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The Investment FAQ (part 2 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/part2
Version: $Id: part02,v 1.62 2005/01/05 12:40:47 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 2 of 20.  The web site
always has the latest version, including in-line links. Please browse

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 2005 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.


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
Please send comments and new submissions to the compiler.

--------------------Check for updates------------------

Subject: Advice - Beginning Investors

Last-Revised: 1 Aug 1998
Contributed-By: Steven Pearson, E.  Green, Chris Lott ( contact me )

Investing is just one aspect of personal finance.  People often seem to
have the itch to try their hand at investing before they get the rest of
their act together.  This is a big mistake.  For this reason, it's a
good idea for "new investors" to hit the library and read maybe three
different overall guides to personal finance - three for different
perspectives, and because common themes will emerge (repetition implies
authority?).  Personal finance issues include making a budget, sticking
to a budget, saving money towards major purchases or retirement,
managing debt appropriately, insuring your property, etc.  Appropriate
books that focus on personal finance include the following (the links
point to

   * Andrew Tobias
     The Only Investment Guide You'll Ever Need
   * Eric Tyson
     Personal Finance for Dummies (4th edn.)
   * Janet Bamford et al. 
     The Consumer Reports Money Book: How to Get It, Save It, and Spend
     It Wisely (3rd edn) (out of print; used copies available)

Another great resource for learning about investing, insurance, stocks,
etc.  is the Wall Street Journal's Section C front page.  Beginners
should make a special effort to get the Friday edition of the WSJ
because a column named "Getting Going" usually appears on that day and
discusses issues in, well, getting going on investments.  If you don't
want to spend the dollar or so for the WSJ, try your local library. 

What I am specifically NOT talking about is most anything that appears
on a list of investing/stock market books that are posted in
misc.invest.* from time to time.  This includes books like Market Logic,
One Up on Wall Street, Beating the Dow, Winning on Wall Street, The
Intelligent Investor, etc.  These are not general enough.  They are
investment books, not personal finance books. 

Many "beginning investors" have no business investing in stocks.  The
books recommended above give good overall money management, budgeting,
purchasing, insurance, taxes, estate issues, and investing backgrounds
from which to build a personal framework.  Only after that should one
explore particular investments.  If someone needs to unload some cash in
the meantime, they should put it in a money market fund, or yes, even a
bank account, until they complete their basic training. 

While I sympathize with those who view this education as a daunting
task, I don't see any better answer.  People who know next to nothing
and always depend on "professional advisors" to hand-hold them through
all transactions are simply sheep asking to be fleeced (they may not
actually be fleeced, but most of them will at least get their tails
bobbed).  In the long run, an individual is the only person ultimately
responsible for his or her own financial situation. 

Beginners may want to look further in The Investment FAQ for the
articles that discuss the basics of mutual funds , basics of stocks ,
and basics of bonds .  For more in-depth material, browse the Investment
FAQ bookshelf with its recommended books about personal finance and

--------------------Check for updates------------------

Subject: Advice - Buying a Car at a Reasonable Price

Last-Revised: 1 Aug 2001
Contributed-By: Kyle Busch (kbusch at

Before making a purchase, especially a large one, most buyers ponder an
equation that goes something like: What is it going to cost me, and will
that equal what I am going to get?

Consider that equation when buying your next vehicle.  Naturally, you
want to get the most vehicle for the money you spend.  Here are several
tips that will help you to get more for your money. 

First, and foremost, consider eliminating some of the steep depreciation
cost incurred during the first three years of vehicle ownership by
purchasing a 2- to 3- year-old used vehicle. 

The price can be further reduced by paying cash.  However, if you need
to finance your next vehicle purchase, consider doing the following to
keep its cost closer to the "as if you were paying cash" figure. 
   * Take the time to carefully identify your current and your future
     transportation needs, and choose an appropriate
     vehicle.Transportation represents different things to different
     people.  For some drivers, it represents status in society.  Other
     drivers place greater emphasis on reliably just getting from point
     A to points B and C.  The more closely that you match your driving
     needs with the vehicle you buy, the more driving pleasure you will
     experience and the more likely you will want to hold on to the
     If you can't fully identify your transportation needs or the
     vehicle that can best satisfy them, consult the April issue of
     Consumer Reports at a public library.  The publication groups
     vehicles into categories, provides frequency-of-repair information
     for many vehicles, and gives vehicle price information.  It is a
     good idea to identify 2 or 3 vehicles in a particular category that
     meet your transportation needs.This enables some latitude when
     shopping for the vehicle.  =
   * Identify how much you can afford to spend per month on
     transportation.  A rule of thumb suggests that the cost to rent an
     apartment per month should not be greater than 25 percent of your
     monthly net pay.The cost of an auto loan should not exceed 10 to 12
     percent of your monthly net pay.  In some instances, leasing a
     vehicle could be a better option than taking out a loan. 
   * The vehicle down payment should be the largest possible, and the
     amount of money borrowed the lowest possible.  In addition,
     borrowing money for the shortest period of time (i.e., a 24-month
     loan rather than a 48-month loan) will reduce the overall cost of
     the loan. 
   * Identify the various loan sources such as banks, savings and loans,
     credit unions, and national lenders (i.e., go online to ask and specify "automobile financing sources").  In regard
     to national financing vs.  local financing, it can be useful to
     determine what the cost of a loan would be from the national
     sources, but accept a loan from a local source if the loan cost is
     comparable or nearly comparable between the two.  Compare the APR
     (annual percentage rate) that each of the sources will charge for
     the loan.  The cost of a loan is negotiable.  Therefore, be certain
     to inform each source what the others have to offer.  In addition
     to the loan's APR, remember to also compare the other costs
     associated with a loan, such as loan insurance and loan processing
   * Be certain to read and understand any fine print contained in the
     loan contract.  Insist that the loan contract gives you the option
     of making payments early and that the payments will be applied on
     the loan principle with no penalty or extra cost if you payoff the
     loan early. 
   * Do not settle for a vehicle that does not entirely meet your
     transportation needs because of low dealer or manufacturer
     incentive financing.Sometimes dealers or manufactures offer
     extremely low APR financing on vehicles that the dealer is having a
     hard time selling.  That's why it helps to have initially
     identified the correct vehicle before encountering the sales
     pitches and other influences of buying a vehicle.  Kyle Busch is
the author of Drive the Best for the Price: How to Buy a Used
Automobile, Sport-Utility Vehicle, or Minivan and Save Money .  To find
out more about the author and this book visit:

