Skip to content

NISM-Series-XV: Research Analyst · Technical Analysis

Moving Averages, MACD and Bollinger Bands Explained

Updated 11 October 2026 · Fact-checked

A moving average smooths price data to show trend direction. SMA weights all days equally; EMA and WMA weight recent days more. MACD is the 12-day EMA minus the 26-day EMA, with a 9-day EMA signal line. Bollinger Bands are a 20-day SMA plus and minus 2 standard deviations.

Understand Moving Averages and Trend Indicators

Daily prices jump around. A moving average (MA) smooths them by averaging the last N closing prices. As each new day arrives, the oldest day drops out and the average moves. This is why it is called moving.

The simple moving average (SMA) gives every day in the window the same weight. The weighted moving average (WMA) gives the most recent day the highest weight, with weights falling for older days. The exponential moving average (EMA) also gives more weight to recent prices, but the weights fall off exponentially and all past prices still count a little. So EMA and WMA react faster than SMA. SMA is smoother but lags more.

All moving averages are lagging indicators. They confirm a trend after it starts; they do not predict. Price above a rising MA suggests an uptrend. Price below a falling MA suggests a downtrend. A shorter MA reacts faster but gives more false signals. A longer MA is slower but steadier. In sideways markets, MAs give many false signals.

A crossover happens when a short-term MA crosses a long-term MA. A golden cross is a short-term MA (commonly 50-day) crossing above a long-term MA (commonly 200-day). It is a bullish signal. A death cross is the short-term MA crossing below the long-term MA. It is a bearish signal.

MACD (Moving Average Convergence Divergence) is a trend and momentum indicator built from EMAs. The MACD line is the 12-period EMA minus the 26-period EMA. The signal line is a 9-period EMA of the MACD line. The histogram is MACD minus signal. Bollinger Bands put a band around price: a middle line (20-period SMA) with an upper and lower band set 2 standard deviations away. Bands widen when volatility rises and narrow when it falls.

Key formulas to remember

Simple moving average
SMA = (P1 + P2 + ... + Pn) ÷ n
Usually uses closing prices. Every day has equal weight.
EMA smoothing factor
k = 2 ÷ (n + 1)
For a 10-day EMA, k = 2 ÷ 11 ≈ 0.1818.
EMA
EMA today = (Price today × k) + (EMA yesterday × (1 − k))
The first EMA value is usually seeded with an SMA.
WMA
WMA = Σ(weight × price) ÷ Σ(weights)
For a 3-day WMA with weights 3, 2, 1, the latest price gets 3.
MACD line
MACD = 12-period EMA − 26-period EMA
Standard default settings.
Signal line and histogram
Signal = 9-period EMA of MACD; Histogram = MACD − Signal
MACD crossing above signal is bullish; below is bearish.
Bollinger Bands
Middle = 20-period SMA; Upper = Middle + 2σ; Lower = Middle − 2σ
σ is the standard deviation of the same 20 prices. Defaults can be changed.
Crossover signals
Golden cross = short MA above long MA (bullish); Death cross = short MA below long MA (bearish)
Commonly 50-day and 200-day.

How to solve Moving Averages and Trend Indicators questions

Use this method for calculation and concept questions on moving averages and trend indicators.

  1. 1Identify the indicator asked: SMA, EMA, WMA, MACD, crossover or Bollinger Bands.
  2. 2Note the period (n) and which prices are used, usually closing prices.
  3. 3If a calculation is needed, write the correct formula first and check the weights or k.
  4. 4Substitute the numbers carefully and compute step by step.
  5. 5For MACD, subtract the 26-period EMA from the 12-period EMA. Do not reverse it.
  6. 6Read the signal: direction of the MA, crossover type, MACD versus signal line, or price versus band.
  7. 7Check the options for trap wording such as leading versus lagging, or bullish versus bearish.
  8. 8Pick the option that matches both your number and the interpretation.

Quickest way: Shortcut: match the keyword to the rule

When to use it: Use for theory MCQs where no long calculation is needed.

  1. Faster reaction to recent prices means EMA or WMA. Smoothest and slowest means SMA.
  2. Short MA crosses above long MA means golden cross, bullish. Below means death cross, bearish.
  3. MACD = 12 EMA − 26 EMA. Signal = 9 EMA of MACD.
  4. Bands narrow means low volatility. Bands wide means high volatility.
  5. All these indicators are lagging, based on past prices.
  6. For EMA, compute k = 2 ÷ (n + 1) first, then eliminate options that do not fit.

