Indices. 1 of 47 March 25, Christopher Ting

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1 Indices 1 of 47 March 25, 2017

2 Motivation Financial and economic indices have evolved into important multi-purpose tools that help investors track the investment performance estimate risk evaluate the performance of investment managers. Indices also form the basis for new investment products. Developing and providing indices can be a viable business Good starting point to learn portfolio management: construction and rebalancing 2 of 47 March 25, 2017

3 Uses of Market Indices Gauges of market sentiment Proxies for measuring and modeling returns, systematic risk, and risk-adjusted performance Proxies for asset classes in asset allocation models Benchmarks for actively managed portfolios Model portfolios for such investment products as index funds and exchange-traded funds (ETFs) 3 of 47 March 25, 2017

4 Major Companies in the Indexing Business S&P Dow Jones MSCI FTSE Russell 4 of 47 March 25, 2017

5 Introduction Define a security market index and explain how to calculate the price return and total return of an index for a single period and over multiple periods. Describe how indices are constructed and managed. Differentiate between price return and total return Discuss the use of market indices. Describe various types of indices. 5 of 47 March 25, 2017

6 What is an Index? In general, an index is a quantitative gauge that provides an eclectic, single-value summary of all endogenous and exogenous factors affecting and driving the state of a system. Example: Temperature Typically involving many constituent sub-systems Example: Dow Jones Industrial Average 6 of 47 March 25, 2017

7 Price! Price is an index! Reflects the forces of supply and demand through the market mechanism Efficient Market Hypothesis Prices already incorporate and reflect all relevant information about a company stock. 7 of 47 March 25, 2017

8 Index Construction and Management Which target market should the index represent? Which securities should be selected from that target market? How much weight should be allocated to each security in the index? When should the index be rebalanced? When should the security selection and weighting decision be reexamined? 8 of 47 March 25, 2017

9 Target Market Selection Defined broadly or narrowly? Other characteristics? Target market Based on an asset class? Based on an exchange? Based on geographic region? 9 of 47 March 25, 2017

10 Different Weighting Methods Market capitalization weighted Equally weighted Price weighted Index Fundamentally weighted 10 of 47 March 25, 2017

11 An Example of Price-Weighted Index The first stock index in the world is the Dow Jones Industrial Average, which was unveiled on May 26, 1896 The precursor of DJIA can be traced back to May 4, At the start, DJIA had only 12 component stocks. In 1916, DJIA had 20 stocks. From 1928, the number of component stocks is fixed at of 47 March 25, 2017

12 Dow Jones Industrial Average in Log Scale Source: Perspective.php 12 of 47 March 25, 2017

13 Another Example of Price-Weighted Index Nikkei 225 index is also price weighted, with some nuances to the par value. The Nikkei 225 index began on September 7, Retroactively could be back-calculated to May 16, of 47 March 25, 2017

14 Examples of Market-Cap Weighted Index S&P 500 Index MSCI Singapore Free Index Hang Seng Index Most if not all stock market indexes 14 of 47 March 25, 2017

15 Index Calculation: Price versus Market Cap Let P i be the price of a component stock and n i the number of its shares used for index calculation. I N i 1 D P i N is the total number of components. I N i 1 n P D is the divisor needed to scale the sum into a value called index I of an appropriate value. D i i 15 of 47 March 25, 2017

16 Index Construction: Price Weighted To construct a price-weighted index, buy the same number of shares for every component stock. If you buy 1 share of every stock, at inception or initially, D = N. The resulting I is the average price of N stocks Suppose you have $40,000 and you wan to construct a price-weighted portfolio with the following 4 stocks: Stock Name W X Y Z Price per Share $8 $12 $20 $24 Shares Issued 200, , , ,000 The number of shares, x, to buy for every stock is found by x ($8 + $12 + $20 + $24) = $40,000. Hence, x = $40,000/$64 = 625 shares 16 of 47 March 25, 2017

17 Tutorial Question For the example in the previous slide, if you want the price-weighted index to be equal to $16, what should be the value of the divisor? 17 of 47 March 25, 2017