--------------------Check for updates------------------

Subject: Advice - Errors in Investing

Last-Revised: 2 Aug 1999
Contributed-By: Chris Lott ( contact me ), Thomas Price (tprice at

The Wall Street Journal of June 18, 1991 had an article on pages C1/C10
on Investment Errors and how to avoid them.  As summarized from that
article, the errors are:
   * Not following an investment objective when you build a portfolio. 
   * Buying too many mutual funds. 
   * Not researching a one-product stock before you buy. 
   * Believing that you can pick market highs and lows (time the
   * Taking profits early. 
   * Not cutting your losses. 
   * Buying the hottest {stock, mutual fund} from last year. 

Here's a recent quote that underscores the last item.  When asked
"What's the biggest mistake individual investors make?" on Wall $treet
Week, John Bogle, founder and senior chairman of Vanguard mutual funds,
said "Extrapolating the trend" or buying the hot stock. 

On a final note, get this quote on market timing:
     In the 1980s if you were out of the market on the ten best
     trading days of the decade you missed one-third of the total

--------------------Check for updates------------------

Subject: Advice - Using a Full-Service Broker

Last-Revised: 23 Mar 1998
Contributed-By: Bill Rini (bill at, Chris Lott ( contact
me )

There are several reasons to choose a full-service broker over a
discount or web broker.  People use a full-service broker because they
may not want to do their own research, because they are only interested
in long-term investing, because they like to hear the broker's
investment ideas, etc.  But another important reason is that not
everybody likes to trade.  I may want retirement planning services from
my broker.  I may want to buy 3 or 4 mutual funds and have my broker
worry about them.  If my broker is a financial planner, perhaps I want
tax or estate advice on certain investment options.  Maybe I'm saving
for my newborn child's education but I have no idea or desire to work
out a plan to make sure the money is there when she or he needs it. 

A huge reason to stick with a full-service broker is access to initial
public offerings (IPOs).  These are generally reserved for the very best
clients, where best is defined as "someone who generates lots of
revenue," so someone who trades just a few times a year doesn't have a
chance.  But if you can afford to trade frequently at the full-service
commission rates, you may be favored with access to some great IPOs. 

And the real big one for a lot of people is quite simply time .  Full
service brokerage clients also tend to be higher net worth individuals
as well.  If I'm a doctor or lawyer, I can probably make more money by
focusing on my business than spending it researching stocks.  For many
people today, time is a more valuable commodity than money.  In fact, it
doesn't even have to do with how wealthy you are.  Americans, in
general, work some pretty insane hours.  Spending time researching
stocks or staying up on the market is quality time not spent with
family, friends, or doing things that they enjoy.  On the other hand
some people enjoy the market and for those people there are discount

The one thing that sort of scares me about the difference between full
service and discount brokers is that a pretty good chunk of discount
brokerage firm clients are not that educated about investing.  They look
at a $20 commission (discount broker) and a $50 commission (full service
broker) and they decide they can't afford to invest with a full service
broker.  Instead they plow their life savings into some wonder stock
they heard about from a friend (hey, it's only a $20 commission, why
not?) and lose a few hundred or thousand bucks when the investment goes
south.  Not that a broker is going to pick winners 100% of the time but
at least the broker can guide or mentor a beginning investor until they
learn enough to know what to look for and what not to look for in a
stock.  I look at the $30 difference in what the two types of brokerage
firms charge as the rebate for education and doing my own research.  If
you're not going to educate yourself or do your own research, you don't
deserve the rebate. 

--------------------Check for updates------------------

Subject: Advice - Mutual-Fund Expenses

Last-Revised: 16 Feb 2003
Contributed-By: Austin Lemoine

This article discusses stealth erosion of wealth, more specifically how
mutual-fund expenses erode wealth accumulation. 

Mutual fund expense ratios, and similar investment-related fees, can
seriously erode wealth accumulation over time.  Those fees and expenses
are stealthy, and they go largely unnoticed by investors while steadily
diminishing the value of their investments in both up and down markets. 

