Investments and Portfolio Management WEEK 5 1

Introducing Market Indexes Objectives : Discuss the major uses of indexes Determine what causes indexes to differ Evaluate the major indexes and their characteristics Evaluate the relationship between indexes 2

What is an Index? An index tracks the value of a basket of shares (or other securities) over time. It does not actually have ownership of the shares within it. The “basket” will typically include companies of a similar size, location or industry. E.g. FTSE100 is a large-cap index of UK listed securities. They can also be used to track shares suggested for a particular investment strategy; growth, balanced or income. A share can be included in more than one index. 3

Uses of Security-Market Indexes To provide a benchmark for the performance of individual portfolios The benchmark can be used to judge the performance of asset managers 1 The creation of index funds where a portfolio tracks the performance of an index over time Index funds exist for common stock (equity) and bonds 2 To examine factors that influence aggregate market returns This allows performance comparison of different asset classes 3 For ‘technicians’ to predict future price movements based upon past index performance Is the past a good predictor of the future? 4 As a substitute for the market portfolio of risky assets when calculating the required return of an asset 5 ke=rf + β(rm – rf) 4

Factors Affecting Market Indexes The Sample – size, breadth and source Weighting of Sample Members Price weighted index Market cap weighted index Equally weighted (or un-weighted) index Fundamental weighted index based on operating variables, e.g. sales, ROE Computational procedure Arithmetic mean Geometric mean 5

Price-weighted Index Simple ‘Arithmetic Mean’ of current stock prices This means that index movements are influenced by the differential prices of the components E.g. Dow Jones Industrial Average (DJIA) DJIA is made up of 30 large, well known industrial stocks (blue chip stocks) The divisor may need to be adjusted to maintain the index value after changes in the sample over time, e.g. a stock split (bonus issue in the UK) 6

Wall Street Journal - DJIA 7 Company Price Change % Change Volume Time (ET) Microsoft Corp 38.16 +0.80 +2.13% 44,957,611 20:10:00 Home Depot Inc/The 77.60 +1.42 +1.86% 7,065,617 20:04:08 Walt Disney Co/The 68.97 +1.20 +1.77% 5,691,005 20:04:05 Pfizer Inc 31.87 +0.49 +1.56% 27,179,902 20:04:06 UnitedHealth Group Inc 71.01 +1.06 +1.52% 3,880,757 20:04:07 NIKE Inc 77.85 +0.98 +1.27% 2,401,072 Cisco Systems Inc 24.00 +0.27 +1.12% 75,234,897 Travelers Cos Inc/The 87.22 +0.78 +0.90% 2,081,857 Procter & Gamble Co/The 83.50 +0.70 +0.85% 7,582,173 Visa Inc 199.78 +1.51 +0.76% 2,050,456 Intel Corp 24.60 +0.17 +0.70% 22,990,316 Boeing Co/The 133.17 +0.84 +0.63% 3,578,750 Coca-Cola Co/The 40.12 +0.24 +0.60% 11,771,162 American Express Co 81.44 +0.41 +0.51% 2,828,191 McDonald's Corp 98.11 +0.45 +0.46% 4,164,823 Caterpillar Inc 84.20 +0.35 +0.42% 3,953,342 General Electric Co 27.15 +0.10 +0.37% 34,393,647 JPMorgan Chase & Co 54.14 +0.31% 22,121,852 International Business Machines Corp 183.55 +0.48 +0.26% 4,711,276 Wal-Mart Stores Inc 78.90 +0.19 +0.24% 8,289,973 3M Co 128.59 +0.23 +0.18% 2,426,280 Chevron Corp 120.09 +0.09 +0.08% 6,214,448 Goldman Sachs Group Inc/The 162.94 +0.05 +0.03% 3,398,763 United Technologies Corp 107.46 +0.01 +0.01% 2,797,564 Exxon Mobil Corp 92.59 -0.08 -0.09% 9,285,719 Johnson & Johnson 93.34 -0.22 -0.24% 8,954,791 AT&T Inc 35.07 -0.10 -0.28% 22,332,041 Verizon Communications Inc 49.99 -0.17 -0.34% 10,915,592 Merck & Co Inc 47.34 -0.25 -0.53% 14,162,665 EI du Pont de Nemours & Co 60.94 -1.11 -1.79% 6,692,518

