Part 04
Part 04
Part 04
1
Introduction
Standard question asked on a daily basis by:
Investors
Traders
Market Analysts
2
Introduction (cont…)
The term “market” refers to the Stock Market.
3
Introduction
Why focus on the market as a whole?
The market consists of a multitude of
assets.
The performance of each asset cannot be
realistically tracked at the same time to draw
meaningful conclusions.
Thus there is a tendency to focus on a
summary measure of the market’s
performance.
4
Types of Indices
5
Stock Indices
6
Types of Indices
computing stock
market indices.
Price Value Equally
Weighted Weighted Weighted
Indices Indices Indices
7
Price Weighted Indices
8
Formula
A price weighted index consists of N
stocks
The day of computation = t
The value of the index = It
9
Hypothetical Example
Take an index consisting of 5 stocks
Assume that we are standing on the
base date.
The Base Date is the date on which the
index is being computed for the first time.
On the Base Date, the Divisor can be set
equal to any value.
A logical value for the Divisor is the number
of stocks in the index.
10
Prices of Constituent Stocks
STOCK PRICE
ACC 907
Bombay Dyeing 81
Colgate Palmolive 211
Escorts 68
Hindustan Lever 732
TOTAL 1999
11
Initial Index Value
1999
It = ______ = 399.80
5
12
The Following Day
2065
It+1 = ______ = 413
5
14
Conclusion
15
Changing the Divisor
16
Stock Split - A Different Scenario
17
Second Day’s Prices - Post Split
STOCK PRICE
ACC 308
Bombay Dyeing 90
Colgate Palmolive 225
Escorts 75
Hindustan Lever 750
TOTAL 1448
18
Comparison of Prices -
With & Without the Split
STOCK PRICE - If no PRICE - With
split split
ACC 925 308
Bombay Dyeing 90 90
20
Calculation of Index After the Split
using the Existing Divisor
1448
It+1 = ______ = 289.60
5
21
Erroneous Conclusion
22
Reason For Wrong Deduction
23
Adjusting the Divisor
24
Theoretical Post-Split Prices
STOCK PRICE
ACC 302.33
Bombay Dyeing 81
Colgate Palmolive 211
Escorts 68
Hindustan Lever 732
TOTAL 1394.33
25
The New Divisor
(1394.33 / X) = 399.80
The new divisor is 3.4876
26
The New Divisor (Cont…)
27
The New Divisor - Conclusion
28
Situations Warranting Re-calculation
of Divisor
29
Handling Stock Dividends
From a mathematical standpoint, a stock
split and a stock dividend are identical
20% stock dividend 1 new share will be issued
for every 5 existing shares
This is exactly analogous to a 6:5 split.
30
Changing the Composition of the
Index
Assume that
Escorts, which has a price of 75, is deleted
at the end of the 2nd day
It is replaced with Ranbaxy which has a
price of 120.
STOCK PRICE
ACC 308
Bombay Dyeing 90
Colgate Palmolive 225
Ranbaxy 120
Hindustan Lever 750
TOTAL 1493 31
Changes in Composition and Divisor
Adjustment
32
Price weighted indices
33
Examples of Price Weighted Indices
34
The Importance of Price
High priced stocks carry more weight
in the case of price weighted indices
than low priced stocks.
35
Illustration of Relative
Importance
price of ACC
36
Illustration of Relative
Importance
STOCK Day 1 Day 2: Day 2:
Case A Case B
ACC 900 1080 900
Bombay Dyeing 90 90 90
38
Value weighted indices
39
Value Weighted Indices
40
Formula
41
Explanation of Symbols
Pib ≡ Price of stock i on the base date
Qib ≡ Number of shares outstanding of stock i on the
base date
Pit ≡ Price of stock i on date t
Qit ≡ No. of shares outstanding of stock i on day t
M ≡ No. of companies constituting the index on the
base date
N ≡ No. of companies constituting the index on day t
42
Starting Index Value
43
The Divisor
44
Hypothetical Example
45
Market Capitalizations on the
Base Date
STOCK Price No. of Market Cap.
(P) Shares (Q)
46
Total Market Capitalization
ΣPiQi = 2,206,800,000
47
Market Capitalizations on the Next
Day
STOCK Price No. of Market Cap.
(P) Shares (Q)
ACC 925 1,000,000 925,000,000
Bombay Dyeing 90 500,000 45,000,000
ΣPiQi = 2,267,500,000
49
Conclusion
Reverse Splits
Stock Dividends
51
Rationale – a theoretical
standpoint
The below will not have any impact on the
market capitalization of the stock
Stock splits
Reverse splits
Stock dividends
The decrease/increase in the stock price
will be exactly offset by an
increase/decrease in the no. of shares
outstanding 52
Example
53
Change in Composition and
the Divisor
The divisor will have to be adjusted if
there is a change in the composition.
Assume that Escorts is replaced by
Ranbaxy.
Escorts Ranbaxy
Price 75 120
No. of shares 200,000 100,000
outstanding
54
Post-Change Market Cap.
STOCK Price (P) No. of Market Cap.