What you pay for investing in a mutual fund, exclusive of any sales
charges, is indicated by the "expense ratio" of the fund.  The expense
ratio is the percentage of mutual fund assets paid for operating
expenses, management fees, administrative fees, and all other
asset-based costs incurred by the fund, except brokerage costs.  Those
expenses are reflected in the fund's net asset value (NAV), and they are
not really visible to the fund investor.  The reported net return equals
the fund's gross return minus its costs.  (And expense ratios do not
account for every cost mutual fund investors bear: additional costs
include any sales charges, brokerage commissions paid by the fund and
other significant kinds of indirect trading costs.)

Mutual fund expense ratios range from less than 0.20 percent for
low-cost index funds to well over 2 percent for actively managed funds. 
The average is 1.40 percent for the more than 14,000 stock and bond
mutual funds currently available, according to Morningstar.  In dollar
terms, that's $14 a year in fees for each $1,000 of investment value; or
a net value of $986.  That might not seem like a big deal, but over time
fees compound to erode investment value. 

Let's say the gross return in real terms (after inflation) of a broadly
diversified stock mutual fund will be 7 percent a year, excluding
expenses.  (The 7 percent figure is consistent with returns for the U.S. 
stock market from 1802 through 2001, as reported in Jeremy Siegel's
book, Stocks for the Long Run, 3rd edition.) Say the fund has an expense
ratio of 1.25 percent.  And say you invest $1,000 in the fund at the
start of every year.  (The figure of $1,000 is arbitrary, and investment
values below can be extrapolated to any annual contribution amount.)

Compounding at 7 percent, your gross investment value would be $6,153
after 5 years; $14,783 after 10 years; $43,865 after 20 years; $101,073
after 30 years; and $213,609 after 40 years.  But with a 1.25 percent
expense ratio, your investment compounds at 7.0 minus 1.25 or 5.75
percent, not 7 percent.  So your investment would actually be worth
$5,931 after 5 years; $13,776 after 10 years; $37,871 after 20 years;
$80,015 after 30 years; and $153,727 after 40 years.  Fund expenses
account for the difference in value over time, with greater expenses
(and/or lower returns) having a greater negative impact on net
investment value. 

That 1.25 percent expense ratio consumes $222 (or 3.6 percent) of the
$6,153 gross value over 5 years; 6.8 percent of gross value over 10
years; 13.6 percent over 20 years; and 20.8 percent over 30 years.  Over
40 years, the $59,882 of fund expenses devour 28.0 percent of the
$213,609 gross value.  In other words, only 72.0 percent of gross
investment value is left after 40 years, a withering erosion of wealth. 

By contrast, let's say there's a broad-based index fund with 7 percent
real return but a 0.25 percent expense ratio.  Putting $1,000 at the
start of each year into that fund, the 0.25 percent expense ratio would
consume just 2.9 percent of gross investment value after 20 years.  Over
40 years, index fund expenses would total $13,759, a modest 6.4 percent
of gross value; so that the fund would earn 93.6 percent of gross value. 
With expenses included, investment value is 30 percent higher after 40
years with the lower cost fund.  (Even lower expense ratios can be found
among lowest-cost index funds and broad-based exchange-traded funds. 
And funds with higher expenses do not outperform comparable funds with
lower expenses.)

Over the next ten to twenty years, expense ratios and similar fees could
be a huge millstone on wealth accumulation and wealth preservation.  To
see why, let's review what's happened since March 2000. 

Like a massive hurricane, the stock market has inflicted damage on
almost every portfolio in its path.  From the peak of March 2000 to the
lows of early October 2002, it's estimated that falling stock prices
wiped out over $7 trillion in market value.  While the market has moved
off its lows, we hope the worst is over. 

How long will the market take to "heal itself?" It could take a long
time.  A growing consensus holds that stocks just won't deliver the
returns we grew accustomed to from 1984 to 1999.  If history is a guide,
real stock returns could average 2 to 4 percent a year over the 10 to 20
years following March 2000. 

If lower expectations for stock returns materialize, mutual fund fees
and expenses will have an even greater adverse impact on wealth
accumulation, and especially on wealth preservation and income security
at retirement. 

Let's say you'll want $40,000 income from your 401(k) assets without
drawing down principal.  If real investment return is 4 percent you'll
need $40,000 divided by 0.04 or $1 million principal.  But if you're
paying 1 percent in fees your real return is 3 percent, so you'll need
$40,000 divided by 0.03 or $1.333 million principal; and if 2 percent,
$2 million.  The arithmetic is brutal!

It's clear that mutual fund costs and similar fees can be detrimental to
investment values over time.  Fund sales charges exacerbate the problem. 
Consider investing in lower-cost funds wherever possible. 

For more insights from Austin Lemoine, please visit the web site for
Austin Lemoine Capital Management:

--------------------Check for updates------------------

Subject: Advice - One-Line Wisdom

Last-Revised: 22 Aug 1993
Contributed-By: Maurice Suhre

This is a collection of one-line pieces of investment wisdom, with brief
explanations.  Use and apply at your own risk or discretion.  They are
not in any particular order. 

