-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathindex.html
310 lines (267 loc) · 8.13 KB
/
index.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2024-09-17 Tue 09:56 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Stock Market Indices</title>
<meta name="author" content="Matt Brigida, Ph.D." />
<meta name="generator" content="Org Mode" />
<link rel="stylesheet" type="text/css" href="https://fniessen.github.io/org-html-themes/src/readtheorg_theme/css/htmlize.css"/>
<link rel="stylesheet" type="text/css" href="https://fniessen.github.io/org-html-themes/src/readtheorg_theme/css/readtheorg.css"/>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
<script type="text/javascript" src="https://fniessen.github.io/org-html-themes/src/lib/js/jquery.stickytableheaders.min.js"></script>
<script type="text/javascript" src="https://fniessen.github.io/org-html-themes/src/readtheorg_theme/js/readtheorg.js"></script>
<script>
window.MathJax = {
tex: {
ams: {
multlineWidth: '85%'
},
tags: 'ams',
tagSide: 'right',
tagIndent: '.8em'
},
chtml: {
scale: 1.0,
displayAlign: 'center',
displayIndent: '0em'
},
svg: {
scale: 1.0,
displayAlign: 'center',
displayIndent: '0em'
},
output: {
font: 'mathjax-modern',
displayOverflow: 'overflow'
}
};
</script>
<script
id="MathJax-script"
async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">
</script>
</head>
<body>
<div id="content" class="content">
<h1 class="title">Stock Market Indices</h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#orgdb85e50">1. Price-Weighted Index (DJIA)</a></li>
<li><a href="#org645f318">2. Value-Weighted (S&P 500)</a>
<ul>
<li><a href="#orgc35221e">2.1. Index Creation</a></li>
</ul>
</li>
<li><a href="#org99161e3">3. Equal-Weight Indices</a></li>
</ul>
</div>
</div>
<p>
Here we'll take a look at price and value-weighted stock indices. Say our index covers two stocks (A and B) with the following number of shares outstanding.
</p>
<table id="org93b731e" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Stock</th>
<th scope="col" class="org-right">Shares Outstanding</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">A</td>
<td class="org-right">50</td>
</tr>
<tr>
<td class="org-left">B</td>
<td class="org-right">300</td>
</tr>
</tbody>
</table>
<p>
We'll consider the price of each stock over two days:
</p>
<table id="orga2a40c9" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Stock</th>
<th scope="col" class="org-right">Price Day 1 ($)</th>
<th scope="col" class="org-right">Price Day 2 ($)</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">A</td>
<td class="org-right">200</td>
<td class="org-right">190</td>
</tr>
<tr>
<td class="org-left">B</td>
<td class="org-right">30</td>
<td class="org-right">35</td>
</tr>
</tbody>
</table>
<div id="outline-container-orgdb85e50" class="outline-2">
<h2 id="orgdb85e50"><span class="section-number-2">1.</span> Price-Weighted Index (DJIA)</h2>
<div class="outline-text-2" id="text-1">
<p>
To construct a price-weighted index we can simply average the prices each day (sum them and here divide by 2). The only complication arises when a stock in the index splits. We don't want the split to affect the index value, so we adjust the divisor.
</p>
<p>
For example, say stock A splits on day 2. For the index value to stay the same, we have to make the divisor (d):
</p>
<p>
\[112.5=\frac{35 + 95}{d} \Rightarrow d = \frac{130}{112.5} = 1.1555\]
</p>
<p>
Obviously, in a price-weighted index
</p>
<blockquote>
<p>
The stock with the highest price has the largest effect on the index.
</p>
</blockquote>
<p>
This may be undesirable, depending on your use for the index, because a stock's price is not a meaningful value—a high price does not mean a large market cap.
</p>
<p>
A price weighted-index tracks:
</p>
<blockquote>
<p>
The performance of a portfolio comprised of one share of each stock in the index.
</p>
</blockquote>
<table id="orgad6edc8" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Day</th>
<th scope="col" class="org-right">Index Value</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-right">115</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-right">112.5</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-right">% Change</td>
<td class="org-right">-0.021739130</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org645f318" class="outline-2">
<h2 id="org645f318"><span class="section-number-2">2.</span> Value-Weighted (S&P 500)</h2>
<div class="outline-text-2" id="text-2">
<p>
A value-weighted index considers the market cap of a firm, rather than its price. This is a more reasonable measure than price. Note the market cap of a firm is not its total size (which is the enterprise value and includes debt).
</p>
<blockquote>
<p>
The stock with the highest market cap has the largest effect on the index.
</p>
</blockquote>
<p>
Generally, the larger your portfolio the more similar your portfolio weights for each stock will be to the weights in the market index. This is why the performance of large portfolios are compared to the market index (which is value-weighted).
</p>
<table id="orgcebe3d2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Day</th>
<th scope="col" class="org-right">Market Cap A</th>
<th scope="col" class="org-right">Market Cap B</th>
<th scope="col" class="org-right">Total Market Cap</th>
<th scope="col" class="org-right">Index Value</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-right">10000</td>
<td class="org-right">9000</td>
<td class="org-right">19000</td>
<td class="org-right">100</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-right">9500</td>
<td class="org-right">10500</td>
<td class="org-right">20000</td>
<td class="org-right">105.26316</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-right">% Change</td>
<td class="org-right"> </td>
<td class="org-right"> </td>
<td class="org-right"> </td>
<td class="org-right">0.0526316</td>
</tr>
</tbody>
</table>
</div>
<div id="outline-container-orgc35221e" class="outline-3">
<h3 id="orgc35221e"><span class="section-number-3">2.1.</span> Index Creation</h3>
<div class="outline-text-3" id="text-2-1">
<p>
To create a market-value index we choose some start date and starting value—commonly 100.
</p>
<p>
\(100*\frac{P_1}{P_0}\frac{P_2}{P_1}\frac{P_3}{P_2}\frac{P_4}{P_3}\frac{P_5}{P_4} = 100\frac{P_5}{P_0}\)
</p>
</div>
</div>
</div>
<div id="outline-container-org99161e3" class="outline-2">
<h2 id="org99161e3"><span class="section-number-2">3.</span> Equal-Weight Indices</h2>
<div class="outline-text-2" id="text-3">
<p>
There is a class of indices where each asset in the index has an equal weight in the index value. These indices are fairly unimportant.
</p>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Matt Brigida, Ph.D.</p>
<p class="date">Created: 2024-09-17 Tue 09:56</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>