What is the Capital Asset Pricing Model (CAPM)?
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The CAPM model establishes a relation between returns investors can expect relative to the risk taken for an asset or a portfolio.
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What is the Capital Asset Pricing Model (CAPM)?
By Bajaj Broking Team
May 06, 2025
11 mins read
Investment
With numerous applications in financial risk management, the capital asset pricing model prescribes a methodology to determine the required rate of return and cost of capital. It connects two concepts - systematic risk and expected return - and describes the interconnection while investing in a security. Essentially, the capital asset pricing model explains the linear relationship between risk and expected return on a particular investment. This linear relationship is described in terms of the security’s volatility relative to market risk, expected return, risk-free rate, and risk premium. The risk-free rate subtracted from the expected market return gives the market risk premium.
The CAPM model ties all the terms together and states that the expected returns from a security is equal to the risk-free rate added to the product of risk of the security relative to market risk and the risk-free premium. This model is a way to determine systematic risk. One of the most widely used models in finance, its specific use cases pertain to valuing securities that are risky and finding expected returns for assets. The objective of using the CAPM model is to evaluate whether a security is fairly valued while comparing its risk and time value of money with expected return. As an investor, you must know about the share market before using CAPM. Using CAPM, you can comment on whether the current value of a security is aligned with its expected returns. Let us understand the CAPM formula, relationship between CAPM and beta, CAPM example and limitations, the concept of the efficient frontier, security market line concept, CAPM applications, origins of CAPM, assumptions of CAPM, alternative models, and ICAPM.
CAPM Formula Explained
The CAPM relationship linking risk and expected returns is given by -
Ei = Rrf + {βi x (Em - Rrf)}
where:
Ei = returns expected on the investment
Rrf = Risk-free rate of return
βi = beta of the investment
Em = returns expected from the market
Ei represents the expected returns on investment in an asset over the period by considering the effect of other variables in the CAPM formula. Returns expected from an asset is an assumption of returns over the asset’s invested lifetime. Rrf, the risk-free rate of return, implies the returns expected on an invested carrying practically no risk. A usual benchmark would be the yield rate on a 10-year government bond. Based on the investment geography, the risk-free rate of return must correspond to the 10-year government bond yield rate for that geography. A more precise way is to match the maturity period of the bond with the investment duration. Βi, also known as “beta,” is a metric of asset volatility relative to the overall market volatility. Beta measures the sensitivity of the asset value fluctuations in response to market fluctuations. Em - Rrf is defined as the market risk premium which is an additional incentive to compensate investors for investing in a risky asset class. More the volatility of the market, more the market risk premium for the investor.
Relationship Between CAPM and Beta
Beta indicates the security risk or portfolio risk relative to the overall market risk. It is a measure of sensitivity or correlation between the security risk and market risk. When the risk for an asset is more than that for the overall market, the asset will have a beta >1. On the other hand, an asset with a beta <1 indicates that it incurs less risk than the market. For a security that If an asset has a beta of 1.1 or 110%, the asset is 10% more volatile than the market and expected return for the asset behaves according to the beta. A negative beta indicates a negative correlation between market returns and asset returns. The asset beta multiplied by the market risk premium and then added to the risk-free rate provides the estimated returns from that asset as per the capital asset pricing model.
Example of CAPM
Example 1
Suppose an investor is evaluating an investment opportunity in a security that is currently valued at ₹120 per unit paying a 4% dividend annually. It is known that this security has a beta of 1.25, indicating that it is 25% more volatile than a broad market index such as NIFTY 50. Assume the risk-free rate is 4% and the market, say NIFTY 50 index, is expected to appreciate by 12% every year. Find the returns on the investment using CAPM.
Here, Ei = 4 + 1.25(12 - 4) = 14%. Now, this expected return is utilized to discount capital appreciation and dividends over the estimated holding period of assets. If the discounted value of the future cash flows is equal to ₹120, then the model represents that the security is fairly valued relative to the risk.
Example 2
Assume that a security trading on NIFTY 50 has a beta of 1.1. Also, let the 10-year G-sec bond yield rate be 6.4% and the NIFTY 50 appreciates by 12.5% every year. Calculate the returns expected on this investment using CAPM.