Hang up on cold calls. 
     While it is theoretically possible that someone is going to offer
     you the opportunity of a lifetime, it is more likely that it is
     some sort of scam.  Even if it is legitimate, the caller cannot
     know your financial position, goals, risk tolerance, or any other
     parameters which should be considered when selecting investments. 
     If you can't bear the thought of hanging up, ask for material to be
     sent by mail. 
Don't invest in anything you don't understand. 
     There were horror stories of people who had lost fortunes by being
     short puts during the 87 crash.  I imagine that they had no idea of
     the risks they were taking.  Also, all the complaints about penny
     stocks, whether fraudulent or not, are partially a result of not
     understanding the risks and mechanisms. 
If it sounds too good to be true, it probably is [too good to be true]. 
     Also stated as ``There ain't no such thing as a free lunch
     (TANSTAAFL).'' Remember, every investment opportunity competes with
     every other investment opportunity.  If one seems wildly better
     than the others, there are probably hidden risks or you don't
     understand something. 
If your only tool is a hammer, every problem looks like a nail. 
     Someone (possibly a financial planner) with a very limited
     selection of products will naturally try to jam you into those
     which s/he sells.  These may be less suitable than other products
     not carried. 
Don't rush into an investment. 
     If someone tells you that the opportunity is closing, filling up
     fast, or in any other way suggests a time pressure, be very leery. 
Very low priced stocks require special treatment. 
     Risks are substantial, bid/asked spreads are large, prices are
     volatile, and commissions are relatively high.  You need a broker
     who knows how to purchase these stocks and dicker for a good price. 

--------------------Check for updates------------------

Subject: Advice - Paying for Investment Advice

Last-Revised: 25 Apr 1997
Contributed-By: Chris Lott ( contact me )

I'm no expert, but there's a simple rule that you should use to evaluate
all advice that is offered to you, especially advice for which someone
who doesn't know you is asking significant sums of money.  Ask yourself
why the person is selling or giving it to you.  If it sounds like a sure
ticket to riches, then why is the person wasting their time on YOU when
they could be out there making piles of dough?

Of course I'm offering advice here in this article, so let's turn the
tables on me right now.  What's in it for me? Well, if you're reading
this article from my web site, look up at the top of the page.  If you
have images turned on, you'll see a banner ad.  I get a tiny payment
each time a person loads one of my pages with an ad.  So my motivation
is to provide informative articles in order to lure visitors to the
site.  Of course if you're reading this from the plain-text version of
the FAQ, you won't see any ads, but please do stop by the site sometime!

So if someone promises you advice that will yield 10-20% monthly
returns, perhaps at a price of some $3,000, you should immediately get
suspicious.  If this were really true - i.e., if you pay for the advice
you'll immediately start getting these returns - you would be making
over 300% annually (compounded).  Hey, that would sure be great, I
wouldn't have a day job anymore.  And if it were true, wouldn't you
think that the person trying to sell it to you would forget all about
selling and just watch his or her money triple every year? But they're
not doing that, which should give you a pretty good idea about where the
money's being made, namely from you . 

I'm not trying to say that you should never pay for advice, just that
you should not overpay for advice.  Some advice, especially the sort
that comes from $15 books on personal finance and investments can easily
be worth ten times that sum.  Advice from your CPA or tax advisor will
probably cost you a 3 or even 4-digit figure, but since it's specialized
to your case and comes from a professional, that's probably money well

It seems appropriate to close this article with a quote that I learned
from Robert Heinlein books, but it's probably older than that:
     TANSTAAFL - there ain't no such thing as a free lunch. 

--------------------Check for updates------------------

Subject: Advice - Researching a Company

Last-Revised: 3 Jun 1997
Contributed-By: George Regnery (regnery at

This article gives a basic idea of some steps that you might take to
research a company.  Many sites on the web will help you in your quest
for information, and this article gives a few of them.  You might look
for the following. 
  1. What multiple of earnings is the company trading at versus other
     companies in the industry? The site does
     this comparison reasonably well, and they base it on forward
     earnings instead of historical earnings, which is also good. 
  2. Is the stock near a high or low, and how has it done recently. 
     This is usually considered technical analysis.  More sophisticated
     (or at least more complicated) studies can also be performed. 
     There are several sites that will give you historical graphs; one
     is Yahoo.
  3. When compared with other companies in the industry, how much times
     the book value or times sales is the company trading? For this
     information, the site is a good place to
  4. Does the company have good products, good management, good future
     prospects? Are they being sued? Do they have patents? What's the
     competition like? Do they have long term contracts established? Is
     their brand name recognized? Depending on the industry, some or all
     of these questions may be relevant.  There isn't a simple web site
     for this information, of course.  The Hoover's profiles have some
     limited information to at least let you get a feel for the basics
     of the company.  And the SEC has lots of information in their Edgar
  5. Management.  Does the company have competent people running it? The
     backgrounds of the directors can be found in proxy statements
     (14As) in the Edgar database.  Note that proxies are written by the
     companies, though.  Another thing I would suggest looking at is the
     compensation structure of the CEO and other top management.  Don't
     worry so much about the raw figure of how they are paid -- instead,
     look to see how that compensation is structured.  If the management
     gets a big base but bonuses are a small portion, look carefully at
     the company.  For some industries, like electric utilities, this is
     OK, because the management isn't going to make a huge difference
     (utilities are highly regulated, and thus the management is
     prevented from making a lot of decisions).  However, in a high tech
     industry, or many other industries, watch your step if the mgmt. 
     gets a big base and the bonus is insignificant.  This means that
     they won't be any better off financially if the company makes a lot
     of profits vs.  no profits (unless, of course, they own a lot of
     stock).  This information is all in the proxies at the SEC.  Also
     check to see if the company has a shareholder rights plan, because
     if they do, the management likely doesn't give a damn about
     shareholder rights, but rather cares about their own jobs.  (These
     plans are commonly used to defend against unfriendly takeovers and
     therefore provide a safety blanket for management.) These
suggestions should get you started.  Also check the article elsewhere in
this FAQ on free information sources for more resources away from the

--------------------Check for updates------------------

Subject: Advice - Target Stock Prices

Last-Revised: 25 Jun 2000
Contributed-By: Uncle Arnie (blash404 at

A target price for a stock is a figure published by a securities
industry person, usually an analyst.  The idea is that the target price
is a prediction, a guess about where the stock is headed.  Target prices
usually are associated with a date by which the stock is expected to hit
the target.  With that explanation out of the way.. 

