Archive-name: investment-faq/general/part2
Version: $Id: faq-p2,v 1.35 1996/09/18 12:47:54 lott Exp lott $
Compiler: Christopher Lott, cml@cs.umd.edu

This is the general FAQ for misc.invest, part 2 of 7.

Compilation copyright (c) 1996 by Christopher Lott.  Use and copying
of this information, distribution of the information on electronic
media, and preparation of derivative works based upon this information
are permitted, so long as the following conditions are met:
    + No fees or compensation are charged for this information,
      excluding charges for the media used to distribute it.
    + Proper attribution is given to the authors of individual articles.
    + This copyright notice is included intact.

Disclaimer: This information is made available AS IS, and no
warranty is made about its quality or correctness.

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Subject: Advice - Beginning Investors
Last-Revised: 16 Nov 1993
From: pearson_steven@tandem.com, egreen@east.sun.com

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 read
three different overall guides to personal finance - three for different
perspectives, and because common themes will emerge (repetition implies
authority?).  Anyway, what I'm talking about are books like:

  Madigan and Kasoff,
      The First-Time Investor,
      ISBN 0-13-942376-1
or
  Andrew Tobias,
      The Only Investment Guide You Will Ever Need
      (3 versions, have slightly different titles)
or
  Sylvia Porter,
      New Money Book for the 80s.

Another good source is the Mutual Fund Education Alliance (MFEA); write
them at MFEA, 1900 Erie Street, Suite 120, Kansas City, MO 64116.

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.  You know, 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, you are the only person ultimately responsible
for your own financial situation.

All beginners should read the article about Charles Givens in this FAQ.
Advanced beginners should also check the recommended list of books
about stocks and other investments that also appears in this FAQ.


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Subject: Advice - One-Line Wisdom
Last-Revised: 22 Aug 1993
From: suhre@trwrb.dsd.trw.com

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.  

1.  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.

2.  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.

3.  If it sounds too good to be true, it probably is [too good to be true].
3a. There's no such thing as a free lunch (TNSTAAFL).

    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.

4.  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.

5.  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.

6.  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.


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Subject: Analysis - Annual Reports
Last-Revised: 31 Oct 1995
From: jerry.bailey@stoicbbs.com, investor@cais.com

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 & 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 & 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 method?

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.

Also try an easy-to-read but informative book by John A. Tracy named
_How to Read a Financial Report_ (4th edn., Wiley, 1994).  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. 


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Subject: Analysis - Beta
Last-Revised: 11 Dec 1992
From: RKSHUKLA@SUVM.SYR.EDU, ajayshah@almaak.usc.edu, rbp@investor.pgh.pa.us

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 < 0		Negative beta is possible but not likely.  People thought gold
		stocks should have negative betas but that hasn't been true

b = 0		Cash under your mattress, assuming no inflation

0 < b < 1	Dull investments (e.g., utility stocks)

b = 1		Matching the index (e.g., for the S&P 500, an index fund) 

b > 1		Anything more volatile than the index (e.g., small cap. funds)

b -> 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. 

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

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.
	===========================================
	  #     Date   Price   Dividend(*)   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 even *doesn't* 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 performance.

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 1.5.

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 different.

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
portfolio.

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 1.

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 computations.

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


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Subject: Analysis - Book-to-Bill Ratio
Last-Revised: 19 Aug 1993
From: tcmay@netcom.com

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 = ougoing 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.


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Subject: Analysis - Computing the Rate of Return on Monthly Investments
Last-Revised: 8 May 1995
From: jedwards@ms.uky.edu 

Q: Assume $X is invested at the beginning of the year into some mutual
   fund or like account, with $Y added to the account every month. 
   Now, down the road, if the value at any given month "i" is Vi, what
   conclusions can be drawn from it ?

The relevant formula is F = P(1+i)**n - p((1+i)**n - 1)/i where F is
the future value of your investment (i.e., the value after n periods),
P is the present value of your investment (i.e., the amount of money
you invest initially), p is the payment each period (p is negative if
you are adding money to your account and positive if you are taking
money out of your account), n is the number of periods you are
interested in, and i is the interest rate per period.  Again, this
formula represents investments as negative and withdrawals as
positive, which I believe is in keeping with standard practice.  This
forumula is often used to compute loan payments (the p's with F = 0
and P = the amount borrowed) and that definition results in positive
payments.  

Remember that you cannot manipulate this formula to get a formula for i;
you have to use some sort of iterative method or buy a financial
calculator.  Also keep in mind that i is the interest rate *per period*.   
You may need to compound the rate to obtain a number you can compare
apples-to-apples with other rates.  For instance, a 1 year CD paying 
12% interest is not as good an investment as an investment paying 1%
per month for a year.  If you put $1000 into each, you'll have $1120
in the CD at the end of the year but $1000*(1.01)**12 = $1126.82 in
the other investment due to compounding.  I always convert interest
rates of any kind into a "simple 1-year CD equivalent" for the purposes
of comparison.

