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The Investment FAQ (part 12 of 20)

( Part1 - Part2 - Part3 - Part4 - Part5 - Part6 - Part7 - Part8 - Part9 - Part10 - Part11 - Part12 - Part13 - Part14 - Part15 - Part16 - Part17 - Part18 - Part19 - Part20 )
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Archive-name: investment-faq/general/part12
Version: $Id: part12,v 1.61 2003/03/17 02:44:30 lott Exp lott $
Compiler: Christopher Lott

See reader questions & answers on this topic! - Help others by sharing your knowledge
The Investment FAQ is a collection of frequently asked questions and
answers about investments and personal finance.  This is a plain-text
version of The Investment FAQ, part 12 of 20.  The web site
always has the latest version, including in-line links. Please browse
http://invest-faq.com/


Terms of Use

The following terms and conditions apply to the plain-text version of
The Investment FAQ that is posted regularly to various newsgroups.
Different terms and conditions apply to documents on The Investment
FAQ web site.

The Investment FAQ is copyright 2003 by Christopher Lott, and is
protected by copyright as a collective work and/or compilation, 
pursuant to U.S. copyright laws, international conventions, and other
copyright laws.  The contents of The Investment FAQ are intended for
personal use, not for sale or other commercial redistribution.
The plain-text version of The Investment FAQ may be copied, stored,
made available on web sites, or distributed on electronic media
provided the following conditions are met: 
    + The URL of The Investment FAQ home page is displayed prominently.
    + No fees or compensation are charged for this information,
      excluding charges for the media used to distribute it.
    + No advertisements appear on the same web page as this material.
    + Proper attribution is given to the authors of individual articles.
    + This copyright notice is included intact.


Disclaimers

Neither the compiler of nor contributors to The Investment FAQ make
any express or implied warranties (including, without limitation, any
warranty of merchantability or fitness for a particular purpose or
use) regarding the information supplied.  The Investment FAQ is
provided to the user "as is".  Neither the compiler nor contributors
warrant that The Investment FAQ will be error free. Neither the
compiler nor contributors will be liable to any user or anyone else
for any inaccuracy, error or omission, regardless of cause, in The
Investment FAQ or for any damages (whether direct or indirect,
consequential, punitive or exemplary) resulting therefrom.  

Rules, regulations, laws, conditions, rates, and such information
discussed in this FAQ all change quite rapidly.  Information given
here was current at the time of writing but is almost guaranteed to be
out of date by the time you read it.  Mention of a product does not
constitute an endorsement. Answers to questions sometimes rely on
information given in other answers.  Readers outside the USA can reach
US-800 telephone numbers, for a charge, using a service such as MCI's
Call USA.  All prices are listed in US dollars unless otherwise
specified. 
                          
Please send comments and new submissions to the compiler.

--------------------Check http://invest-faq.com/ for updates------------------

Subject: Retirement Plans - Traditional IRA

Last-Revised: 24 Jan 2003
Contributed-By: Chris Lott ( contact me ), Dave Dodson, David Hinds
(dhinds at hyper.stanford.edu), Rich Carreiro (rlcarr at
animato.arlington.ma.us), L.  Williams (taxhelp at hawaiicpa.com), John
Schussler (jeschuss at erols.com), John Lourenco (decals at
autodecals.com)

This article describes the provisions of the US tax code for traditional
IRAs as of mid 2001, including the changes made by the Economic Recovery
and Tax Relief Reconciliation Act of 2001.  Also see the articles
elsewhere in the FAQ for information about Roth IRA and Education IRA
accounts. 

An individual retirement arrangement (IRA) allows a person, whether
covered by an employer-sponsored pension plan or not, to save money for
use in retirement while allowing the savings to grow tax-free.  Stated
differently, a traditional IRA converts investment earnings (interest,
dividends, and capital gains) into ordinary income. 

Funds in an IRA may be invested in a broad variety of vehicles such as
stocks, mutual funds, and bonds.  Because an IRA must be administered by
some trustee, most people are limited to the investment choices offered
by that trustee.  For example, an IRA at a bank at one time pretty much
was limited to CDs from that bank.  Similarly, if you open an IRA
account with a mutual-fund company, that account is probably restricted
to owning funds run by that company.  Certain investments are not
allowed in an IRA, however; for example, options trading is restricted
and you cannot go short. 

IRA contributions are limited, and the limits are quite low in
comparison to arrangements that permit employee contributions such as a
401(k) (see the article elsewhere in the FAQ for extensive information
about those accounts).  For tax year 2002, an individual may contribute
the lesser of US$3,000 or the amount of wage income from US sources to
his or her IRA account(s).  In other words, an individual may have both
a traditional and a Roth IRA, but can only contribute $3,000 total to
those accounts, divided up any way he or she pleases. 

There is one notable exception that was introduced in 1997, namely a
provision for a spousal IRA.  Under this provision, married couples with
only one wage earner may each contribute the full $3,000 to their
respective IRA accounts.  Note that total contributions are still
limited to the couple's total gross income, so you cannot contribute $3k
each if together you earned less than $6k. 

Annual IRA contributions can be made between January 1 of that year and
April 15 of the following year.  Because of the extra three and a half
months, if you send in a contribution to your IRA custodian between
January and April, be sure to indicate the year of the contribution so
the appropriate information gets sent to the IRS. 

Many people can deduct their IRA contributions from their gross income. 
Eligibility for this deduction is determined by the person's modified
adjusted gross income (MAGI), the person's filing status on their
1040(-A, -EZ) form, and whether the person is eligible to participate in
an employer-sponsored pension plan or contributory plan such as a
401(k).  To compute MAGI, you include your federally taxable wages
(i.e., salary after any 401(k) contributions), investment income,
business income, etc., then subtract your adjustments (not to be
confused with deductions) other than the proposed IRA deduction.  In
essence, the MAGI is the last line on the front side of a Form 1040 with
no IRA deductions. 