Why do people suddenly think that the term du jour "target price" has
any meaning?? Consider the sources of these numbers.  They're ALWAYS
issued by someone who has a vested interest in the issue: It could be an
analyst whose firm was the underwriter, it could be an analyst whose
firm is brown-nosing the company, it could be a firm with a large
position in the stock, it could be an individual trying to talk the
stock up so he can get out even, or it could be the "pump" segment of a
pump-and-dump operation.  There is also a chance that the analyst has no
agenda and honestly thinks the stock price is really going places.  But
in all too many cases it's nothing more than wishful guesswork (unless
they have a crystal ball that works), so the advice here: ignore target
prices, especially ones for internet companies. 

--------------------Check for updates------------------

Subject: Analysis - Amortization Tables

Last-Revised: 16 Feb 2003
Contributed-By: Hugh Chou

This article presents the formula for computing monthly payments on
loans.  A listing of thed full series of payments (principal and
interest) that show how a loan is paid off is known as a loan
amortization table.  This article will explain how these tables are
generated for the U.S.  system in which interest is compounded monthly. 

First you must define some variables to make it easier to set up:

P = principal, the initial amount of the loan
I = the annual interest rate (from 1 to 100 percent)
L = length, the length (in years) of the loan, or at least the length
over which the loan is amortized. 

The following assumes a typical conventional loan where the interest is
compounded monthly.  First I will define two more variables to make the
calculations easier:

J = monthly interest in decimal form = I / (12 x 100)
N = number of months over which loan is amortized = L x 12

Okay now for the big monthly payment (M) formula, it is:
         M  =  P  x ------------------------
                      1  - ( 1 + J ) ^ -N
where 1 is the number one (it does not appear too clearly on some

So to calculate it, you would first calculate 1 + J then take that to
the -N (minus N) power, subtract that from the number 1.  Now take the
inverse of that (if you have a 1/X button on your calculator push that). 
Then multiply the result times J and then times P.  Sorry for the long
way of explaining it, but I just wanted to be clear for everybody. 

The one-liner for a program would be (adjust for your favorite
         M = P * ( J / (1 - (1 + J) ** -N))
So now you should be able to calculate the monthly payment, M.  To
calculate the amortization table you need to do some iteration (i.e.  a
simple loop).  I will tell you the simple steps :

  1. Calculate H = P x J, this is your current monthly interest
  2. Calculate C = M - H, this is your monthly payment minus your
     monthly interest, so it is the amount of principal you pay for that
  3. Calculate Q = P - C, this is the new balance of your principal of
     your loan. 
  4. Set P equal to Q and go back to Step 1: You thusly loop around
     until the value Q (and hence P) goes to zero.  Programmers will see
how this makes a trivial little loop to code, but I have found that many
people now surfing on the Internet are NOT programmers and still want to
calculate their mortgages!

Note that just about every PC or Mac has a spreadsheet of some sort on
it, and they are very good tools for doing mortgage analysis.  Most of
them have a built-in PMT type function that will calculate your monthly
payment given a loan balance, interest rate, and the number of terms. 
Check the help text for your spreadsheet. 

Please visit Hugh Chou's web site for a calculator that will generate
amortization tables according to the forumlas discussed here.  He also
offers many other calculators:

--------------------Check for updates------------------

Subject: Analysis - Annual Reports

Last-Revised: 31 Oct 1995
Contributed-By: Jerry Bailey, Chris Lott ( contact me )

The June 1994 Issue of "Better Investing" magazine, page 26 has a
three-page article about reading and understanding company annual
reports.  I will paraphrase:

  1. Start with the notes and read from back to front since the front is
     management fluff. 
  2. Look for litigation that could obliterate equity, a pension plan in
     sad shape, or accounting changes that inflated earnings. 
  3. Use it to evaluate management.  I only read the boring things of
     the companies I am holding for long term growth.  If I am planning
     a quick in and out, such as buying depressed stocks like BBA, CML,
     CLE, etc.), I don't waste my time. 
  4. Look for notes to offer relevant details; not "selected" and
     "certain" assets.  Revenue and operating profits of operating
     divisions, geographical divisions, etc. 
  5. How the company keeps its books, especially as compared to other
     companies in its industry. 
  6. Inventory.  Did it go down because of a different accounting
  7. What assets does the company own and what assets are leased?

If you do much of this, I really recommend just reading the article. 