Shares (Q)
57
Examples of Value Weighted
Indices
58
Equally weighted indices
59
Equally Weighted Indices
The value of an equally weighted index consisting of N stocks is given
by
60
Prices & Returns
61
The Formula in Terms of Returns
It =
62
Explanation of Formula
Thus
Value of the index =
(Index level on the previous day) * (average
return on all the stocks)
63
Tracking portfolois
64
Mimicking Portfolios
65
Replication Techniques
index
66
To track…
Price weighted Equally Value weighted
index weighted index index
68
Portfolio Rebalancing
Once a tracking portfolio is formed it will
not continue to track the index
automatically forever
There are circumstances under which the index
ought to be rebalanced if it is to maintain its
property of being a tracking portfolio.
The circumstances under which the portfolio
has to be rebalanced depend on the nature of
the index.
69
Events that Warrant Rebalancing
Price weighted Equally weighted index Value
index weighted
index
One of the Has to be rebalanced every If there is a
constituent stocks in day, unless none of the change in
the index: component stocks changes the
Undergoes a split in price - because a price composition
Undergoes a change in even 1 stock is of the index
reverse split adequate to ensure that the
Or pays a stock portfolio is no longer equally
dividend weighted.
If there is a change
in the composition of 70
Equally Weighted Tracking
Portfolio
71
An Equally Weighted Tracking
Portfolio
Assume that
We have Rs. 500,000
73
Equally Weighted …(Cont…)
If we assume that the index level is 100 our
portfolio will be worth 5000 times the index
Assume that the prices on the next day are as
follows.
STOCK PRICE
Alfa Laval 40
Atlas Copco 125
Sandvik 50
Sulzer 100
74
Equally Weighted …(Cont…)
75
Equally Weighted …(Cont…)
The percentage of each stock in the portfolio
STOCK PERCENTAGE
Sandvik 30.49%
Sulzer 19.51%
76
Equally Weighted… (Cont…)
The portfolio is no longer equally weighted.
The total portfolio value is 512,500
We need to invest 128,125 in each stock
Sandvik
Invest the proceeds in Buy 703.125 shares of
Alfa Laval & Sulzer Alfa Laval
77
Buy 281.25 shares of
Rebalancing at Zero Cost
If we assume that there are no transactions
costs, we can rebalance at no cost.
78
The New Index Level
It+1 = It x (1 + )
= 100 x (1 + )
It+1 = 102.50
79
Mimicking Property
80
Price Weighted Tracking
Portfolio
81
A Price Weighted Tracking
Portfolio
Assume that we wish to form a price weighted
tracking portfolio by buying 1000 shares
STOCK PRICE
Alfa Laval 50
Atlas Copco 100
Sandvik 40
Sulzer 125
82
Price Weighted…(Cont…)
Assume that the divisor is 4.0, the index
level will be:
50 + 100 + 40 + 125
It =________________ = 78.75
4.0
83
Price Weighted…(Cont…)
The value of our tracking portfolio will be:
{1000 x (50 + 100 + 40 + 125)} = 315,000
= 4000 x 78.75
84
Stock Split
Assume that Atlas Copco undergoes a 2:1 split
The post split theoretical value of the stock will be 50
85
Rebalancing
In order to ensure that our portfolio continues to
mimic the index, we need to rebalance in such a
way that the portfolio value remains unchanged.
86
Rebalancing (Cont…)
The portfolio value = 4000 x 78.75
= 1000 X 4 x 78.75
87
Rebalancing (Cont…)
Therefore:
1000 x 4
N = ______ = 1188.672
3.3651
88
Rebalancing (Cont…)
Assume that fractional shares can be
bought & sold
We need to buy
188.672 shares of Alfa Laval, Sandvik, and
Sulzer,
We need to sell
811.328 shares of Atlas Copco
Because we would have 2000 shares after the
split and we need only 1188.672 shares
89
Rebalancing (Cont…)
Inflow:
811.328 x 50 = 40,566.40
Outflow:
188.672 x (50 + 40 + 125) = 40,564.48
91
A Value Weighted Tracking Portfolio
Consider a value weighted portfolio
consisting of the following 4 stocks.
STOCK Price No. of Market
(P) Shares Cap.
(Q)
MRF 20 100,000 2,000,000
93
Value Weighted… (Cont…)
Consider a person with a capital of
200,000
2,000,000
________ x 200,000 = 40,000 in MRF
10,000,000
94
Value Weighted…(Cont…)
2,000,000
_________ x 200,000 = 40,000 in J.K. Tyres
10,000,000
5,000,000
_________ x 200,000 = 100,000 in Apollo Tyres
10,000,000
1,000,000
________ x 200,000 = 20,000 in Vikrant Tyres
10,000,000
95
Value Weighted… (Cont…)
1 x 12,500,000 x 100
__ _________ = 62.50
X 16,000,000
⇒ X = 1.25
98
Value Weighted…(Cont…)
For the portfolio to remain value
weighted, the investor must have:
2,000,000
_________ x 200,000 = 32,000 in MRF
12,500,000
100
Value Weighted…(Cont…)
The investor requires The investor needs to
102
Base period capitalization
103
Changing the Base Period
Capitalization
104
Base Period…(Cont…)
Adjust the Divisor Keep the Divisor fixed
at 1.0
This is the approach used In India we follow this
for the S&P500 procedure for the Sensex
and the Nifty
105
Base Period…(Cont…)
In our illustration when the market capitalization
changed from 10,000,000 to 12,500,000 we
changed the divisor to 1.25 to keep the index
level fixed at 62.50.
In India we would have changed the base period
capitalization instead.
12,500,000
_________ x 100 = 62.50 ⇒ X = 20,000,000
X
106
Base Period…(Cont…)
composition.
107