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Q: Capital Asset Pricing Model and Beta ( Answered,   0 Comments )
Question  
Subject: Capital Asset Pricing Model and Beta
Category: Business and Money > Finance
Asked by: lost4words-ga
List Price: $75.00
Posted: 06 Nov 2006 08:55 PST
Expires: 06 Dec 2006 08:55 PST
Question ID: 780519
In relation to CAPM, I need a clear definition of beta and explain how
a beta is determined and also how a beta is obtained. I would also
like to understand the limitations of a beta.

Note: Although I do understand the concepts of each, I am having a
hard time understanding how the two mesh. Non technical but detailed
responses would be appreciated, along with an easy to understand
example, as I would like to fully understand and learn about these
concepts.
Answer  
Subject: Re: Capital Asset Pricing Model and Beta
Answered By: omnivorous-ga on 06 Nov 2006 13:00 PST
 
Lost4words ?

A little history may help you understand how measures of beta came
about and what they mean.  Until the mid-1970s there was considerable
debate over what a company?s ?cost of capital? was.  It is important
in investment decisions like ?buy vs. lease?; it is important in
pricing; in fact it turns out to be a key factor in almost all
business decisions.


HISTORY
=========

Until William F. Sharpe?s work was fully accepted (by the mid-1970s),
there was continual debate over financial structures.  A friend used
to argue telephone rate cases for GTE (back in the days when the
telephone monopoly was highly regulated by states) and a critical
issue was always:
a.  is the cost-of-money the after-tax cost of bond debt (the lowest number)?
b.  how do we account for shareholder investment in the
cost-of-capital?  Do we add dividends?  Or some other number?

As we know from experience, a company can?t use all debt for projects:
at some point it becomes too risky to have too high a debt level.  But
the key issue was always: what return is fair for shareholders?

Sharpe reasoned that there is a risk-free rate that anyone could
obtain.  That?s now taken to be the Treasury bill rate, rf.  Investors
in the market should expect a higher return rM, if they?re properly
diversified.  Market returns go up and down as an economy goes through
recessions and boom times but on average the market returns will be
higher than just parking money in a Treasury bill.

But the company has risk of its own: maybe from its financial
structure; from the growth or erratic nature of its markets; and from
quality of management, among other factors.  How do we measure it?

Sharpe?s work on this issue won him the Nobel Prize for the work in 1990:
NobelPrize.org
?THIS YEAR'S LAUREATES ARE PIONEERS IN THE THEORY OF FINANCIAL
ECONOMICS AND CORPORATE FINANCE,? (Oct. 16, 1990)
http://nobelprize.org/economics/laureates/1990/press.html

Even more importantly, it revolutionized the management of finance
within a company.  It enabled the creation of stock options and
futures markets.  And it has even influenced the management of
baseball teams with the increased use of Sabermetrics or statistical
analysis to look at ?expected wins?.  I promise that I won?t take you
that far astream ...


WHAT IS CAPM?
==============

Restated mathematically, the CAPM model says that the return to
investors (and to the corporation, Rc) has to be equal to:
?	the risk-free rate
?	PLUS a premium for stocks as a whole that is higher than the
risk-free rate.  This market return premium is (rM ? rf)
?	And the market return should be multiplied by the risk factor for
the individual company, termed the ?beta of the corporation? (c)


Expressed as a formula, it?s:

Rc = rf + c(rM - rf)

Where,  

Rc is the company's expected return on capital 
rf is the risk-free return rate, usually a long-term U.S. Treasury bill rate 
rM is the expected return on the entire market of all investments. 
Most measures use a common broad index, most often the S&P500 over the
past 5 or 10 years
c is the company's beta, based on its covariance with the market.

Wikipedia
?Capital Asset Pricing Model,? (Sept. 15, 2005)
http://en.wikipedia.org/wiki/Capital_asset_pricing_model


WHAT IS A ?BETA??
=================

Relying on the assumption that markets are efficient, we see investors
vote every day on whether the stock market will rise or fall.  They do
the same thing every day for the company.

