2.5.1 CAPM Basics |
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A widely-used valuation model, known as the Capital
Asset Pricing Model, seeks to value financial
assets by linking an asset's return and its risk.
Armed with two inputs -- the market's overall
expected return and an asset's risk compared to
the overall market -- the CAPM predicts the asset's
expected return and thus a discount rate to determine
price!
To work with the CAPM you have to understand
three things. (1) the kinds of risk implicit in
a financial asset (namely diversifiable and nondiversifiable
risk); (2) an asset's risk compared to the overall
market risk -- its so-called beta coefficient
(ß); (3) the linear formula (or security
market line) that relates return and ß --
this is the CAPM equation.
The CAPM, despite its theoretical elegance, makes
some heady assumptions. It assumes prices of financial
assets (the model's measure of returns) are set
in informationally-efficient markets. It relies
on historical returns and historical variability,
which might not be a good predictor of the future.
In fact, some recent empirical studies have discredited
the CAPM -- actual results simply don't fit the
model. But CAPM continues to be used and offers
a framework to roughly approximate stock risk
and thus value. |
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Diversifiable and non-diversifiable
risk
How is the CAPM derived? The CAPM begins with
the insight that financial assets contain two
kinds of risk. There is risk that is diversifiable
-- it can be eliminated by combining
the asset with other assets in a diversified portfolio.
And there is nondiversifiable risk - risk that
reflects the future is unknowable and cannot
be eliminated by diversification.
As you add financial assets in a portfolio, the
diversifiable risk decreases and begins to approach
zero -- the only risk left is nondiversifiable risk.
In fact, studies show that approximately 15-20 stocks
are sufficient to reduce diversifiable risk nearly
to zero, though more recent studies suggest the
minimum is 40 stocks. See Gerald D. Newbould &
Percy S. Poon, The Minimum Number of Stocks
Needed for Diversification, Financial Practice
and Education at 85-87 (Fall 1993). |
Diversifiable risk
(sometimes called unsystematic risk) |
That part of an asset's risk arising from
random causes that can be eliminated through
diversification. For example, the risk of
a company losing a key account can be diversified
away by investing in the competitor that look
the account. |
Nondiversifiable risk
(sometimes called systematic risk)
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The risk attributable to market
factors that affect all firms and that cannot
be eliminated through diversification. For
example, if there is inflation, all companies
experience an increase in prices of inputs,
and generally their profitability will suffer
if they cannot fully pass the price increase
on to their customers. |
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Beta
coefficient
Since it is possible to create a portfolio that
virtually eliminates all diversifiable risk, the
only question is how much nondiversifiable risk
does an asset add to a portfolio. What is a financial
asset's systematic risk? Financial economists
assume different assets carry different nondiversifiable
risks -- depending on how their volatility compares
to overall market volatility.
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Beta
as a measure of volatility
The measure for this nondiversifiable risk is
the beta coefficient -- which measures
the volatility of an asset's returns compared
to volatility of overall market returns. To understand
this, suppose two stocks and the S&P 500
(a common index of market-traded stocks) had the
following returns:
| Year |
Stock A |
Stock B |
S&P 500 |
1990 |
-6% |
-1.5% |
-3% |
1991 |
60 |
15 |
30 |
1992 |
16 |
4 |
8 |
1993 |
20 |
5 |
10 |
1994 |
2 |
0.5 |
1 |
1995 |
76 |
19 |
38 |
1996 |
46 |
11.5 |
23 |
1997 |
66 |
16.5 |
33 |
1998 |
58 |
14.5 |
29 |
1999 |
42 |
10.5 |
21 |
2000 |
-18 |
-4.5 |
-9 |
Notice that Stock A's returns rise twice as much
as the S&P 500 when it rises, but fall twice
as much when the S&P falls. Stock A is twice
as volatile as the market -- its beta
is 2.0. Stock B's returns were half as volatile
as the S&P 500, and its beta is 0.5.
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Example
Normally, financial assets' returns
are not a precise multiple of overall market
returns. They vary. For example, suppose a more
realistic example:
| Year |
Anheuser
Busch |
Merrill Lynch
|
S&P 500 |
1991 |
13 |
4 |
10 |
1992 |
18 |
38 |
20 |
1993 |
12 |
8 |
5 |
1994 |
6 |
-8 |
0 |
1995 |
14 |
19 |
15 |
1996 |
20 |
27 |
22 |
1997 |
22 |
30 |
24 |
1998 |
18 |
22 |
20 |
Average |
15.4 |
17.5 |
14.5 |
From these data it appears that
Anheuser Busch is less volatile, and Merrill
Lynch more, compared to the S&P 500. But
how much more or less volatile?
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| Computing
beta (ß) coefficient
The beta coefficient is a mathematical
way of expressing the volatiltiy of an asset's
returns compared to a market benchmark. Let's
create a graph comparing Asset Return and Market
Return. The horizontal axis (x) measures
market return, and the vertical axis (y)
measures the asset's return. If we plot the stock's
coordinates for each year, we should notice a
pattern -- that is, a "characteristic line"
that best shows how stock's Asset Return compares
to Market Return. The line that best fits the
coordinates can be derived mathematically using
a regression analysis, easily
performed on a financial calculator or spreadsheet.
We immediately notice that our market benchmark
always has a perfect slope of 1.0 -- for every
change in the market, the benchmark goes up or
down the same amount.
