करेंगे.

L&T के लिए क्लोजिंग प्राइस यहां दिए गए हैं:

कुल = ₹3,120.50 + ₹3,145.75 + ₹3,110.20 + ₹3,135.60 + ₹3,160.40 ₹15,672.45

5-दिन की औसत क्लोजिंग प्राइस खोजने के लिए, हम कुल 5 से विभाजित करते हैं:

औसत = ₹15,672.45 ÷ 5 = ₹3,134.49

इसलिए, पिछले 5 ट्रेडिंग सेशन में L&T का औसत क्लोजिंग प्राइस ₹3,134.49 है.

यह औसत ट्रेडर को दैनिक कीमत के उतार-चढ़ाव को आसान बनाने और स्टॉक के शॉर्ट-टर्म ट्रेंड की स्पष्ट समझ प्राप्त करने में मदद करता है. टेक्निकल एनालिसिस में, यह मूविंग एवरेज का आधार बनाता है, जिसकी गणना लगातार की जाती है क्योंकि नया डेटा आता है.

13.1 - 'मूविंग' औसत को समझना (सरल मूविंग एवरेज)

मान लें कि आप लेटेस्ट 5 ट्रेडिंग सेशन में Tata कंज्यूमर प्रोडक्ट की औसत क्लोजिंग प्राइस की गणना करना चाहते हैं. क्लोजिंग प्राइस यहां दिए गए हैं:

कुल = ₹875.20 + ₹878.50 + ₹880.10 + ₹882.40 + ₹884.30 ₹4,400.50

5-दिन की औसत क्लोजिंग प्राइस खोजने के लिए, कुल 5 से विभाजित करें:

औसत = ₹4,400.50 ÷ 5 = ₹880.10

इसलिए, इन 5 सेशन में Tata कंज्यूमर की औसत क्लोजिंग कीमत ₹880.10 है.

अब What It है a “Moving” Average?

Let’s say the next trading day is 08/08/25. A new closing price is available: ₹886.50.

To keep the average updated, we include this new data point and drop the oldest one (01/08/25). The new set of dates becomes:

New Total = ₹4,411.80

New Average = ₹4,411.80 ÷ 5 = ₹882.36

As you can see, we’ve moved forward by including the latest closing price and excluding the oldest one. This process continues each day, always using the most recent 5 data points. That’s why it’s called a “moving” average, because it shifts forward with each new trading session.

In the above example the moving average is calculated using closing prices which are commonly preferred by traders and investors. The closing price represents the final value at which the stock trades for the day which makes it a reliable indicator of market sentiment. While closing prices are used most frequently , moving averages also can be computed using other data points such as OHL data which means opening, High and Low prices depending on the specific analysis or strategy. Moving averages are highly flexible and can be applied across various time frames.

For those who frequently use excel can calculate average within minutes. Observe how the cell reference moves in the average formula, eliminating the oldest to include the latest data points. Here is a screenshot of excel calculation.

The moving average adjusts dynamically with each new closing price, reflecting the latest market trends. This type of average is known as a Simple Moving Average (SMA). When calculated using the most recent five days of data, it’s specifically referred to as the 5-Day SMA.

आमतौर पर 5, 10, 50, 100, या 200 दिनों की एक निश्चित संख्या में औसत की गणना करके - परिणामी मूल्यों को एक सुगम, प्रवाह लाइन बनाने के लिए प्लॉट किया जा सकता है जिसे मूविंग एवरेज लाइन कहा जाता है. This line evolves continuously over time, offering a clearer view of price direction and helping to filter out short-term fluctuations.

Here is a chart which shows 50, 100 and 200 days Simple Moving Average is plotted.

What does a moving average tell us, and how is it used? In fact, moving averages have a wide range of applications in financial analysis and trading. Now it’s important to understand another powerful variation—the Exponential Moving Average.

आपके लिए ऐक्टिविटी

वर्तमान कीमत ₹930.65 है, which is above the SMA 100 (₹854.14) and SMA 200 (₹809.32), and equal to the SMA 50.

प्रश्न: If you’re a trader and you observe the price staying above all three SMAs, what could this indicate?

• A) Weak market momentum
• B) Potential continuation of bullish trend
• C) Imminent breakdown
• D) No relevance to trend

सही उत्तर: B) Potential continuation of bullish trend 

क्यों: When the price remains above the SMA 50, SMA 100, and SMA 200, it typically signals strength and supports the possibility of an ongoing uptrend.

13.2  Understanding the Exponential Moving Average (EMA)

Let’s consider a fresh set of closing prices:

When we calculate a simple average of these values, we’re assuming each data point carries equal weight. That means the price on 22nd July is treated as just as important as the price on 28th July. But in the context of financial markets, this assumption doesn’t always hold.

