WFU Law School
Law & Valuation
2.5 Capital Asset Pricing Model (CAPM)

2.5.1 CAPM Basics

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.


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)
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.

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.

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.

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?

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.

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
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?


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.

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?

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].

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>>)

2.5 Capital Asset Pricing Model (CAPM)

©2003 Professor Alan R. Palmiter

This page was last updated on: March 16, 2004