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Formula sheet/NISM Series XV: Research Analyst/Technical Analysis
[ TECHNICAL ANALYSIS ]

Simple Moving Average (SMA) & Exponential Moving Average (EMA)

SMAt=(Pt+Pt−1+...+Pt−n+1)/nSMA_{t} = ( P_{t} + P_{t-1} + ... + P_{t-n+1} ) / n
Multiplier(Smoothing Factor)=2/(n+1)Multiplier (\text{Smoothing Factor}) = 2 / (n + 1)
EMAt=[Pricet×(2/(n+1))]+[EMAt−1×(1−2/(n+1))]EMA_{t} = [ Price_{t} \times ( 2 / (n + 1) ) ] + [ EMA_{t-1} \times ( 1 - 2 / (n + 1) ) ]
Variables

n: Time period (e.g., 13, 21, 34 Fibonacci EMAs; 50, 200 DMAs). PtP_{t}: Price at time t.

Exam note

EMA accords higher weighting to recent prices, reacting faster to trend momentum shifts than SMA.

Worked examples
Exponential Moving Average (EMA) Calculation

A stock's 10-day EMA yesterday was Rs 450.00. Today's closing price is Rs 472.00. Calculate the smoothing multiplier and today's new 10-day EMA.

Relative Strength Index (RSI) Calculation

Over a 14-day lookback period, a stock's average daily gain on up-days is Rs 18.00 and its average daily loss on down-days is Rs 6.00. Calculate the Relative Strength (RS) and the 14-period RSI.