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From:
[email protected] (Christopher Lott)
Newsgroups: misc.invest.misc,misc.invest.stocks,misc.invest.technical,misc.invest.options,misc.answers,news.answers
Subject: The Investment FAQ (part 3 of 19)
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Reply-To: lott at invest-faq dot com
Summary: Answers to frequently asked questions about investments.
Should be read by anyone who wishes to post to misc.invest.*
Organization: The Investment FAQ publicity department
Keywords: invest, finance, stock, bond, fund, broker, exchange, money, FAQ
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Archive-name: investment-faq/general/part3
Version: $Id: part03,v 1.58 2002/08/14 10:20:04 lott Exp lott $
Compiler: Christopher Lott, lott at invest-faq dot com
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 3 of 19. The web site
always has the latest version, including in-line links. Please browse
http://invest-faq.com/
Terms of Use
The following terms and conditions apply to the plain-text version of
The Investment FAQ that is posted regularly to various newsgroups.
Different terms and conditions apply to documents on The Investment
FAQ web site.
The Investment FAQ is copyright 2001 by Christopher Lott, and is
protected by copyright as a collective work and/or compilation,
pursuant to U.S. copyright laws, international conventions, and other
copyright laws. The contents of The Investment FAQ are intended for
personal use, not for sale or other commercial redistribution.
The plain-text version of The Investment FAQ may be copied, stored,
made available on web sites, or distributed on electronic media
provided the following conditions are met:
+ The URL of The Investment FAQ home page is displayed prominently.
+ No fees or compensation are charged for this information,
excluding charges for the media used to distribute it.
+ No advertisements appear on the same web page as this material.
+ Proper attribution is given to the authors of individual articles.
+ This copyright notice is included intact.
Disclaimers
Neither the compiler of nor contributors to The Investment FAQ make
any express or implied warranties (including, without limitation, any
warranty of merchantability or fitness for a particular purpose or
use) regarding the information supplied. The Investment FAQ is
provided to the user "as is". Neither the compiler nor contributors
warrant that The Investment FAQ will be error free. Neither the
compiler nor contributors will be liable to any user or anyone else
for any inaccuracy, error or omission, regardless of cause, in The
Investment FAQ or for any damages (whether direct or indirect,
consequential, punitive or exemplary) resulting therefrom.
Rules, regulations, laws, conditions, rates, and such information
discussed in this FAQ all change quite rapidly. Information given
here was current at the time of writing but is almost guaranteed to be
out of date by the time you read it. Mention of a product does not
constitute an endorsement. Answers to questions sometimes rely on
information given in other answers. Readers outside the USA can reach
US-800 telephone numbers, for a charge, using a service such as MCI's
Call USA. All prices are listed in US dollars unless otherwise
specified.
Please send comments and new submissions to the compiler.
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Subject: Analysis - Paying Debts Early versus Making Investments
Last-Revised: 14 July 2000
Contributed-By: Gary Snyder, Thomas Price (tprice at engr.msstate.edu),
Chris Lott ( contact me ), John A. Weeks III (john at johnweeks.com)
This article analyzes the question of whether you should apply any extra
cash you might have lying around to making extra payments on a debt, or
whether you should instead leave the debt on its regular payment
schedule and invest the cash instead. An equivalent question is whether
you should cash out an existing investment to pay down debt, or just let
it ride. We'll focus on the example of a first mortgage on a house, but
the analysis works (with some changes) for a car loan, credit-card debt,
etc.
Before we compare debts with investments, it's important to frame the
debate. A bit of financial planning is appropriate here; there are
several articles in the FAQ about that. To start with, an individual
should have an emergency fund of 3-6 months of living expenses.
Emergency funds need to be readily available (when was the last
emergency that you could plan for), like in a bank, credit union, or
maybe a money market fund. And most people would not consider these
investments. So the first thing to do with cash is arguably to
establish this sort of rainy-day fund. If you have to cash out a stock
to get this fund, that's ok; remember, emergencies rarely happen at
market tops.
Before we run numbers, I'd like to point out two important issues here.
The most important issue to remember is risk. Making early payments to
a loan exposes you to relatively few risks (once the loan is paid, it
stays paid), but two notable risks are liquidity and opportunity. The
liquidity risk is that you might not have cash when you need it (but see
above for the mitigation strategy of a rainy-day fund). The opportunity
risk is the possibility that a better opportunity might present itself
and you would be unable to take advantage of it since you gave the bank
your extra cash. And when you invest money, you generally expose
yourself to market risk (the investment's price might fall) as well as
other risks that might cause you to lose money. Of course the other
important issue (you probably guessed) is taxes. The interest paid on
home mortgages is deductable, so that acts to reduce the cost of the
loan below the official interest rate on the loan. Not true for
credit-card debt, etc. Also, monies earned from an investment are
taxed, so that acts to reduce the return on the investment.
One more caveat. If you simply cannot save; i.e., you would cash out
the investments darned quick, then paying down debt may be a good
choice! And owning a home gives you a place to live, especially if you
plan to live in it on a modest income.
Finally, all you can do in advance is estimate, guess, and hope. No one
will never know the answer to "what is best" until long after it is too
late to take that best course of action. You have to take your shot
today, and see where it lands tomorrow.
