Portfolio Theory and Financial Engineering - PowerPoint PPT Presentation

1 / 23
About This Presentation
Title:

Portfolio Theory and Financial Engineering

Description:

Dow Jones Industrial Average. Best-known, oldest, most popular series ... Price-weighted series formulated by Dow Jones and Company ... – PowerPoint PPT presentation

Number of Views:196
Avg rating:3.0/5.0
Slides: 24
Provided by: stude285
Category:

less

Transcript and Presenter's Notes

Title: 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
Write a Comment
User Comments (0)
About PowerShow.com