Here, Ei = 6.4 + 1.1(12.5 - 6.4) = 13.11%. Following the same principle of discounting, if the discounted value of future cash flows is equal to the asset’s current value, then the asset is fairly valued relative to the risk.
Limitations of CAPM
The CAPM concept has several underlying assumptions as mentioned below -
Equity markets are efficient
Investors are rational and risk-averse
However, using beta as it is has emerged as a key bone of contention. It has been discovered that betas, over an extended duration, do not represent the performance of assets. When the time periods are shorter, the linear relationship between expected returns and beta does not hold true. Also, the CAPM model assumes that risk can be readily measured by measuring asset volatility. However, both positive and negative movements in asset values do not carry the same risk and the CAPM model fails to take this into account. The CAPM model takes for granted that the risk-free rate of return is constant, but in reality, the rate may change because the bond yield rates for government bonds keep changing over a period of time. A rise in the risk-free rate also increases the cost of capital which may represent the security to be undervalued.
CAPM and the Concept of the Efficient Frontier
For an investor to utilize the CAPM model to manage his investments relative to risk, he would have to refer to a curve known as the “Efficient Frontier.” As per the figure, the expected return increases with the expected risk. Any asset or a portfolio starts at an expected return more than zero on the Y-axis because there is always the case of risk-free returns. Theoretically, the Capital Market Line (CML) represents better returns for a portfolio than any portfolio to its right. An investor needs to go beyond this line and understand the returns relative to risk taken. CML and Efficient Frontier, though cannot be defined conceptually, highlight an important takeaway for investors: more the risk incurred, more the returns. So, there is always a tradeoff between rewards and risk.
As shown above, portfolio 1 has an expected return of 12% for a risk level of 10%, whereas portfolio 2 has an expected return of 15% for a risk level of 20%. The returns for portfolio 2 does not increase commensurate with the risk taken and therefore, portfolio 1 is a better investment option than portfolio 2.
Security Market Line (SML) in Relation to CAPM
The assumptions of the CML are the same as of CAPM and it only exists theoretically. Also, any portfolio that lies on the efficient frontier will provide maximum returns for the risk taken. Since future returns cannot be accurately estimated, it is not possible to determine if a portfolio is on the line of efficient frontier. In order to manage these limitations, a modified version of the CML is more practically suited for investors which is known as the Security Market Line (SML).
The risk and return tradeoff that applies to CAPM also applies to the SML. In the SML, β is used instead of the risk. As the portfolio or the asset β increases, the return also increases. The SML and the CAPM theories establish a relationship between the returns and the β.
Practical Applications of CAPM
CAPM is used widely in performance assessment, pricing of securities, capital budgeting, and risk management. Some of the important application of CAPM are mentioned below -
Evaluation of performance
Various metrics used for performance evaluations are derived from the CAPM concept. Such metrics are used to evaluate the performance of portfolios. Managers of active fund portfolios are expected to exceed the market performance and there are different ratios to track portfolio performance.
Selection of securities
After the estimated returns are calculated by CAPM, if the future discounted cash flows of the security is equal to the current price of the security, then the security is fairly valued relative to the risk. Using the SML, the undervalued security will be to the left of the SML, whereas a fairly valued security will be on the SML. An overvalued security will be to the right of the SML. This information aids in the decision-making to add or shelve off securities from a portfolio.
Construction of portfolio
A market portfolio may consist of a large number of securities and it may not be feasible for an investor to go through all of them and compute their valuations relative to risks. An index may serve as an indicator to which securities should be bought or sold.
Origin and Developers of the CAPM Theory
The CAPM theory was developed by William Sharpe, Jack Treynor, John Lintner, and Jan Mossin in the early 1960s providing a fundamental relationship of returns with respect to risks. The idea behind CAPM was that not every risk affects the price of a security and a portfolio can be hedged by diversifying risks across asset classes and securities. Risk, as a concept or empirical evidence, was understood very superficially in the 1960s even though the security and option markets had existed since 1602. Fisher and Lorie reported average returns on securities listed on the New York Stock Exchange for different holding periods since 1926, but they did not provide any insight on the risk or the market risk premium. In a way, the CAPM concept was developed at a time when the understanding of decision-making under uncertainty was still in its infancy.