A program 'irr' which helps calculate this is discussed in the article
"Software - Investment-Related Programs."


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Subject: Analysis - Computing Compound Return
Last-Revised: 30 Dec 1995
From: bakken@cs.arizona.edu, chen@digital.sps.mot.com, prand@po.harenet.or.jp

To calculate the compounded return, just figure out the factor by which
the investment multiplied.  For examle, $1000 became $3200 in 10 years.
The multiplying factor is 1000/32000 or 3.2.  Now take the 10th root
of 3.2 (the multiplying factor) and you get a compounded return of
1.1233498 (12.3% per year).  To see that this works, note that
1.1233498**10 = 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. To calculate annualized
return, the following formula applies:
        AR = (10 ** ( Log(TR) / 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:
        = 10^(LOG(TR)/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.


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Subject: Analysis - Future and Present Value of Money
Last-Revised: 28 Jan 1994
From: cml@cs.umd.edu

This note explains briefly two concepts concerning the time-value-of-money,
namely future and present value.

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

    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)
    where
    	principal = dollar value you have now
    	termy     = term, in years
    	rrate     = annual rate of return in decimal (i.e., use .05 for 5%)

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

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

* 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:
		          future-sum 
	 pv =  ----------------------------------
	       (1 + rrate/12) ** (12 * termy)
	 where
	     future-sum = dollar value you want in termy years
	     termy = term, in years
	     rrate = annual rate of return that you can expect, in decimal

	 Example:
	     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 8%.  

Case 1b: This formulation can also be used to estimate the effects of
	 inflation; i.e., compute 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.

	 Example:
	     In 30 years I will receive 1,000,000 (a gigabuck).  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.

	 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)/ 12)
	 pv = SUM                ---------------------------------------------
	      month = 1               (1 + rrate/12) ** (month - 1)
	 where
	     month = 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
	     int() function = keep integral part; compute yr nr from mo nr 

	 Example:
	     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

Two small C programs for computing future and present value are available.
See the article "Software - Investment-Related Programs" for more information.


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Subject: Analysis - Goodwill
Last-Revised: 18 Jul 1993
From: keefej@panix.com

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
company. 
 
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 stocks.  


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Subject: Analysis - P/E Ratio
Last-Revised: 22 Jan 1993
From: egreen@east.sun.com, schindler@csa2.lbl.gov

P/E is shorthand for Price/Earnings Ratio.  The price/earnings ratio is
a tool for determining the value the market has placed on a common stock. 
A lot can be said about this little number, but in short, companies
expected to grow and have higher earnings in the future should have a
higher P/E than companies in decline.  For example, if Amgen has a lot
of products in the pipeline, I wouldn't mind paying a large multiple of
its current earnings to buy the stock.  It will have a large P/E.  I am
expecting it to grow quickly. 

P/E is determined by dividing the current market price of one share
of a company's stock by that company's per-share earnings (after-tax
profit divided by number of outstanding shares).  For example, a company
that earned $5M last year, with a million shares outstanding, had
earnings per share of $5.  If that company's stock currently sells for
$50/share, it has a P/E of 10.  Investors are willing to pay $10 for
every $1 of last year's earnings.

P/Es are traditionally computed with trailing earnings (earnings from
the year past, called a trailing P/E) but are sometimes computed with
leading earnings (earnings projected for the year to come, called a
leading P/E).  Like other indicators, it is best viewed over time, 
looking for a trend.  A company with a steadily increasing P/E is being
viewed by the investment community as becoming more and more speculative.

PE is a much better comparison of the value of a stock than the price. 
A $10 stock with a PE of 40 is much more "expensive" than a $100 stock
with a PE of 6.  You are paying more for the $10 stock's future earnings
stream.  The $10 stock is probably a small company with an exciting product
with few competitors.  The $100 stock is probably pretty staid - maybe a
buggy whip manufacturer.


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Subject: Analysis - Renting versus Buying a Home
Last-Revised: 21 Nov 1995
From: jmincy@avid.com, cml@cs.umd.edu

This note will explain one way to compare the monetary costs of renting
vs. buying a home.  It is extremely prejudiced towards the US system.
A few small C programs for computing future value, present value, and
loan amortization schedules (used to write this article) are available. 
See the article "Software - Investment-Related Programs" for information
about obtaining them.


1. Abstract

    - If you are guaranteed an appreciation rate that is a few points
      above inflation, buy.
    - If the monthly costs of buying are basically the same as
      renting, buy. 
    - The shorter the term, the more advantageous it is to rent.
    - Tax consequences in the US are fairly minor in the long term.