Anyhow, if your filing status is single, head of household, or
equivalent, the income test has limits that are lower when compared to
filing status married filing jointly (MFJ).  These income tests are
expressed as ranges.  Briefly, if your MAGI is below the lower number,
you can deduct everything.  If your MAGI falls within the range, you can
deduct some portion of your IRA contribution.  And if your MAGI is above
the upper number, you cannot deduct any portion.  (No longer does
coverage of one spouse by an employer-maintained retirement plan
influence the other's eligibility.) The income tests for 1998 look like
this:

   * Not covered by a pension plan: fully deductible. 
   * Covered by a pension plan:
        * MAGI less than 30k (MFJ 50k): fully deductible
        * MAGI in the range 30-40k (MFJ 50-60k): partially deductible
        * MAGI greater than 40k (MFJ 60k): not deductible

If your filing status is "Married Filing Separately" (MFS), then the
income restriction is much tighter.  If your filing status is MFS and
both spouses have a MAGI of $10,000 or more, then neither spouse can
deduct an IRA contribution. 

It's important to understand what it means to be "covered" by a pension
plan.  If you are eligible for a defined benefit plan, that's enough;
you are considered covered.  If you are eligible to participate in a
defined contribution plan, then either you or your employer must have
contributed some money to the account before you are considered covered. 
IRS Notice 87-16 gives all the gory details about who is considered
covered by a pension plan. 

Here's an excerpt from Fidelity's IRA disclosure statement concerning
retirement plans. 
     
     An "employer-maintained retirement plan" includes any of the
     following types of retirement plans:
        * a qualified pension, profit-sharing, or stock bonus plan
          established in accordance with Section 401(a) or 401(k)
          of the Code. 
        * a Simplified Employee Pension Plan (SEP) (Section 408(k)
          of the Code). 
        * a deferred compensation plan maintained by a governmental
          unit or agency. 
        * tax sheltered annuities and custodial accounts (Section
          403(b) and 403(b)(7) of the Code). 
        * a qualified annuity plan under Section 403(a) of the
          Code.  You are an active participant in an
     employer-maintained retirement plan even if you do not have a
     vested right to any benefits under your employer's plan. 
     Whether you are an "active participant" depends on the type of
     plan maintained by your employer.  Generally, you are
     considered an active participant in a defined contribution
     plan if an employer contribution or forfeiture was credited to
     your account under the plan during the year.  You are
     considered an active participant in a defined benefit plan if
     you are eligible to participate in the plan, even though you
     elect not to participate.  You are also treated as an active
     participant for a year during which you make a voluntary or
     mandatory contribution to any type of plan, even though your
     employer makes no contribution to the plan. 



If you can't deduct your contribution, think about making a full
contribution to a Roth IRA (see the article elsewhere in this FAQ for
more information).  The power of untaxed, compound interest should not
be underestimated.  But if you insist on making a non-deductible
contribution into a traditional IRA in any calendar year, you must file
IRS form 8606 with your return for that year. 

For tax purposes, each person has exactly one (1) regular IRA.  It may
be composed of as many, or as few, separate accounts as you wish.  There
are basically only four justifiable reasons for having more than one
regular IRA account:
  1. Legitimate investment purposes such as diversification. 
  2. Estate planning purposes. 
  3. Preserving roll-over status.  If you have rolled a former
     employer's 401K money into an IRA and you wish to retain the right
     to re-roll that money into a new employer's 401k, plan (if allowed
     by that new plan), then you must keep that money in a separate
     account. 
  4. Added flexibility when making penalty-free early withdrawals from
     your IRA via the "substantially equal payments" method, since there
     are IRS private letter rulings (which, admittedly, are only binding
     on the addressees) that strongly hint the IRS takes the position
     that for this purpose, you can make the calculation on an
     account-by-account basis.  See your tax professional if you think
     this applies to you.  In short, you cannot separate deductible and
nondeductible IRA contributions by keeping separate IRA accounts.  There
simply is no way to keep money from deductible and non-deductible
contributions "separate." As far as the IRS is concerned, when you go to
withdraw money from an IRA, all they care about is the total amount of
non-deductible contributions (your "basis") and the total current value
of your IRA's.  Any withdrawal you make, regardless of whether it is
from an account that was started with deductible or non-deductible
contributions, will be taxed the same, based on the fraction of the
current value of all your IRA's that was already taxed.  Stated more
formally, whether or not you put deductible and non-deductible IRA
contributions into the same account, IRS says that any subsequent
withdrawals are considered to be taken ratably from each, regardless of
which account you withdraw from. 

Here's an example.  Let's say that you go so far as to have IRA accounts
with 2 different companies and alternate years as follows:
   * Odd years: contribute the maximum deductible amount to fund A and
     deduct it all. 
   * Even years: contribute $2000 to fund B and deduct none of it. 
     (Yes, you are allowed to decline taking an IRA deduction you are
     eligible for.  You just need to include the actual amount of
     contributions you made - the amount you're deducting on Form 8606.)
Given the above scheme, there is no possibility of nondeductible
contributions (NDC) actually being in fund A, all of them went directly
into fund B.  If fund A is $12,000 with $0 from nondeductible
contributions, and fund B is $18,000 (you put more in) with $6,000 from
nondeductible contributions, and you roll fund B to a Roth, the Form
8606 calculation goes as follows:

Total IRA = $12,000 + $18,000 = $30,000
Total NDC = $0 + $6,000 = $6,000
Ratio = $6,000 / $30,000 = 1/5
Amount transferred = $18,000
NDC transferred = 1/5 of $18,000 = $3,600. 

Unfortunately, you can't just say "All of my nondeductible contributions
are in fund B" (even though it's demonstable that this must be so) and
pay taxes on $18,000 - $6,000 = $12,000.  You have to go through the
above math and pay taxes on $18,000 - $3,600 = $14,400. 

So, once you make a non-deductible contribution, you're committed to
doing the paperwork when you take any money out of the IRA.  On the
upside, the tax "problem" never gets any more complicated.  You don't
have to keep track of where different contributions came from: all you
need to do is keep track of your basis, the sum of all your
non-deductible contributions.  This number is on the most recent Form
8606 that you've filed (the form serves as a cumulative record, perhaps
once of the more taxpayer-friendly forms from the IRS). 

Occasionally the question crops up as to exactly why people cannot go
short (see the article elsewhere in the FAQ explaining short sales) in
an IRA account.  The restriction comes from the combination of the
following three facts.  First, the law governing IRAs says that if any
part of an IRA is used as collateral, the entire IRA is considered
distributed and thus subject to income tax and penalties.  Second, the
rules imposed by the Federal Reserve Board et al.  say that short sales
have to take place in a margin account.  Third and finally, margin
accounts require that you pledge the account as collateral.  So if you
try to turn an IRA into a margin account, you'll void the IRA; but
without a margin account, you can't sell short. 