Now we'll run some numbers. If you have debt as well as cash that you
will invest, then maintaining the debt (instead of paying it) costs you
whatever the interest rate on the loan is minus whatever you make from
the investment. So to justify your choice of investing the cash,
basically you're trying to determine whether you can achieve a return on
your investment that is better than the interest rate on the debt. For
example, you might have a mortgage that has an after-tax rate of 6%, but
you find a very safe investment with a guaranteed, after-tax return of
9% (I should be so lucky). In this case, you almost certainly should
invest the money. But the analysis is never this easy -- it invariably
depends on knowing what the investments will yield in the future.
But don't give up hope. Although it is impossible to predict with
certainty what an investment will return, you can still estimate two
things, the likely return and the level of risk. Since paying down any
debt entails much lower risk than making an investment, you need to get
a higher level of return to assume the market risk (just to name one) of
an investment. In other words, the investment has to pay you to assume
the risk to justify the investment. It would be foolish to turn down a
risk-free 10% (i.e., to pay off a debt with an after-tax interest rate
of 10%) to try to get an after-tax rate of 10.5% from an investment in
the stock market, but it might make very good sense to turn down a
risk-free 6.5%. It is a matter of personal taste how big the difference
between the return on the investment and the risk-free return has to be
(it's called the risk premium), but thinking like this at least lets you
frame the question.
Next we'll characterize some investments and their associated risks.
Note that characterizing risk is difficult, and we'll only do a
relatively superficial job it. The purpose of this article is to get
you thinking about the options, not to take each to the last decimal
point.
Above we mentioned that paying the debt is a low-risk alternative. When
it comes to selecting investments that potentially will yield more than
paying down the debt, you have many options. The option you choose
should be the one that maximizes your return subject to a given level of
risk (from one point of view). Paying off the loan generates a
rock-solid guaranteed return. The best option you have at approximately
this level of risk is to invest in a short-term, high-grade corporate
bond fund. The key market risk in this investment is that interest
rates will go up by more than 1%; another risk of a bond fund is that
companies like AT&T will start to default on their loans. Not quite
rock-solid guaranteed, but close. Anyway, these funds have yielded
about 6% historically.
Next in the scale of risk is longer-term bonds, or lower rated bonds.
Investing in a high-yield (junk) bond fund is actually quite safe,
although riskier than the short-term, high grade bond fund described
above. This investment should generate 7-8% pre-tax (off the top of my
head), but could also lose a significant amount of money over short
periods. This happened in the junk bond market during the summer of
1998, so it's by no means a remote possibility.
The last investment I'll mention here are US stock investments.
Historically these investments have earned about 10-11%/year over long
periods of time, but losing money is a serious possibility over periods
of time less than three years, and a return of 8%/year for an investment
held 20 years is not unlikely. Conservatively, I'd expect about an 8-9%
return going forward. I'd hope for much more, but that's all I'd count
on. Stated another way, I'd choose a stock investment over a CD paying
6%, but not a CD paying 10%.
Don't overlook the fact that the analysis basically attempted to answer
the question of whether you should put all your extra cash into the
market versus your mortgage. I think the right answer is somewhere in
between. Of course it's nice to be debt free, but paying down your
debts to the point that you have no available cash could really hurt you
if your car suddenly dies, etc. You should have some savings to cushion
you against emergencies. And of course it's nice to have lots of
long-term investments, but don't neglect the guaranteed rate of return
that is assured by paying down debt versus the completely unguaranteed
rate of return to be found in the markets.
The best thing to do is ask yourself what you are the most comfortable
with, and ignore trying to optimize variables that you cannot control.
If debt makes you nervous, then pay off the house. If you don't worry
about debt, then keep the mortgage, and keep your money invested. If
you don't mind the ups and downs of the market, then keep invested in
stocks (they will go up over the long term). If the market has you
nervous, pull out some or all of it, and ladder it into corporate bonds.
In short, each person needs to find the right balance for his or her
situation.
--------------------Check
http://invest-faq.com/ for updates------------------
Subject: Analysis - Price-Earnings (P/E) Ratio
Last-Revised: 27 Jan 1998
Contributed-By: E. Green, Aaron Schindler, Thomas Busillo, Chris Lott (
contact me )
P/E is shorthand for the ratio of a company's share price to its
per-share earnings. For example, a P/E ratio of 10 means that the
company has $1 of annual, per-share earnings for every $10 in share
price. Earnings by definition are after all taxes etc.
A company's P/E ratio is computed by dividing the current market price
of one share of a company's stock by that company's per-share earnings.
A company's per-share earnings are simply the company's 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. Stated differently, at this price, 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 past 12 months, called a trailing P/E) but are sometimes computed
with leading earnings (earnings projected for the upcoming 12-month
period, called a leading P/E). Some analysts will exclude one-time
gains or losses from a quarterly earnings report when computing this
figure, others will include it. Adding to the confusion is the
possibility of a late earnings report from a company; computation of a
trailing P/E based on incomplete data is rather tricky. (I'm being
polite; it's misleading, but that doesn't stop the brokerage houses from
reporting something.) Even worse, some methods use so-called negative
earnings (i.e., losses) to compute a negative P/E, while other methods
define the P/E of a loss-making company to be zero. The many ways to
compute a P/E may lead to wide variation in the reporting of a figure
such as the "P/E for the S&P whatever." Worst of all, it's usually next
to impossible to discover the method used to generate a particular P/E
figure, chart, or report.
Like other indicators, P/E 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. And of
course a company's P/E ratio changes every day as the stock price
fluctuates.