2. Introduction

The three important factors that affect the analysis the most are the
following: 
    1) Relative cash flows; e.g., rent compared to monthly ownership expenses
    2) Length of term
    3) Rate of appreciation

The approach used here is to determine the present value of the money
you will pay over the term for the home.  In the case of buying, the
appreciation rate and thereby the future value of the home is estimated. 
For home appreciate rates, find something like the tables published by
Case Schiller that show changes in house prices for your region.  The
real estate section in your local newspaper may print it periodically.
This analysis neglects utility costs because they can easily be the
same whether you rent or buy.  However, adding them to the analysis
is simple; treat them the same as the costs for insurance in both cases.

Opportunity costs of buying are effectively captured by the present
value.  For example, pretend that you are able to buy a house without
having to have a mortgage.  Now the question is, is it better to buy
the house with your hoard of cash or is it better to invest the cash
and continue to rent?  To answer this question you have to have
estimates for rental costs and house costs (see below), and you have a
projected growth rate for the cash investment and projected growth
rate for the house.  If you project a 4% growth rate for the house and
a 15% growth rate for the cash then holding the cash would be a much
better investment.

First the analysis for renting a home is presented, then the analysis
for buying.  Examples of analyses over a long term and a short term
are given for both scenarios.


3. Renting a Home.

    * Step 1: Gather data. You will need:
      - monthly rent
      - renter's insurance 	(usually inexpensive)
      - term 			(period of time over which you will rent)
      - estimated inflation rate to compute present value (historically 4.5%)
      - estimated annual rate of increase in the rent (can use inflation rate)

    * Step 2: Compute the present value of the cash stream that you will
      pay over the term, which is the cost of renting over that term.
      This analysis assumes that there are no tax consequences
      (benefits) associated with paying rent.   


3.1 A long-term example of renting

    Rent  		=  990 / month 
    Insurance	 	=  10 / month
    Term		=  30 years
    Rent increases	=  4.5% annually
    Inflation	 	=  4.5% annually
    For this cash stream, present value = 348,137.17.


3.2 A short-term example of renting

    Same numbers, but just 2 years.  Present value = 23,502.38


4. Buying a Home.

  * Step 1: Gather data. You need a lot to do a fairly thorough analysis:  
    - purchase price
    - down payment & closing costs
    - other regular expenses, such as condominium fees
    - amount of mortgage
    - mortgage rate
    - mortgage term
    - mortgage payments (this is tricky for a variable-rate mortgage)
    - property taxes
    - homeowner's insurance (Note: this analysis neglects extraordinary
	risks such as earthquakes or floods that may cause the homeowner
	to incur a large loss due to a high deductible in your policy. 
	All of you people in California know what I'm talking about.)
    - your marginal tax bracket (at what rate is the last dollar taxed)
    - the current standard deduction which the IRS allows

  Other values have to be estimated, and they affect the analysis critically:
    - continuing maintenance costs (I estimate 1/2 of PP over 30 years.)
    - estimated inflation rate to compute present value (historically 4.5%)
    - rate of increase of property taxes, maintenance costs, etc. (infl. rate)
    - appreciation rate of the home (THE most important number of all)

  * Step 2: compute the monthly expense.  This includes the mortgage
    payment, fees, property tax, insurance, and maintenance.  The
    mortgage payment is fixed, but you have to figure inflation into
    the rest.  Then compute the present value of the cash stream.

  * Step 3: compute your tax savings.  This is different in every
    case, but roughly you multiply your tax bracket times the amount
    by which your interest plus other deductible expenses (e.g.,
    property tax, state income tax) exceeds your standard deduction.
    No fair using the whole amount because everyone, even a renter,
    gets the standard deduction for free.  Must be summed over the
    term because the standard deduction  will increase annually, as
    will your expenses.  Note that late in the mortgage your interest
    payments will be be well below the standard deduction.  I compute
    savings of about 5% for the 33% tax bracket. 

  * Step 4: compute the present value.  First you compute the future
    value of the home based on the purchase price, the estimated
    appreciation rate, and the term.  Once you have the future value,
    compute the present value of that sum based on the inflation rate
    you estimated earlier and the term you used to compute the future
    value.  If appreciation is greater than inflation, you win.  Else
    you break even or even lose.  

    Actually, the math of this step can be simplified as follows:

                             / periods + appr_rate/100 \ ^ (periods * yrs)
    prs-value = cur-value * |  -----------------------  |
                             \ periods + infl_rate/100 /

  * Step 5: Compute final cost.  All numbers must be in present value.
    Final-cost = Down-payment + S2 (expenses) - S3 (tax sav) - S4 (prop value)


4.1  Long-term example Nr. 1 of buying 

  * Step 1 - the data:
    Purchase price   =  145,000
    Down payment etc =  10,000
    Mortgage amount  =  140,000
    Mortgage rate    =  8.00%
    Mortgage term    =  30 years
    Mortgage payment =  1027.27 / mo
    Property taxes   =  about 1% of valuation; I'll use 1200/yr = 100/mo
			(which increases same as inflation, we'll say)
    Homeowner's ins. =  50 / mo
    Condo. fees etc. =  0 
    Tax bracket	     =  33%
    Standard ded.    =  5600