Withdrawals can be made from a traditional IRA account at any time, but
a 10% penalty is imposed by the IRS on withdrawals made before the magic
age of 59 1/2.  Note that taxes are always imposed on those portions of
withdrawals that can be attributed to deductible contributions. 
Withdrawals from an IRA must begin by age 70 1/2.  There are also
various provisions for excess contributions and other problems. 

The following exceptions define cases when withdrawals can be made
subject to no penalty:

   * The owner of the IRA becomes disabled or dies. 
   * A withdrawal program is set up as a series of "substantially equal
     periodic payments" (known as SEP) that are taken over the owner's
     life expectancy.  Part of the deal with SEP is that the person also
     must continue to take that amount for a period of 5 years before he
     or she is allowed to change it. 
   * The funds are used to pay unreimbursed medical expenses that exceed
     7.5% of the owner's adjusted gross income. 
   * The funds are used to pay medical insurance premiums provided the
     owner of the IRA has received unemployment for more than 12 weeks. 
   * The funds are used to pay for qualified higher-education expenses. 
   * The funds are used to pay for a first-time home purchase, subject
     to a lifetime maximum of 10,000.  Note that a husband and wife can
     both take distributions from their IRAs for a total of 20k to apply
     to a first-time home purchase (lots of strings attached, read IRS
     publication 590 carefully). 

When an IRA account holder dies, the account becomes the property of the
named beneficiary, and is subject to various minimum distribution rules. 

The IRS issued new regulations in April 2002 for minimum distributions
from traditional IRAs.  The rules (which are retroactive to 1 April
2001) simplify the old, complex rules and reduce the minimum
distribution amounts for many people.  First, IRA trustees are required
to report minimum required distributions to the IRS each year (to make
certain Uncle Sam gets his share).  Second, account holders can name
beneficiaries at practically any time -- even after the death of the
account holder.  Third, major changes were made to the calculation of
required minimum distributions.  According to the 2002 rules, the IRA
owner is required (as before) to begin minimum distributions at age 70
and 1/2, or suffer tax penalties.  However, these distributions are
calculated based on one of three new tables:
  1. Single Life Table: This (depressingly) is used after the owner
     dies. 
  2. Joint and Last Survivor Table: Used when the named beneficiary is a
     spouse younger than the owner by at least 10 years (lucky them). 
  3. Uniform Lifetime Table: Used in nearly all other cases (i.e., when
     the named beneficiary is close in age to the owner). 

The traditional IRA permits a distribution to be treated as a rollover. 
This means that you can withdraw money from an IRA account with no tax
effect as long as you redeposit it (into any of your IRA accounts, not
necessarily the one you took the money from) within 60 days of the
withdrawal.  Any monies not redeposited are considered a distribution,
subject to income tax and the penalty tax if applicable.  You are
permitted one rollover every 12 months per IRA account. 

The rules changed in mid 2001 in the following ways:
   * The contribution limit is $3,000 in 2002; reaches $4,000 in 2005,
     and finally hits $5,000 in 2008. 
   * Investors over 50 can put an extra $500 per year (in 2002) and
     eventually an extra 1,000 (in 2006) per year; this is called a
     catch-up provision. 

Order IRS Publication 590 for complete information.  You can also get a
PDF version of Pub 590 from the IRS web site:
http://www.irs.ustreas.gov/


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Software - Archive of Free Investment-Related Programs

Last-Revised: 20 Aug 1996
Contributed-By: Chris Lott ( contact me )

This article lists two archives of investment-related programs.  Most of
these programs are distributed in source-code form, but some include
binaries.  Anyhow, if all that is available is source, then before you
can run them on your PC at home you will need a C compiler to create
executable versions. 

Ed Savage maintains an archive of programs which are available here:
ftp://metalab.unc.edu/pub/archives/misc.invest/programs

The compiler of this FAQ maintains an archive of programs (both source
code and PC binaries) for a number of investment-related programs.  The
programs include:

   * 401-calc: compute value of a 401(k) plan over time
   * commis: compute commisions for trades at selected discount brokers
   * fv: compute future value
   * irr: compute rate of return of a portfolio
   * loan: calculate loan amortization schedule
   * prepay: analyze prepayments of a mortgage loan
   * pv: calculate present value
   * returns: analyze total return of a mutual fund
   * roi: compute return on investment for mutual funds

These programs are available from The Investment FAQ web site at URL
http://invest-faq.com/sw.html . 


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Software - Portfolio Tracking and Technical Analysis

Last-Revised: 2 Jul 2001
Contributed-By: Chris Lott ( contact me )

Many software packages are available that support basic personal finance
and investment uses, such as managing a checkbook, tracking expenses,
and following the value of a portfolio.  Using a package can be handy
for tracking transactions in mutual funds and stocks, especially for
active traders at tax time.  Many packages support various forms of
technical analysis by drawing charts using historical data, applying
various T/A decision rules, etc.  Those packages usually include a large
amount of historical data, with many provisions for fetching current
data via the 'net. 

With the advent of online banking, many banks are offering software at
no charge, so be sure to ask locally. 

This page lists a few resources that will help you find a package to
meet your needs. 
   * A decent collection of links for portfolio software is available on
     The Investment FAQ web site:
     http://invest-faq.com/links/software.html
   * A yearly compendium is part of AAII's Computerized Investing
     Newsletter. 
   * Anderson Investor's Software, 130 S.  Bemiston.  Ste 101, St. 
     Louis MO 63105, USA; Sales 800-286-4106, Info 314-918-0990, FAX
     314-918-0980. 
     http://www.investorsoftware.com/
   * Nirvana Systems of Austin, TX specializes in investment- and
     finance-related software.  +1 (512) 345-2545, 800-880-0338. 
   * Money$earch maintains a collection of links to software packages. 
     The following URL will run a search on their site so you get the
     latest results. 
     http://www.moneysearch.com/docs/software.html
   * BobsGuide.com is an online showcase for technologies and services
     in the banking and finance industry.  The target users are
     primarily those in the banking and finance community responsible
     for purchasing software and hardware technology. 
     http://www.bobsguide.com/


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - Basics

Last-Revised: 26 Aug 1994
Contributed-By: Art Kamlet (artkamlet at aol.com), Edward Lupin

Perhaps we should start by looking at the basics: What is stock? Why
does a company issue stock? Why do investors pay good money for little
pieces of paper called stock certificates? What do investors look for?
What about Value Line ratings and what about dividends?

