How does the CAPM model work and can it be used?

The capital asset pricing model (CAPM) is an idealized depiction of how financial markets price securities and thereby determine the expected return on capital investments. The model provides a methodology for quantifying risk and translating that risk into an estimate of the expected return on equity.

The main advantage of CAPM is the objective nature of the estimated cost of capital. CAPM cannot be used in isolation because it necessarily simplifies the world of financial markets. But financial managers can use this model in addition to other methods and their own judgment in their attempts to develop realistic and useful estimates of stock prices.

Although the use of the CAPM continues to stimulate vigorous debate, modern financial theory now takes the model for granted when it comes to investment management.

CAPM embodies the theory. Among financial managers, the popularity of CAPM raises the following questions:

• What is CAPM?
• How can you use this model?
• And most importantly, does it work?

CAPM is a theoretical understanding of the behavior of financial markets and can be used in estimating a company's cost of equity.

Despite its limitations, the model can be a useful addition to a financial manager's analytical arsenal.

Work on the theory and practice of using CAPM has led to the emergence of many complex, and often very complex, versions of this simple model. But in solving the above issues, we will focus exclusively on its simple version. Finding answers to these questions requires understanding the theory behind CAPM.

What is CAPM?

Modern financial theory is based on two assumptions:

• (1) securities markets are highly competitive and efficient (that is, relevant information about companies is quickly and widely distributed and absorbed);
• (2) these markets are dominated by rational, risk-averse investors who seek to maximize the return on their investments.

The first assumption assumes a financial market filled with sophisticated, well-informed buyers and sellers. The second assumption describes wealth-conscious investors who prefer more to less. Moreover, the hypothetical investors of modern financial theory demand a premium in the form of higher expected returns for the risks they take.

Although these two assumptions constitute the cornerstones of modern financial theory, the formal development of the CAPM is associated with other, more specialized, restrictive assumptions. These include ideal markets without imperfections such as transaction costs, taxes, and restrictions on borrowing and short selling.

The model also requires marginal assumptions regarding the statistical nature of security returns and investor preferences. Finally, investors are expected to agree on the likely performance and risk of the securities based on a common time frame.

An experienced financial manager may have difficulty recognizing the world described by this theory. Much research has been devoted to relaxing these restrictive assumptions. The result is more complex versions of the model, which, however, are quite consistent with the simple version of CAPM, which we will consider below.

Although the CAPM assumptions are obviously unrealistic, this simplification of reality is often necessary to develop useful models. Testing the validity of a model is not only about the validity of the underlying assumptions, but also about the validity and usefulness of the model's recipe. Tolerating the CAPM's assumptions, as fantastical as they may be, provides a concrete, albeit idealized, model of how financial markets measure risk and turn it into expected return.

Portfolio diversification.

CAPM looks at the risks and returns of financial securities and determines their exact value. The rate of return that an investor receives from buying common stock and holding it over a period of time is:

• amount of dividends received
• plus capital gain (or minus capital loss) during the holding period,
• divided by the purchase price of the shares.

While investors may expect a certain return when they buy certain stocks, they may be disappointed or pleasantly surprised as fluctuations in stock prices lead to fluctuations in earnings. Therefore, common shares are considered risky securities. Conversely, because the return on some securities, such as Treasury bills, does not differ from the expected return, they are considered risk-free securities.

Financial theory defines risk as the possibility that actual returns will deviate from expected returns, and the degree of potential deviation determines the degree of risk.

The fundamental basis of CAPM is the observation that risky securities can be combined in such a way that the combination (portfolio) is less risky than any of its components. Although such diversification is a familiar concept, it is useful to consider how diversification reduces risk.

Suppose there are two companies located on an isolated island whose main industry is tourism. One company produces suntan lotion. Its shares predictably perform well in sunny years and poorly in rainy years. Another company makes disposable umbrellas. Its shares, on the contrary, sell poorly in sunny years and well in rainy years. Each company brings in an average of 12% profit.

When purchasing shares of any of these companies, investors are exposed to great risk due to share price volatility caused by fluctuating weather conditions. However, investing half in a suntan lotion maker and half in an umbrella maker results in a 12% return no matter what weather conditions prevail. Thus, portfolio diversification turns two risky investments with an average return of 12% into a risk-free portfolio that is expected to return 12%.

Unfortunately, a perfect negative relationship between the stock returns of these two companies is very rare in the real world. To some extent, corporate securities move together so that complete elimination of risk through simple portfolio diversification is not possible. However, as long as there is some lack of synchronicity in security returns, diversification will always reduce risk.