  Estimates:
    Maintenance      =  1/2 PP is 72,500, or 201/mo; I'll use 200/mo
    Inflation rate   =  4.5% annually
    Prop. taxes incr =  4.5% annually
    Home appreciates =  6% annually (the NUMBER ONE critical factor)

  * Step 2 - the monthly expense, both fixed and changing components: 
    Fixed component is the mortgage at 1027.27 monthly.  
    Present value = 203,503.48 
    Changing component is the rest at   350.00 monthly.  
    Present value = 121,848.01 
    Total from Step 2: 325,351.49

  * Step 3 - the tax savings.
    I use my loan program to compute this.  Based on the data given
    above, I compute the savings: Present value = 14,686.22.  
    Not much when compared to the other numbers.

  * Step 4 - the future and present value of the home.
    See data above.  Future value = 873,273.41 and present value =
    226,959.96 (which is larger than 145k since appreciation is larger
    than inflation).  Before you compute present value, you should
    subtract reasonable closing costs for the sale; for example, a
    real estate broker's fee. 

  * Step 5 - the final analysis for 6% appreciation.
    Final = 10,000 + 325,351.49 - 14,686.22 - 226,959.96
          = 93,705.31

So over the 30 years, assuming that you sell the house in the 30th
year for the estimated future value, the present value of your total
cost is 93k. (You're 93k in the hole after 30 years ~~ you only paid
260.23/month.) 


4.2  Long-term example Nr. 2 of buying 

All numbers are the same as in the previous example, however the home
appreciates 7%/year.  
Step 4 now comes out FV=1,176,892.13 and PV=305,869.15
Final = 10,000 + 325,351.49 - 14,686.22 - 305,869.15
      = 14796.12

So in this example, 7% was an approximate break-even point in the
absolute sense; i.e., you lived for 30 years at near zero cost in
today's dollars. 


4.3  Long-term example Nr. 3 of buying

All numbers are the same as in the previous example, however the home
appreciates 8%/year.  
Step 4 now comes out FV=1,585,680.80 and PV=412,111.55
Final = 10,000 + 325,351.49 - 14,686.22 - 412,111.55
      = -91,446.28

The negative number means you lived in the home for 30 years and left
it in the 30th year with a profit; i.e., you were paid to live there.


4.4 Long-term example Nr. 4 of buying 

All numbers are the same as in the previous example, however the home
appreciates 2%/year.  
Step 4 now comes out FV=264,075.30 and PV=68,632.02
Final = 10,000 + 325,351.49 - 14,686.22 - 68,632.02
      = 252,033.25

In this case of poor appreciation, home ownership cost 252k in today's
money, or about 700/month.  If you could have rented for that, you'd
be even. 


4.5 Short-term example Nr. 1 of buying

All numbers are the same as long-term example Nr. 1, but you sell the
home after 2 years.  Future home value in 2 years is 163,438.17 
Cost  = down&cc + all-pymts - tax-savgs - pv(fut-home-value - remaining debt)
      = 10,000  + 31,849.52 - 4,156.81  - pv(163,438.17 - 137,563.91)
      = 10,000  + 31,849.52 - 4,156.81  - 23,651.27
      = 14,041.44


4.6 Short-term example Nr. 2 of buying

All numbers are the same as long-term example Nr. 4, but you sell the
home after 2 years.  Future home value in 2 years is 150,912.54 
Cost  = down&cc + all-pymts - tax-savgs - pv(fut-home-value - remaining debt)
      = 10,000  + 31,849.52 - 4,156.81  - pv(150912.54 - 137,563.91)
      = 10,000  + 31,849.52 - 4,156.81  - 12,201.78
      = 25,490.93


5.  A Question

Q: Is it true that you can usually rent for less than buying?

Answer 1:  It depends.  It isn't a binary state.  It is a fairly
complex set of relationships.

In large metropolitan areas, where real estate is generally much more
expensive than elsewhere, then it is usually better to rent, unless
you get a good appreciation rate or if you are going to own for a long
period of time.  It depends on what you can rent and what you can buy.
In other areas, where real estate is relatively cheap, I would say it
is probably better to own.  

On the other hand, if you are currently at a market peak and the
country is about to go into a recession it is better to rent and let
property values and rent fall.  If you are currently at the bottom of
the market and the economy is getting better then it is better to own.

Answer 2:  When you rent from somebody, you are paying that person to
assume the risk of homeownership.  Landlords are renting out property
with the long term goal of making money.  They aren't renting out
property because they want to do their renters any special favors.
This suggests to me that it is generally better to own.


6. Conclusion

Once again, the three important factors that affect the analysis the
most are cash flows, term, and appreciation.  If the relative cash
flows are basically the same, then the other two factors affect the
analysis the most.  