To start with, if a company wants to raise capital (money), one of its
options is to issue stock.  A company has other methods, such as issuing
bonds and getting a loan from the bank.  But stock raises capital
without creating debt; i.e., without creating a legal obligation to
repay borrowed funds. 

What do the buyers of the stock -- the new owners of the company --
expect for their investment? The popular answer, the answer many people
would give is: they expect to make lots of money, they expect other
people to pay them more than they paid themselves.  Well, that doesn't
just happen randomly or by chance (well, maybe sometimes it does, who
knows?). 

The less popular, less simple answer is: shareholders -- the company's
owners -- expect their investment to earn more, for the company, than
other forms of investment.  If that happens, if the return on investment
is high, the price tends to increase.  Why?

Who really knows? But it is true that within an industry the
Price/Earnings (i.e., P/E) ratio tends to stay within a narrow range
over any reasonable period of time -- measured in months or a year or
so. 

So if the earnings go up, the price goes up.  And investors look for
companies whose earnings are likely to go up.  How much?

There's a number -- the accountants call it Shareholder Equity -- that
in some magical sense represents the amount of money the investors have
invested in the company.  I say magical because while it translates to
(Assets - Liabilities) there is often a lot of accounting trickery that
goes into determining Assets and Liabilities. 

But looking at Shareholder Equity, (and dividing that by the number of
shares held to get the book value per share) if a company is able to
earn, say, $1.50 on a stock whose book value is $10, that's a 15%
return.  That's actually a good return these days, much better than you
can get in a bank or C/D or Treasury bond, and so people might be more
encouraged to buy, while sellers are anxious to hold on.  So the price
might be bid up to the point where sellers might be persuaded to sell. 

A measure that is also sometimes used to assess the price is the
Price/Book (i.e., P/B) ratio.  This is just the stock price at a
particular time divided by the book value. 

What about dividends? Dividends are certainly more tangible income than
potential earnings increases and stock price increases, so what does it
mean when a dividend is non-existent or very low? And what do people
mean when they talk about a stock's yield?

To begin with the easy question first, the yield is the annual dividend
divided by the stock price.  For example, if company XYZ is paying $.25
per quarter ($1.00 per year) and XYZ is trading at $10 per share, the
yield is 10%. 

A company paying no or low dividends (zero or low yield) is really
saying to its investors -- its owners, "We believe we can earn more, and
return more value to shareholders by retaining the earnings, by putting
that money to work, than by paying it out and not having it to invest in
new plant or goods or salaries." And having said that, they are expected
to earn a good return on not only their previous equity, but on the
increased equity represented by retained earnings. 

So a company whose book value last year was $10 and who retains its
entire $1.50 earnings, increases its book value to 11.50 less certain
expenses.  The $1.50 in earnings represents a 15% return.  Let's say
that the new book value is 11.  To keep up the streak (i.e., to earn a
15% return again), the company must generate earnings of at least $1.65
this year just to keep up with the goal of a 15% return on equity.  If
the company earns $1.80, the owners have indeed made a good investment,
and other investors, seeking to get in on a good thing, bid up the
price. 

That's the theory anyway.  In spite of that, many investors still buy or
sell based on what some commentator says or on announcement of a new
product or on the hiring (or resignation) of a key officer, or on
general sexiness of the company's products.  And that will always
happen. 

What is the moral of all this: Look at a company's financials, look at
the Value Line and S&P charts and recommendations, and do some homework
before buying. 

Do Value Line and S&P take the actual dividend into account when issuing
their "Timeliness" and "Safety" ratings? Not exactly.  They report it,
but their ratings are primarily based on earnings potential, performance
in their industry, past history, and a few other factors.  (I don't
think anyone knows all the other factors.  That's why people pay for the
ratings.)

Can a stock broker be relied on to provide well-analyzed, well thought
out information and recommendations? Yes and no. 

On the one hand, a stock broker is in business to sell you stock.  Would
you trust a used-car dealer to carefully analyze the available cars and
sell you the best car for the best price? Then why would you trust a
broker to do the same?

On the other hand, there are people who get paid to analyze company
financial positions and make carefully thought out recommendations,
sometimes to buy or to hold or to sell stock.  While many of these folks
work in the "research" departments of full-service brokers, some work
for Value Line, S&P etc, and have less of an axe to grind.  Brokers who
rely on this information really do have solid grounding behind their
recommendations. 

Probably the best people to listen to are those who make investment
decisions for the largest of Mutual Funds, although the investment
decisions are often after the fact, and announced 4 times a year. 

An even better source would be those who make investment decisions for
the very large pension funds, which have more money invested than most
mutual funds.  Unfortunately that information is often less available. 
If you can catch one of these people on CNN for example, that could be
interesting. 


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - American Depositary Receipts (ADRs)

Last-Revised: 19 Feb 2002
Contributed-By: Art Kamlet (artkamlet at aol.com), George Regnery
(regnery at yahoo.com)

An American Depositary Receipt (ADR) is a share of stock of an
investment in shares of a non-US corporation.  The shares of the non-US
corporation trade on a non-US exchange, while the ADRs, perhaps somewhat
obviously, trade on a US exchange.  This mechanism makes it
straightforward for a US investor to invest in a foreign issue.  ADRs
were first introduced in 1927. 

Two banks are generally involved in maintaining an ADR on a US exchange:
an investment bank and a depositary bank.  The investment bank purchases
the foreign shares and offers them for sale in the US.  The depositary
bank handles the issuance and cancellation of ADRs certificates backed
by ordinary shares based on investor orders, as well as other services
provided to an issuer of ADRS, but is not involved in selling the ADRs. 

To establish an ADR, an investment bank arranges to buy the shares on a
foreign market and issue the ADRs on the US markets. 

For example, BigCitibank might purchase 25 million shares of a non-US
stock.  Call it EuroGlom Corporation (EGC).  Perhaps EGC trades on the
Paris exchange, where BigCitibank bought them.  BigCitibank would then
register with the SEC and offer for sale shares of EGC ADRs. 

EGC ADRs are valued in dollars, and BigCitibank could apply to the NYSE
to list them.  In effect, they are repackaged EGC shares, backed by EGC
shares owned by BigCitibank, and they would then trade like any other
stock on the NYSE. 