Watching a long series of measures we should be able to see a
relationship between a change in stock prices and the market.  If the
market rises 10% over a one-year period, a firm with a beta of 2.0
will rise at a faster rate.  And if the market falls by the same 10%,
your company with a beta of 2.0 will fall faster too.

We want a long series of measures (at least two or three years) in
order to eliminate the ?noise? of dramatic news on the short-term. 
For example, oil prices have an impact on all companies but since jet
fuel is a significant portion of airlines cost you wouldn?t want to
measure the beta only during the month that oil prices shot above the
$70 per barrel.  You?d want a longer-term picture that also shows what
happens during periods of falling oil prices.

Beta is the non-diversified risk of holding a single stock.  But it
turns out that companies in similar markets have similar risks.  After
all, airlines are all selling a similar product and have similar cost
structures:

Wikipedia
Beta Coefficient (undated)
http://en.wikipedia.org/wiki/Beta_coefficient

A beta of 1.0 matches the market portfolio.  A beta of more than 1.0
is a ?riskier? or more highly variable company.  Companies with betas
lower than 1.0 are less risky, usually because their markets and
returns are highly predictable.  These would include electric
utilities and consumer product companies where sales don?t fall as
quickly in economic downturns.


HOW DO WE CALCULATE A BETA?
============================

Linear regressions are typically used to track a company?s daily
returns against the stock market.  The Goldman Sachs chart on page 2
of the linked page below is a classic example, showing Bloomberg?s
estimate of the beta for Goldman Sachs (NYSE: GS).  Bloomberg does its
estimate with WEEKLY returns for Goldman Sachs measured against the
S&P500:

Babson College
?Finding beta?? (Fall 2004)
http://www3.babson.edu/CutlerCenter/upload/beta_data_finder.pdf

Bloomberg happens to be one of the shorter time horizons used for beta
calculation, using only two years of data.  Both Value Line and
Baseline use five year worth of data.  I?ll come back to that issue in
the section on limitations of beta coefficients.

As you can see from the measures in the Babson College brief, there
can be large differences in beta.  The three measures are 1.03
(Bloomberg); 1.35 (Value Line) and 1.36 (Baseline).  Clearly Goldman
Sachs is riskier than a market portfolio ? but is it 3% riskier?  Or
36% riskier?



HOW IS IT USED?
================

The most important use of beta is to set a cost of money for the
company so that employees, shareholders and managers can evaluate
investments.  Within the firm the cost of equity should be used for
all business decisions.  ANYTHING that has a positive return or net
present value (NPV) should be funded, as it adds wealth to the
corporation.  I?ll give some examples in the next section, but let?s
calculate a beta for GS first.

Here are some Treasury bill rates from today?s Wall Street Journal:
10-year T-bill: 4.731%
2-year: 4.845%
6-month: 4.955%
90-day: 4.975%

The yield curve is pretty flat today but sometimes there are major
differences between short- and long-term rates.  We?d match our
cost-of-capital calculations to the length of the investment ? using a
2-year rate if we?re go lease a car for two years and a 10-year (or
longer) rate if the decision were on building a new corporate
headquarters.

For rM, we?d look at some long-term returns.  Being an investment
banking firm, Goldman Sachs? finance officers would have a strong
sense of beta and even whether their business has become more or less
risky in the past 5 years, but we?ll use 1.35.

They would also have a good idea of what market index makes sense, as
they are constantly invested in these same markets.  They might choose
the widely-used S&P500 Index, which captures most of the value of
publicly-owned companies.  Or they might want to use a ?broader?
measure like the Wilshire 5000, which includes more over-the-counter
and small capitalization stocks.
(Goldman Sachs is sophisticated enough that they might even tailor the
rM to local markets or a basket of worldwide securities.)