The longer you hold the house, the less appreciation you need to beat
renting.  This relationship always holds, however, the scale changes.
For shorter holding periods you also face a risk of market downturn.
If there is a substantial risk of a market downturn you shouldn't buy
a house unless you are willing to hold the house for a long period.

If you have a nice cheap rent controlled apartment, then you should
probably not buy.

There are other variables that affect the analysis, for example, the
inflation rate.  If the inflation rate increases, the rental scenario
tends to get much worse, while the ownership scenario tends to look
better.


-----------------------------------------------------------------------------

Subject: Analysis - Same-Store Sales
Last-Revised: 9 Jan 1996
From: stevemack@beta.delphi.com

When earnings for retail outlets like KMart, Walmart, Best Buy, etc.
are reported, we see two figures, namely total sales and same-store
sales.  Same-store comparisons measure the growth in sales, excluding
the impact of newly opened stores.  Generally, sales from new stores
are not reflected in same-store comparisons until those stores have
been open for fifty three weeks.  With these comparisons, analysts can
measure sales performance against other retailers that may not be as
aggresive in opening new locations during the evaluated period.


-----------------------------------------------------------------------------

Subject: Analysis - Technical
Last-Revised: 12 Feb 1994
From: suhre@trwrb.dsd.trw.com

The following material introduces technical analysis and is intended to
be educational.  If you are intrigued, do your own reading.  The answers
are brief and cannot possibly do justice to the topics.  The references
provide a substantial amount of information.  The contributions of the
reviewers is appreciated.

First, the references:

  1. Technical Analysis of the Futures Markets, by John J. Murphy. 
     New York Institute of Finance.
  
  2. Technical Analysis Explained, by Martin Pring. 
     McGraw Hill.
  
  3. Stan Weinstein's Secrets for Profiting in Bull and Bear Markets, by
     Stan Weinstein.  Dow Jones-Irwin.

Next, the discussion:

1.  What is technical analysis?

Technical analysis attempts to use *past* stock price and volume
information to predict *future* price movements.  Note the emphasis.
It also attempts to time the markets.

2.  Does it have any chance of working, or is it just like reading tea leaves?

There are a couple of plausibility arguments.  One is that the chart
patterns represent the past behavior of the pool of investors.  Since
that pool doesn't change rapidly, one might expect to see similar chart
patterns in the future.  Another argument is that the chart patterns
display the action inherent in an auction market.  Since not everyone
reacts to information instantly, the chart can provide some predictive
value.  A third argument is that the chart patterns appear over and over
again.  Even if I don't know why they happen, I shouldn't trade or invest
against them.  A fourth argument is that investors swing from overly
optimistic to excessively pessimistic and back again.  Technical analysis
can provide some estimates of this situation.

A contrary view is that it is just coincidence and there is little, if
any, causality present.  Or that even if there is some sort of causality
process going on, it isn't strong enough to trade off of.

A very contrary view:  The past and future performance of a stock may
be correlated, but that does not mean or imply causality. So, relying
on technical analysis to buy/sell a stock is like relying on the position
of the stars in the atmosphere or the phases of the moon to decide whether
to buy or sell.

3.  I am a fundamentalist.  Should I know anything about technical analysis?

Perhaps.  You should consider delaying purchase of stocks whose chart
patterns look bad, no matter how good the fundamentals.  The market is
telling you something is still awry.  Another argument is that the
technicians won't be buying and they will not be helping the stock move
up.  On the other hand (as the economists say), it makes it easy for
you to buy in front of them.  And, of course, you can ignore technical
analysis viewpoints and rely solely on fundamentals.

4.  What are moving averages?

Observe that a period can be a day, a week, a month, or as little as 1
minute.  Stock and mutual fund charts normally are daily postings or
weekly postings.  An N period (simple) moving average is computed by
summing the last N data points and dividing by N.  Moving averages are
normally simple unless otherwise specified.

An exponential moving average is computed slightly differently.  Let
X[i] be a series of data points.  Then the Exponential Moving Average
(EMA) is computed by

    EMA[i] = (1 - sm) * EMA[i-1] + sm * X[i]

    where sm = 2/(N+1), and EMA[1] = X[1].

"sm" is the smoothing constant for an N period EMA.  Note that the EMA
provides more weighting to the recent data, less weighting to the old data.

4a.  What is Stage Analysis?

Stan Weinstein [Ref 3] developed a theory (based on his observations)
that stocks usually go through four stages in order.  Stage 1 is a time
period where the stock fluctuates in a relatively narrow range.  Little
or nothing seems to be happening and the stock price will wander back
and forth across the 200 day moving average.  This period is generally
called "base building".  Stage 2 is an advancing stage characterized by
the stock rising above the 200 and 50 day moving averages.  The stock
may drop below the 50 day average and still be considered in Stage 2.
Fundamentally, Stage 2 is triggered by a perception of improved conditions
with the company.  Stage 3 is a "peaking out" of the stock price action. 
Typically the price will begin to cross the 200 day moving average, and
the average may begin to round over on the chart.  This is the time to
take profits.  Finally, the Stage 4 decline begins.  The stock price drops
below the 50 and 200 day moving averages, and continues down until a new
Stage 1 begins.  Take the pledge right now:  hold up your right hand and
say "I will never purchase a stock in Stage 4".  One could have avoided
the late 92-93 debacle in IBM by standing aside as it worked its way
through a Stage 4 decline.