BigCitibank would take a management fee for their efforts, and the
number of EGC shares represented by EGC ADRs would effectively decrease,
so the price would go down a slight amount; or EGC itself might pay
BigCitibank their fee in return for helping to establish a US market for
EGC.  Naturally, currency fluctuations will affect the US Dollar price
of the ADR. 

BigCitibank would set up an arrangement with another large financial
institution for that institution to act as the depositary bank for the
ADRs.  The depositary would handle the day-to-day interaction with
holders of the ADRs. 

Dividends paid by EGC are received by BigCitibank and distributed
proportionally to EGC ADR holders.  If EGC withholds (foreign) tax on
the dividends before this distribution, then BigCitibank will withhold a
proportional amount before distributing the dividend to ADR holders, and
will report on a Form 1099-Div both the gross dividend and the amount of
foreign tax withheld. 

Most of the time the foreign nation permits US holders (BigCitibank in
this case) to vote their shares on all or most issues, and ADR holders
will receive ballots which will be received by BigCitibank and voted in
proportion to ADR Shareholder's vote.  I don't know if BigCitibank has
the option of voting shares which ADR holders failed to vote. 

The depositary bank sets the ratio of US ADRs per home country share. 
This ratio can be anywhere, and can be less than or greater than 1. 
Basically, it is an attempt to get the ADR within a price that Americans
are comfortable with, so upon issue, I would assume that most ADRs range
between $15 and $75 per share.  If, in the home country, the shares are
worth considerably less, than each ADR would represent several real
shares.  If, in the home country, shares were trading for the equivalent
of several hundred dollars, each ADR would be only a fraction of a
normal share. 

Now, concerning who sets the price: yes, it floats on supply and demand. 
However, if the US price gets too far off from the price in the home
country (Accounting for the currency exchange rate and the ratio of ADRs
to home country shares), then an arbitrage opportunity will exist.  So,
yes, it does track the home country shares, but probably not exactly
(for there are transaction costs in this type of arbitrage).  However,
if the spread gets too big, arbitragers will step in and then of course,
the arbitrage opportunities will soon cease to exist. 

Having said this, however, for the most part ADRs look and feel pretty
much like any other stock. 

The following resources offer more information about ADRs. 
   * Citicorp offers in-depth information about ADRs:
     http://www.citibank.com/corpbank/adr
   * JP Morgan runs a web site devoted to ADRs (with a truly lovely
     legal disclaimer you must accept before visiting the site):
     http://www.adr.com/
   * Site-By-Site offers information about specific ADR issues:
     http://www.site-by-site.com/adr/toc.htm
   * CoBeCo lists background information and current quotes for ADRs:
     http://www.cobeconet.com/global/adr/news/adrpr.cfm


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - Cyclicals

Last-Revised: 9 Apr 1995
Contributed-By: Bill Sullivan (sully at postoffice.ptd.net)

Cyclical stocks, in brief, are the stocks of those companies whose
earnings are strongly tied to the business cycle.  This means that the
prices of the stocks move up sharply when the economy turns up, move
down sharply when the economny turns down. 

Examples:

Cyclical companies: Caterpillar (CAT), US Steel (X), General Motors
(GM), International Paper (IP); i.e., makers of products for which the
demand curve is fairly flexible. 

Non-Cyclical companies: CocaCola (KO), Proctor & Gamble (PG), and Quaker
Oats (OAT); i.e., makers of products for which the demand curve is
fairly inflexible; after all, everyone has to eat!


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - Dividends

Last-Revised: 29 Sep 1997
Contributed-By: Art Kamlet (artkamlet at aol.com), Rich Carreiro (rlcarr
at animato.arlington.ma.us)

A company may periodically declare cash and/or stock dividends.  This
article deals with cash dividends on common stock.  Two paragraphs also
discuss dividends on Mutual Fund shares.  A separate article elsewhere
in this FAQ discusses stock splits and stock dividends. 

The Board of Directors of a company decides if it will declare a
dividend, how often it will declare it, and the dates associated with
the dividend.  Quarterly payment of dividends is very common, annually
or semiannually is less common, and many companies don't pay dividends
at all.  Other companies from time to time will declare an extra or
special dividend.  Mutual funds sometimes declare a year-end dividend
and maybe one or more other dividends. 

If the Board declares a dividend, it will announce that the dividend (of
a set amount) will be paid to shareholders of record as of the RECORD
DATE and will be paid or distributed on the DISTRIBUTION DATE (sometimes
called the Payable Date). 

Before we begin the discussion of dates and date cutoffs, it's important
to note that three-day settlements (T+3) became effective 7 June 1995. 
In other words, the SEC's T+3 rule states that all stock trades must be
settled within 3 business days. 

In order to be a shareholder of record on the RECORD DATE you must own
the shares on that date (when the books close for that day).  Since
virtually all stock trades by brokers on exchanges are settled in 3
(business) days, you must buy the shares at least 3 days before the
RECORD DATE in order to be the shareholder of record on the RECORD DATE. 
So the (RECORD DATE - 3 days) is the day that the shareholder of record
needs to own the stock to collect the dividend.  He can sell it the very
next day and still get the dividend. 

If you bought it at least 3 business days before the RECORD date and
still owned it at the end of the RECORD DATE, you get the dividend. 
(Even if you ask your broker to sell it the day after the (RECORD DATE -
3 days), it will not have settled until after the RECORD DATE so you
will own it on the RECORD DATE.)

So someone who buys the stock on the (RECORD DATE - 2 days) does not get
the dividend.  A stock paying a 50c quarterly dividend might well be
expected to trade for 50c less on that date, all things being equal.  In
other words, it trades for its previous price, EXcept for the DIVidend. 
So the (RECORD DATE - 2 days) is often called the EX-DIV date.  In the
financial listings, that is indicated by an x. 

How can you try to predict what the dividend will be before it is
declared?

Many companies declare regular dividends every quarter, so if you look
at the last dividend paid, you can guess the next dividend will be the
same.  Exception: when the Board of IBM, for example, announces it can
no longer guarantee to maintain the dividend, you might well expect the
dividend to drop, drastically, next quarter.  The financial listings in
the newspapers show the expected annual dividend, and other listings
show the dividends declared by Boards of directors the previous day,
along with their dates. 