The price/earnings ratio is commonly used as 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.
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.
It's difficult to say whether a particular P/E is high or low, but there
are a number of factors you should consider. First, a common rule of
thumb for evaluating a company's share price is that a company's P/E
ratio should be comparable to that company's growth rate. If the ratio
is much higher, then the stock price is high compared to history; if
much lower, then the stock price is low compared to history. Second,
it's useful to look at the forward and historical earnings growth rate.
For example, if a company has been growing at 10% per year over the past
five years but has a P/E ratio of 75, then conventional wisdom would say
that the shares are expensive. Third, it's important to consider the
P/E ratio for the industry sector. For example, consumer products
companies will probably have very different P/E ratios than internet
service providers. Finally, a stock could have a high trailing-year P/E
ratio, but if the earnings rise, at the end of the year it will have a
low P/E after the new earnings report is released. Thus a stock with a
low P/E ratio can accurately be said to be cheap only if the
future-earnings P/E is low. If the trailing P/E is low, investors may
be running from the stock and driving its price down, which only makes
the stock look cheap.
--------------------Check
http://invest-faq.com/ for updates------------------
Subject: Analysis - Risks of Investments
Last-Revised: 15 Aug 1999
Contributed-By: Chris Lott ( contact me ), Eugene Kononov (eugenek at
ix.netcom.com)
Risk, in general, is the possibility of sustaining damage, injury, or
loss. This is true in the world of investments also, of course.
Investments that are termed "high risk" have a significant possibility
that their value will drop to zero.
You might say that risk is a measure of whether a surprise will occur.
But in the world of investments, positive as well as negative surprises
happen. Sometimes a company's revenue and profits explode suddenly and
the stock price zooms upward, a very pleasant and positive surprise for
the stockholders. Sometimes a company implodes, and the stock crashes,
a not very pleasant and decidedly negative surprise for the
stockholders.
Because investments can rise or fall unexpectedly, the primary risk
associated with an investment (the market risk) is characterized by the
variability of returns produced by that investment. For example, an
investment with a low variability of return is a savings account with a
bank (low market risk). The bank pays a highly predictable interest
rate. That interest rate also happens to be quite low. An internet
stock is an investment with a high variability of return; it might
quintuple, and it might fall 50% (high market risk).
The standard way to calculate the market risk of investing in a
particular security is to calculate the standard deviation of its past
prices. So, the academic definition is:
market risk = volatility = StdDev(price history)
However, it has long been noticed that the standard deviation may not be
appropriate to use in many instances. Consider a hypothetical asset
that always goes up in price, in very small and very large increments.
The standard deviation of the prices (and returns) for that asset may be
large, but where is the market risk?
For practical purposes (trading and system evaluation), a much better
measure of market risk is the distribution of the drawdowns. Given the
history of the prices, and assuming some investment strategy (be it
buy-and-hold or market timing), what is the maximum loss that would have
been suffered? How frequent are the losses? What is the longest
uninterrupted string of losses? What is the average gain/loss ratio?
Other risks in the investment world are the risk of losing purchasing
power due to inflation (possibly by making only risk-free investments),
and the risk of underperforming the market (of special concern to mutual
fund mangers). Occasionally you may see "liquidity risk" which
basically means that you might need your money at a time when an
investment is not liquid; i.e., not easily convertible to cash. The
best example is a certificate of deposit (CD) which is payable in full
when it matures but if you need the money before then, you will pay a
penalty.
Bond holders face several risks unique to bonds, the most prominent
being interest rate risk. Because the price of bonds drops as the
prevailing interest rates rise, bond holders tend to worry about rising
interest rates. Other risks more-or-less unique to bonds are the risk
of default (i.e., the company that issued the bond decides it cannot pay
the obligation), as well as call (or prepayment) risk. What's that last
one? Well, in a nutshell, a bond issuer can call (prepay) the bond
before the bond matures, depending of course whether the terms and
conditions associated with the bond allow it. A bond that can be repaid
before the maturity date is called "callable" and a bond that cannot is
called "non callable" (see the basics of bonds article elsewhere in this
FAQ for more details). Hmm, you might be saying to yourself, the bond
holder got the money back, where's the risk? Because the investor will
have to reinvest the money at some random time, the risk is that the
investor might not be able to find as good of a deal as the old bond.
Market risk has additional components for investments outside your home
country. To the usual volatility of the markets you have to add the
volatility of the currency markets. You might have great gains, but
lose them when you swap the foreign currency for your own. Other risks
(especially in emerging markets) are problems in the economy or
government (that might lead to severe market declines) and the risk of
illiquidity (no one is buying when you want to sell).
This seems like a good place to discuss the classic risk-reward
tradeoff. If we use volatility as our risk measure, then it's clear an
investor will obtain only modest returns from low-volatility (low-risk)
investments. An investor must put his or her money into volatile (i.e.,
risky) investments if he or she hopes to experience returns on
investment that are greater than the risk-free rate of return.
Different individuals will have very different tolerances for risk, and
their tolerance for risk will change during their lifetimes. In
general, if an investor will need cash within a short period of time
(and will be forced to sell investments to raise that cash), the
investor should not put money into high-volatility (i.e., high-risk)
vehicles. Those investments might not be worth very much when the
investor needs to sell. On the other hand, if an investor has a very
long time horizon, such as a young person investing 401(k) monies, he or
she should seriously consider choosing investments that offer the best
possibility of good returns (i.e., investments with significant
historical volatility). The long period of time before that person
needs the money offers an unparalleled chance to allow the investment to
grow; the occasional downturn will most likely be offset by other gains.