One of the key principles of technical analysis is that markets discount everything, meaning the most recent price reflects all known and unknown information. As a result, the latest price i.e 28th July is considered more significant than earlier ones.

To account for this, we assign greater weight to newer data points. So, the closing price on 28th July receives the highest weight, followed by 25th July, then 24th July, and so on. This approach emphasizes recent market behavior while still considering historical data.

By applying these weights, we create a scaled average where newer prices have more influence. The result is the Exponential Moving Average (EMA), a refined version of the moving average that responds more quickly to price changes.

एक्सपोनेन्शियल मूविंग एवरेज की गणना

The Exponential Moving Average (EMA) is a type of moving average that gives more weight to recent prices, making it more responsive to new information than the Simple Moving Average (SMA). It’s widely used in technical analysis to identify trends.

The formula for EMA is:

EMA_t = (P_t×K) +(EMA_t−1×(1−K))

जहां:

• EMA_t= EMA टुडे
• P_t= आज की कीमत
• EMA_t−1 = कल EMA
• K = स्मूथिंग कॉन्स्टेंट = 2/N+1
• n = अवधि की संख्या

भारतीय स्टॉक का उपयोग करने का उदाहरण: इंफोसिस लिमिटेड (इन्फी)

मान लें कि हम Infosys स्टॉक के लिए 10-दिन के EMA की गणना करना चाहते हैं.

चरण 1: अंतिम 10 क्लोजिंग प्राइस प्राप्त करें :

Step 2: Calculate the 10-day SMA (used as the first EMA value):

SMA=1450+1460+1455+ 1470+1465+1475+1480+1490+1495+1500/10= ₹1,474

Step 3: Calculate the multiplier:

K=2/10+1

=0.1818

Step 4: Calculate EMA for Day 11 (assuming closing price is ₹1,510):

EMA_t = (P_t×K) +(EMA_t−1×(1−K)

ईमा₁₁= (1510×0.1818) + (1474×0.8182) = ₹1,480.5

If the EMA is rising, it suggests a bullish trend. Traders often use crossovers (e.g., 10-day EMA crossing above 50-day EMA) as buy/sell signals.

Here is a chart which shows 20, 50, 100 , 200 days EMA Plotted.

13.3 Simple Application of Moving Average

Trading with the 50-Day EMA: A Simple System

The 50-day Exponential Moving Average (EMA) isn’t just a line on a chart—it’s a signal of market sentiment. When price moves in relation to this average, it reflects how traders feel about the stock’s future.

• Price Above EMA: Traders are buying at levels higher than the recent average. That’s a vote of confidence. Momentum is building. Time to consider entering a long position.
• Price Below EMA: Traders are selling below the average. That’s caution, maybe even fear. Momentum is fading. Time to think about exiting or staying out.

The Strategy

Let’s keep it clean and rule-based. कोई अनुमान नहीं. Just two core rules:

• Entry Rule: Go long when the current price climbs above the 50-day EMA. This suggests upward momentum. Stay in the trade until the exit condition is met.
• Exit Rule: Close the position when the price drops below the 50-day EMA. This signals potential weakness or reversal.

This system doesn’t predict the future, it reacts to it. That’s its strength. It’s built to follow trends, not fight them.

Let’s analyze how the Exponential Moving Average (EMA) strategy would have played out on the Nifty 50 index using the chart you provided. We’ll focus on buy and sell signals generated when price crosses above or below key EMAs (like 50 EMA), and how trend behavior influences profitability.

Trade 1: B1 near ~5,727 → S1 near ~7,000

• Buy Signal (B1):Price crosses above the 50 EMA around mid-2013.
• Sell Signal (S1):Exit triggered when price dips below EMA after a rally.
• परिणाम:Approximate gain of ₹1,273 (7000-5727)
• Trend Context:Strong upward breakout from consolidation.

Trade 2: B2 near ~7,000 → S2 near ~7,300

• Buy Signal (B2):Another crossover above EMA, but price moves sideways.
• Sell Signal (S2):Minor dip below EMA.
• परिणाम:Marginal gain of ₹300
• Trend Context:Sideways movement, low momentum.

🔹 Trade 3: B3 near ~7,300 → S3 near ~11,500

• Buy Signal (B3):Clear breakout above EMA, followed by sustained rally.
• Sell Signal (S3):Exit near peak before correction.
• परिणाम:Massive gain of ₹4,200
• Trend Context:Strong bullish trend lasting several months.