5.  What is a whipsaw?

This is where you purchase based on a moving average crossing (or some
other signal) and then the price moves in the other direction giving a
sell signal shortly thereafter, frequently with a loss.  Whipsaws can
substantially increase your commissions for stocks and excessive mutual
fund switching may be prohibited by the fund manager.

5a.  Why a 200 day moving average as opposed to 190 or 210?

Moving averages are chosen as a compromise between being too late to
catch much move after a change in trend, and getting whipsawed.  The
shorter the moving average, the more fluctuations it has.  There are
considerations regarding cyclic stock patterns and which of those are
filtered out by the moving average filter.  A discussion of filters is
far beyond the scope of this FAQ.  See Hurst's book on stock
transactions for some discussion.

6.  Explain support and resistance levels, and how to use them.

Suppose a stock drops to a price, say 35, and rebounds.  And that this
happens a few more times.  Then 35 is considered a "support" level.
The concept is that there are buyers waiting to buy at that price.
Imagine someone who had planned to purchase and his broker talked him
out of it.  After seeing the price rise, he swears he's not going to
let the stock get away from him again.  Similarly, an advance to a
price, say 45, which is repeatedly followed by a pullback to lower
prices because a "resistance" level.  The notion is that there are
buyers who purchased at 45 and have watched a deterioration into a loss
position.  They are now waiting to get out even.  Or there are sellers
who consider 45 overvalued and want to take their profits.

One strategy is to attempt to purchase near support and take profits near
resistance.  Another is to wait for an "upside breakout" where the stock
penetrates a previous resistance level.  Purchase on anticipation of a
further move up.  [See references for more details.]

The support level (and subsequent support levels after rises) can provide
information for use in setting stops.  See the "About Stocks" section of
the FAQ for more details.  

6a.  What would cause these levels to be penetrated?

Abrupt changes in a company's prospects will be reacted to in the stock
market almost immediately.  If the news is extreme enough, the reaction
will appear as a jump or gap in prices.  More modest changes will
result, in general, in more modest changes in price.

6b.  What is an "upside breakout"?

If a stock has traded in a narrow range for some time (i.e. built a
base) and then advances above the resistance level, this is said to be an
"upside breakout".  Breakouts are suspect if they do not occur on high
volume (compared to average daily volume).  Some traders use a "buy stop"
which calls for purchase when a stock rises above a certain price.

6c.  Is there a "downside breakout"?

Not by that name -- the opposite of upside breakout is called
"penetration of support" or "breakdown".  Corresponding to "buy stops,"
a trader can set a "sell stop" to exit a position on breakdown.

7.  Explain breadth measurements and how to use them.

A breadth measurement is something taken across a market.  For example,
looking at the number of advancing stocks compared to declining stocks
on the NYSE is a breadth measurement.  Or looking at the number of stocks
above their 200 day moving average.  Or looking at the percentage of stocks
in Stage 1 and 2 configurations.  In general, a technically healthy market
should see a lot of stocks advancing, not just the Dow 30.  If the breadth
measurements are poor in an advancing sense and the market has been
advancing for some time, then this can indicate a market turning point
(assuming that the advancing breadth is declining) and you should consider
taking profits, not entering new long positions, and/or tightening stops. 
(See the divergence discussion.)

7a.  What is a divergence?  What is the significance?

In general, a divergence is said to occur when two readings are not
moving generally together when they would be expected to.  For example,
if the DJIA moves up a lot but the S&P 500 moves very little or even
declines, a divergence is created.  Divergences can signify turning
points in the market.  At a major market low, the "blue chip" stocks
tend to move up first as investors becoming willing to purchase quality. 
Hence the S&P 500 may be advancing while the NYSE composite is moving
very little.  Divergences, like everything else, are not 100 per cent
reliable.  But they do provide yellow or red alerts.  And the bigger the
divergence, the stronger the signal.  Divergence and breadth are related
concepts.  (See the breadth discussion.)

8.  How much are charting services and what ones are available?

They aren't cheap.  Daily Graphs (weekly charts with daily prices) is
$465 for the NYSE edition, $432 for the AMEX/OTC edition.  Somewhat
cheaper for biweekly or monthly.  Mansfield charts are weekly with weekly
prices.  Mansfield shows about 2.5 years of action, Daily Graphs shows 1
year or 6 months for the less active stocks.