Two types of risk.

Some risk investors believe that risks are specific to individual stocks in their portfolios—for example, a company's earnings could plummet due to a strike. On the other hand, as stock prices and returns rise somewhat, even investors holding widely diversified portfolios are exposed to the risks inherent in the overall performance of the stock market.

Thus, we can divide the total risk of shares into unsystematic (or diversifiable risk, from the English 'unsystematic risk') , i.e. risk that can be diversified, and systematic risk (from the English 'systematic risk') , i.e. uncontrollable, related to the movement of the stock market, and therefore inevitable. Examples of systematic and unsystematic risk factors are given in Example 1.

Example 1. Some systematic and unsystematic risk factors.

The example clearly illustrates the reduction in risk as securities are added to the portfolio. Empirical research has shown that unsystematic risk can be virtually eliminated in portfolios of 30 to 40 randomly selected securities. Of course, if investments are made in closely related industries, more securities are required to eliminate unsystematic risk.

Example 2. Reducing unsystematic risk through diversification.

The investors inhabiting this hypothetical world are assumed to be risk averse. But most of us know that investors demand compensation for taking risk. In financial markets dominated by 'risk-averse investors', higher-risk securities provide higher expected returns than lower-risk securities.

A simple equation expresses the positive relationship between risk and return. The risk-free rate (return on a risk-free investment) establishes the relationship between risk and expected return.

The expected return on a risky security, Rs , can be thought of as the risk-free rate Rf plus the 'risk premium':

Rs = Rf + risk premium

The reward for making unrealistic CAPM assumptions is that one can measure that risk premium and that there is a method for estimating the risk/expected return curve. These assumptions and the risk-reducing effectiveness of diversification lead to an idealized financial market in which, to minimize risk, CAPM investors hold highly diversified portfolios that are sensitive only to market risks.

Since investors can eliminate company-specific risk simply by properly diversifying their portfolios, they are not exposed to unsystematic risk. And since well-diversified investors are only exposed to systematic risk, in the CAPM model, financial market risk represents systematic risk rather than total risk. Thus, the investor receives a higher expected return for risking only the market.

This important result may seem inconsistent with empirical evidence that, despite low-cost diversification mechanisms such as mutual funds, most investors do not maintain sufficiently diversified portfolios.

However, according to the CAPM, large investors who dominate trading on the New York Stock Exchange typically hold portfolios with many securities. These actively trading investors determine the prices of securities and expected returns. If their portfolios are well diversified, their actions may result in market pricing consistent with the CAPM's prediction that only systematic risk matters.

Beta is the standard CAPM measure for systematic risk. It measures the trend in the returns of an individual security that parallel the returns of the stock market as a whole. One way to think about beta is to think of it as a measure of a security's volatility relative to market volatility.

• Stocks with a beta of 1.00—the average level of systematic risk—rise and fall at the same percentage as a broad market index such as the Standard & Poor's 500.
• Stocks with a beta greater than 1.00 tend to rise and fall by a greater percentage than the market, meaning they have a high level of systematic risk and are very sensitive to changes in the market.
• Conversely, stocks with a beta of less than 1.00 have a low level of systematic risk and are less sensitive to market fluctuations.

Securities Market Line (SML).

The CAPM sequence of conceptual blocks culminates in the relationship of risk to expected return. This fundamental result follows from the proposition that only systematic risk, as measured by beta (β), . Securities are valued in such a way that:

Rs = Rf + risk premium

Rs = Rf + βs (Rm - Rf)

Where:

Rs = expected stock return (and company's cost of equity).

Rf = risk free rate.

Rm = expected return on the stock market as a whole.

βs = stock beta.

This relationship between risk and expected return is called the security market line (SML - from the English 'security market line') . Let's illustrate this graphically in Example 3.

As stated above, the expected return of a security as a whole is equal to the risk-free rate plus the risk premium. In the CAPM, the risk premium is measured as beta multiplied by the difference in expected return minus the risk-free rate.

The risk premium of a security depends on the market risk premium (i.e., the difference between Rm and Rf) and is directly related to the level of beta (no measure of unsystematic risk is included in the risk premium because the CAPM assumes that diversification has eliminated it ).

Example 3. Securities market line.

In the freely competitive financial markets described by the CAPM, no security can trade at prices low enough for long to earn a return greater than its corresponding SML line yield. The security will then be very attractive relative to other securities of similar risk, and investors will bid up its price until the expected return falls to the corresponding position on the SML.