18 Index Construction: Price versus Market Cap To construct a market-cap-weighted index, compute the market cap of every component stock sum up N market caps. for every stock, divide its market cap by the total market-cap to obtain its fraction of contribution. Then apportion the fund according to the fraction. Use the apportioned fund to buy the number of shares at the price with which its market cap is computed. Stock Name W X Y Z Price per Share $8 $12 $20 $24 Shares Issued 200, , , ,000 Market Cap $1,600,000 $3,720,000 $12,040,000 $2,640,000 Weight 2/25 1/5 3/5 1/8 18 of 47 March 25, 2017

19 Tutorial Questions Given $40,000, how many shares are to be bought in order to construct a market-cap-weighted portfolio? The amount apportioned to Stock W is (2/25) $40000 = $3,200. With this money, you can buy 3200/8 = 400 shares. Do likewise for Stocks, X, Y, and Z. If you want the market cap to start at 100 at inception, what should the divisor D be? 19 of 47 March 25, 2017

20 Equal Weight Give the same weight to every component stock by having the same dollar amount to buy every stock. With $40,000 and 4 stocks, we allocate $10,000 for each stock How many shares do you buy for every component stock? If you want your index to start at 100, what should the divisor be? 20 of 47 March 25, 2017

21 Factor-Weighted Index In a way, the ubiquitous market cap weighted index is based on the size factor. One can use earnings, for example, to decide the weight for constructing the index. Consider two stocks, A and B Stock A Earnings = 20 Market cap = 200 Market cap weight = 20% Fundamental weight = 40% Stock B Earnings = 30 Market cap = 800 Market cap weight = 80% Fundamental weight = 60% 21 of 47 March 25, 2017

22 Weighting Schemes During Construction How much fund out of the total is allocated? Price weighted w P i N P i1 i P Equally weighted i Market capitalization weighted w M i N j1 n P n i is the number of shares of shares of constituent security i. i n Factor weighted j i P j 1 w E i N 22 of 47 March 25, 2017 w F i N F j1 i F j

23 Very Important After the index is constructed, i.e., the number of shares for each component stock has already been fixed, the index calculation is now based on the shares and not on the weights anymore. For equally weighted index, the weights will become unequal, and the index becomes unequally weighted. Regular rebalancing is needed to make it equally weighted again. Likewise, the factor based index needs to be rebalance to better reflect changes in the factor. But for price- and market-cap-weighted indices, you don t have to, if the component stocks don t change. 23 of 47 March 25, 2017

24 Myth of Using Weight for Market Cap Index Calculation Many people misunderstood that to calculate the market-cap-weighted index even after its inception, you must use the weights of the components. This is wrong! The weights are the results, not the starting data for index calculation. The weight changes as soon as any of the component stock price changes! 24 of 47 March 25, 2017

25 Advantages and Disadvantages Price weighted Equally weighted Market capitalization weighted Fundamentally weighted Simple High price stocks have greater impact Stock splits necessitate a change in divisor Simple Under- and overrepresentation Frequent rebalancing Securities held in proportion to their market value Similar to a momentum strategy Ensures a value or contrarian tilt Data intensive 25 of 47 March 25, 2017

26 Real World Example: Singapore MSCI Index The MSCI Singapore Free Index is a free-float adjusted market capitalization weighted index that is designed to track the equity market performance of Singapore securities listed on Singapore Stock Exchange. The MSCI Singapore Free Index is constructed based on the MSCI Global Investable Market Indexes Methodology targeting a free-float market capitalization coverage of 85%. The index has a base date of December 31, ance.html 26 of 47 March 25, 2017

27 Reconstitution Change constituent securities? Reconstitution date Beginning index Reconstituted index 27 of 47 March 25, 2017

28 Equity Indices Broad market Wilshire 5000 Total Market Index Equity indices Multimarket Sector Style MSCI Emerging Markets GSTI Semiconductor Index Dow Jones U.S. Small-Cap Value Index 28 of 47 March 25, 2017

29 Challenges Facing Fixed Income Index Construction Number of securities Illiquid securities Lack of pricing data 29 of 47 March 25, 2017