All things being equal, it's reasonable to expect that a young worker
will tolerate more risk than a retired person.
A commonly accepted quantification of market risk is beta, which is
explained in another article in this FAQ.
--------------------Check
http://invest-faq.com/ for updates------------------
Subject: Analysis - Return on Equity versus Return on Capital
Last-Revised: 7 June 1999
Contributed-By: John Price (johnp at sherlockinvesting.com)
This article analyzes the question of whether return on equity (ROI) or
return on capital (ROC) is the better guide to performance of an
investment.
We'll start with an example. Two brothers, Abe and Zac, both inherited
$10,000 and each decided to start a photocopy business. After one year,
Apple, the company started by Abe, had an after-tax profit of $4,000.
The profit from Zebra, Zac's company, was only $3,000. Who was the
better manager? I.e., who provided a better return? For simplicity,
suppose that at the end of the year, the equity in the companies had not
changed. This means that the return on equity for Apple was 40% while
for Zebra it was 30%. Clearly Abe did better? Or did he?
There is a little more to the story. When they started their companies,
Abe took out a long-term loan of $10,000 and Zac took out a similar loan
for $2,000. Since capital is defined as equity plus long-term debt, the
capital for the two companies is calculated as $20,000 and $12,000.
Calculating the return on capital for Apple and Zebra gives 20% (= 4,000
/ 20,000) for the first company and 25% (= 3,000 / 12,000) for the
second company.
So for this measure of management, Zac did better than Abe. Who would
you invest with?
Perhaps neither. But suppose that the same benefactor who left money to
Abe and Zac, also left you $100 with the stipulation that you had to
invest in the company belonging to one or other of the brothers. Who
would it be?
Most analysts, once they have finished talking about earnings per share,
move to return on equity. For public companies, it is usually stated
along the lines that equity is what is left on the balance sheet after
all the liabilities have been taken care of. As a shareholder, equity
represents your money and so it makes good sense to know how well
management is doing with it. To know this, the argument goes, look at
return on equity.
Let's have a look at your $100. If you loan it to Abe, then his capital
is now $20,100. He now has $20,100 to use for his business. Assuming
that he can continue to get the same return, he will make 20% on your
$100. On the other hand, if you loan it to Zac, he will make 25% on
your money. From this perspective, Zac is the better manager since he
can generate 25% on each extra dollar whereas Abe can only generate 20%.
The bottom line is that both ratios are important and tell you slightly
different things. One way to think about them is that return on equity
indicates how well a company is doing with the money it has now, whereas
return on capital indicates how well it will do with further capital.
But, just as you had to choose between investing with Abe or Zac, if I
had to choose between knowing return on equity or return on capital, I
would choose the latter. As I said, it gives you a better idea of what
a company can achieve with its profits and how fast its earnings are
likely to grow. Of course, if long-term debt is small, then there is
little difference between the two ratios.
Warren Buffett (the famous investor) is well known for achieving an
average annual return of almost 30 percent over the past 45 years.
Books and articles about him all say that he places great reliance on
return on equity. In fact, I have never seen anyone even mention that
he uses return on capital. Nevertheless, a scrutiny of a book The
Essays of Warren Buffett and Buffett's Letters to Shareholders in the
annual reports of his company, Berkshire Hathaway, convinces me that he
relies primarily on return on capital. For example, in one annual
report he wrote,"To evaluate [economic performance], we must know how
much total capital—debt and equity—was needed to produce these
earnings." When he mentions return on equity, generally it is with the
proviso that debt is minimal.
If your data source does not give you return on capital for a company,
then it is easy enough to calculate it from return on equity. The two
basic ways that long-term debt is expressed are as long-term debt to
equity DTE and as long-term debt to capital DTC. (DTC is also referred
to as the capitalization ratio.) In the first case, return on capital
ROC is calculated from return on equity ROE by
ROC = ROE / (1 + DTE),
and in the second case by:
ROC = ROE * (1 - DTC)
For example, in the case of Abe, we saw DTE = 10,000 / 10,000 = 1 and
ROE = 40% so that, according to the first formula, ROC = 40% / ( 1 + 1)
= 20%. Similarly, DTC = 10,000 / 20,000 = 0.5 so that by the second
formula, ROC = 40% (1 – 0.5) = 20%. You might like to check your
understanding of this by repeating the calculations with the results for
Zac's company.
If you compare return on equity against return on capital for a company
like General Motors with that of a company like Gillette, you'll see one
of the reasons why Buffett includes the latter company in his portfolio
and not the former.
For more articles, analyses, and insights into today's financial markets
from John Price, visit his web site.
http://www.sherlockinvesting.com/
--------------------Check
http://invest-faq.com/ for updates------------------
Subject: Analysis - Rule of 72
Last-Revised: 19 Feb 1998
Contributed-By: Chuck Cilek (ccilek at nyx10.nyx.net), Chris Lott (
contact me ), Richard Alpert
The "Rule of 72" is a rule of thumb that can help you compute when your
money will double at a given interest rate. It's called the rule of 72
because at 10%, money will double every 7.2 years.
To use this simple rule, you just divide the annual interest into 72.
