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 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. 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 divisorP N i it / 1 ∑ = i 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 – 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 ititt PnMV 1 t MV t n 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 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 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 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 Development of index funds ? Vanguard Index Trust S&P 500 mutual funds in the U.S. – Offered in 1976 – Founder: John Bogle; – Biggest index fund; – Grew from less than $2 billion in assets to over $100 billion over 1990s ? In the U.S., inflows into equity index funds grow from $1.8 billion (14% of total equity fund inflows) in 1990 to $54.3 billion (28.9% of total equity fund inflows) in 1999 Mechanics of indexing ? Fully indexed fund – An index fund attempts to replicate a market index. It is relatively simple to create, once the index to be replicated has been identified. (Example: S&P500) ? Identify the index to be replicate (S&P500) ? Estimate the total market values of equity of the firms in the index ? Create a market-value weighted portfolio of stocks in the index ? This fund will replicate the index and is self correcting. It will need to be adjusted only if stocks enter or leave the index. Mechanics of indexing ? Sampled index fund: – Here, you sample an index because the index contains too many stocks like the Wilshire 5000 or it is too expressive to index the assets in a funds. – Cover each economic sector adequately. – Optimization ? Based on risk model. ? Risk exposures similar to index. Index fund management ? Stock index assumes that there is no cost associated with – Purchase and sales of stocks – Reinvestment of dividends and timing – Adjustment of the index portfolio in response to additions and deletions from the index ? Managing index fund – Have extra cash for redemption – Do not rush to buy and sell in response to index changes – Use futures and derivatives to lock in trades. Can active managers outperform the index? ? Yes, in index is based on the subset of securities; ? Some good securities could be outside the index; ? If active managers pick up good securities, they could outperform the index Can active managers outperform the index? ? No. if index is based on the universe of securities. ? Index performance=average gross performance of active managers (good and bad). ? Therefore, index performance>average net (after transaction cost) performance of active managers. Index fund fundamentalist John Bogle ? Investors should invest in low-cost index funds. The magnitudes of difference (of index over actively managed funds) are so large and so consistent as to devastate the concept of high cost active management. ? Implications are enormous.—If index fund proponents are correct, it will make actively managed funds unattractive. Beware of Index Fundamentalist Dylan Minor ? This issue may have a paradoxical conclusion: If Bogle is right, he will be wrong; and if he is wrong, he will be right. ? If more people become convinced that they can beat the market (Bogle is wrong), the more efficient the market becomes. Less likely they will outerperform it. ? If investor believe active management is a waste of money (Bogle is right), fund managers will be replaced by index funds, that will worsen the market efficiency. The remaining fund managers will have a better chance of outperforming the market. What is tracking error? ? Active return (alpha) – Average return on the portfolio-average return on the index ? Active risk(tracking error) – Expected volatility of the difference between the portfolio return and the index return. – Measured as the annualized standard deviation of these differential returns. Tracking error analysis ? An active manager expects to outperform his benchmark by 1.3% annualized with an active risk of 3.5%. What is the range of active return for the portfolio with a 68% probability? What about the range of the expected returns with a 95% probability. ? Active risk (σ)=3.5% ? Alpha( expected active return)=1.3% ? Range of active return: ? 68% probability: 1.3% 3.5%=(-2.2%, 4.8%) ? 95% probability: 1.3 2(3.5%) ± ± Tracking error analysis ? Indexes are widely used to be benchmark the performance of portfolio managers. The idea is that a skillful manager should be able to outperform a passive index that invested in stocks with similar risk characteristics. Consequently, portfolio managers often focus on the variance of their tracking error rather than the overall variance of returns. ?Let Rpt and Rit denote the return on the managers’ portfolio and the return on the index, respectively. We have ? Tracking error= Rpt-Rit ? That is, the tracking error is simply the deviation of the return on the manger’s portfolio from that on the index. Portfolio optimization using tracking error ? Similar to portfolio optimization using total return, we could do the portfolio optimization using tracking error. ? One possibility is to ? Minimize var(Rpt-Rit) ? Subject to E(Rpt-Rit)=target level of out performance