Portfolio Theory and Financial Engineering

1
Portfolio Theory and Financial Engineering

• FIN 428
• Lecture Three Index Funds and Passive Portfolio
  Management
• Tuesday, January 16, 2007

2
Uses of Security-Market Indexes

• As benchmarks to evaluate the performance of
  professional money managers
• To create and monitor an index fund
• To measure market rates of return in economic
  studies
• For predicting future market movements by
  technicians
• As a substitute for the market portfolio of risky
  assets when calculating the systematic risk of an
  asset

3
Construction of Market Indices

• Weighting schemes
• price-weighted series
• value-weighted series
• unweighted (equally weighted) series

4
Price Weighted Indices

• Dow Jones Industrial Average
• Best-known, oldest, most popular series
• Price-weighted average of thirty large well-known
  industrial stocks, leaders in their industry, and
  listed on NYSE
• Total the current price of the 30 stocks and
  divide by a divisor (adjusted for stock splits
  and changes in the sample)
• Nikkei-Dow Jones Average
• Arithmetic average of prices for 225 stocks on
  the First Section of the Tokyo Stock Exchange
  (TSE)
• Best-known series in Japan
• Price-weighted series formulated by Dow Jones and
  Company
• The 225 stocks represent 15 percent of all stocks
  on the First Section

5
Example of Change in DJIA Divisor When a Sample
Stock Splits
Exhibit 5.1

• After Three-for One
• Before Split Split by Stock A
• Prices Prices
• A 30 10
• B 20 20
• C 10 10
• 60 3 20 40
  X 20
• X 2 (New Divisor)

6
Criticism of the DJIA (and price weighting)

• Limited to 30 non-randomly selected blue-chip
  stocks
• Does not represent a vast majority of stocks
• The divisor needs to be adjusted every time one
  of the companies in the index has a stock split
• Introduces a downward bias by reducing weighting
  of fastest growing companies whose stock splits

7
Value weighted indices

• Derive the initial total market value of all
  stocks used in the series
• Market Value Number of Shares Outstanding
• X Current Market Price
• Assign an beginning index value (100) and new
  market values are compared to the base index
• Automatic adjustment for splits
• Weighting depends on market value
• Most popular indices are value weighted (e.g. the
  SP 500 and the NASDAQ)

8
Value weighted indices (cont)
where Indext 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
9
Unweighted indices

• All stocks carry equal weight regardless of price
  or market value
• May be used by individuals who randomly select
  stocks and invest the same dollar amount in each
  stock
• Some use arithmetic average of the percent price
  changes for the stocks in the index
• Value Line and the Financial Times Ordinary Share
  Index compute a geometric mean of the holding
  period returns and derive the holding period
  yield from this calculation

10
Global Equity Indexes

• There are stock-market indexes available for most
  individual foreign markets
• These are closely followed within each country
• These are difficult to compare due to differences
  in sample selection, weighting, or computational
  procedure
• Groups have computed country indexes

11
FT/SP-Actuaries World Indexes

• Jointly compiled by The Financial Times Limited,
  Goldman Sachs Company, and Standard Poors 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
• Includes actively traded medium and small
  corporations along with major international
  equities
• Securities included must allow direct holdings of
  shares by foreign nationals
• Index is market-value weighted with a base date
  of December 31, 1986 100
• Index results are reported in U.S. dollars, U.K.
  pound sterling, Japanese yen, German mark, and
  the local currency of the country included
• Results are calculated daily after the New York
  markets close and published the following day in
  the Financial Times
• Geographic subgroups are also published

12
Morgan Stanley Capital International (MSCI)
Indexes

• Three international, nineteen national, and
  thirty-eight international industry indexes
• Include 1,375 companies listed on stock exchanges
  in 19 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-value weighted
• Reporting is in U.S. dollars and the countrys
  local currency
• Also provides
• price to book value (P/BV) ratio
• price to cash earnings (earnings plus
  depreciation) (P/CE) ratio
• price to earnings (P/E) ratio
• dividend yield (YLD)
• The Morgan Stanley group index for Europe,
  Australia, and the Far East (EAFE) is used as the
  basis for futures and options contracts on the
  Chicago Mercantile Exchange and the Chicago Board
  Options Exchange

13
Dow Jones World Stock Index

• Introduced in January 1993
• 2,200 companies worldwide
• Organized into 120 industry groups
• Includes 33 countries representing more than 80
  percent of the combined capitalization of these
  countries
• Countries are grouped into three major
  regionsAsia/Pacific, Europe/Africa, and the
  Americas
• Each countrys index is calculated in its own
  currency as well as in the U.S. dollar

14
Comparison of World Stock Indexes

• Correlations between the three series since
  December 31, 1991 to December 31, 2003, indicates
  an average correlation coefficient among them in
  excess of 0.99

15
Comparison of World Stock Indexes

• Passive equity portfolio management
• Long-term buy-and-hold strategy
• Usually tracks an index over time
• Designed to match market performance
• Manager is judged on how well they track the
  target index
• Active equity portfolio management
• Attempts to outperform a passive benchmark
  portfolio on a risk-adjusted basis

16
An Overview of Passive Equity Portfolio
Management Strategies

• Replicate the performance of an index
• May slightly underperform the target index due to
  fees and commissions
• Costs of active management (1 to 2 percent) are
  hard to overcome in risk-adjusted performance
• Many different market indexes are used for
  tracking portfolios

17
Index Portfolio Construction Techniques

• Full replication
• Sampling
• Quadratic optimization or programming

18
Full Replication

• All securities in the index are purchased in
  proportion to weights in the index
• This helps ensure close tracking
• Increases transaction costs, particularly with
  dividend reinvestment

19
Sampling

• Buys a representative sample of stocks in the
  benchmark index according to their weights in the
  index
• Fewer stocks means lower commissions
• Reinvestment of dividends is less difficult
• Will not track the index as closely, so there
  will be some tracking error

20
Expected Tracking Error
Exhibit 16.2
Expected Tracking Error (Percent)
4.0
3.0
2.0
1.0
500
400
300
200
100
0
Number of Stocks
21
Quadratic Optimization (or programming
techniques)

• Historical information on price changes and
  correlations between securities are input into a
  computer program that determines the composition
  of a portfolio that will minimize tracking error
  with the benchmark
• This relies on historical correlations, which may
  change over time, leading to failure to track the
  index

22
Discussion

• Q16.1 Why have passive portfolio management
  strategies increased in use over time?
• Q5.10 You learn that the Wilshire 5000
  market-value weighted index increased by 16
  percent during a specified period, whereas a
  Wilshire 5000 equal-weighted index increased by
  23 percent during the same period. Discuss what
  this difference implies.

23
Before the Next Class

• Readings
• Chapter 16 (pp 615-641)
• Chan and Lakonishok reading
• Topics to be discussed in the next class
• Equity Portfolio Management Strategies