STOCK PRICE INDEX

R. Srinivasan

• S&P CNX Nifty– Comprises of 50 stocks– Selection Criteria

• Market Capitalization• Liquidity: Each should have traded at least 85% of the

trading days at an impact cost of < 1.5%• Impact Cost: %age mark up suffered while buying/

selling the desired quantity of shares, as compared to the ideal price (Avg. of Bid & Ask Price)

Impact CostExample: Order Book of a broker

Bid (Buy) Ask (Sell)Qty Price (Rs.) Qty Price (Rs.)100

098 100

099

2000

97 1500

100

1000

96 1000

101Actual Buy price = (1000 x 99 + 500 x 100) / 1500 = Rs. 99.33Impact Cost = {(99.33 – 98.50) / 98.5} = 0.84%

If the impact cost is consistently > 1% then the stock moves out of the index. This is another indicator of liquidity.

Calculate Impact Cost for buying 1500 shares

Ideal Price = (98+99) / 2 = Rs. 98.50

Company Weightage in Index• Shares bear a weight in the index in proportion of their M. Cap.• Example: Base Period Index = 1.000X 1000 = 1000

• Suppose current M Cap = Rs. 880000 (due to market price changes)• Current Index = (Current Cap / Base Cap) x 1000

= 1.073 x 1000=1073

Share Price Issue Size Cap WeightA 20 4000 80000 0.098

B 60 5000 300000 0.366

C 145 2000 290000 0.354

D 15 10000 150000 0.182

Total 820000 1.000

Index Maintenance

• Index should remain constantIt = (Mt /M0) x I0

M0 = Mt x ( I0 / It )

I0 - Index Today; It - Base Index

M0 - Base year M Cap; Mt - M Cap today

∆M0 = ∆Mt x ( I0 / It )

M’0 (New Base Cap) = M0 X ∆M0

= M0 + ∆Mt x ( I0 / It )

• Example:On 5 April: M0 = Rs. 195000 crores

Mt = Rs. 197500 crores

It = (Mt / M0) x I0 = (197500 / 195000) x 1000

= 1012.82Scrip A with a Cap of Rs. 1000 crores, gets replaced with Scrip B with a Cap of

Rs 900 croresM’0 (New Base Cap) = M0 + ∆Mt x ( I0 / It )

=195000 + (900 – 1000) x (1000/1012.82)= 194901 crores

Mt = 197500 – 100 = 197400 crores

It = (197400 / 194901) x 1000

= 1012.82

Index Maintenance (Contd…)

Efficient Market Hypothesis

• EMH– Security prices incorporate all past/new

information in a rapid and unbiased manner– Investors will not b able to systematically

outperform the market by following conventional approaches (use of charts/trends or in search for mispriced securities)

– Refers to only informational efficiency

EMH (Weak Form)

• Three forms of EMH– Weak Form: Security prices fully reflect the information implied

by all prior price movements – successive price movements are independent

• AKA Random Walk Hypothesis• Common testable form of RWH

– lnPt = lnPt-1 + έ

– Where E (έ) = 0 & Cov (έt, έt-1) = 0

– Or ln(Pt /Pt-1) = έt

• The model considers only the linear independence – meaning thereby that investors immediately react to new information – investors do not react react in a cumulative fashion to a series of events.

• Stock process follows a Brownian Motion

EMH (Contd…)

• Traditional Tests of RWH– Serial Correlation Test– Runs test

• Evidence against EMH – Market Anomalies– Day-of-the-week effect– January effect– P/E effect– Small-firm effect– Reversal effect – losers rebound and winners fade

away

• Biased Random Walk of stock prices– Stock returns found to be skewed and

leptokurtotic (fat tails & high peaks)• Information shows up in infrequent lumps, which

explains non-normal distribution of price movements

– Several studies found volatility of stock returns to be unstable overtime

• High volatility followed by even higher volatility; while low volatility is followed more lower volatility.

EMH (Contd…)

• Most investors react to information in a non-linear way – wait for confirming information and do not react until a trend is established– Influence of past – a clear violation of EMH

EMH (Contd…)

EMH (Other Forms)

• Semi Strong Form: Security prices reflect fully all publicly available information – not possible to consistently outperform the market from any analysis of published data

• Strong Form: Security prices not only reflect fully the published information but also privileged information – even insiders cannot consistently outperform the market

Dow Theory• The ideas of Charles Dow, the first editor of the Wall Street Journal, form the

basis of technical analysis today.

He believed that the behavior of the averages reflected the hopes and fears of the entire market. The behavior patterns that he observed apply to markets throughout the world.

Dow Theory• Three Movements – Markets fluctuate in more than one time frame at the

same time:1. The daily variation due to local causes and the balance of buying and selling at

that particular time (Ripple). 2. The secondary movement covers a period ranging from days to weeks,

averaging probably between six to eight weeks (Wave). 3. The third move is the great swing covering anything from a few months to a

few years. (Tide).

Primary Movements have Three Phases

• Look out for these general conditions in the market:Bull markets• Bull markets commence with reviving confidence as business conditions improve. • Prices rise as the market responds to improved earnings • Rampant speculation dominates the market and price advances are based on hopes

and expectations rather than actual results. Bear markets• Bear markets start with abandonment of the hopes and expectations that sustained

inflated prices. • Prices decline in response to disappointing earnings. • Distress selling follows as speculators attempt to close out their positions and securities

are sold without regard to their true value. Ranging Markets• A secondary reaction may take the form of a ‘line’ which may endure for several weeks. • Price fluctuates within a narrow range of about five per cent.