For example, if you get 6% on an investment and that rate stays
constant, your money will double in 72 / 6 = 12 years. Of course you
can also compute an interest rate if you are told that your money will
double in so-and-so many years. For example, if your money has to
double in two years so that you can buy your significant other that
Mazda Miata, you'll need 72 / 2 = 36% rate of return on your stash.
Like any rule of thumb, this rule is only good for approximations. Next
we give a derivation of the exact number for the case of an interest
rate of 10%. We want to know how long it takes a given principal P to
double given either the interest rate r (in percent per year) or the
number of years n. So, we are solving this equation:
P * (1 + r/100) ** n = 2P
Note that the symbol '**' is used to denote exponentiation (2 ** 3 = 8).
Since we said we'll try the case of r = 10%, we're solving this:
P * (1 + 10/100) ** n = 2P
We cancel the P's to get:
(1 + r/100) ** n = 2
Continuing:
(1 + 10/100) ** n = 2
1.1 ** n = 2
From calculus we know that the natural logarithm ("ln") has the
following property:
ln (a ** b) = b * ln ( a )
So we'll use this as follows:
n * ln(1.1) = ln(2)
n * (0.09531) = 0.693147
Finally leaving us with:
n = 7.2725527
Which means that at 10%, your money doubles in about 7.3 years. So the
rule of 72 is pretty darned close.
You can solve the equation for other values of r to see how rough of an
approximation this rule provides. Here's a table that shows the actual
number of years required to double your money based on different
interest rates, along with the number that the rule of 72 gives you.
% Rate Actual Rule 72
1 69.66 72
2 35.00 36
3 23.45 24
4 17.67 18
5 14.21 14.4
6 11.90 12
7 10.24 10.29
8 9.01 9
9 8.04 8
10 7.27 7.2
. .. ..
15 4.96 4.8
20 3.80 3.6
25 3.11 2.88
30 2.64 2.4 (note: 10pct error)
40 2.06 1.8
50 1.71 1.44 (note: 19pct error)
75 1.24 0.96
100 1.00 0.72 (note: 38pct error)
--------------------Check
http://invest-faq.com/ for updates------------------
Subject: Analysis - Same-Store Sales
Last-Revised: 9 Jan 1996
Contributed-By: Steve Mack
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.
--------------------Check
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Subject: Bonds - Basics
Last-Revised: 5 Jul 1998
Contributed-By: Art Kamlet (artkamlet at aol.com), Chris Lott ( contact
me )
A bond is just an organization's IOU; i.e., a promise to repay a sum of
money at a certain interest rate and over a certain period of time. In
other words, a bond is a debt instrument. Other common terms for these
debt instruments are notes and debentures. Most bonds pay a fixed rate
of interest (variable rate bonds are slowly coming into more use though)
for a fixed period of time.
Why do organizations issue bonds? Let's say a corporation needs to build
a new office building, or needs to purchase manufacturing equipment, or
needs to purchase aircraft. Or maybe a city government needs to
construct a new school, repair streets, or renovate the sewers.
Whatever the need, a large sum of money will be needed to get the job
done.
One way is to arrange for banks or others to lend the money. But a
generally less expensive way is to issue (sell) bonds. The organization
will agree to pay some interest rate on the bonds and further agree to
redeem the bonds (i.e., buy them back) at some time in the future (the
redemption date).
Corporate bonds are issued by companies of all sizes. Bondholders are
not owners of the corporation. But if the company 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.
Municipal bonds are issued by cities, states, and other local agencies
and may or may not be as safe as corporate bonds. Some municipal bonds
are backed by the taxing authority of the state or town, while others
rely on earning income to pay the bond interest and principal.
Municipal bonds are not taxable by the federal government (some might be
subject to AMT) and so don't have to pay as much interest as equivalent
corporate bonds.
U.S. Bonds are issued by the Treasury Department and other government
agencies and are considered to be safer than corporate bonds, so they
pay less interest than similar term corporate bonds. Treasury bonds are
not taxable by the state and some states do not tax bonds of other
government agencies. Shorter term Treasury bonds are called notes and
much shorter term bonds (a year or less) are called bills, and these
have different minimum purchase amounts (see the article elsewhere in
this FAQ for more details about US Treasury instruments.)
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.
Interest payments are usually made every 6 months.
A bond with a maturity of less than two years is generally considered a
short-term instrument (also known as a short-term note). A medium-term
note is a bond with a maturity between two and ten years. And of
course, a long-term note would be one with a maturity longer than ten
years.
The price of a bond is a function of prevailing interest rates. As
rates go up, the price of the bond goes down, because that particular
bond becomes less attractive (i.e., pays less interest) when compared to
current offerings. As rates go down, the price of the bond goes up,
because that particular bond becomes more attractive (i.e., pays more
interest) when compared to current offerings. The price also fluctuates
in response to the risk perceived for the debt of the particular
organization. For example, if a company is in bankruptcy, the price of
that company's bonds will be low because there may be considerable doubt
that the company will ever be able to redeem the bonds. When you buy a
bond, you may pay a premium. In other words, you may pay more than the
face value (also called the "par" value). For example, a bond with a
face value of $1,000 might sell for $1050, meaning at a $50 premium.
Or, depending on the markets and such, you might buy a bond for less
than face value, which means you bought it at a discount.
