Mathematical Indicators in Security Analysis

1. Mathematical
indicators

2. Rationale
• Erratic movement of share
prices
• Difficulty to guage the
trend.
• So wee need some
mathematical tools to
smoothen out the erratic
movements
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3. Solutions
SMA EMA Oscillators
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4. SimpleMovingAverageMethod
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Year Value
1994 2
1995 5
1996 2
1997 2
1998 7
1999 6

5. ExponentialMovingAverageMethod
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• EMA is calculated using the following formula;
• EMA = 𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝒄𝒍𝒐𝒔𝒊𝒏𝒈 𝒑𝒓𝒊𝒄𝒆 − 𝑷𝒓𝒆𝒗𝒊𝒐𝒖𝒔 𝑬𝑴𝑨 × 𝑭𝒂𝒄𝒕𝒐𝒓 + 𝑷𝒓𝒆𝒗𝒊𝒐𝒖𝒔 𝑬𝑴𝑨
• 𝑭𝒂𝒄𝒕𝒐𝒓 =
𝟐
𝒏+𝟏
• n = Number of days for which the average is to be calculated.

6. Oscillators
Used when the stock’s chart is
not showing a definite trend
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Most useful when the
movement is horizontal
The readings from an
oscillator will fluctuate either
between -1 and 1 or 0 to 100

7. RateofChangeIndicator(ROC)
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• ROC is calculated using the following formula;
• ROC=
𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝑷𝒓𝒊𝒄𝒆
𝑷𝒓𝒊𝒄𝒆 𝒏′ ′ 𝒑𝒆𝒓𝒊𝒐𝒅𝒔 𝒂𝒈𝒐
- 1
• n = Number of days for which the oscillator is to be calculated.

8. Days Closing Price Closing Price 4 days ago Price Ratio ROC
1 112 -
2 114 -
3 114 -
4 115 112 115/112 = 1.02 1.02 – 1 = 0.02
5 116 114
6 115 114
7 114 115
8 113 116
9 111 115
ROC–4dayoscillator
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9. Oscillator-Interpretation
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10. MACD(MovingAverageConvergenceDivergence)
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• The MACD is a trend derived
from the relationship between
two moving averages of prices.
• It measures the convergence
and divergence between two
exponential moving averages.

11. 11
 MACD: The 12-period exponential
moving average (EMA) minus the 26-
period EMA.
 MACD Signal Line: A 9-period EMA of
the MACD.
 MACD Histogram: The MACD minus
the MACD Signal Line
MACD-Components

12. MACD–Keytakeaways
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MACD is calculated by subtracting the 26-period EMA from the
12-period EMA.
MACD triggers technical signals when it crosses above (to buy) or
below (to sell) its signal line.
When the 12 day EMA crosses over the 26 day EMA line from below,
the MACD will cross over the zero line from below and vice versa.
MACD helps investors understand whether the bullish or bearish
movement in the price is strengthening or weakening.

13. 13

14. 14
Market
Indicators

15. A market indicator refers to anything used to project future financial or
economic trends.
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MarketIndicators
ADL RSI MFI BPI TRIN
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16.  Popular indicator of market
breadth that is used to determine
the direction of the stock market.
 It is a cumulative sum of the
differences between number of
stocks closing higher (Advance)
and those closing lower (decline)
 This indicator includes the data
from the entire market and hence
can be used to measure the
strength of the market
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Advance –Decline Line

17. 17
 Market breadth indicators analyse
the number of stocks advancing
relative to those that are declining in
a given index or on a stock exchange
 Positive market breadth occurs
when more stocks are advancing
than which are declining.

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19. 19
A rising ADL means more
stocks are advancing than
those which decline and
signals a strong market.
A falling ADL means more
stocks are declining than
those advancing and
signals a weak market.