How much do the other stocks go up and down
compared to the market? The slope of each of their
lines gives us their beta -- a measure of how
volatile or nonvolatile they are compared to the
market. A steeper line (such as that of Merrill
Lynch) has a slope greater than 1.0, indicating
the asset's returns are more responsive to market
changes -- it is riskier than the market. A flatter
line (such as that of Anheuser Busch) has a slope
less than 1.0, indicating the asset's returns
are less responsive to market changes -- it is
less risky.
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Interpreting
beta (ß) coefficient
The beta for Merrill Lynch is approximately
1.61. Why are its returns more volatile than the
market? Well, if the market is bullish (suggesting
good times ahead), investors in a securities firm
are ecstatic about the firm's future. They anticipate
more stock trading, more companies going public,
more financial deal-making. Merrill Lynch's returns
outperform the market. But when the market turns
bearish (suggesting bad times ahead), investors
in a securities firm become apoplectic. They worry
that stock-related activities will decline, deals
will whither, the firm will announce layoffs.
Merrill Lynch's returns underperform the already
lethargic market.
But the story for Anheuser Busch is different.
Its beta of 0.58 indicates that people
will drink beer no matter what. Maybe there will
be more profitability in premium brands when the
market (and the economy) are booming. But there
will also be profitability for Budweiser when
the market turns bearish. Steady returns, like
barrels of beer, will keep rolling out.
Although it is possible to imagine a company with
a negative beta -- that is, its returns
are counter-cyclical and move opposite to the market
-- the beta of most companies' stock is
positive. Of course, some financial assets are designed
to have negative betas. For example, funds
that engage exclusively in short-selling make money
when the market is falling and lose when the market
is rising. Including these assets in a portfolio
decreases volatility.
How do you find an asset's beta -- short
of performing your own regression analysis? There
are many sources, such as Value Line Investment
Surveys. For example, moneychimp.com
will allow you to look up a company’s beta
by ticker symbol. |
Portfolio betas. The
beta (ß) of a portfolio is the
sum of the weighted betas of all the
assets in the portfolio. For example, assume you
hold of portfolio of five stocks in different
proportions:
| Asset |
Proportion |
Asset's beta |
Weighted beta |
Boston Edison
|
15% |
0.70 |
0.105 |
Callaway Golf
|
10% |
1.45 |
0.145 |
Intel |
25% |
1.10 |
0.275 |
Proctor &
Gamble |
20% |
1.05 |
0.210 |
Xerox Corporation |
30% |
1.00 |
0.300 |
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Total |
1.035 |
Your portfolio will move approximately with the
market. Notice, though, we have not yet talked
about returns. Can you expect your slightly more
volatile portfolio to outperform the market?
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CAPM
equation - security market line
The CAPM provides an equation that relates an
asset's beta to its expected return. The formula
says:
| E(r)
= Rf + ß x (Rm -
Rf ) |
| E(r) |
required return on asset |
| Rf |
risk-free rate of return (commonly based
on U.S. Treasury bill) |
| ß |
beta coefficient (nondiversifiable
risk of asset) |
| Rm |
market return (measured by market portfolio
of assets) |
If it works, this is fantastic! If you know a
financial asset's expected volatility compared
to the market, and you know what the expected
market return is supposed to be, you can compute
the expected return for the asset -- and thus
the discount rate to determine its price.
FOr a useful description of CAPM,
see MoneyChimp.
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Let's try an example. Suppose that
AT&T has an expected ß = .92, and Microsoft
has a ß = 1.23 (both based on past stock
price volatility). Further, assume that analysts
are predicting the S&P 500 will go up 14.7%
over the next year, and currently the return on
a one-year Treasury bill is 5.2%. What return
should I expect for AT&T and Microsoft?
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Risk-free
return [Rf] |
Asset's
beta [ß] |
Market
return [Rm] |
Expected
return
[Rf + ß*(Rm
- Rf)] |
| AT&T |
5.2% |
.92 |
14.7% |
.052+
0.92(.147-.052)
= 13.94% |
| Microsoft |
5.2% |
1.23 |
14.7% |
.052+
1.23(.147-.052)
= 16.88% |
We now have a market-adjusted discount
rate for each company. If we know the company's
expected returns (earnings) and their growth rate,
we can determine their present value -- that is,
the company's price. For example, if Microsoft's
eanings for its most recent year were $3.12 per
share and we anticipated a growth rate of 10%
into the foreseeable future, we can capitalize
earrnings using the Gordon model to compute its
price -- $3.12(1 + .10) / (.1688 - .10) = $49.88
[see 1.3.6
- Present value of constantly growing perpetuity].
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Example
Tad's Enterprises ran 6 steakhouses
in the NY area. It also owned an algae production
and marketing company, as well as a geothermal
power production company. In short, the company's
managers had no idea what they wanted to be.
In 1987 Tad's sold its steakhouses
for $9.75 million and then took the remaining
businesses private -- that is, it cashed out
the company's public shareholders and the majority
insiders retained a controlling interest of
the reduced company. In the transaction, public
shareholders received $13.25 per share.
The Ryan brothers, owners of 5.5%
of Tad's shares, dissented from the transaction
and sought an appraisal of their shares. They
later amended their complaint to add claims
that the Tad board breached its fiduciary duties
in approving the two-step transaction. (More>>)
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2.5 Capital Asset Pricing Model (CAPM)