Other companies declare less regular dividends, so try to look at how
well the company seems to be doing.  Companies whose shares trade as
ADRs (American Depositary Receipts -- see article elsewhere in this FAQ)
are very dependent on currency market fluctuations, so will pay
differing amounts from time to time. 

Some companies may be temporarily prohibited from paying dividends on
their common stock, usually because they have missed payments on their
bonds and/or preferred stock. 

On the DISTRIBUTION DATE shareholders of record on the RECORD date will
get the dividend.  If you own the shares yourself, the company will mail
you a check.  If you participate in a DRIP (Dividend ReInvestment Plan,
see article on DRIPs elsewhere in this FAQ) and elect to reinvest the
dividend, you will have the dividend credited to your DRIP account and
purchase shares, and if your stock is held by your broker for you, the
broker will receive the dividend from the company and credit it to your
account. 

Dividends on preferred stock work very much like common stock, except
they are much more predictable. 

Tax implications:

   * Some Mutual Funds may delay paying their year-end dividend until
     early January.  However, the IRS requires that those dividends be
     constructively paid at the end of the previous year.  So in these
     cases, you might find that a dividend paid in January was included
     in the previous year's 1099-DIV. 
     
     
   * Sometime before January 31 of the next year, whoever paid the
     dividend will send you and the IRS a Form 1099-DIV to help you
     report this dividend income to the IRS. 
     
     
   * Sometimes -- often with Mutual Funds -- a portion of the dividend
     might be treated as a non-taxable distribution or as a capital
     gains distribution.  The 1099-DIV will list the Gross Dividends (in
     line 1a) and will also list any non-taxable and capital gains
     distributions.  Enter the Gross Dividends (line 1a) on Schedule B. 
     
     
   * Subtract the non-taxable distributions as shown on Schedule B and
     decrease your cost basis in that stock by the amount of non-taxable
     distributions (but not below a cost basis of zero -- you can deduct
     non-taxable distributions only while the running cost basis is
     positive.) Deduct the capital gains distributions as shown on
     Schedule B, and then add them back in on Schedule D if you file
     Schedule D, else on the front of Form 1040. 

Finally, just a bit of accounting information.  Earnings are always
calculated first, and then the directors of a company decide what to do
with those earnings.  They can distribute the earnings to the
stockholders in the form of dividends, retain the earnings, or take the
money and head for Brazil (NB: the last option tends to make the
stockholders angry and get the local district attorney on the case :-). 
Utilities and seasonal companies often pay out dividends that exceed
earnings - this tends to prop up the stock price nicely - but of course
no company can do that year after year. 


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - Dramatic Price Changes

Last-Revised: 18 Sep 1994
Contributed-By: Maurice Suhre, Lynn West, Fahad A.  Hoymany

One frequently asked question is "Why did my stock in X go down/up by
this large amount in the past short time ?

The purpose of this answer is not to discourage you from asking this
question in misc.invest, although if you ask without having done any
homework, you may receive a gentle barb or two.  Rather, one purpose is
to inform you that you may not get an answer because in many cases no
one knows. 

Stocks surge for a variety of reasons ranging from good company news,
improving investors' sentiment, to general economic conditions.  The
equation which determines the price of a stock is extremely simple, even
trivial.  When there are more people interested in buying than there are
people interested in selling, possibly as a result of one or more of the
reasons mentioned above, the price rises.  When there are more sellers
than buyers, the price falls.  The difficult question to answer is, what
accounts for the variations in demand and supply for a particular stock?
Naturally, if all (or most) people knew why a stock surges, we would
soon have a lot of extremely rich people who simply use that knowledge
to buy and sell different stocks. 

However, stocks often lurch upward and downward by sizable amounts with
no apparent reason, sometimes with no fundamental change in the
underlying company.  If this happens to your stock and you can find no
reason, you should merely use this event to alert you to watch the stock
more closely for a month or two.  The zig (or zag) may have meaning, or
it may have merely been a burp. 

A related question is whether stock XYZ, which used to trade at 40 and
just dropped to 25, is good buy.  The answer is, possibly.  Buying
stocks just because they look "cheap" isn't generally a good idea.  All
too often they look cheaper later on.  (IBM looked "cheap" at 80 in 1991
after it declined from 140 or so.  The stock finally bottomed in the
40's.  Amgen slid from 78 to the low 30's in about 6 months, looking
"cheap" along the way.) Technical analysis principles suggest to wait
for XYZ to demonstrate that it has quit going down and is showing some
sign of strength, perhaps purchasing in the 28 range.  If you are
expecting a return to 40, you can give up a few points initially.  If
your fundamental analysis shows 25 to be an undervalued price, you might
enter in.  Rarely do stocks have a big decline and a big move back up in
the space of a few days.  You will almost surely have time to wait and
see if the market agrees with your valuation before you purchase. 


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - Holding Company Depositary Recepits (HOLDRs)

Last-Revised: 16 July 2000
Contributed-By: Chris Lott ( contact me )

A Holding Company Depositary Receipt (HOLDR) is a fixed collection of
stocks, usually 20, that is used to track some industry sector.  For
example, HOLDRs exist for biotech, internet, and business-to-business
companies, just to pick some examples.  A HOLDR is a way for an investor
to gain exposure to a market sector with at a low cost, primarily the
comission to purchase the HOLDR.  All HOLDR securities trade on the
American Stock Exchange; their ticker symbols all end in 'H'. 

Although a HOLDR may sound a bit like a mutual fund, it really is quite
different.  One important difference is that nothing is done to a HOLDR
after it is created (mutual funds are usually managed actively).  So,
for example, if one of the 20 companies in a HOLDR gets bought,
thereafter the HOLDR will have just 19 stocks.  This keeps the annual
expenses very low (currently about $0.08 or less per share). 

So maybe a HOLDR is much more like a stock? Yes, but also with some
differences.  Like stocks, HOLDRs can be bought on margin or shorted. 
But unlike stocks, investors can only buy round lots (multiples of 100
shares) of HOLDR securities.  So buying into a HOLDR can be fairly
expensive for a small investor. 

Interestingly, an owner of a HOLDR is considered to own the stocks in
the HOLDR directly, even though they were purchased via the HOLDR.  So
the HOLDR holder (sorry, bad joke) receives quarterly and annual reports
from the companies directly, receives dividends directly, etc.  And, if
the investor decides it's a good idea (and is willing to pay the
associated fees), he or she can ask the HOLDR trustee to deliver the
shares represented by the HOLDR; the HOLDR then is gone (cancelled), and
the investor holds the shares as if he or she had purchased them
directly. 