The following list of resources may also help. 
   * John A.  Tracy has written an an easy-to-read and informative book
     named How to Read a Financial Report (4th edn., Wiley, 1993).  This
     book should give you a good start.  You won't become a graduate
     student in finance by reading it, but it will certainly help you
     grasp the nuts and bolts of annual reports. 
   * IBM offers a web site with much information about understanding
     financial reports:

--------------------Check for updates------------------

Subject: Analysis - Beta and Alpha

Last-Revised: 22 Oct 1997
Contributed-By: Ajay Shah ( ), R.  Shukla
(rkshukla at, Bob Pierce (rbp at

Beta is the sensitivity of a stock's returns to the returns on some
market index (e.g., S&P 500).  Beta values can be roughly characterized
as follows:

   * b less than 0
     Negative beta is possible but not likely.  People thought gold
     stocks should have negative betas but that hasn't been true. 
   * b equal to 0
     Cash under your mattress, assuming no inflation
   * beta between 0 and 1
     Low-volatility investments (e.g., utility stocks)
   * b equal to 1
     Matching the index (e.g., for the S&P 500, an index fund)
   * b greater than 1
     Anything more volatile than the index (e.g., small cap.  funds)
   * b much greater than 1 (tending toward infinity)
     Impossible, because the stock would be expected to go to zero on
     any market decline.  2-3 is probably as high as you will get. 

More interesting is the idea that securities MAY have different betas in
up and down markets.  Forbes used to (and may still) rate mutual funds
for bull and bear market performance. 

Alpha is a measure of residual risk (sometimes called "selecting risk")
of an investment relative to some market index.  For all the gory
details on Alpha, please see a book on technical analysis. 

Here is an example showing the inner details of the beta calculation

Suppose we collected end-of-the-month prices and any dividends for a
stock and the S&P 500 index for 61 months (0..60).  We need n + 1 price
observations to calculate n holding period returns, so since we would
like to index the returns as 1..60, the prices are indexed 0..60.  Also,
professional beta services use monthly data over a five year period. 

Now, calculate monthly holding period returns using the prices and
dividends.  For example, the return for month 2 will be calculated as:
    r_2 = ( p_2 - p_1 + d_2 ) / p_1
Here r denotes return, p denotes price, and d denotes dividend.  The
following table of monthly data may help in visualizing the process. 
(Monthly data is preferred in the profession because investors' horizons
are said to be monthly.)

Nr.  Date Price Div.(*) Return
0 12/31/86 45.20 0.00 --
1 01/31/87 47.00 0.00 0.0398
2 02/28/87 46.75 0.30 0.0011
.  ...  ...  ...  ... 
59 11/30/91 46.75 0.30 0.0011
60 12/31/91 48.00 0.00 0.0267
(*) Dividend refers to the dividend paid during the period.  They are
assumed to be paid on the date.  For example, the dividend of 0.30 could
have been paid between 02/01/87 and 02/28/87, but is assumed to be paid
on 02/28/87. 

So now we'll have a series of 60 returns on the stock and the index
(1...61).  Plot the returns on a graph and fit the best-fit line
(visually or using some least squares process):

          |         *   /
   stock  |  *    *  */ *
   returns|    *  * /      *
          |   *   /    *
          | *   /*  *     *
          |   /  *  *
          | /    *
          +------------------------- index returns

The slope of the line is Beta.  Merrill Lynch, Wells Fargo, and others
use a very similar process (they differ in which index they use and in
some econometric nuances). 

Now what does Beta mean? A lot of disservice has been done to Beta in
the popular press because of trying to simplify the concept.  A beta of
1.5 does not mean that is the market goes up by 10 points, the stock
will go up by 15 points.  It doesn't even mean that if the market has a
return (over some period, say a month) of 2%, the stock will have a
return of 3%.  To understand Beta, look at the equation of the line we
just fitted:

stock return = alpha + beta * index return

Technically speaking, alpha is the intercept in the estimation model. 
It is expected to be equal to risk-free rate times (1 - beta).  But it
is best ignored by most people.  In another (very similar equation) the
intercept, which is also called alpha, is a measure of superior

Therefore, by computing the derivative, we can write:
Change in stock return = beta * change in index return

So, truly and technically speaking, if the market return is 2% above its
mean, the stock return would be 3% above its mean, if the stock beta is

One shot at interpreting beta is the following.  On a day the (S&P-type)
market index goes up by 1%, a stock with beta of 1.5 will go up by 1.5%
+ epsilon.  Thus it won't go up by exactly 1.5%, but by something

The good thing is that the epsilon values for different stocks are
guaranteed to be uncorrelated with each other.  Hence in a diversified
portfolio, you can expect all the epsilons (of different stocks) to
cancel out.  Thus if you hold a diversified portfolio, the beta of a
stock characterizes that stock's response to fluctuations in the market

So in a diversified portfolio, the beta of stock X is a good summary of
its risk properties with respect to the "systematic risk", which is
fluctuations in the market index.  A stock with high beta responds
strongly to variations in the market, and a stock with low beta is
relatively insensitive to variations in the market. 

E.g.  if you had a portfolio of beta 1.2, and decided to add a stock
with beta 1.5, then you know that you are slightly increasing the
riskiness (and average return) of your portfolio.  This conclusion is
reached by merely comparing two numbers (1.2 and 1.5).  That parsimony
of computation is the major contribution of the notion of "beta". 
Conversely if you got cold feet about the variability of your beta = 1.2
portfolio, you could augment it with a few companies with beta less than

If you had wished to figure such conclusions without the notion of beta,
you would have had to deal with large covariance matrices and nontrivial

Finally, a reference.  See Malkiel, A Random Walk Down Wall Street , for
more information on beta as an estimate of risk. 