On the redemption date, bonds are usually redeemed at "par", meaning the
company pays back exactly the face value of the bond. Most bonds also
allow the bond issuer to redeem the bonds at any time before the
redemption date, usually at par but sometimes at a higher price. This
is known as "calling" the bonds and frequently happens when interest
rates fall, because the company can sell new bonds at a lower interest
rate (also called the "coupon") and pay off the older, more expensive
bonds with the proceeds of the new sale. By doing so the company may be
able to lower their cost of funds considerably.
A bearer bond is a bond with no owner information upon it; presumably
the bearer is the owner. As you might guess, they're almost as liquid
and transferable as cash. Bearer bonds were made illegal in the U.S.
in 1982, so they are not especially common any more. Bearer bonds
included coupons which were used by the bondholder to receive the
interest due on the bond; this is why you will frequently read about the
"coupon" of a bond (meaning the interest rate paid).
Another type of bond is a convertible bond . This security can be
converted into shares of the company that issues the bond if the
bondholder chooses. Of course, the conversion price is usually chosen
so as to make the conversion interesting only if the stock has a pretty
good rise. In other words, when the bond is issued, the conversion
price is set at about a 15--30% premium to the price of the stock when
the bond was issued. There are many terms that you need to understand
to talk about convertible bonds. The bond value is an estimate of the
price of the bond (i.e., based on the interest rate paid) if there were
no conversion option. The conversion premium is calculated as ((price -
parity) / parity) where parity is just the price of the shares into
which the bond can be converted. Just one more - the conversion ratio
specifies how many shares the bond can be converted into. For example,
a $1,000 bond with a conversion price of $50 would have a conversion
ratio of 20.
Who buys bonds? Many individuals buy bonds. Banks buy bonds. Money
market funds often need short term cash equivalents, so they buy bonds
expiring in a short time. People who are very adverse to risk might buy
US Treasuries, as they are the standard for safeness. Foreign
governments whose own economy is very shaky often buy Treasuries.
In general, bonds pay a bit more interest than federally insured
instruments such as CDs because the bond buyer is taking on more risk as
compared to buying a CD. Many rating services (Moody's is probably the
largest) help bond buyers assess the riskiness of any bond issue by
rating them. See the FAQ article on bond ratings for more information.
Listed below are some additional resources for information about bonds.
* The Bond Market Association runs an information site.
http://www.investinginbonds.com
--------------------Check
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Subject: Bonds - Amortizing Premium
Last-Revised: 12 Jul 2001
Contributed-By: Chris Lott ( contact me )
The IRS requires investors who purchase certain bonds at a premium
(i.e., above par, which means above face value) to amortize that premium
over the life of the bond. The reason is fairly straightforward. If
you bought a bond at 101 and were redeemed at 100, that sounds like a
capital loss -- but of course it really isn't, since it's a bond (not a
stock). So the IRS prevents you from buying lots and lots of bonds
above par, taking the interest and a phony loss that could offset a bit
of other income.
Here's a bit more discussion, excerpted from a page at the IRS. If you
pay a premium to buy a bond, the premium is part of your cost basis in
the bond. If the bond yields taxable interest, you can choose to
amortize the premium. This generally means that each year, over the
life of the bond, you use a part of the premium that you paid to reduce
the amount of interest that counts as income. If you make this choice,
you must reduce your basis in the bond by the amortization for the year.
If the bond yields tax-exempt interest, you must amortize the premium.
This amortized amount is not deductible in determining taxable income.
However, each year you must reduce your basis in the bond by the
amortization for the year.
To compute one year's worth of amortization for a bond issued after 27
September 1985 (don't you just love the IRS?), you must amortize the
premium using a constant yield method. This takes into account the
basis of the bond's yield to maturity, determined by using the bond's
basis and compounding at the close of each accrual period. Note that
your broker's computer system just might do this for you automatically.
--------------------Check
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Subject: Bonds - Duration Measure
Last-Revised: 19 Feb 1998
Contributed-By: Rich Carreiro (rlcarr at animato.arlington.ma.us)
This article provides a brief introduction to the duration measure for
bonds. The duration measure for bonds is a invention that allows bonds
of different maturities and coupon rates to be compared directly.
Everyone knows that the maturity of a bond is the amount of time left
until it matures. Most people also know that the price of a bond swings
more violently with interest rates the longer the maturity of the bond
is. What many people don't know is that maturity is actually not that
great a measure of the lifetime of a bond. Enter duration.
The reason why maturity isn't that great a measure is that it does not
account for the differences in bond coupons. A 10-year bond with a 5%
coupon will be more sensitive to interest rate changes than a 10-year
bond with an 8% coupon. A 5-year zero-coupon bond may well be more
sensitive than a 7-year 6% bond, and so forth.
Faced with the inadequacy of maturity, the investment gurus came up with
a measure that takes both maturity and coupon rate into account in order
to make apples-to-apples comparisons. The measure is called duration.
There are different ways to compute duration. I will use one of the
common definitions, namely:
Duration is a weighted average of the times that interest
payments and the final return of principal are received. The
weights are the amounts of the payments discounted by the
yield-to-maturity of the bond.
The final sentence may be alternatively stated:
The weights are the present values of the payments, using the
bond's yield-to-maturity as the discount rate.
Duration gives one an immediate rule of thumb -- the percentage change
in the price of a bond is the duration multiplied by the change in
interest rates. So if a bond has a duration of 10 years and
intermediate-term interest rates fall from 8% to 6% (a drop of 2
percentage points), the bond's price will rise by approximately 20%.
In the examples and formulas that follow, I make the simplifying
assumptions that:
1. Interest payments occur annually (they actually occur every 6
months for most bonds).