S&P Trendline Chart Guide is about $145 per year.  It provides over 4,000
charts.  These charts show one year of weekly price/volume data and do not
provide nearly the detail that Daily Graphs do.  You get what you pay for.

There are other charting services available.  These are merely representative.

9.  Can I get charts with a PC program?

Yes.  There are many programs available for various prices.  Daily quotes
run about $35 or so a month from Dial Data, for example.  Or you can
manually enter the data from the newspaper.

10.  What would a PC program do that a charting service doesn't?

Programs provide a wide range of technical analysis computations in
addition to moving averages.  RSI, MACD, Stochastics, etc., are routinely
included.  See Murphy's book [Ref 1] for definitions.  Frequently you can
change the length of the moving averages or other parameters.  As another
example, AIQ StockExpert provides an "expert rating" suggesting purchase
or short depending on the rating.  Intermediate values of the rating are
less conclusive.

11.  What does a charting service do that PC doesn't?

Charts generally contain a fair amount of fundamental information such
as sales, dividends, prior growth rates, institutional ownership.

11a.  Can I draw my own charts?

Of course.  For example, if you only want to follow a handful of mutual
funds of stocks, charting on a weekly basis is easy enough.  EMAs are
also easy enough to compute, but will take a while to overcome the lack
of a suitable starting value.

12.  What about wedges, exhaustion gaps, breakaway gaps, coils, saucer
     bottoms, and all those other weird formations?

The answer is beyond the scope of this FAQ article.  Such patterns can be
seen, particularly if you have a good imagination.  Many believe they are
not reliable.  There is some discussion in Murphy [Ref 1].

13.  Are there any aspects of technical analysis that don't seem quite
     so much like hokum or tea leaf reading?

RSI (Relative Strength Indicator) is based on the observation that a
stock which is advancing will tend to close nearer to the high of the day
than the low.  The reverse is true for declining stocks.  RSI is a formula
which attempts to provide a number which will indicate where you are in
the declining/advancing stage.

14.  Can I develop my own technical indicators?

Yes.  The problem is validating them via some sort of backtesting procedure. 
This requires data and work.  One suggestion is to split the data into
two time periods.  Develop your indicator on one half and then see if it
still works on the other half.  If you aren't careful, you end up
"curve fitting" your system to the data.


-----------------------------------------------------------------------------

Subject: Bonds - Basics
Last-Revised: 7 Jan 1993
From: a_s_kamlet@att.com

Bonds are debt instruments.   Let's say a corporation needs to build
a new office building, or needs to purchase manufacturing equipment,
or needs to purchase aircraft, they will have to raise money.

One way is to arrange for banks or others to lend them money. But a
generally less expensive way is to issue (sell) bonds.  The corporation
will agree to pay dividends on these bonds and at some time in the
future to redeem these bonds.

In the U.S., corporate bonds are often issued in units of $1,000.
When municipalities issue bonds, they are usually in units of $5,000.
Dividends are usually paid every 6 months.

Bondholders are not owners of the corporation.  But if the corporation
gets in financial trouble and needs to dissolve, bondholders must be
paid off in full before stockholders get anything.

If the corporation defaults on any bond payment, any bondholder can
go into bankruptcy court and request the corporation be placed in
bankruptcy.

The price of a bond is a function of prevailing interest rates (as
rates go up, the price of the bond goes down, and vice versa) as
well as the risk perceived for the debt of the particular
corporation.  For example, if the company is in bankruptcy, the
price of the bond will be low.


-----------------------------------------------------------------------------

Subject: Bonds - Moody Bond Ratings
Last-Revised: 7 Nov 1995
From: Bill Rini <billman@centcon.com>

Moody's Bond Ratings are intended to characterize the risk of holding
a bond.  These ratings, or risk assessments, in part determine the
interest that an issuer must pay to attract purchasers to the bonds.
All information herein was obtained from Moody's Bond Record.

Aaa: Bonds which are rated Aaa are judged to be of the best quality.
     They carry the smallest degree of investment risk and are
     generally referred to as "gilt edged."  Interest payments are
     protected by a large or an exceptionally stable margin and
     principal is secure.  While the various protective elements are
     likely to change, such changes as can be visualized are most
     unlikely to impair the fundamentally strong position of such
     issues. 

Aa:  Bonds which are rated Aa are judged to be of high quality by all
     standards. Together with the Aaa group they comprise what are
     generally known as high grade bonds.  They are rated lower than
     the best bonds because margins of protection may not be as large
     as in Aaa securities or fluctuation of protective elements may be
     of greater amplitude or there may be other elements present which
     make the long-term risk appear somewhat larger than the Aaa
     securities. 

A:   Bonds which are rated A possess many favorable investment
     attributes and are considered as upper-medium-grade obligations.
     Factors giving security to principal and interest are considered
     adequate, but elements may be present which suggest a
     susceptibility to impairment some time in the future. 