Key Assumptions Underlying CAPM
For all its applications, there are several assumption underlying the CAPM model such as -
Portfolio diversification
The CAPM model assumes that investors require returns only for the systematic portion of their risk because the unsystematic portion has already been taken care of by portfolio diversification and therefore need not be accounted for. In a way, the CAPM model considers all investors to be rational and risk-averse in behavior. Practically, it is possible for investors to diversify their portfolios but the level of diversification varies across investors. An investor who has invested across 10 securities has less diversification than the one with 100 securities. In the case of the former, the unsystematic risk cannot be ignored.
Transaction horizon
The holding period in the CAPM model is considered to be standardized and a holding period of one year is generally used. However, returns for a 1-year holding period cannot be compared with that for a 5-year holding period. Also, investors hold securities for more than a year in many cases.
Borrowing and lending rates
The CAPM model assumes no transaction charges for borrowing and lending so there is always a minimum return at the risk-free rate. But in the real world, investors cannot borrow and lend at risk-free rates because transaction charges and a risk premium are added to the interest rates for debt.
Perfect markets
CAPM assumes perfect capital markets, therefore, there is no information asymmetry along with taxes. So, all investors want to maximize their gains using the same information in a risk-averse manner. However, the reality is markets are not perfect and information asymmetry always exists.
Alternative Models to CAPM
Because of the simplistic assumptions of the CAPM model, other alternative models establishing the connection between risks and returns have been developed of which the Arbitrage Pricing Theory (APT) and Fama-French 3-factor model are the important ones.
Arbitrage Pricing Theory (APT)
The APT is generally used in value investing style and it proposes that the returns can be estimated through a linear relationship between expected returns and different macroeconomic variables. Developed in 1976 by Stephen Ross, an economist, the APT considers that markets are imperfect and sometimes misprice assets before correcting so that the asset value reverts to the fair value. APT considers inflation, gross national product, changes in yield curve, and spreads in bonds as macroeconomic factors affecting an asset’s returns.
Fama-French 3-factor model
Developed in 1992, the Fama-French 3-factor model considers value risk factors and size risk to systematic risks in CAPM. The three factors used in this model are firm size, book-to-market value, and excess returns on the market. Fama and French, the brains behind this model, added two more factors in 2014 to the existing three. Those two factors are profitability and investment.
Introduction to the International Capital Asset Pricing Model (ICAPM)
The International Capital Asset Pricing Model (ICAPM) is an extension of the CAPM model in the sense that it applies CAPM to global investments. In addition to market risk and time value of money, the ICAPM incorporates risks due to exposure to foreign currency. The ICAPM model accounts for the fact that investors should be compensated more for exposure to foreign currency risks.
Conclusion
As an investor, you should be aware of the types of risks you will be encountering while investing in securities. The CAPM model offers you a view on the returns you can expect given the risk that you take. Though the CAPM model has its limitations, it was the first to connect the concepts of risks and returns. You need to look at the CAPM formula as an indicator rather than a perfect metric and account for other factors as you go along in your investing journey.
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Frequently Asked Questions
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How is the CAPM formula derived?
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The CAPM formula is derived from the fact that expected returns must be equal to the risk-free rate added to the product of asset risk and market risk premium.
What are the key assumptions of CAPM?
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The key assumptions of CAPM are perfect markets, rational investors, absence of unsystematic risk due to diversification, and a standard holding period.
How does CAPM calculate expected returns?
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The CAPM adds the risk-free rate to the product of asset risk and market risk premium in order to arrive at expected returns for an asset or a portfolio.
What are the limitations of using CAPM in investment decisions?
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CAPM does not consider that markets could be imperfect. Neither does it consider the fact that unsystematic risk could be present.
How does CAPM compare to other asset pricing models?
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Some of the limitations of CAPM have been adjusted for in other asset pricing models developed later after CAPM.
Can CAPM be applied to all types of investments?
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No, CAPM is usually applicable only for securities in the equity market.
What is the significance of beta in the CAPM formula?
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The beta in the formula measures the risk of the asset relative to the overall market risk.
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