2. The final interest payment occurs on the date of maturity.
3. It is always one year from now to the first interest payment.
It turns out that (especially for intermediate- and long-term bonds)
these simplifications don't affect the final numbers that much --
duration is well less than a year different from its "true" value, even
for something as short as a duration of 5 years.
Example 1:
Bond has a $10,000 face value and a 7% coupon. The yield-to-maturity
(YTM) is 5% and it matures in 5 years. The bond thus pays $700 a year
from now, $700 in 2 years, $700 in 3 years, $700 in 4 years, $700 in 5
years and the $10,000 return of principal also in 5 years.
As you may recall, to compute the weighted average of a set of numbers,
you multiply the numbers by the weights and add those products up. You
then add all the weights up and divide the former by the latter. In
this case the weights are $700/1.05, $700/1.05^2, $700/1.05^3,
$700/1.05^4, $700/1.05^5, and $10,000/1.05^5, or $666.67, $634.92,
$604.69, $575.89, $548.47, and $7,835.26. The numbers being average are
the times the payments are received, or 1 year, 2 years, 3 years, 4
years, 5 years, and 5 years. So the duration is:
1*$667.67 + 2*$634.92 + 3*$604.69 + 4*$575.89 + 5*$548.47 +
5*$7,835.26
D =
-----------------------------------------------------------------------
$667.67 + $634.92 + $604.69 + $575.89 + $548.47 + $7,835.26
D = 4.37 years
Example 2:
Bond has a face value of $P, coupon of c, YTM of y, maturity of M years.
1Pc/(1+y) + 2Pc/(1+y)^2 + 3Pc/(1+y)^3 + ... + MPc/(1+y)^M +
MP/(1+y)^M
D =
---------------------------------------------------------------------------
Pc/(1+y) + Pc/(1+y)^2 + Pc/(1+y)^3 + ... + Pc/(1+y)^M +
P/(1+y)^M
We can use summations to condense this equation:
M
Pc*Sum i/(1+y)^i + MP/(1+y)^M
i=1
D = ------------------------------
M
Pc*Sum 1/(1+y)^i + P/(1+y)^M
i=1
We can cancel out the face value of P, leaving a function only of
coupon, YTM and time to maturity:
M
c*Sum i/(1+y)^i + M/(1+y)^M
i=1
D = -----------------------------------
M
c*Sum 1/(1+y)^i + 1/(1+y)^M
i=1
It is trivial to write a computer program to carry out the calculation.
And those of you who remember how to find a closed-form expression for
Sum{i=1 to M}(x^i) and Sum{i=1 to M}(ix^i) can grind through the
resulting algebra and get a closed-form expression for duration that
doesn't involve summation loops :-)
Note that any bond with a non-zero coupon will have a duration shorter
than its maturity. For example, a 30 year bond with a 7% coupon and a
6% YTM has a duration of only 14.2 years. However, a zero will have a
duration exactly equal to its maturity. A 30 year zero has a duration
of 30 years. Keeping in mind the rule of thumb that the percentage
price change of a bond roughly equals its duration times the change in
interest rates, one can begin to see how much more volatile a zero can
be than a coupon bond.
--------------------Check
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Subject: Bonds - Moody Bond Ratings
Last-Revised: 7 Nov 1995 Contributed-By: Bill Rini (bill at
moneypages.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.
--------------------Check
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Subject: Bonds - Municipal Bond Terminology
Last-Revised: 7 Nov 1995
Contributed-By: Bill Rini (bill at moneypages.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%
YieldA 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. For more insights from
Bill Rini, visit The Syndicate:
http://www.moneypages.com
--------------------Check
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Subject: Bonds - Relationship of Price and Interest Rate
Last-Revised: 28 Oct 1997
Contributed-By: Rich Carreiro (rlcarr at animato.arlington.ma.us), Chris
Lott ( contact me )
The basic relationship between the price of a bond and prevailing market
interest rates is an inverse relationship. This is actually pretty
straightforward. For example, if you have a 6% bond (this means that it
pays $60 annually per $1000 of face value) and interest rates jump to
8%, wouldn't you agree that your bond should be worth less now if you
were to sell it?
If this isn't clear, think about it this way. If the rate of interest
being paid on newly issued bonds stands at 8%, a bond buyer would get
paid $80 annually for each $1,000 investment in one of those bonds. If
that bond buyer instead bought your old 6% bond for the price you
originally paid, that bond would yield $20 less per year when compared
to bonds on the market. Clearly that's not a very attractive offer for
the buyer (although it would be a great deal for you).
To quantify the inverse relationship between the price and the interest
rate, you really need the concept of the present value of money (also
see the article elsewhere in the FAQ on this topic). Computing present
value figures helps you answer questions like "what's better, $95 today
or $100 one year from now?" The beginnings of it go something like this.
Pretend that you have $100. Also pretend that you can invest it in
something that will pay a 5% annual return. So, one year from now you
have:
$100 * (1 + 0.05) = $105
This can be turned around. Let's say that you want to know how much
money you need to have today in order to have $200 a year from now, if
you can earn 5%:
X * (1 + 0.05) = $200 or X = $200/(1 + 0.05) = $190.48
Therefore, we can say that the present value of $200 one year from now,
assuming a "discount rate" (this is what the assumed interest rate in a
present-value calculation is called) of 5% is $190.48.