--------------------Check for updates------------------

Subject: Analysis - Book-to-Bill Ratio

Last-Revised: 19 Aug 1993
Contributed-By: Timothy May

The book-to-bill ration is the ratio of business "booked" (orders taken)
to business "billed" (products shipped and bills sent). 

A book-to-bill of 1.0 implies incoming business = outgoing product. 
Often in downturns, the b-t-b drops to 0.9, sometimes even lower.  A
b-t-b of 1.1 or higher is very encouraging. 

--------------------Check for updates------------------

Subject: Analysis - Book Value

Last-Revised: 23 Mar 1998
Contributed-By: Art Kamlet (artkamlet at

In simplest terms, Book Value is Assets less Liabilities. 

The problem is Assets includes, as stated, existing land & buildings,
inventory, cash in the bank, etc.  held by the company. 

The problem in assuming you can sell off these assets and receive their
listed value is that such values are accounting numbers, but otherwise
pretty unrealistic. 

Consider a company owning a 40 year old building in downtown Chicago. 
That building might have been depreciated fully and is carried on the
books for $0, while having a resale value of millions.  The book value
grossly understates the sell-off value of the company. 

On the other hand, consider a fast-changing industry with 4-year-old
computer equipment which has a few more years to go before being fully
depreciated, but that equipment couldn't be sold for even 10 cents on
the dollar.  Here the book value overstates the sell-off value. 

So consider book value to be assets less liabilities, which are just
numbers, not real items.  If you want to know how much a company should
be sold off for, hire a good investment banker, which is often done on
take-over bids. 

--------------------Check for updates------------------

Subject: Analysis - Computing Compound Return

Last-Revised: 12 Dec 2004
Contributed-By: Paul Randolph (paulr22 at juno dot com), Chris Lott (
contact me )

This article discusses how to compute the effective annual percentage
rate earned by a single investment after a number of years have passed. 
A related concept called "average annual return" is frequently seen when
reading about mutual funds but is computed very differently; it is
discussed briefly at the end of this article.  Another related concept
called "internal rate of return" is used to calculate the percentage
rate earned by an investment made as a series of purchases, such as
monthly investments in a mutual fund; also see the article on that topic
elsewhere in this FAQ. 

To calculate the compound return on an investment, just figure out the
factor by which the original investment multiplied.  For example, if
$1,000 became $3,200 in 10 years, then the multiplying factor is
3,200/1,000 or 3.2.  Now take the 10th root of 3.2 (the multiplying
factor) and you get a compound return of 1.1233498, which means
approximately 12.3% per year.  To see that this works, note that
1.233498 raised to the 10th power equals 3.2. 

Here is another way of saying the same thing.  This calculation assumes
that all gains are reinvested, so the following formula applies:
     TR = (1 + AR) ** YR

where TR is total return (present value/initial value), AR is the
compound annualized return, and YR is years.  The symbol '**' is used to
denote exponentiation (e.g., 2 ** 3 = 8). 

To calculate annualized return, the following formula applies:
     AR = (TR ** (1/YR)) - 1

Thus a total return of 950% in 20 years would be equivalent to an
annualized return of 11.914454%.  Note that the 950% includes your
initial investment of 100% (by definition) plus a gain of 850%. 

For those of you using spreadsheets such as Excel, you would use the
following formula to compute AR for the example discussed above (the
common computer symbol used to denote exponentiation is the caret or hat
on top of the 6). 
     = TR ^ (1 / YR) - 1

where TR = 9.5 and YR = 20.  If you want to be creative and have AR
recalculated every time you open your file, you can substitute something
like the following for YR:
     ( (*cell* - TODAY() ) / 365)

Of course you will have to replace '*cell*' by the appropriate address
of the cell that contains the date on which you bought the security. 

Don't confuse a compound return with something called an average annual
return, which is a simple arithmetic mean (also see the FAQ article on
this topic).  That method simply adds the annual rates and divides by
the number of years.  For example, 5% one year and 10% the next year,
average is 7.5% over those two years. 

Let's compare the two methods with a contrived example.  You invest
$100.  After one year, you have $200, which means in that first year,
the investment returned 100%.  At the end of the second year, you have
$100, which means in that second year, the investment lost 50%.  (In
short, you're back where you started.) Do the calculations for the
compound return and you'll get 0%.  Calculate the average annual return
and you get 25%.  So this contrived example yields a big difference. 
However, common scenarios yield less striking differences, and the
average annual return is a useful approximation. 

Here's the one thing to remember from this article.  When you read an
investment company's statements about their "average return", you should
check carefully just exactly what they calculated. 

--------------------Check for updates------------------

Subject: Analysis - Future and Present Value of Money

Last-Revised: 28 Jan 1994
Contributed-By: Chris Lott ( contact me )

This note explains briefly two concepts concerning the
time-value-of-money, namely future and present value.  Careful
application of these concepts will help you evaluate investment
opportunities such as real estate, life insurance, and many others. 

Future Value
Future value is simply the sum to which a dollar amount invested today
will grow given some appreciation rate. 

To compute the future value of a sum invested today, the formula for
interest that is compounded monthly is:
fv = principal * [ (1 + rrate/12) ** (12 * termy) ]
     fv = future value
     principal = dollar value you have now
     termy = term, in years
     rrate = annual rate of return in decimal (i.e., use .05 for

Note that the symbol '**' is used to denote exponentiation (2 ** 3 = 8). 