We?ll use the most-widely used of market indexes: the S&P500, used in
most finance studies.  The returns for the past 10 years have averaged
10.73%:

Vanguard Historic Returns
S&P500 Index (1991-2005)
https://flagship.vanguard.com/VGApp/hnw/FundsHistoricalReturns?FundId=0040&FundIntExt=INT


So, Goldman Sachs cost of capital can be estimated at:

10-year:
Rc = 4.73% + 1.35* (10.73 ? 4.73) = 12.83%


2-year:
Rc = 4.85% + 1.35*(10.73 ? 4.73) = 12.95%

Historically short- and long-term investments have much different
?hurdle? rates but we live in a time of flat yield curves.

There are other uses of beta in financial markets, including pricing
of options, futures and even in some instances, for bonds.  They are
not minor but Black-Scholes and option pricing is the next chapter in
finance, so I?ll leave that out until you get there:
Yahoo! Finance
Goldman Sachs Options
http://finance.yahoo.com/q/op?s=GS


EXAMPLES
===========

Q.	 Goldman Sachs wants to expand retail office presence across the
country and will provide cars to 50 local managers.  They can lease
the cars at a 6% rate or pay cash?  Which should they do?

A.	The rate to borrow is far lower than their 12.95% cost of capital,
particularly after taxes.  Lease.

Q.	Goldman Sachs operates a printing plant for financial documents. 
It has $100 million invested in the plant and believes that it saves
$2.5 million versus  outsourcing the printing.  Should it sell the
plant or continue operating it?

A.  The $100 million invested in the plant has an investment cost of
$12.83 million each year.  If the company isn?t generating that much
in savings each year ? or if there?s not another strategic reason
(perhaps for security of important financial information) ? it is
actually decreasing shareholders? wealth.  Sell the plant.


WHAT ARE THE LIMITATIONS?
===========================

Every aspect of the use of beta and CAPM has been called into
question, so you could take each part of the formula for it and attack
the assumptions behind it or the specific number that you choose. 
Many start with one of Sharpe?s key assumptions: that transactions can
be performed without cost, since every time we buy stocks or even
mutual funds we?re incurring some cost.  For stock it is in the
commission paid; for mutual funds in the management fees.

The Wikipedia CAPM link above has some of the more academic
limitations.  But there are much more debated issues including:
* what will future market returns be?  rM numbers for the S&P500 were
very high in the late 1990s when interest rates were higher.  With a
fall in interest rates during the first five years of this century, it
would be reasonable to expect rM returns to fall as well.  And they
have.
* you?ve seen with the Goldman Sachs example that the beta can vary
widely ? in this case between 1.03 and 1.36, depending on what data
sources are used and the measurement period.
* market volatility can change in periods of economic instability,
which changes the firm volatility as well.
* typical beta measures are over a 5-year period.  During that time
the businesses in which a company is involved can change dramatically.
 Divisions get sold; managers change; new ventures started;
competitive pricing changes.  The beta may measure the 2001 Goldman
Sachs more than it does the company of today.

Finally, there is one academic study that has created a new wave of
examination of beta coefficients.  The paper has the boring title of
"The Cross-Section of Expected Stock Returns" by Eugene F. Fama and
Kenneth R. French, Journal of Finance (1992).  Fama and French
discovered in this study that that value stocks have higher returns
than growth stocks; smaller stocks higher returns than growth stocks;
and that small value stocks have the highest returns.  It led to a
series of articles declaring that ?beta is dead?.

Much of the criticism has been that Fama and French ignored
transactions costs, leading to flawed results.

If you?d like to see more on it, a summary is here:
Google Answers
?Cross-Section of Expected Stock Returns,? (Omnivorous, Nov. 8, 2003)
http://answers.google.com/answers/threadview?id=273817


Google search strategy:
CAPM + ?beta coefficient?
calculating beta coefficient
S&P500 historic returns

---

With a question this involved, there may still be issues that need
clarification.  Please don?t hesitate to use a Clarification Request
before rating this Answer.

Best regards,

Omnivorous-GA
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