Merrill Lynch created the first HOLDR in 1998 to track the Brazilian
phone company when it was broken up.  Merrill (or some other big
financial institution) serves as the trustee, the agency that purchases
shares in the companies and issues the HOLDR shares.  When a HOLDR is
first issued, the event is considered an IPO. 

Here are a few resources with more information. 
   * The Merrill Lynch site:
     http://www.holdrs.com/
   * The Street.com printed a comprehensive introduction to HOLDRs in
     June 2000:
     http://www.thestreet.com/funds/deardagen/968391.html


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - Income and Royalty Trusts

Last-Revised: 24 Jul 2001
Contributed-By: John Carswell (webmaster at finpipe.com)

Income and Royalty Trusts are special-purpose financing vehicles that
are created to make investments in operating companies or their cash
flows.  Investors supply capital to a trust, a legal entity that exists
to hold assets, by purchasing "trust units".  The trust then uses these
funds to purchase an interest in the operating company.  The trust then
distributes all its income to holders of the trust units. 

Income and Royalty trusts are neither stocks nor bonds, although they
share some of their characteristics.  Investment trusts are created to
hold interests in operating assets which produce income and cash flows,
then pass these through to investors.  A "trust" is a legal instrument
which exists to hold assets for others.  A "trust" investment which uses
a trust (the legal entity) to hold ownership of an asset and pass
through income to investors is called a "securitization" or an
"asset-backed security". 

The trust can purchase common shares, preferred shares or debt
securities of an operating company.  Royalty trusts purchase the right
to royalties on the production and sales of a natural resource company. 
Real estate investment trusts purchase real estate properties and pass
the rental incomes through to investors. 

Royalty and Income Trusts are attractive to investors because they
promise high yields compared to traditional stocks and bonds.  They are
attractive to companies wishing to sell cash flow producing assets
because they provide a much higher sale price, or proceeds, than would
be possible with conventional financings.  The investment
characteristics of both types of trusts flow from their structure.  To
understand the risks and returns inherent in these investments we must
go beyond their promised yield and examine their purpose and structure. 

Cashflow Royalty Created!

For example, let's say that we own an oil company,CashCow Inc., that has
many mature producing oil wells.  The prospect for these wells is fairly
mundane.  With well known rates of production and reserves, there is not
much chance to enhance production or lower costs.  We know that we will
produce and sell 1,000,000 barrels per year at the prevailing oil price
until it runs out in a forecasted 20 years.  At the current price of $25
per barrel, we will make $25,000,000 per year until the wells run dry in
2017. 

We're getting a bit tired of the oil business.  We want to sell.  Our
investment bank, Sharp & Shooter, suggest that we utilize a royalty
trust.  They explain the concept to us.  CashCow Inc., our company,
sells all the oil wells to a "trust", the CashCow Royalty Fund.  The
trust will then pay CashCow Inc a management fee to manage and maintain
the wells.  The CashCow Royalty Fund then gets all the earnings from the
wells and distributes these to the trust unit holders.  We ask, "Why we
just wouldn't sell shares in our company to the public".  Sharp &
Shooter tells us that we will get more money by setting up the trust
since investors are "starved for yield".  We agree. 

Sharp & Shooter then do the legals and proceed with an issue.  They
offer a cash yield of 10%, based on their projections for oil prices,
the cost structure, and management fee to CashCow Inc.  This means they
hope to raise $250,000,000.  We're rich!!

Yield to the Poor Tired Investment Masses

What about the poor tired investment masses? Starving for yield in the
low interest rate revolution, the CashCow Royalty Fund lets them have
their investment cake and eat it too.  Thanks to the royalty courtiers
of Sharp & Shooter, yield starved investors can buy a piece of a "high
yield" investment.  Sounds a bit strange, but the royalty trust turns
the steady income that made the operating company CashCow Inc. 
financially mundane and boring into a scintillating geyser of high
yield. 

Since the operating company, CashCow Inc., no longer has to explore for
oil or develop technologies to increase production, its expenditures
will be much lower under the royalty trust structure.  Remember, the
purposes of the trust is to pay out the earnings from the oil sales
until the oil fields are exhausted.  No more analysts and shareholders
complaining about "depleting" resources.  Paying out the steadily
depleting oil sales are now the idea.  This means that none of the
revenues and profits from production have to be expended on securing new
supplies.  The continuing operations of CashCow Inc.  can be downsized
now that maintenance is the only need.  No more exploration department,
huge head office staff, or worldwide travel bills. 

The investor, who might shun a low dividend yield of 3% on an oil stock
or worry about the risk of a lower grade corporate bond, sees the bright
lights of high yield beckoning.  Our $25,000,000 in revenues is only
reduced by a management contract of $1,000,000 paid to the now shrunken
CashCow Inc.  to keep the fields maintained.  All the earnings will be
passed through to the CashCow Royalty Trust which will be taxed in the
hands of the investors.  We can offer a 10% yield to the trust unit
holders which means that we can raise $250,000,000. 

What's Wrong with this Investment Picture?

One of the first questions to ask about an investment is, "What's in it
for them?".  Why would the owners of CashCow Inc.  part with their
$25,000,000 in income? Not just to provide a higher yield for the yield
starved investment masses.  Logically, the owners of an operating
company would only sell their interest if they could use the money to
more effect somewhere else.  Think about it for a minute.  If the owner
of CashCow Inc.  can take $250,000,000 and put it into another
investment with a higher yield, it should be done.  The fixed return of
10% on established, tired wells might be a tad low next to the upside on
a new oil field, or a well diversified portfolio of growth stocks. 

Another question to ask is,"Why didn't the owner just sell the company
to another oil company?".  The simple answer is that they get more money
by selling to the income trust.  Which begs the question, "Why is the
price so high?".  Other companies realize that the price of oil goes up
and down and that the price of $25 a barrel today is very high compared
to the $10 it was a few years ago.  At $10 per barrel, the cash flow
would only be $10,000,000 a year.  That is why the prospectus for these
trust deals talks about 'forecasted' revenues and earnings.  The other
oil companies also realize that 'proven reserves' has an element of
guesswork, and that there might be less oil in the ground, or it may be
'more difficult to recover' than expected. 