Conversely, investors would sell any security at a price high enough to reduce the expected return below its corresponding position. As a result, the price decline will continue until the expected return reaches a level justified by the systematic risk.

The pricing adjustment mechanism may be sufficient to justify the SML relationship with less restrictive assumptions than the traditional CAPM model. Therefore, SML can be derived from models other than CAPM.

One perhaps controversial aspect of the CAPM is that stocks exhibit a lot of total risk but very little systematic risk.

An example would be a company that mines precious metals. Considered in isolation, the company would be very risky, but much of its overall risk is unsystematic and can be diversified. A well-diversified CAPM investor would view these stocks as low-risk stocks. In SML, a low stock beta will result in a low risk premium. Despite the high level of total risk in the stock market, the market will price these stocks with low expected returns.

In practice, such contradictory examples are rare—most companies with high overall risk also have high betas, and vice versa. Systematic risk, as measured by beta, usually matches intuitive estimates of risk for specific stocks. However, there is no general risk equivalent to SML for pricing securities and determining expected returns in financial markets where investors are free to diversify their portfolios.

Summarize the conceptual components of CAPM. If a model correctly describes market behavior, the appropriate measure of risk is its market or systematic risk, as measured by its beta. If a security's return has a strong positive relationship with market returns and thus has a high beta, it will be priced with a high expected return; if it has a low beta, it will be priced with a low expected return.

Because unsystematic risk can be easily eliminated through diversification, it does not increase the security's expected return. According to the model, financial markets only influence systematic risk and stock prices, so expected returns lie along the stock market line.

How can you use the CAPM model?

Due to its sensitivity to expected returns and security prices in financial markets, the CAPM model has legitimate investment management rights. Its use in this area has advanced to a level of sophistication beyond the scope of this introductory review.

CAPM has important applications in corporate finance. Financial literature defines the cost of capital as a company's expected earnings per share (EPS). Expected stock returns are the shareholders' opportunity cost of equity capital employed by the company.

In theory, a company must earn this value on the equity portion of its investment, or its stock price will fall. If a company does not expect to earn at least its cost of equity capital, it must return funds to shareholders, who can earn that expected return on other securities at the same level of risk in the financial market. Because the cost of capital is tied to market expectations, it is very difficult to measure. Several methods are used for this.

Measuring the cost of capital.

This complexity is very inconvenient for the role of 'cost of equity' in such vital tasks as estimating capital budgets and assessing potential acquisitions. The cost of equity is one component of the weighted average cost of capital (WACC), which corporate managers often use as a hurdle rate when evaluating investments. Financial managers can use the CAPM to obtain an estimate of the cost of equity.

If the CAPM correctly describes market behavior, the stock market line gives the stock's expected return. With this expected return, Rs , SML also provides an estimate of the cost of capital, ke . Thus:

ke = Rs = Rf + βs (Rm - Rf)

Applying the resulting cost of capital to estimate future cash flows requires estimating future values ​​of the risk-free rate Rf , the expected market return, Rm , and beta, βs .

Over the past 50 years, the T-bill rate (risk-free rate) has approximately equaled the annual inflation rate. In recent years, due to short-term inflation expectations, the T-bill rate has fluctuated widely. While sophisticated methods can be used to estimate future inflation and the T-bill rate, for the purposes of this review we will make a rough estimate of 10%.

Estimating expected returns in the market is more difficult. The general approach is to assume that investors expect the same risk premium (Rm - Rf) in the future as they did in the past. From 1926 to 1978, the risk premium for the Standard & Poor's 500% index averaged 8.9%. An estimate of 9% for the risk premium and 10% for the T-bill rate implies that Rm is 19%.

This is significantly higher than the historical average of 11.2%. The difference reflects the long-term 10% inflation rate included in our T-bill rate estimate. The future inflation rate is projected to be 7.5% higher than the 2.5% average for the period 1926-1978. Expected profits (in nominal terms) must increase to compensate investors for the expected loss of purchasing power. As elsewhere, more sophisticated methods exist, but the 19% estimate for Rm is roughly consistent with historical spreads between equity returns and yields on Treasuries, long-term government bonds and corporate bonds.

Statistical methods that estimate a security's past volatility relative to the market can estimate beta. Many brokerage and investment firms also estimate beta. If a company's previous level of systematic risk is likely to continue, beta calculations from historical data can be used to estimate the cost of capital.

Example 4 calculates the estimated stock price of three hypothetical companies.

Example 4. Calculation of the cost of equity capital.

