Beta and the Capital Asset Pricing Model
A fundamental principal of finance is that investors prefer:
 A higher expected return (note that expected return does not mean guaranteed return and
it applies to the future – not the past)
and
 Less risk (which we will define as volatility and measure as standard deviation)
When investors combine stocks into a portfolio, the expected return of the portfolio is simply an
average of the expected returns of each of the stocks in the portfolio.
However,
The volatility (standard deviation) of the portfolio will always be less than an average of the
standard deviations of each of the stocks in the portfolio.
The lower the correlations between the stocks (the less that they tend to move in tandem with
each other), the lower will be the risk of the portfolio.
We can see this with the exercise: “Am I Diversified?”
Larger portfolios of stocks have less volatility because if something bad happens to one stock in
the portfolio, it is likely offset by something good happening to another stock in the portfolio. Of
course, this only applies to events that affect stocks in isolation – like accounting fraud or poor
management decisions. Events that affect the entire economy (such as a recession) will affect all
stocks (though not all to the same degree).
Since diversification is a “free” way to reduce risk (which investors like), most professionally
managed money is held in well-diversified portfolios.
The most well-diversified portfolio you can achieve is called the market portfolio. It is a
portfolio that technically consists of all the assets in the world, but realistically can be any large,
well-diversified portfolio of stocks (and/or other assets).
Since the market portfolio is what most money is invested in, we should define the riskiness of a
stock by how it affects the volatility (standard deviation) of the market portfolio and not the
standard deviation of the stock when it is held in isolation.
The beta of a stock tells us how it affects the market portfolio’s standard deviation. Simply put, if
a stock has a beta > 1.0, when it is added to the market portfolio it increases the risk of that
portfolio (investors don’t like that). But if a stock has a beta < 1.0, when it is added to the market
portfolio, it decreases the risk of that portfolio (investors like that).
Since investors don’t like the way that stocks with a high beta increase their portfolio’s risk, the
price of these stocks goes down (compared to what they would otherwise be) – pushing up their
expected returns.
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On the other hand, stocks with a low beta, which decreases the risk of the portfolio are in
demand, thus increasing their price and pushing down their expected returns.
So what we end up with is a world where low-beta stocks offer less risk to the portfolio, but have
lower expected returns while high-beta stocks lead to more risk in the portfolio, but offer higher
expected returns.
That is the essence of the Capital Asset Pricing Model (The CAPM).
The CAPM says that the expected return for all stocks is at least equal to the rate of return you
can get on a risk-free investment such as a U.S. Treasury instrument. Beyond that, investors
should (on average) expect to get a risk-premium – an extra return – based on how that stock
contributes to the riskiness of the portfolio. High-beta stocks will receive a larger risk premium
and low-beta stocks will only receive a small risk premium. There is quite a bit of disagreement
over what an “average” risk premium is, but historically, a diversified portfolio of stocks have
tended to average 3% to 8% more than risk-free treasuries when measured over a long (50-100
years) period of time.
So if the CAPM says that a stock’s beta determines its expected return, how do find the beta for a
stock? Unfortunately, a stock’s beta can change over time and what you really want to know is
what its beta will be over the next few years. Unless you have a time machine, you can only
estimate what a stock’s beta will be in the future based on what it has been in the not-too-distant
past (the last 2-5 years).
Most analysts will look at a stock’s monthly returns over the past five years (60 months) and
observe how they have correlated with the returns of a broad market index like the S&P 500 over
that same period of time. A linear regression, where the dependent variable is the return on the
stock and the independent variable is the return on the S&P 500 will tell us what the stock’s beta
has been over the fairly recent past and what it most likely will be in the near future.
In summary, almost all financial experts agree that you can’t forecast a stock’s returns over the
next year or two simply by expecting it to continue on the upward or downward trend it has been
on in the past. The CAPM says that its expected return is a function of the amount of risk it
brings to a well-diversified portfolio. Stocks with high betas bring more risk and thus investors
expect (on average) a higher return from them as compensation for that additional risk. Low-beta
stocks will have lower expected returns.
The CAPM is certainly not a perfect pricing model. There are other, more complex models out
there (such as the Fama/French multifactor model) which some prefer. However, it is certainly
the most widely-used model and serves as the basis for other more complex models.
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