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07/15/11 Chapter 20:30
Capital Asset Pricing Model
In todays lecture, we learn a formula which is used to determine the
correct rate of return of a companys stock
The key result is a simple formula, which many company managers use
References Corporate Finance: An Introduction (Welch, 2009, Prentice Hall)
6-1B
Some Example Portfolios
Stocks
Probability
Portfolios
State of
World
A
B
C
A, B
A, C
1/4
Yellow
10%
8%
-9%
9%
0.5%
1/4
Red
5%
4%
-5%
4.5%
0%
1/4
Green
-2%
0%
7%
-1%
2.5%
1/4
Blue
-3%
-4%
15%
-3.5%
6%
E[r]
2.25%
2%
2%
2.25%
2.25%
St.Dev.[r]
6.14%
5.16%
11.02%
5.61%
2.72%
The second portfolio, split evenly between A and C, is better than the
first, split evenly between A and B --- same return, half the risk.
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Individual vs. Portfolio Risk
8-1
Look at the table again. C is clearly riskiest of three stocks.
C is also the least desirable stock. A and B have at least as high
return, and about half the risk
But, a portfolio combining A and C has half the risk of a
portfolio combining A and B!
C is a better addition to a portfolio than B, because it contributes more
to reducing portfolio risk.
This is because C is negatively correlated with A (i.e., moves in
opposite direction), while B is positively correlated
Key point: when adding stock to portfolio, individual risk does
not matter. Contribution to portfolio risk does.
But how do we measure risk contribution? And what
does this have to do with stock returns?
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CAPM, Logic
8-1
You already knew: investments which are riskier have to offer
higher rate of return to induce people to buy
You just learned: riskier stocks are those which are more
highly correlated (i.e., move in same direction) as other stocks
in portfolio
Now, a big assumption: investors are smart, and also have
same beliefs about how each stock will perform in future
Implication: all investors will hold the market portfolio
This portfolio is highly diversified. It contains a little bit of
each stock trading on stock exchange (e.g., index fund)
Key result of CAPM model: each stock's return depends on
correlation with market portfolio
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CAPM Equation
8-1
The key equation of the CAPM model is:
E [ri ] = rF + * ( E [rM ] rF )
Each stock's expected return equals:
risk-free rate
plus correlation with market portfolio
multiplied by equity premium (the difference between
return on market minus risk-free rate)
You can think of equity premium as added compensation
investors demand for holding market portfolio
Beta is contribution of individual stock to risk of portfolio
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Inputs into Equation
8-1
We have already discussed the risk-free rate. In practice,
people use return on U.S. Treasury bond
Only question is which bond to use. May be best to use
bond with similar duration to your company's project
In theory, market portfolio should contain all investments. In
practice, people use S&P 500 or similar measure of stocks
The trickiest input is equity premium. It is the expected return
on S&P 500, minus risk-free rate.
Some use people historical return on stocks (~8%). But
what if future is different from past?
Different analysts use different estimates. In 2005
survey, estimates ranges from 1.5% to 5.2%
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What about Beta?
8-1
You can think of Beta as the correlation between the
individual stock and the market portfolio
It essentially captures the degree to which the individual
stock moves together with the market
Beta = 1 firm's stock moves in step with market.
Beta > 1 firm's stock amplifies market. Beta < 1
firm's stock moves less than one-to-one with market
To be precise, beta is the coefficient in a regression of the
individual stock on the market portfolio
Beta is the slope of the best fit line in a scatterplot with
market return on x-axis and individual return on y-axis
You don't have to know how to compute beta, or exactly
what it means
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Q1: Suppose the r_f rate is .02, the Beta is 1, and E[r_m] = .1.
What is the expected rate of return for the individual stock?
Q2: Suppose the r_f rate is .05, the Beta is 2, and E[r_m] = .1.
What is the expected rate of return for the individual stock?
Q3: The r_f rate is still .05, and E[r_m] = .1. The expected rate
of return for the individual stock is .075. What is Beta?
So what is the CAPM?
8-1
A primary goal of finance research is to explain stock prices -- why some companies prices are higher, some lower.
Statistical models which try to do this are called asset
pricing models. They are based on economic theory.
Good asset pricing model could help investors figure out the
correct stock price of a company
Investors could figure out which prices are too high or
too low, and therefore make money on the stock market.
The CAPM was the first attempt by economists to develop an
asset pricing model.
Economists really like the CAPM, because the logic
seems to make a lot of sense.
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But, it doesn't work
8-1
About 20 years ago, economists concluded the model is
wrong. The data clearly reject CAPM's predictions
CAPM says that only correlation with market portfolio should
matter. Data shows that many other things do.
Smaller companies have higher stock returns. So do
value and momentum companies.
Economists have no theory for why these characteristics
affect stock returns
Big puzzle in finance is explaining stock returns. Despite
much effort, we really don't have good understanding of them.
Many quant funds now do value or momentum investing
But they only know that these factors worked in past.
(momentum effect changed suddenly in 2009)
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So was today pointless?
8-1
For a company manager, the CAPM formula gives an
estimate of the E[r] which goes in the NPV formula.
Knowing the opportunity cost of capital is crucial helps
managers decide which projects are worth taking
Although CAPM is wrong, it remains quite popular in the
finance industry.
The formula is simple and convenient. Many people use
it as a rule of thumb.
73% of CFOs say they usually use CAPM for NPV
It is sometimes the best estimate of E[r] managers have.
In many cases, it is reasonably accurate.
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