The betas in Example 4 are for companies in the three industries shown. Many electric utilities have low systematic risk and low betas due to relatively modest fluctuations in their revenues and earnings. Airline revenues are closely tied to passenger miles, which are highly sensitive to changes in economic activity.

Compounding this systematic earnings variability is high operating and financial leverage. The results are returns that vary widely and produce high betas for these stocks. Large chemical companies exhibit an intermediate degree of systematic risk.

It must be emphasized that the methodology shown in Example 4 provides only rough estimates of the cost of capital. Complex refinements can help evaluate each input of a formula. Sensitivity analysis using different input values ​​can result in a fairly good range of cost of capital estimates. However, the calculations in this example show how a simple model can generate benchmark data.

Exhibit 5 shows a risk/expected return spectrum using average betas for companies in more than three dozen industries. The result is an equity pricing schedule that reflects the risk function. The spectrum represents the ratio of risk to expected return in financial markets and therefore alternative shareholder options for a particular company.

Example 5. Risk/expected return spectrum.

Application of CAPM.

The applications of CAPM concepts are simple. For example, when a manager calculates a division's cost of capital or hurdle rate, the cost of capital should reflect the risk inherent in the division's operations rather than the risk of the parent company. If the division is in one of the risky businesses, a cost of capital commensurate with that risk should be used, even though it may be much higher than the parent company's cost of capital.

One approach to estimating a division's cost of capital is to calculate CAPM estimates of the cost of capital for similar independent companies operating in the same industry. The betas of these companies reflect the level of risk in the industry. Of course, adjustments may be required to adjust for differences in financial leverage and other factors.

The second area of ​​application concerns acquisitions. When estimating discounted cash flows on an acquisition, the appropriate cost of capital should reflect the risks inherent in the discounted cash flows. Again, ignoring the refinements required by changes in capital structure and the like, the cost of capital should reflect the risk level of the target company, not the acquirer.

Basic Earnings per Share

The basic earnings per share ratio is defined as the ratio of basic profit (loss) for the reporting period to the weighted average number of ordinary shares outstanding during the reporting period.

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Number of Common Shares Outstanding

The basic profit of the reporting period is determined by reducing the profit of the reporting period remaining at the disposal of the organization after taxation by the amount of dividends on preferred shares accrued for the reporting period.

Does CAPM work?

As an idealized theory of financial markets, the model's assumptions are clearly unrealistic. But the true test of CAPM, naturally, is how well it works.

There have been many empirical tests of the CAPM. Most have studied the past to determine the extent to which stock returns and betas have followed the stock market's predicted line. With some exceptions, the main empirical studies in this area have concluded that:

• As a measure of risk, beta is related to past returns. The close relationship between total and systematic risk makes it difficult to distinguish their effects empirically. However, the inclusion of a factor representing unsystematic risk appears to do little to explain the strength of the risk-return relationship.
• The relationship between past returns and beta is linear—that is, reality matches what the model predicts. The relationship is also positively sloped, that is, there is a positive relationship between them (high risk equals high return, low risk equals low return).
• The empirical SML line slopes less steeply than the theoretical SML line. As shown in Exhibit 6, low-beta securities generate returns that are slightly higher than predicted by the CAPM, while high-beta securities generate lower returns than predicted. Various shortcomings in the CAPM and/or in the statistical methodologies used have been hypothesized to explain this phenomenon.

Example 6. Theoretical and estimated lines of the securities market.

While these empirical tests provide unequivocal support for the CAPM, they do also support its major limitations. A measure of systematic risk, beta appears to be related to past returns; there is a positive relationship between risk and return; and this risk-return relationship appears to be linear. The controversial finding regarding the slope of the SML is the subject of ongoing research. Based on these results, some researchers propose using a more gradually sloping “empirical market line” instead of the theoretical SML.

Problems with applying the CAPM model.

There are several potential sources of error in enterprise applications of CAPM.

First, a simple model may not be an adequate description of the behavior of financial markets. (As noted above, empirical work to date has unequivocally supported the validity of the CAPM.) In attempts to improve their realism, researchers have developed many extensions of the model.

The second problem is that betas are not stable over time. This fact creates difficulties when betas derived from historical data are used to calculate the cost of capital when estimating future cash flows. Betas should change as fundamentals and capital structures change. In addition, betas estimated from past data are subject to statistical error. There are several methods to help deal with these sources of instability.

Estimates of the future risk-free rate and expected market returns are also subject to error. The focus here is also on developing methods to reduce potential errors associated with SML inputs.

