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Stock Market IndexesStock Market Indexes
If we want to know how the stockmarket did today, what should we
look at?
The Dow Jones Industrial
Average? The S! "## Index? The $asda% &om'osite Index?
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(hat (e $eed to )now to(hat (e $eed to )now to*nderstand an Index*nderstand an Index The num+er of stocks in the
index
The ty'es of stocks in the index
The weighting method used tocalculate the index value
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!rice (eighting!rice (eighting
Start +y calculating the average 'rice-arithmetic
mean. of the stocks in the index at time
t
$
Index valuet / ∑ !i,t divided +y $
i / 0
where the stocks in the index at time t go from 0 1 $
3
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!rice (eighting2 An!rice (eighting2 An
3xam'le3xam'le Price Price
Stock Day 1 Day 2 Shrs
Out. A 40## 400# 0##,###
5 4 0# 4 0# 0,###,###
$ote that the market ca' of each stockis 40# million on Day 0
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!rice (eighting2 An!rice (eighting2 An
3xam'le3xam'leIndex 6alue0 / -0## 7 0#.89 / ""Index 6alue9 / -00# 7 0#.89 / :#
; &hange Index / -:# < "".8"" /=0;
A 0#; increase in the 'rice of stockA caused a =0; increase in theindex
5
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(hat if Instead(hat if Instead
Price Price
Stock Day 1 Day 2 SharesOut.
A 40## 40##0##,###
5 4 0# 4 000,###,###
6
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3xam'le -cont.3xam'le -cont.
Index 6alue0 / -0## 7 0#.89 / ""
Index 6alue9 / -0## 7 00.89 / """
; &hange in Index / -""" < "".8""/ =0;
A 0#; increase in the 'rice of stock5 caused a #=0; increase in theindex
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!rice (eighting!rice (eightingStock A>s !rice is 0# times higher so
it gets a 0# times larger weighting
5ut +oth com'anies are the samesie
Stock 'rices can +e altered +ychanging shares outstandingthrough s'lits and re'urchases
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!rice (eighting2 Another!rice (eighting2 Another3xam'le3xam'le Price Price
Stock Day 1 Day 2 SharesOut
A 40## 4 "" 9##,###
5 4 0# 4 0# 0,###,###
!rice of Stock A goes u' to 400# on day 9,
and at the close of trading, it has a 9
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!rice (eighting Index!rice (eighting Index
Index 6alue0 / -0## 7 0#.89 / ""
Index 6alue9 / -"" 7 0#.89 / @9"
; &hange / -@9" < "".8"" / < #=;
The index is down, +ut stock Agained 0#; and stock 5 wasunchanged
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The Solution2 AdBust the The Solution2 AdBust the
DivisorDivisorAdjust the Divisor so that the indexgives us the value it would have hadwithout the split:
5efore the S'lit, the index would have +een2
00# 7 0# / 09# and 09#89 / !
After the S'lit, sum of 'rices Day 9 / "" 70#/ :" :"8-adBusted divisor. / :#
AdBusted Divisor / 0#C@@@@
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The AdBusted Divisor The AdBusted Divisor
rom now on, we need to add the 'rices of thestocks in the index and divide +y the adBusteddivisor to get the index value
(e continue to use this adBusted divisor untilanother stock s'lits, or until one of the stocksin the index is re'laced, or if there is a s'ins 'rice
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!rice (eighting!rice (eighting
Do any maBor indexes use a !rice(eighting System?