But what if you wanted to know how much you needed today to have $200
two years from now, again assuming you could earn 5%? Here's the
computation.
[ X * (1 + 0.05) ] * (1 + 1.05) = $200
X represents the original amount, and the quantity "X * (1 + 0.05)"
represents the amount after 1 year. Solving for X we get:
X = 200/(1 + 1.05)^2 = $181.41
So, the present value of $200 two years hence, at a discount rate of 5%
is $181.41. It should be clear that the present value of $200 N years
from now at a discount rate of 5% is:
PV = 200/(1 + 0.05)^N
And this can be generalized to the present value of an amount C, N years
from now, at a discount rate of r:
PV = C/(1 + r)^N
Now you can combine these. Let's say I promise to pay you $300 a year
from today and $500 two years from today. What could I have paid you
today that would have made you just as happy as what I promised? Assume
you can earn 7% on your money. To solve this, just sum the present
value of each payment. This sum is called the "net present value" (NPV)
of a series of cash flows.
NPV = $300/(1+0.07) + $500/(1+0.07)^2 = $717.09
So, given the 7% discount rate, the payments I scheduled are equivalent
to a payment of $717.09 made today.
Let's get a little fancier. What if I'm willing to promise to pay you
$50 per year for 4 years, starting a year from now, and further promise
to pay you $1000 five years from now. What's the most you'd be willing
to pay me now to make you that promise. Assume a discount rate of 6%.
NPV = $50/(1+0.06) + $50/(1+0.06)^2 + $50/(1+0.06)^3 +
$50/(1+0.06)^4 + $1000/(1+0.06)^5 = $920.51
Let's say you want to wait until tomorrow. You have a dream that night
that makes you believe that you'll now be able to earn 10% on your
money. When I come back to you, you now tell me you'll only pay me
NPV = $50/(1 + 0.10) + $50/1.1^2 + $50/1.1^3 + $50/1.1^4 +
$1000/1.1^5 = $779.41
My promise is now worth quite a bit less. You should be able to see
that if your dream had led you to believe you could earn less on your
money, then my promise would have been worth more to you than it did
yesterday.
At this point, it's probably clear that my "promise" is effectively what
a bond is -- I'm agreeing to pay you a fixed amount each year (actually,
the bond would pay half that fixed amount twice a year) and then the
principal amount at maturity. Given what you think you can earn on your
money, the price you should pay for the bond is well-defined. The
question is what affects what you think you'll be able to earn on your
money? Fed policy might. What you think the chances of inflation are
might. Lots of other things might. This is where the fun starts. :-)
Also note that you can turn the equation around. Let's say that you
have a $1000 bond paying $75 per year. The bond matures in 10 years.
Someone is willing to sell it to you for $850. What will I have earned
on my investment? The net present value equation always holds, so $850
equals the net present value of the yearly payments and principal
payment.
Obviously, since we know everything except the discount rate, this
equation must define the discount rate that makes it true. The problem
is that the rate cannot be simply calculated. You must make a guess,
compute the net present value, see how different it is from $850, use
that to adjust your guess, and try again until the sides of the equation
balance. The discount rate you come up with is called the "internal
rate of return" (IRR) and in the bond world is called the "yield to
maturity" (YTM). In fact, if you know the initial value of some
portfolio, all cash flows into and out of the portfolio, and the final
value of the portfolio, you can compute your IRR, thus answering the
common misc.invest.* question of "I put $N into a fund on date X, but
then added $D on date Y and $F on date W. My account is today worth $B.
What's my return?"
As a final note, here's a bit of a stumper to spring on someone:
Assuming you could earn 5% on your money, would you rather be paid $1000
annually (first payment is today, next is a year from now, etc.) forever
(assume you are immortal :-) or $25000 today? Believe it or not, you
should take the $25000 today. Here's the analysis why.
NPV = $1000 + $1000/1.05 + $1000/1.05^2 ...
or
NPV = $1000*(1 + 1/1.05 + 1/1.05^2 + ...)
A math reference book can tell you (or you might remember or derive it)
that the infinite sum:
1 + x + x^2 + x^3 + ... = 1/(1 - x) if |x| < 1
In this case, x = 1/1.05, so
NPV = $1000*[1/(1 - 1/1.05)] = $21000
So believe it or not, you'd be better off taking $25000 today then
taking $1000 per year forever, given the 5% discount rate assumption.
--------------------Check
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Subject: Bonds - Tranches
Last-Revised: 22 Oct 1997
Contributed-By: (anonymous), Chris Lott ( contact me )
A 'tranche' (derived from the French for 'slice') is used in finance to
define part of an asset that is divided (sliced, hence the term) into
smaller pieces. A common example is a mortgage-backed security. One
bank may only be interested in the payments at the longer end of the
security's maturity, while another investment firm may want only the
cash flows due in the near term. An investment bank can split the
original asset into 'tranches' where each party (the bank and the
investment firm) receive rights to the expected cash payments for
particular periods. The two new assets are repriced, and the investment
bank usually makes a tidy profit. This can be done with many assets,
the goal being better marketablity of typically larger assets. If you
want more information on how this is used in specific, I would think
there would be data on the debt of less developed countries that has
been consolidated, then sold in 'tranches' to investors in the developed
worlds. The London Club is a group of commercial creditors which holds
claim on the debt of Russia, for example.
--------------------Check
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Compilation Copyright (c) 2002 by Christopher Lott.