The resulting set of problems is unique to the application of CAPM in the corporate finance of a particular company. There are practical and theoretical problems associated with using the CAPM or any financial market model in capital budgeting decisions involving real assets. These challenges continue to be a fertile area of ​​research.

Dividend growth model.

The disadvantages of CAPM may seem serious. However, they should be evaluated in comparison with other approaches to estimating the cost of equity capital. The most commonly used of these is the simple discounted cash flow (DCF) method , which is known as the dividend growth model or the Gordon-Shapiro model).

This approach is based on the assumption that the price of a company's shares is equal to the present value of future dividends per share, discounted by the value of the company's equity. Assuming that future dividends per share will grow at a constant rate and that this growth rate will continue forever, the general formula for present value comes down to a simple expression.

P = dps / (ke - g)

Where:

P = current price of the security.

dps = next year's dividend per share.

g = growth rate (constant rate).

ke = the company's cost of equity.

Calculation of return on equity:

ke = dps / P + g

The cost of capital implied by the current share price and model assumptions is simply the dividend yield plus the constant growth rate.

Like the CAPM, two model assumptions limit the dividend growth method. One of them is the assumption of a constant growth rate of dividends per share. The second is that the constant growth rate must be less than the company's cost of capital. If this is not the case, the equation is invalid.

These two assumptions severely limit the applicability of the dividend growth model. The model cannot be used in estimating the cost of capital for companies with an unstable dividend pattern or for high-growth companies where g is likely to be greater than ke . (Obviously, the model also doesn't apply to companies that don't pay dividends.) Unlike the CAPM, the model is limited primarily to companies that enjoy slow, steady dividend growth. However, more sophisticated DCF methods can be applied to a wider range of companies.

Another problem with using the dividend growth model to estimate the cost of capital is the estimation of g . To get a reasonable cost of capital, you need to estimate the growth rate that investors use to value a stock. Thus, what is important is the current valuation of the market at the moment, not the company. This is a major source of error in the dividend growth model.

Unlike the dividend model, the only company-specific input in the SML model is the beta coefficient, which is derived by an objective statistical method. Even more complex DCF methods require as an input parameter a market estimate of the company's future dividends per share.

Compared to the dividend growth model and other DCF approaches, the disadvantages of the CAPM do not appear to be as severe. However, there is no reason to view the CAPM and the dividend growth model as competitors. There are not many technologies available for the complex task of measuring the cost of capital. Despite the shortcomings, investors should use both the DCF and CAPM models, as well as sound judgment, to estimate the cost of capital.

Book value of the share (Book value, BV)

This indicator is defined as the ratio of the company’s net assets to the number of outstanding shares:

Book Value per Share = (Total Shareholders' Equity - Preferred Shares) / Total Number of Outstanding Shares

BV = Net assets / Number of outstanding shares

In the Russian literature, you can also find a slightly different calculation of the book value of a share, which determines the value of share capital (defined as the difference between total assets, or the balance sheet currency, and liabilities, or the sum of short-term and long-term borrowings of the issuing organization):

BV = Share capital / Number of shares outstanding

The company's net asset value per share (Price/Book Value Ratio, Price-to-book Ratio) shows how much investors pay for the company's net assets per share.

P/B Ratio = Stock Price per Share / Shareholders' Equity per Share

P/BV Ratio = Stock Price / Total Assets - Intangible Assets and Liabilities

If the share price is below the net asset value per share, the following two conclusions can be drawn, depending on which approach investors use:

1. The share price has been unfairly or mistakenly depressed for some reason, but since the company has sufficient growth potential, the shares should be bought as the price will rise.
2. If the low valuation of the company's shares is correct, then investing in this company is extremely risky, since either its fortunes are on the verge of decline, or investing in the company will not bring dividends.

CAPM is imperfect, but useful.

Investment managers have widely used the simple CAPM and more complex extensions. Although CAMP has been used in many utility rate setting processes, it has not yet gained widespread acceptance in corporate circles for estimating companies' costs of capital.

Because of its shortcomings, financial managers should not rely on the CAPM as an accurate algorithm for estimating the cost of equity capital. However, tests of the model confirm that it has a lot to say about how returns are determined in financial markets.

Because of the inherent difficulty in measuring the cost of capital, the disadvantages of CAPM appear to be no worse than those of other approaches. Its key advantage is that it quantifies risk and provides a broadly applicable and relatively objective approach for translating risk measures into estimates of expected returns.

Financial decision makers can use this model in combination with traditional methods and sound judgment to develop realistic and useful estimates of the cost of equity.