Fes
The Dow Jones IndustrialAverage does
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DJIA2 GistoryDJIA2 Gistory
htt'288wwwdBindexescom8mdsidx8?event/showAverages
Hldest +arometer of the stockmarket!rice (eighted IndexStarted in 0C=: +y &harles Dow
with 09 stocks -Ge and Jonesstarted Dow Jones &om'any.3 is the only original stock still in
the index 14
http://www.djindexes.com/mdsidx/?event=showAverageshttp://www.djindexes.com/mdsidx/?event=showAverageshttp://www.djindexes.com/mdsidx/?event=showAverageshttp://www.djindexes.com/mdsidx/?event=showAverages
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DJIA2 &om'ositionDJIA2 &om'osition
Today, there are @# &om'anies
e'resent a+out @#; of the
market value of *S Stocks
9K stocks trade on the $FS3@ stocks -MST, I$T&, and &S&H.
trade on $ASDAL
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DJIA2 &om'ositionDJIA2 &om'osition
As of Jan 0, 9#0#2@M, Alcoa, American 3x'ress, ATT,
5ank of America,5oeing, &ater'illar,
&hevron, &isco, &oca
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DJIA2 &om'ositionDJIA2 &om'osition
Gow are the rms in the indexselected?
3ditors of the Dow Jones
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Hther Dow JonesHther Dow Jones!rice (eighted Indexes!rice (eighted Indexes
Trans'ortation -9# rms.
*tilities -0" rms.
&om'osite -:" rms.
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DJIA2 Index 6alueDJIA2 Index 6alue
Su''ose the Dow closes at0#,"C="#
Gow did they arrive at this value?
@#
∑ !i,t
i / 0
DJIA Indext /
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Market &a' (eightedMarket &a' (eighted
IndexesIndexes Market &a'italiation / Market
6alue
D"#$%$&$O%:
Nshares outstanding O !rice 'erShare
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Index 6alueIndex 6alue tt n
∑ -! i,t . x -NHut Shrsi,t .
i / 0
Indext /
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Index 6alueIndex 6alue tt
t indexes days+ is the +ase dayi indexes stocks
5ase day value needs to +ear+itrarily set to something +y
the rm starting the index 0# or0## are common
22
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5ack to 3xam'le2 &ase 05ack to 3xam'le2 &ase 0
Price Price
Stock Day 1 Day 2 SharesOut.
A 40## 400# 0##,### 5 4 0# 4 0# 0,###,###
Again, note that each stock has thesame market value on day 0
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Market 6alue 3xam'le 1Market 6alue 3xam'le 1
Day 0Day 0Index 6alue0 /
-0##.-0##,###. 7 -0#.-0,###,###.
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Market 6alue 3xam'le 1Market 6alue 3xam'le 1
Day 9Day 9Index 6alue9 /
-00#.-0##,###. 7 -0#.-0,###,###.
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Market 6alue 3xam'leMarket 6alue 3xam'le
; &hange /-0#" < 0##.80## / "#;
$HT32 a0#; increase in Stock Acaused a
"; increase in the index
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(hat if InsteadP&ase 9(hat if InsteadP&ase 9
Price Price SharesStock Day 1 Day 2Outstanding
A 40## 40## 0##,### 5 4 0# 4 00 0,###,###
Instead of stock A going u' +y 0#;,stock 5 does
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3xam'le -cont.3xam'le -cont.
Index 6alue9 /
-0##.-0##,###. 7 -00.-0,###,###.
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(hat if a stock s'lits?(hat if a stock s'lits?
Price Price Stock Day 1 Day 2 ShrsOut
A 40## 4 ""9##,###
5 4 0# 4 0#0,###,###
Stock A goes u' to 400# and then hasa 9
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Market 6alue 3xam'leMarket 6alue 3xam'le
Index 6alue9 /
-"".-9##,###. 7 -0#.-0,###,###.
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Market 6alue 3xam'leMarket 6alue 3xam'le
; &hange /-0#" < 0##.80## / "#;
Since stocks A and 5 have thesame market value, they receivethe same weight in the index
(hat indexes use this weightingsystem?
