EquityIndexing.docx

1、EquityIndexingEquity IndexingThe term “efficient capital market” generally refers to pricing efficiency, or externally efficient.Pricing efficiency refers to a market where prices, at all times, fully reflect all available information that is relevant to valuation.When a market is price-efficient, p

2、ursuing investment strategies in an attempt to outperform a broad-based index will not consistently produce superior returns after adjusting for: Risk Transactions costsAvailable information sets: Only past prices All public information All public and private informationActive Portfolio Strategies t

3、ry to take advantage of “perceived” market inefficiencies. Fundamental Analysis Technical AnalysisPassive Portfolio Strategies try to take advantage of “perceived” market efficiencies. Buy and Hold IndexingOur Focus here is on Index Fund Management, commonly called IndexingIn an indexing approach, a

4、 fund manager does not try to identify under-priced securities or over-priced securities.Instead, the “indexer” invokes a trading strategy designed to create a portfolio that “mimics,” “replicates,” or “tracks” the performance of an index.The goal here is to show how an indexed portfolio is construc

5、ted and maintained.The motivation for indexing comes from capital market theory, i.e., the market or tangency portfolio. The portfolio is capturing market efficiency. Buy and hold may not capture market efficiency. Why?(Later, when we talk more about factor risks, you will see that one can use much

6、of this material there, as well.)Is the market efficient? Pockets of inefficiency exist. Difficult to outperform the market consistently after accounting for risk and transactions costs.Keep in mind, many professional money managers under-perform popular indexes, like the S&P 500. Also, see Table 14

7、.2 in Fabozzi. Bange and Miller (Working Paper)Selecting the Index (or Benchmark) Many broad-based and special indexes exist today Boutique funds require a specially constructed index Problems with the S&P 500 as a benchmarko Stocks selected by committeeo Not necessarily based on future performance

8、Constructing an Index-Replicating PortfolioTracking Error: The difference between the performance of the benchmark and the replicating portfolio.Performance is generally measured by the total return of the portfolio in question.Tracking Error = Total Return on Replicating Portfolio - Total Return on

9、 Benchmark PortfolioTracking Error can be positive or negative.The goal in Index-Replication is to have a tracking error of zero.Example: Tracking Error of the S&P 500. Tracking the S&P 500 with 50 stocks results in a tracking error of about 2.5% (annualized). Tracking the S&P 500 with 100 stocks re

10、sults in a tracking error of about 1.5% (annualized). Tracking the S&P 500 with 175 stocks results in a tracking error of about 1.0% (annualized).A Nettlesome Issue: Transactions Costs. The number of stocks included in the replicating portfolio affects transactions costs. Holding fewer than the numb

11、er of stocks in the replicating portfolio generates tracking error.Sources of Tracking Error Other than the Number of Stocks Odd-Lot Purchases are cumbersome (computer trading generally uses 100 shares). Rebalancing the portfolio generates transactions costs:o Market Impact, or liquidity, Risko Bid-

12、ask spreadso Brokerage commissionso TimingIn theory, rebalancing can be avoided if all stocks are held in the index, proportionate to their value in the benchmark (if the benchmark is value-weighted). Capital Weighted = Value WeightedBut, because of the odd-lot nature introduced by capital-weighting

13、, it is difficult to begin with a capital-weighted replicating portfolio.Benchmark Construction and the Replicating PortfolioThree basic weighting schemes:1. Capitalization-Weighting (AKA Value Weighting or Market-Value Weighting): Stocks held in proportion to their value in the Benchmark Portfolio.

14、a. Large-cap companies have more influence on the index, but are the most liquid.b. Therefore, under/over-weighting in the large-caps generates more tracking error. 2. Price Weighting: Equal number of shares invested in each stock, therefore, the price is the weight.a. The highest-priced stocks have

15、 the largest weight.b. Berkshire Hathaway3. Equal Dollar Weighting: Same dollar investment in each stock. a. The lowest-priced stocks have more influence.Weighting Schemes, In-Class Example, Data from 3/11/94 (Fabozzi, Pg. 258) Assume a $1,000,000 Replicating PortfolioValue-Weighting:Shares = $1,000

16、,000*Weight / PricePrice-Weighting(Shares = $1,000,000 / 334.50 = 2,990) Equal WeightingShares = $1,000,000*0.20 / PriceFactors that also influence weights (and therefore, rebalancing): There is a merger Company may be added to or deleted from the benchmark There might be a stock split or a stock di

17、vidend New stock may be issued Current stock may be repurchasedMethods to Construct a Replicating Portfolio Modified Capitalization Method. Assume 200 firms account for 85% of the value of the index. Value-weight these and equally weight the remainder. Stratified Method.o Define a factor by which th

18、e stocks making up the index may be classified. Typically: An industry Betao Suppose industry is chosen: Each company is assigned to an industry. Attempt to minimize residual risk by diversifying across industry sectors in the same proportion as the benchmark. Selection of stocks in each stratum? Qu

19、adratic Optimizationo Use a quadratic optimization procedure to generate a Markowitz efficient set.o That is, minimize risk given a return level. This is known as constrained optimization.o Recall that in mean-variance space, the efficient set is a parabola, which can be described by a quadratic equ

20、ation.Links to Active Equity Management “Enhanced” Indexing. Design a well-diversified portfolio that takes advantage of superior estimates of return.o Tilted Portfolio. Emphasizes a particular industry sector, performance factor, or economic factor: Tech Earnings momemtum Inflationo Use Index Futures to Enhance Returns (See Chapter 19). This involves identifying short-term instances when futures prices are underpriced relative to the index. Instead of buying more stock, buy synthetic stock using futures and an investment in T-bills.