Common mistakes in Moving Averages and Trend Indicators

  • Saying EMA ignores older prices.

    Students hear that EMA weights recent prices more and assume old prices drop out.

    Fix: EMA still includes all past prices with shrinking weights. Only SMA drops the oldest price completely.

  • Calling moving averages leading indicators.

    Crossovers feel like predictions.

    Fix: They are built from past prices, so they are lagging. They confirm trends.

  • Reversing the MACD subtraction.

    Students subtract the short EMA from the long one by habit.

    Fix: MACD = 12-period EMA − 26-period EMA. Short minus long.

  • Confusing golden cross and death cross.

    The names sound alike and direction is easy to flip.

    Fix: Golden is good: short MA moves above long MA. Death is the short MA falling below.

  • Using k = 2 ÷ n for the EMA factor.

    The +1 is easily forgotten.

    Fix: Always k = 2 ÷ (n + 1). For n = 9, k = 0.2.

  • Treating a Bollinger Band touch as an automatic buy or sell.

    Students read the upper band as overbought without context.

    Fix: Price can ride a band in a strong trend. Bands show relative volatility and price position, so confirm with other signals.

Worked examples

Example 1

Closing prices of a stock over the last 5 days are ₹100, ₹102, ₹104, ₹106 and ₹108 (latest). Find the 5-day SMA and the 3-day WMA using weights 3, 2, 1 (3 for the latest day).

Show the solution
  1. 5-day SMA = (100 + 102 + 104 + 106 + 108) ÷ 5 = 520 ÷ 5 = ₹104.
  2. 3-day WMA uses the last three prices: 108 (weight 3), 106 (weight 2), 104 (weight 1).
  3. Weighted sum = 108 × 3 + 106 × 2 + 104 × 1 = 324 + 212 + 104 = 640.
  4. Sum of weights = 3 + 2 + 1 = 6.
  5. WMA = 640 ÷ 6 = ₹106.67 (approximately).

Answer: 5-day SMA = ₹104; 3-day WMA ≈ ₹106.67. The WMA is higher because it weights the latest, higher prices more.

Example 2

A stock's 10-day EMA yesterday was ₹200. Today's close is ₹211. Find today's 10-day EMA.

Show the solution
  1. k = 2 ÷ (10 + 1) = 2 ÷ 11 ≈ 0.1818.
  2. Today's price part = 211 × 0.1818 ≈ 38.36.
  3. Yesterday's EMA part = 200 × (1 − 0.1818) = 200 × 0.8182 ≈ 163.64.
  4. EMA today = 38.36 + 163.64 = 202.00.
  5. Check: EMA = 200 + k × (211 − 200) = 200 + 0.1818 × 11 = 202.00.

Answer: Today's 10-day EMA = ₹202 (approximately).

Exam tips

  • Know the default settings cold: 12, 26 and 9 for MACD; 20 and 2 standard deviations for Bollinger Bands; 50 and 200 for golden and death cross.
  • Expect direct definition questions: which average reacts fastest, which is a lagging indicator, what a death cross signals.
  • For EMA numbers, compute k first and use the shortcut EMA = old EMA + k × (price − old EMA).
  • Watch the wording: narrowing bands mean falling volatility, not a falling price.
  • With negative marking of 25% of the marks, skip a question only if you cannot eliminate at least two options.

Practice questions from Technical Analysis

Moving Averages and Trend Indicators in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Moving Averages and Trend Indicators: frequently asked questions

What is the difference between SMA and EMA?

SMA gives equal weight to every price in the period. EMA gives more weight to recent prices, so it reacts faster to price changes. SMA is smoother but lags more.

How do you calculate MACD?

Subtract the 26-period EMA from the 12-period EMA to get the MACD line. Then take a 9-period EMA of the MACD line to get the signal line. The histogram is MACD minus the signal line.

What do golden cross and death cross mean?

A golden cross is when a short-term moving average, often the 50-day, crosses above a long-term one, often the 200-day. It is read as bullish. A death cross is the opposite crossing and is read as bearish.

How are Bollinger Bands explained simply?

They are a 20-period SMA with bands 2 standard deviations above and below. Wide bands show high volatility and narrow bands show low volatility. Price near a band shows where it sits relative to recent volatility.