Baa: Bonds which are rated Baa are considered as medium-grade
     obligations (i.e., they are neither highly protected not poorly
     secured).  Interest payments and principal security appear
     adequate for the present but certain protective elements may be
     lacking or may be characteristically unreliable over any great
     length of time.  Such bonds lack outstanding investment
     characteristics and in fact have speculative characteristics as
     well. 

Ba:  Bonds which are rated Ba are judged to have speculative elements;
     their future cannot be considered as well-assured.  Often the
     protection of interest and principal payments may be very
     moderate, and thereby not well safeguarded during both good and
     bad times over the future.  Uncertainty of position characterizes
     bonds in this class.

B:   Bonds which are rated B generally lack characteristics of the
     desirable investment.  Assurance of interest and principal
     payments of of maintenance of other terms of the contract over
     any long period of time may be small.

Caa: Bonds which are rated Caa are of poor standing.  Such issues may
     be in default or there may be present elements of danger with
     respect to principal or interest.

Ca:  Bonds which are rated Ca represent obligations which are
     speculative in a high degree.  Such issues are often in default
     or have other marked shortcomings.

C:   Bonds which are rated C are the lowest rated class of bonds, and 
     issues so rated can be regarded as having extremely poor
     prospects of ever attaining any real investment standing.

This article is copyright 1995 by Bill Rini.


-----------------------------------------------------------------------------

Subject: Bonds - Municipal bond terminology
Last-Revised: 7 Nov 1995
From: Bill Rini <billman@centcon.com>

These definitions of municipal bond terminology are at best
simplifications.  They should only be used as a stepping stone,
leading to further education about municipal bonds.

Act of 1911 and 1915:  Used for developments within a particular
    district and are secured by special assessment taxes set at a
    fixed dollar amount for the life of the bond.  1911 Act Bonds are
    secured by individual parcels, while 1915 Act Bonds are secured by
    all properties within the district. 

Ad Valorem Tax:  A tax based on the value of the property

Advance Refunding:  The replacement of debt prior to the original call
    date via the issuance of refunding bonds.

Authority (Lease Revenue):  A bond secured by the lease between the
    authority and another agency.  The lease payments from the "city"
    to the agency are equal to the debt service.

Callable Bond:  A bond that can be redeemed by the issuer prior to its
    maturity. Usually a premium is paid to the bond owner when the
    bond is called.

Certificate of Participation (COP):  Financing whereby an investor
   purchases a share of the lease revenues of a program rather than
   the bond being secured by those revenues.  Usually issued by
   authorities through which capital is raised and lease payments are
   made.  The authority usually uses the proceeds to construct a
   facility that is leased to the municipality, releasing the
   municipality from restrictions on the amount of debt that they can
   incur. 

Crossover Refunded:  The revenue stream originally pledged to secure
    the securities being refunded continues to be used to pay debt
    service on the refunded securities until they mature or are
    called.  At that time, the pledged revenues pay debt service on
    the refunding securities. 

Discount Bond:  A bond that is valued at less than its face amount.

Double Barrelled:  Bonds secured by the pledge of two or more sources
    of repayment. 

Face Value: The stated principal amount of a bond.

General Obligations:  Voter approved bonds that are backed by the full
    faith, credit and unlimited taxing power of the issuer.

Mello Roo's:  Bonds used for developments that benefit a particular
    district (schools, prisons, etc.) and are secured by special taxes
    based on the assessed value of the properties within the district.
    Tax assessment is included on the county tax bill.

Par Value:  The face value of a bond, generally $1,000.

Premium Bond:  A bond that is valued at more than its face amount.

Principal:  The amount owed; the face value of a debt.

Redevelopment Agency (Tax Allocation):  Bonds secured by all of the
    property taxes on the increase in assessed valuation above the
    base, on properties in the project. 

Revenue Bonds:  Bonds secured by the revenues derived from a
    particular service provided by the issuer.

Sinking Fund:  A bond with special funds set aside to retire the term
    bonds of a revenue issue each year according to a set schedule.
    Usually takes effect 15 years from date of issuance.  Bonds are
    retired through either calls, open market purchases, or tenders.

Taxable Equivalent Yield:  The taxable equivalent yield is equal to
    the tax free yield divided by the sum of 100 minus the current tax
    bracket.  For example the taxable equivalent yield of a 6.50% tax
    free bond for someone in the 32% tax bracket would be:
    6.5/(100-32) = 0.0955882 or 9.56% 

Yield:  A measure of the income generated by a bond. The amount of
    interest paid on a bond divided by the price.

Yield to Maturity:  The rate of return anticipated on a bond if it is
    held until the maturity date.

This article is copyright 1995 by Bill Rini.


-----------------------------------------------------------------------------

Compilation Copyright (c) 1996 by Christopher Lott, cml@cs.umd.edu
-- 
Christopher Lott	Compiler of the FAQ for misc.invest, misc.invest.stocks
cml@cs.umd.edu		http://www.cs.umd.edu/users/cml/