For interest that is compounded annually, use the formula:
fv = principal * [ (1 + rrate) ** (termy) ]

     I invest 1,000 today at 10% for 10 years compounded monthly. 
     The future value of this amount is 2707.04. 

Note that the formula for future value is the formula from Case 1 of
present value (below), but solved for the future-sum rather than the
present value. 

Present Value
Present value is the value in today's dollars assigned to an amount of
money in the future, based on some estimate rate-of-return over the
long-term.  In this analysis, rate-of-return is calculated based on
monthly compounding. 

Two cases of present value are discussed next.  Case 1 involves a single
sum that stays invested over time.  Case 2 involves a cash stream that
is paid regularly over time (e.g., rent payments), and requires that you
also calculate the effects of inflation. 

Case 1a: Present value of money invested over time. 
     This tells you what a future sum is worth today, given some rate of
     return over the time between now and the future.  Another way to
     read this is that you must invest the present value today at the
     rate-of-return to have some future sum in some years from now (but
     this only considers the raw dollars, not the purchasing power). 
     To compute the present value of an invested sum, the formula for
     interest that is compounded monthly is:
      pv = ------------------------------
           (1 + rrate/12) ** (12 * termy)
             * future-sum = dollar value you want to have in termy
             * termy = term, in years
             * rrate = annual rate of return that you can expect,
               in decimal
          I need to have 10,000 in 5 years.  The present value of
          10,000 assuming an 8% monthly compounded rate-of-return
          is 6712.10.  I.e., 6712 will grow to 10k in 5 years at
Case 1b: Effects of inflation
     This formulation can also be used to estimate the effects of
     inflation; i.e., compute the real purchasing power of present and
     future sums.  Simply use an estimated rate of inflation instead of
     a rate of return for the rrate variable in the equation. 
          In 30 years I will receive 1,000,000 (a megabuck).  What
          is that amount of money worth today (what is the buying
          power), assuming a rate of inflation of 4.5%? The answer
          is 259,895.65
Case 2: Present value of a cash stream. 
     This tells you the cost in today's dollars of money that you pay
     over time.  Usually the payments that you make increase over the
     term.  Basically, the money you pay in 10 years is worth less than
     that which you pay tomorrow, and this equation lets you compute
     just how much less. 
     In this analysis, inflation is compounded yearly.  A reasonable
     estimate for long-term inflation is 4.5%, but inflation has
     historically varied tremendously by country and time period. 
     To compute the present value of a cash stream, the formula is:
          month=12 * termy   paymt  * (1 + irate) ** int ((month - 1)/ 
     pv = SUM                
          month=1                (1 + rrate/12) ** (month - 1)
             * pv = present value
             * SUM (a.k.a.  sigma) means to sum the terms on the
               right-hand side over the range of the variable
               'month'; i.e., compute the expression for month=1,
               then for month=2, and so on then add them all up
             * month = month number
             * int() = the integral part of the number; i.e., round
               to the closest whole number; this is used to compute
               the year number from the month number
             * termy = term, in years
             * paymt = monthly payment, in dollars
             * irate = rate of inflation (increase in
               payment/year), in decimal
             * rrate = rate of return on money that you can expect,
               in decimal
          You pay $500/month in rent over 10 years and estimate
          that inflation is 4.5% over the period (your payment
          increases with inflation.) Present value is 49,530.57

Stefan Heizmann offers a calculator for NPV on the web.

Two small C programs for computing future and present value on a PC are
also available, which may be convenient if you have a large amount of
data.  See the article Software - Archive of Investment-Related Programs
in this FAQ for more information. 

--------------------Check for updates------------------

Subject: Analysis - Goodwill

Last-Revised: 18 Jul 1993
Contributed-By: John Keefe

Goodwill is an asset that is created when one company acquires another. 
It represents the difference between the price the acquiror pays and the
"fair market value" of the acquired company's assets.  For example, if
JerryCo bought Ford Motor for $15 billion, and the accountants
determined that Ford's assets (plant and equipment) were worth $13
billion, $2 billion of the purchase price would be allocated to goodwill
on the balance sheet.  In theory the goodwill is the value of the
acquired company over and above the hard assets, and it is usually
thought to represent the value of the acquired company's "franchise,"
that is, the loyalty of its customers, the expertise of its employees;
namely, the intangible factors that make people do business with the

What is the effect on book value? Well, book value usually tries to
measure the liquidation value of a company -- what you could sell it for
in a hurry.  The accountants look only at the fair market value of the
hard assets, thus goodwill is usually deducted from total assets when
book value is calculated. 

For most companies in most industries, book value is next to
meaningless, because assets like plant and equipment are on the books at
their old historical costs, rather than current values.  But since it's
an easy number to calculate, and easy to understand, lots of investors
(both professional and amateur) use it in deciding when to buy and sell

--------------------Check for updates------------------

Compilation Copyright (c) 2005 by Christopher Lott.

User Contributions:

Gerri Pisciotta
Report this comment as inappropriate
Nov 9, 2012 @ 9:09 am
My employer accidentally advised the company handling the 401k investment that I had been terminated, when in fact I had not. As a result, withdrawals discontinued from my pay and I missed a couple years of contributions. Since I never withdrew from the plan, is my employer liable for making up these contributions? If I made a lump sum catchup contribution,could they do the same?

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