What is the new index value? The adjusted divisor Assume the price-weighted index consists of three stocks, A, B, and C. Stock A issues a 3-for-1 stock split, i.e. if you hold 1 share you will receive an additional 2 shares to end up with 3 shares. Stock Price Before Issue Price After Issue A 30 10 B 20 20 C 10 10 Index 60 / 3 = 20 Divisor 3 3 What is the new index value? 8

If the divisor were not adjusted…. Stock Price Before Issue Price After Issue A 30 10 B 20 20 C 10 10 Index 60 / 3 = 20 40 / 3 = 13.33 Divisor 3 3 Note: Whilst the price of Stock A has reduced to a third of the original price there are now 3 times the number of shares in issue. Therefore, the total market value of the shares remains the same. Yet the value of the index has fallen from 20 to 13.33?! This cannot be correct, therefore we need to change the divisor. 9

With an adjusted divisor Note: If the total market value remains the same after a stock split then the index should not change. Stock Price Before Issue Price After Issue A 30 10 B 20 20 C 10 10 Index 60 / 3 = 20 40 / X = 20 Divisor 3 X=2 The divisor is only changed when there is a change in the sample make-up of the index: it started at 30 in 1896 but as at 11.03.2016 stands at 0.14602128057775 10 Wall Street Journal - DJIA

Price weighted Index – Effect of differently priced shares The index is price weighted, therefore a stock with a high price carries more weight than one with a low price Case A = 10% increase in share price of A Case A Period T (T+1 week) A 100 110 B 50 50 C 30 30 Sum 180 190 Divisor 3 3 Index 60 63.3 Percentage Change 5.5% 11

Price weighted Index – Impact of differently priced shares Case B = 10% increase in share price of C Case A Case B Period T (T+1 week) (T+1 week) A 100 110 100 B 50 50 50 C 30 30 33 Sum 180 190 183 Divisor 3 3 3 Index 60 63.3 61 Percentage Change 5.5% 1.7% A change in a higher priced stock will have a greater impact on a price-weighted index than a similar change in a lower priced stock 12

DJIA Criticism of the DJIA 30 non-randomly selected blue chip stocks not representative of the market Stock splits reduce share price distorting weight in the index Stock splits mean constant revisions of the divisor 13

Market cap weighted Index Derive the initial total market value of all stocks used in the series Market Cap = Number of Shares Outstanding * Current Market Price E.g. S&P500, FTSE100 S&P uses only freely floating shares (excluding those held by insiders) Assign a beginning index value (typically 100) and new market values are compared to the base index 14

Market Cap Weighted Index where: Index t = index value on day t Pt = ending prices for stocks on day t Qt = number of outstanding shares on day t Ph = ending price for stocks on base day Qh = number of outstanding shares on base day 15

Market Cap Weighted Index example Stock share price(£) number of shares Market Value 31/12/2012 (£) A 10 1,000,000 10,000,000 B 15 6,000,000 90,000,000 C 20 5,000,000 100,000,000 Base value equal to an Index of 100 200,000,000 16

Market Cap Weighted Index example B – Issue a two-for-one stock split during the year = 6,000,000 x 2 = 12,000,000 = £15 / 2 = £7.50 Stock share price(£) number of shares Market Value 31/12/2013 (£) B 7.50 12,000,000 90,000,000 17

Market Cap Weighted Index example After the changes: Stock share price(£) number of shares Market Value 31/12/2013 (£) A 10 1,000,000 10,000,000 B 7.50 12,000,000 90,000,000 C 20 5,000,000 100,000,000 Index remains at 100 200,000,000 In a market cap weighted index there is an automatic adjustment for stock splits as a decrease in stock price is offset by an increase in the number of shares. 18

Market Cap Weighted Index example 2 Now let’s assume that the stock of B remains in demand after the capital change leading to increased prices Stock share price(£) number of shares Market Value 31/12/2013 (£) A 12 12,000,000 B 10 C 20 5,500,000 Calculate the new index as at 31.12.2013 19

Market cap weighted Index example 2 After the changes: Stock share price(£) number of shares Market Value 31/12/2013 (£) A 12 1,000,000 12,000,000 B 10 120,000,000 C 20 5,000,000 100,000,000 232,000,000 New Market Cap Market cap weighted index = Beginning index value Original Market Cap 20