Summary Table (Based on Chart)

Insights from the Chart

1. EMA works best in trending markets—Trade 1 and 3 show strong gains.
2. Sideways phases generate weak signals—Trade 2 had minimal returns.
3. Big winners compensate for small losses or flat trades.
4. Consistency is key—Don’t skip signals; the next one could be the breakout.
5. EMA helps ride long-term trends—Trade 3 lasted several months, ideal for positional investors.

13.4 मूविंग एवरेज क्रॉसओवर सिस्टम

A moving average crossover system is a popular method used by traders to identify potential buy and sell signals in the stock market. Instead of relying on just one moving average, this system uses two, one that reacts quickly to price changes (called the short-term or fast moving average) and another that reacts more slowly (called the long-term or slow moving average). The idea is to observe how these two lines interact with each other on a price chart.

मूविंग एवरेज क्रॉसओवर सिस्टम

Moving Average Crossover System is a more refined strategy. It uses two moving averages: a faster one (e.g., a 9-day EMA) and a slower one (e.g., a 21-day EMA)

Bullish Crossover: When the faster EMA crosses over the slower EMA, it indicates a possible upward trend and generates a buy signal. Bearish Crossover: When the faster EMA crosses below the slower EMA, it indicates a possible decline and generates a sell signal.

This approach helps cut down on the noise or erroneous signals that frequently surface during sideways times and is quite successful in trending markets.

The fast moving average, such as a 50-day EMA (Exponential Moving Average), stays closer to the current market price because it uses fewer data points. The slow moving average, like the 100-day EMA, uses more data points and therefore moves more gradually. When the fast moving average crosses above the slow moving average, it signals that momentum is picking up, this is considered a buy signal. On the other hand, when the fast moving average crosses below the slow one, it indicates that the trend may be weakening—this becomes a sell signal.

This crossover method helps traders avoid false signals that often occur in sideways markets. In a basic moving average system, where only one average is used, traders might receive too many signals during periods of low volatility, leading to small or unprofitable trades. The crossover system filters out much of this noise by requiring confirmation from both averages, making it more reliable during trending phases.

Different combinations of moving averages can be used depending on the trader’s goals. For short-term trades, a 9-day and 21-day EMA might be used. For medium-term trades, combinations like 25-day and 50-day EMA’s are common. Long-term investors might prefer using 100-day and 200-day EMA’s to identify major trends that can last for months or even years. The longer the time frame, the fewer signals you will get, but those signals tend to be stronger and more meaningful.

This system can also be applied to intraday trading by using shorter time frames, such as 5-minute and 10-minute EMAs. Aggressive traders often use these to catch quick moves during the trading day. Regardless of the time frame, the principle remains the same: when the fast average overtakes the slow one, it’s a sign to enter the trade; when it falls below, it’s time to exit.

In summary, the moving average crossover system is a simple yet effective way to follow market trends. It helps traders stay invested during strong moves and avoid getting caught in choppy, directionless markets. By using two averages instead of one, this system offers better timing and more confidence in trading decisions—especially for beginners who are learning to spot trends and manage risk.

आपके लिए ऐक्टिविटी

वर्तमान कीमत ₹950.15 है, which is slightly below the EMA 9 line at ₹964.62.

प्रश्न: If you’re a trader and you notice the price dropping below the EMA 9 after a recent uptrend, what could this signal?

• A) Strong bullish momentum
• B) Potential short-term bearish shift
• C) Market indecision
• D) No relevance to trend

सही उत्तर: B) Potential short-term bearish shift क्यों: When price falls below a short-term EMA like EMA 9, it may indicate weakening momentum and a possible short-term reversal or pullback.

13.5 मुख्य टेकअवे

• Moving averages are trend indicators used in technical analysis to help traders smooth out short-term price fluctuations and identify trends more clearly.
• A moving average is calculated by taking the average closing price of a stock over a set number of days.
• The “moving” part of a moving average means that as a new day’s closing price is added, the oldest data point is dropped from the calculation to keep the average updated.
• An average is just an estimate and doesn’t account for the full range of price behaviour, as there will be days when the price is higher or lower than the average.
• The Moving Average Crossover System uses two different moving averages to generate buy and sell signals.
• In a bullish crossover, a faster-moving average (like a 9-day) crosses above a slower-moving average (like a 21-day), signaling a potential upward trend and a buy opportunity.
• In a bearish crossover, the faster-moving average crosses below the slower one, signaling a potential downtrend and an exit or sell opportunity.
• This crossover system helps traders stay invested during strong moves and avoid getting caught in choppy, directionless markets.
• Different combinations of moving averages are used depending on the trading time frame: short-term traders might use 9-day and 21-day EMAs, while long-term investors might use 100-day and 200-day EMAs.
• The longer the time frame, the fewer signals you will get, but those signals tend to be stronger and more meaningful.