20. During a Bull
market, if the
breadth declines
to new lows
while the
market index
continues to
grow, a peak is
suggested
followed by a
downturn
Breadth may
also signal
recovery. This
happens when
the breadth line
begins to rise
even as the
market index is
reaching new
lows
ADL–Keytakeaways
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21. Day Advancing Declining Net ADL
1 1198 882 316 316
2 1183 965 218 534
3 882 1251 ? ?
4 706 1411 ? ?
5 1139 1033 ? ?
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22.  RSI is an indicator, which helps to
indicate overbought and over
sold conditions.
 It is plotted in a range between
zero and hundred.
RSI = 𝟏𝟎𝟎 − [
𝟏𝟎𝟎
𝟏+𝑹𝑺
]
Where RS =
Average gain per day
Average loss per day
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Relative strength
index

23. An RSI reading above 70 is used to suggest that the
security is overbought.
A reading below 30 may indicate that the security is
oversold
Thus RSI helps to identify whether a security price is
pushed/dragged to unreasonable heights or depths
Keytakeaways
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24. DAY CLOSING
PRICE
CHANGES OVER
PREVIOUS DAY
Gain Loss
1 130 - -
2 132 2 -
3 130 - 2
4 135 5 -
5 137 2 -
6 134 - 3
7 136 2 -
8 140 4 -
…….
Calculationofa14dayRSI
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25.  A momentum indicator
measuring the strength of
money flowing into and out of a
stock.
 RSI looks only at stock prices,
but MFI also considers volume
of trade.
 MFI in the 70-80 range indicates
an overbought condition and
that in the 20-30 range indicates
an oversold one.
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MoneyFlowIndex

26.  The TRIN indicator, also known as
the ARMS index because it was
developed by Richard Arms.
 Functionally it is an oscillator-type
indicator that is primarily used to
identify short-term overbought or
oversold conditions in the stock
market.
 TRIN has an inverse relationship
with the market because a rising
TRIN is bearish and a declining one
is bullish!
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TRINIndex

27. TRIN = =
Advancing issues/Declining issues
Advancing volume/Declining volume
Calculationof TRIN
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Day 1 Day 2 Day 3
Advances 2000 2100 2100
Declines 1000 700 700
Adv/Decl. Ratio 2 3 3
Adv. Volume 40,000 35,000 48,000
Decl. Volume 20,000 25,000 12,000
Volume ratio 2 1.4 4

28. A TRIN above 1 indicates that the volume in declining stocks
outpaced volume in advancing stocks and signals a bearish market.
A TRIN below 1 indicates that there is high volume transactions
in bullish stocks than in bearish ones.
According to Mr. Arms, a reading of 0.8 or below in the 10 day
moving avg. of TRIN indicates an overbought situation.
A reading above 1.2 in the 10-day moving avg. will indicate an
oversold market
Keytakeaways
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29.  A market breadth indicator, that is
applied on a group of stocks/a
particular industry.
 Calculated by dividing the number
of bullish stocks in the group with
the total number of stocks in the
group.
 A percentage above 70 & below 30
indicates overbought and oversold
conditions.
 Reversal by 6% triggers buy/sell
decisions 29
BullishPercent Index

30. 30
Behavioural
Finance

31. Areyouarational person?
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32. ConsiderLauraSmith.Sheis31,single,smartandvery
bright.Shemajoredineconomicsatuniversityand,asa
student,shewaspassionateabouttheissuesofequality
anddiscrimination.
IsitmorelikelythatLauraworksatabank?
Or,isitmorelikelythatsheworksatabankANDis
activeinthefeministmovement?
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33. Behavioural finance -
Meaning
BF is the study of the influence of
psychology on the behaviour of
investors or financial analysts.
It also includes the subsequent effects
on the markets.
It focuses on the fact that investors are
not always rational, have limits to their
self-control, and are influenced by their
own biases.
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34. Representative Bias
Overconfidence Bias
Anchoring Bias
Aversion to ambiguity Bias
Innumeracy Bias
HeuristicBias
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35. Frame Dependence
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36. Paper loss & Realized loss
Instant sale of losers
Extending the sale of winners
MentalAccounting
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37. BehaviouralPortfolios
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38. 38

39. Emotional Time
line
Group Instincts
and
Overreaction
EmotionalandSocialInfluences
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