复旦大学：《投资学讲义》（英文版） Chapter 9 Index and index fund

Index and index fund Fan longzhen

Index and index fund Fan Longzhen

Stock market index Stock market index is an indicator that is designed to reflect the performance of an entire market or a particular market segment Indexes have many uses in investments allow us to quickly and easily assess market performance --Serve as underlying securities for futures and options contracts help us evaluate the performance of fund managers; --facilitate "style analysis for mutual fund m-act as the basis for tracking-error portfolio strategies

Stock market index • Stock market index is an indicator that is designed to reflect the performance of an entire market or a particular market segment. • Indexes have many uses in investments: • --allow us to quickly and easily assess market performance; • --Serve as underlying securities for futures and options contracts; • --help us evaluate the performance of fund managers; • --facilitate “style analysis” for mutual funds; • --act as the basis for “tracking-error” portfolio strategies

Stock indices around the world Lock stock indices: Hang Seng index, Dow Jones Index standard and poor 500 index Nikkei 225 Index International indices: Ftse all-word index FTSE ASia index Investment style indices: Barra Large/ Mid/small cap value/growth. Russell 1000/2000/3000 value/growth Sector indices: Technology Telecom, consumer products, financial index

Stock indices around the world • Lock stock indices: Hang Seng index, Dow Jones Index, Standard and Poor 500 index; Nikkei 225 index. • International indices: FTSE all-word index; FTSE Asia index. • Investment style indices: Barra Large/ Mid/small cap value/growth. Russell 1000/2000/3000 value/growth. • Sector indices: Technology, Telecom, consumer products, financial index

Price-weighted index Price-weighted indexes Less common(e. g. Dow Jones, Nikkei 225 Determined by the average price of the stocks in the Index Stocks are equally weighted by price, i. e. 2P/divisor Where Pit=price of stock i at time t The divisor changes to reflect Changes in index composition Stock splits or stock dividends

Price-weighted index • Price-weighted indexes – Less common(e.g. Dow Jones, Nikkei 225) – Determined by the average price of the stocks in the index; – Stocks are equally weighted by price, i.e. where Pit=price of stock at time t. • The divisor changes to reflect – Changes in index composition; – Stock splits or stock dividends P divisor N i it / 1 ∑= i

Price-weighted index Example. Suppose you begin a price-weighted index of stocks a and b which have, respectively 0 and 100 shares outstanding stock a stock b total price divisor indexlevel 55110.111 0.11 6140.1140 stock a executes a 2-for-1 stock split find a new divisor such that the index level remains the same 100.071140

Price-weighted index • Example. Suppose you begin a price-weighted index of stocks A and B which have, respectively, 10, and 100 shares outstanding t stock A stock B total price divisor index level 0 4 6 10 0.1 100 1 5 5 11 0.1 110 2 6 7 12 0.1 120 3 8 6 14 0.1 140 4 6 10 0.071 140 stock A executes a 2-for-1 stock split find a new divisor such that the index level remains the same

Value-weighted index Value-weighted index More commonly used(e.g S&P 500, Hang Seng Index, NASDAQ, FTSE-100) To determine the index level, we weight each stock according to the ratio of its market value to total market value of all the stocks in the index Mv, is the total market capitalization of all n index stock n, is the number of shares outstanding for stock I at timet The divisor is set such that the base index level equal 100 The index level at time t is computed as The divisor changes whenever the index composition changes

Value-weighted index • Value-weighted index – More commonly used (e.g. S&P 500, Hang Seng Index, NASDAQ, FTSE-100) • To determine the index level, we weight each stock according to the ratio of its market value to total market value of all the stocks in the index – is the total market capitalization of all N index stock – is the number of shares outstanding for stock I at time t – The divisor is set such that the base index level equal 100; – The index level at time t is computed as – The divisor changes whenever the index composition changes ∑= = N i MVt nit Pit 1 MVt nt

Value-weighted index Example. Suppose you begin a price-weighted index of stocks a and b which have, respectively, 10, and 100 shares outstanding stock pric market value stock a stock B stock A stock b total price divisor index level 406006406.410 )7506411875 806006806.41106.25 stock a is removed for C which has 100 shares which has 100 shares(@S10 per share stock c stock c 1061006001160015.05910.25

Value-weighted index • Example. Suppose you begin a price-weighted index of stocks A and B which have, respectively, 10, and 100 shares outstanding t stock A stock B stock A stock B total price divisor index level 0 4 6 40 600 640 6.4 100 1 5 5 60 500 560 6.4 87.5 2 6 7 50 700 750 6.4 117.1875 3 8 6 80 600 680 6.4 106.25 stock C stock C 10 6 1000 600 1600 15.059 106.25 stock prices market value stock A is removed for C which has 100 shares which has 100 shares @$10 per share

Hang Seng Index Comprise 33 constituent stocks which are representative of the market The aggragte market capital ization of these stocks account for about 70% of the total market capitalization of the hong Kong stock market Select criteria Must be amon those that constitute the top 90% of the total market capitalization of all ordinary shares listed on the sehk(market capitalization is expressed as an average of the past 12 months. Must be among those that constitute the top 90% of the total turnover on the sehK Should normally have a listing history of 24 months Should not be a foreign company as defined by the sehK

Hang Seng Index • Comprise 33 constituent stocks which are representative of the market. The aggragte market capitalization of these stocks account for about 70% of the total market capitalization of the Hong Kong stock market. • Select criteria – Must be amon those that constitute the top 90% of the total market capitalization of all ordinary shares listed on the SEHK (market capitalization is expressed as an average of the past 12 months.) – Must be among those that constitute the top 90% of the total turnover on the SEHK. – Should normally have a listing history of 24 months. – Should not be a foreign company as defined by the SEHK

Free-float adjusted market capitalization MSCi and ftse globe indices Consider the proportion of shares outstanding that are deemed to be available for purchase in the public equity markets by international investors Limitations on free float available to international nvestors include Strategic and other shareholdings not considered part of available free float Limits on share ownership for foreigners

Free-float adjusted market capitalization • MSCI and FTSE globe indices • Consider the proportion of shares outstanding that are deemed to be available for purchase in the public equity markets by international investors. • Limitations on free float available to international investors include – Strategic and other shareholdings not considered part of available free float – Limits on share ownership for foreigners

Index funds Index funds are to replicate the performance of the sto ocK index Passive management-driven by risk management consideration rather than the objective of beating the market Index return always available at low cost Investors buying broad market exposure to earn risk premium Opportunity cost is potential for outperformance

Index funds • Index funds are to replicate the performance of the stock index • Passive management—driven by risk management consideration rather than the objective of beating the market. • Index return always available at low cost – Investors buying broad market exposure to earn risk premium; – Opportunity cost is potential for outperformance