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S! "##S! "##
htt'288www9standardand'oorscom8'ortal8site8s'8en8us8'ageto'ic8indicesQ"##89,@,9,9,#,#,#,#,#,9,0,#,#,#,#,#html
Most famous market
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S! "##S! "##
0=9C was S! =# In 0="K it+ecame S! "##
Is used +y =K; of *S moneymanagers and 'ension 'lans'onsors as a 'roxy for the *S
stock market
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S! "##S! "##
Stocks are selected to includeleading com'anies in leadingindustries in the *S*S rms only, though some non<
*S rms are grandfathered intothe index&hanges are made every cou'le of
weeks or soStandard and !oors -a division ofMcraw
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Hther M6 (eightedHther M6 (eighted
IndexesIndexes
%'S" (o)posite2 All $FS3stocks
%ASDA* (o)posite2 All stockslisted on $ASDAL -oughly @,###stocks.
+ilshire ,!!!: All stocks tradedin the *nited States
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Hther M6 (eightedHther M6 (eighted
IndexesIndexes
(ilshire "##2 (ilshire "###stocks with the S! "## stocks
removed
S! ##2 A mid
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Hther M6 (eightedHther M6 (eighted
IndexesIndexes-ussell $ndexes: *S Stocks from
$FS3, AM3O, and $asda%
htt'288wwwrussellcom8indexes
-ussell !!!2 @### largest *S rms
-ussell 2!!!2 9### smallest of ussell@###
-ussell 1!!!2 0### largest of ussell@###
37
http://www.russell.com/indexeshttp://www.russell.com/indexes
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International IndexesInternational Indexes
$nternational "/uity $ndexes2MS&I (orld Index2
Maintained +y Morgan Stanley
0"## stocks from 9@ countries
Hnly com'anies from develo'ed countriesUmarket value weightedlo+al Dow2 0"# stocksU +oth develo'ed
and emerging countries -+ut #; from*S.U unweighted
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*nweighted Indexes*nweighted Indexes
3ach stock receives the sameweight
Indexes done either witharithmetic or geometric averages
of ; changes in stock 'rices
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5ack to 3xam'le2 &ase 05ack to 3xam'le2 &ase 0
Price PriceStock Day 1 Day 2Shares Out.
A 40## 400#0##,###
5 4 0# 4 0#
0,###,###
40
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3xam'le3xam'le
Stock A increased 0#; in 'riceand Stock 5 had a 'rice changeof #;
Assume a starting index value of0## on day 0, so Index 6alue0 /
0##
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3xam'le3xam'le
0sing Arith)etic ean2Average ; &hange / -0#7#.89 /
";
Since the stocks in the index wentu' +y an average of ";, the indexmust go u' +y ";
Index 6alue9 / 0## O 0#" / 0#"
*sed in academic studies
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3xam'le3xam'le
0sing eo)etric ean2Average ; &hange
V-00#.-0#.W089 < 0 / CC;
Index 6alue9 / 0## O 0#CC /
0#CC
*sed +y 6alue Xine
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Index und ormationIndex und ormation
Price +eighted: 3%ual num+erof shares of each stock
arket 3alue +eighted2 Investin 'ro'ortion to marketca'italiation
0nweighted2 3%ual dollaramount in each stock
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$)plications o4$)plications o4
SkewnessSkewnessSu''ose there are only stocks in our
world2
(, O, F Y
W has a 300% return
X has a 25% return
Y has a 5% return
Z has a - 20% return
45
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$)plications o4$)plications o4
SkewnessSkewness(hat if you invested the same amount of
money in each stock?
!ortfolio eturn2
9"-@##;. 7 9"-9";. 7 9"-";. 7 9"-
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$)plications o4$)plications o4
SkewnessSkewness Many indexes have skewed returns Often get a narrow arket!
"trong returns for an index ay #e $riari%y due to one or two industries
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$)plications o4$)plications o4
SkewnessSkewness &or any $ri'e(weighted or va%ue(weighted
index) as a sto'k*s $ri'e goes u$ +re%ative toother sto'ks, it re'eives a higher weighting inthe index!
-his eans that if there is a .#u##%e/ in onese'tor) the index wi%% ti%t ore heavi%y towardthe sto'ks in that se'tor!&or those who invest in the index) it eans
$%a'ing a greater weight on those sto'ks whi'hhave gone u$ in $ri'e the ost!s that good or #ad