All this means that the 10% "yield" is not fixed in stone, as we now
realize.  As with all investments, we must take our time and do our
analysis.  As Uncle Pipeline says, "It's all in the cash flows!"

For more insights from the Financial Pipeline, visit their site:
http://www.finpipe.com/


--------------------Check http://invest-faq.com/ for updates------------------

Subject: Stocks - Types of Indexes

Last-Revised: 10 Jul 1998
Contributed-By: Susan Thomas, Chris Lott ( contact me )

There are three major classes of indexes in use today in the US:

Equally weighted price index
     An example is the Dow Jones Industrial Average. 
Market capitalization weighted index
     An example is the S&P500 Industrial Average. 
Equally weighted returns index
     The only one of its kind is the Value-Line index. 


The first two are widely used.  All my profs in the business school
claim that the equally weighted return indexs is weird and don't
emphasize it too much. 

Now for the details on each type. 



Equally Weighted Price Index
     As the name suggests, the index is calculated by taking the average
     of the prices of a set of companies:
     Index =  Sum (Prices of N companies) / divisor
     In this calculation, two questions crop up:
     
       1. What is "N"? The DJIA takes the 30 large "blue-chip"
          companies.  Why 30? Well, you want a fairly large number so
          the index will (at least to some extent) represent the entire
          market's performance.  Of course, many would argue (and
          rightly so) that 30 is a ridiculously small number in today's
          markets, so a case can be made that it's more of a historical
          hangover than anything else. 
          
          Does the set of N companies change across time? If so, how
          often is the list updated (with respect to the companies that
          are included)? In the case of the DJIA, yes, the set of
          companies is updated periodically.  But these decisions are
          quite judgemental and hence not readily replicable. 
          
          If the DJIA only has 30 companies, how do we select these 30?
          Why should they have equal weights? These are real criticisms
          of the DJIA-type index. 
          
          
       2. The divisor is not always equal to N for N companies.  What
          happens to the index when there is a stock split by one of the
          companies in the set? Of course the stock price of that
          company drops, but the number of shares have increased to
          leave the market capitalization of the shares the same.  Since
          the index does not take the market cap into account, it has to
          compensate for the drop in price by tweaking the divisor.  For
          examples on this, look at pg.  61 of Bodie, Kane, and Marcus,
          Investments .  The DJIA actually started with a divisor of 30,
          but currently uses a number around 0.3 (yes, zero point 3). 
     
     Historically, this index format was computationally convenient.  It
     just doesn't have a very sound economic basis to justify it's
     existence today.  The DJIA is widely cited on the evening news, but
     not used by real finance folks.  I have an intuition that the DJIA
     type index will actually be BAD if the number of companies is very
     large.  If it's to make any sense at all, it should be very few
     "brilliantly" chosen companies.  Because the DJIA is the most
     widely reported index about the U.S.  equity markets, it's
     important to understand it and its flaws. 
     
     
Market capitalization weighted index
     In this index, each of the N companies' price is weighted by the
     market capitalization of the company. 
             Sum (Company market capitalization * Price) over N 
     companies
     Index = 
     ------------------------------------------------------------
            Market capitalization for these N companies
     Here you do not take into account the dividend data, so effectively
     you're tracking the short-run capital gains of the market. 
     
     Practical questions regarding this index:
     
       1. What is "N"? I would use the largest N possible to get as
          close to the "full" market as possible.  By the way, in the
          U.S.  there are companies that make a living on only
          calculating extremely complete value-weighted indexes for the
          NYSE and foreign markets.  CMIE should sell a very complete
          value-weighted index to some such folks. 
          
          Why does S&P use 500? Once again, a large number of companies
          captures the broad market, but the specific number 500 is
          probably due to historical reasons when computating over
          20,000 companies every day was difficult.  Today, computing
          over 20k companies for a Sun workstation is no problem, so the
          S&P idea is obsolete. 
          
          
       2. How to deal with companies entering and exiting the index? If
          we're doing an index containing "every single company
          possible" then the answer to this question is easy -- each
          time a company enters or exits we recalculate all weights. 
          But if we're a value-weighted index like the S&P500 (where
          there are only 500 companies) it's a problem.  For example,
          when Wang went bankrupt, S&P decided to replace them by Sun --
          how do you justify such choices?
     
     The value-weighted index is superior to the DJIA type index for
     deep reasons.  Anyone doing modern finance will not use the DJIA
     type index.  A glimmer of the reasoning for this is as follows: If
     I held a portfolio with equal number of shares of each of the 30
     DJIA companies then the DJIA index would accurately reflect my
     capital gains.  But we know that it is possible to find a portfolio
     which has the same returns as the DJIA portfolio but at a smaller
     risk.  (This is a mathematical fact). 
     
     Thus, by definition, nobody is ever going to own a DJIA portfolio. 
     In contrast, there is an extremely good interpretation for the
     value weighted portfolio -- it yields the highest returns you can
     get for its level of risk.  Thus you would have good reason for
     owning a value-weighted market portfolio, thus justifying it's
     index. 
     
     Yet another intuition about the value-weighted index -- a smart
     investor is not going to ever buy equal number of shares of a given
     set of companies, which is what the equally weighted price index
     tracks.  If you take into consideration that the price movements of
     companies are correlated with others, you are going to hedge your
     returns by buying different proportions of company shares.  This is
     in effect what the market capitalization weighted index does, and
     this is why it is a smart index to follow. 
     
     One very neat property of this kind of index is that it is readily
     applied to industry indexes.  Thus you can simply apply the above
     formula to all machine tool companies, and you get a machine tool
     index.  This industry-index idea is conceptually sound, with
     excellent interpretations.  Thus on a day when the market index
     goes up 6%, if machine tools goes up 10%, you know the market found
     some good news on machine tools. 
     
     
Equally weighted returns index
     Here the index is the average of the returns of a certain set of
     companies.  Value Line publishes two versions of it:
     
        * The arithmetic index:
          ( VLAI / N ) =  Sum (N returns)
          
        * The geometric index:
          VLGI  = { Product (1 + return) over N } ^ { 1 / n },
          which is just the geometric mean of the N returns. 


Notice that these indexes imply that the dollar value on each company
has to be the same.  Discussed further in Bodie, Kane, and Marcus,
Investments , pg 66. 


--------------------Check http://invest-faq.com/ for updates------------------

Compilation Copyright (c) 2003 by Christopher Lott.

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