30 Dimensions of Fixed-Income Indices Market Global Regional Country or currency zone Type Corporate Collateralized Securitized Mortgagebacked Government agency Government Maturity Credit quality For example, 1 3, 3 5, 5 7, 7 10, 10+ years; short-term, medium-term, or long-term For example, AAA, AA, A, BBB, etc.; Aaa, Aa, A, Baa, etc.; investment grade, high yield 30 of 47 March 25, 2017

31 Indices for Alternative Investments Commodities Real estate Indices for alternative investments Hedge funds 31 of 47 March 25, 2017

32 Commodity Indices Risk-free interest rate Changes in futures prices Commodity index return Roll yield 32 of 47 March 25, 2017

33 Real Estate Indices Appraisal indices Repeat sales indices Real estate investment trust (REIT) indices Ownership of properties Investment in mortgages 33 of 47 March 25, 2017

34 The FTSE EPRA/NAREIT Global REIT Index Family Source: FTSE International, FTSE EPRA/NAREIT Global & Global Ex US Indices (Factsheet 2009). 34 of 47 March 25, 2017

35 Hedge Fund Indices Hedge funds are private investment vehicles that typically use leverage and long and short investment strategies. Research organizations maintain databases of hedge fund returns and summarize these returns into indices. Most indices reflect performance on a broad global level or on a strategy level. Most hedge fund indices are equal weighted. 35 of 47 March 25, 2017

36 Source: 36 of 47 March 25, 2017

37 Problems Caused by Voluntary Reporting Voluntary investment performance Survivorship bias Indices reflect different performances for the same time period 37 of 47 March 25, 2017

38 Description of a Security Market Index Constituent securities Security market index Price return index Total return index 38 of 47 March 25, 2017

39 Value of a Price Return Index N i1 VPRI V PRI = the value of the price return index n i = the number of units of constituent securities in the index N = the number of constituent securities in the index P i = the unit price of constituent security i D = the value of the divisor n D i P i 39 of 47 March 25, 2017

40 Calculation of Single-Period Price Return PR I V PR I1 V V PRI 0 PRI 0 N N i1 w ipr i w i i1 i1 Pi 0 P P i0 PR I = the price return of index portfolio I PR i = the price return of constituent security i w i = the weight of security i P i1 = the price of constituent security i at the end of the period P i0 = the price of constituent security i at the beginning of the period 40 of 47 March 25, 2017

41 Security Example of Single-Period Price Return Beginning of Period Price ( ) V V PRI 0 PRI1 PR I Ending of Period Price ( ) Dividends per share ( ) (20010) (100 25) (40015) (20012) (100 24) (40018) % Shares Outstanding LMN OPQ RST Divisor = of 47 March 25, 2017

42 Calculation of Single-Period Total Returns TR I V PRI1 V V PRI 0 PRI 0 Inc I TR I N N 1i 0i w itr i w i i1 i1 P0 i P P Inc i TR I = the total return of the index portfolio Inc I = the total income from all securities in the index TR i = the total return of the constituent security i Inc i = the total income from security i 42 of 47 March 25, 2017

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44 Calculation of Single-Period Total Return Security Beginning of Period Price ( ) Ending of Period Price ( ) Dividends per share ( ) Shares Outstanding LMN OPQ RST Divisor = 100 Inc I [( ) ( ) ( )] TR I % 44 of 47 March 25, 2017

45 Index Values over Multiple Time Periods Calculation of index values over multiple time periods requires geometrically linking the series of index returns. V V PRIT TRIT V V PRI 0 TRI 0 1 PR 1 PR 1 PR I1 1 TR 1 TR 1 TR I1 I 2 I 2 IT IT 45 of 47 March 25, 2017

46 Calculation Example For an index with an inception value set to 1,000 and price returns of 5 percent and 3 percent for Periods 1 and 2 respectively, the values of the price return index would be calculated as follows: Period Return (%) Calculation Ending Value 0 1,000(1.00) 1, ,000(1.05) 1, ,000(1.05)(1.03) 1, of 47 March 25, 2017

47 Summary Price return index Total return index Choices in index construction and management Advantages and disadvantages of different weighting schemes Rebalancing and reconstitution Uses of market indices Equity, fixed income, and alternative investment indices 47 of 47 March 25, 2017