Market cap weighted Index example 3 Base Value Price A increase by 20% Price C increase by 20% Stock number of shares Price Market Value 31.12.2012 31.12.2013 A 1,000,000 10 10,000,000 12 12,000,000 B 6,000,000 15 90,000,000 C 5,000,000 20 100,000,000 24 120,000,000 200,000,000 202,000,000 220,000,000 100 101 110 Price changes in large market value stocks will influence the index to a greater degree than those with smaller market values. 21

Equally-Weighted Index (un-weighted) All stocks carry equal weight regardless of price or market value May be used by individuals who randomly select stocks and/or invest the same amount in each stock Typically use arithmetic mean of the percentage price changes for the stocks in the index The FT30 Share Index uses a geometric mean of the holding period returns 22

Equally-Weighted Index example Base Value Price increases Stock number of shares Price Market Cap Percentage change 31.12.2012 31.12.2013 A 1,000,000 10 10,000,000 15 15,000,000 50.0% B 6,000,000 90,000,000 20 120,000,000 33.3% C 5,000,000 100,000,000 22 110,000,000 10.0% 200,000,000 245,000,000 93.3% Index value 100 100x1.311 = 131.1 93.3/3 = 31.1 Market cap weighted index would be (245/200)x100 = 122.5. 23

Global Equity Indexes Stock market indexes found in most individual foreign markets Local therefore difficult to compare due to different samples, weighting and computation To overcome this some investment data firms have created consistent stock indexes to allow comparison 24

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FT/S&P-Actuaries World Indexes Jointly compiled by The Financial Times Limited, Goldman Sachs & Co., and S&P’s in conjunction with the Institute of Actuaries and the Faculty of Actuaries Measures 2,271 securities in 30 countries Covers 70% of the total value of all listed companies in each country Securities included must allow direct holdings of shares by foreign nationals Index is market cap weighted with a base date of December 31, 1986 = 100 Index results are reported in U.S. dollars, U.K. pound sterling, Japanese yen, and the local currency of the country included 26

Morgan Stanley Capital International (MSCI) Indexes Include over 1,500 companies listed on stock exchanges in 22 countries with a combined capitalization representing approximately 60 percent of the aggregate market value of the stock exchanges of these countries All the indexes are market cap weighted Reporting is in U.S. dollars and the country’s local currency http://www.msci.com/products/indices/tools/ 27

Dow Jones Wiltshire Global Indexes Introduced in January 1993 2,200 companies worldwide Organized into 120 industry groups Includes 33 countries representing more than 80 percent of the combined capitalisation of these countries Countries are grouped into three major regions: Asia/Pacific, Europe/Africa, and the Americas Each country’s index is calculated in its own currency as well as in the U.S. dollar 28

Summary Indexes track the value of a basket of shares over time. There are different ways of weighting and computing the value; price-weighted, market cap weighted and equally-weighted, using arithmetic or geometric means. The method used will determine how much influence the change in the price of one share has on an index. Given the different methods, indexes tend to be difficult to compare. For this reason, investment companies create global indexes 29

Reading The slides for this week’s lecture have been based on: Reilly, F. K. and Brown, K. C. (2012) Analysis of Investments and Management of Portfolios, 10th edition, Cengage Learning – Chapter 5 Stafford Johnson, R. (2014), Equity Markets and Portfolio Analysis, John Wiley & Sons – Chapters 1 & 5 Other sources: http://www.londonstockexchange.com/exchange/prices-and-markets/stocks/indices/ftse-indices.html http://money.cnn.com/data/afterhours/ http://www.bloomberg.com/markets/stocks/world-indexes/ http://markets.ft.com/research/Markets/Equity-Indices http://quotes.wsj.com/index/DJIA 30

Useful Bloomberg Functions SECF <GO> and in ‘category’ select ‘index/stats’. Select whichever tab you want and can search on various fields. Clicking on the selected index will take you to a menu offering such functions as: MEMB <GO> Member weightings GP <GO> Price graph COMP <GO> comparative returns of different indexes WEI <GO> world equity indexes 31

Useful Bloomberg Functions SECF <GO> ‘S&P 500’ followed by COMP <GO>, added FTSE 100 as a comparator. Note that I selected different currencies. 32

Useful Bloomberg Functions Now I have included the FTSE 100 both in GBP and USD. The yellow line is in USD. i.e. the pound has weakened against the dollar so the value in USD has dropped more than the value in GBP In GBP In USD 33

Useful Bloomberg Functions MEMB <GO> ‘UKX’ sorted by industry (one industry expanded to show data) 34 Note: UKX is FTSE 100 index