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Capital Asset Pricing Model (CAPM): Definition, Examples, Formula, and Calculation
The Capital Asset Pricing Model (CAPM) is the most widely used formula to assess the returns of a security against its risks. It has undertaken a lot of criticism in recent years but remains a constant in every economics 101 university course.
QUOTE
Perhaps the most important job of a financial advisor is to get their clients in the right place on the efficient frontier in their portfolios. But their № 2 job, a very close second, is to create portfolios that their clients are comfortable with.
Big ideas
- CAPM fits in neatly with Modern Portfolio Theory (MPT) and is also based on the concept of the Time Value of Money (TVM).
- CAPM calculates the expected return for an asset taking into account its risk as well as the risk-free rate of return.
- Despite its limitations, CAPM remains one of the most popular tools for comparing one security (or portfolio of securities) against another, due to its simplicity and ease of use.
What is the Capital Asset Pricing Model (CAPM)?
DEFINITION
CAPM was conceived in the 1960s as a means for determining the expected return on an investment based on its relative risk level to the market.
The concept is basically that the more risk associated with a security, the greater the return needs to be to compensate you for that to make it worthwhile investing.
The concept is basically that the more risk associated with a security, the greater the return needs to be to compensate you for that to make it worthwhile investing.
Overview of the CAPM formula
The CAPM formula has four major components. These are the risk-free rate (Rf), the beta (β), the market risk premium (RM), and the expected return E(Ri).
- Risk-free rate (Rf) - this is typically measured against a government bond, the closest thing to risk-free we can get within the financial markets. Some contend that government bonds are not as safe as they once were, but it is still a near-guaranteed return with the lowest possible risk and is thus described as risk-free.
- Beta (β) - this is a measure of systemic risk. Systemic risk is the risk that cannot be reduced through diversification. A beta above 1.0 has more risk than the wider market. A beta of 0.5 has half the risk of the wider market, while a beta of 2.0 has twice the risk.
- Market risk premium (RM) - this is a theoretical return of the wider market (as gauged by a large and well-known benchmark such as the FTSE 100 for UK stocks or S&P 500 for US stocks) minus the risk-free rate of return.
- Expected return E(Ri) - this is the total expected return from investing in an asset taking the risk-free rate, beta, and market risk premium into account. This is compared to other rates to analyse which security offers the best investment.
Capital Asset Pricing Model (CAPM) components
The chart above shows expected return E(Ri) relative to risk as measured by beta (β).
So if two stocks had the same return but one had greater risk attached, the lower-risk stock is a better investment. Equally if two stocks had the same risk but one is expected to return more, the higher return choice is preferable to the other. The model enables investors to get to grips with the fair value of an asset, balancing risk vs reward.
So if two stocks had the same return but one had greater risk attached, the lower-risk stock is a better investment. Equally if two stocks had the same risk but one is expected to return more, the higher return choice is preferable to the other. The model enables investors to get to grips with the fair value of an asset, balancing risk vs reward.
CAPM formula
The expected rate of return is the risk-free rate (such as government bonds) added to the beta (systemic risk) multiplied by the market risk premium (judged by a strong market index).
FORMULA
E(Ri) = (Rf) + (β x (RM – Rf))
Where:
• E(Ri): Expected return on a given asset
• Rf: Risk-free rate, or the return on a Treasury security/government bond
• β: Beta of the asset (its risk relative to the market)
• RM: Market return, or return on a comparable market index
Where:
• E(Ri): Expected return on a given asset
• Rf: Risk-free rate, or the return on a Treasury security/government bond
• β: Beta of the asset (its risk relative to the market)
• RM: Market return, or return on a comparable market index
In terms of the formula, it is best to keep in mind that some analysts use different notations to represent the same thing, such as RPM to represent RM. Yet the underlying formula always remains constant.
CAPM example
EXAMPLE
A UK stock has the following characteristics:
• Risk-Free Rate (Rf): 2% (0.02)
• Market Return (RM): 8% (0.08)
• Stock Beta (β): 1.3
Calculation
Expected Return = Rf + β × (RM − Rf) = 0.02 + 1.3 × (0.08 - 0.02) = 0.098 = 9.8%
Interpretation
If you bought this stock with a beta of 1.3, you would expect a return of 9.8% based on this model, given that the risk-free rate is 2% and the expected market return is 8%.
If you were investing £1,000, you could expect a return of £98 for that year.
• Risk-Free Rate (Rf): 2% (0.02)
• Market Return (RM): 8% (0.08)
• Stock Beta (β): 1.3
Calculation
Expected Return = Rf + β × (RM − Rf) = 0.02 + 1.3 × (0.08 - 0.02) = 0.098 = 9.8%
Interpretation
If you bought this stock with a beta of 1.3, you would expect a return of 9.8% based on this model, given that the risk-free rate is 2% and the expected market return is 8%.
If you were investing £1,000, you could expect a return of £98 for that year.
CAPM assumptions
The CAPM model operates on a few key assumptions and these assumptions need to be understood to gauge the strengths and weaknesses of the wider framework. If these assumptions do not hold true, it means the framework will not be fully effective.
Efficient Markets Hypothesis (EMH)
The Efficient Markets Hypothesis (EMH) is a foundation for CAPM. It assumes that asset prices reflect all known information. In an efficient market, no investor consistently beats the market through superior stock-picking skills. CAPM depends on this idea because if prices reflect all information, the model can calculate expected returns based on risk alone.
Rational investor behaviour
CAPM assumes investors are rational. They make decisions aimed at maximising their returns relative to the risk they take on. Rational investors understand their risk tolerance and invest accordingly. They diversify their portfolios to reduce unnecessary risk, knowing that only market risk (systematic risk) matters, which the CAPM model addresses directly.
Single-period investment horizon
A key CAPM assumption is that investors have a single-period investment horizon. This means they only plan for one period (e.g., one year) and care only about returns during that time frame. Future returns or changes in investment strategy are not factored into the CAPM model, which simplifies the calculation of expected returns.
Unlimited borrowing and lending at a risk-free rate
CAPM assumes investors can borrow or lend unlimited amounts at the risk-free rate, typically represented by government bonds. This makes it easier for investors to adjust their portfolios to the ideal mix of risk and return. In practice, real-world constraints like credit limits and varying interest rates make this assumption unrealistic.
Absence of taxes and transaction costs
CAPM operates under the assumption that there are no taxes or transaction costs. In other words, investors do not incur extra costs when buying or selling assets. This simplifies calculations since it avoids factoring in these additional expenses, which would reduce net returns and complicate decision-making in real-world investing.
Homogeneous expectations among investors
Another assumption is that all investors have the same expectations regarding future returns and risks. This means everyone agrees on the values of key inputs like the risk-free rate, market return, and the beta of a stock. While this simplifies the model, it does not reflect reality, where investors often have differing opinions and forecasts.
Equal access to information
CAPM assumes that all investors have equal access to the same information. This is closely tied to the efficient markets hypothesis. If everyone has the same data, no single investor has an advantage in predicting asset prices.
CAPM and the efficient frontier
DEFINITION
The efficient frontier is a key concept in modern portfolio theory. It represents a set of investment portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given return.
The idea is that investors want to optimise their portfolios by getting the most return possible without taking on more risk than necessary.
The idea is that investors want to optimise their portfolios by getting the most return possible without taking on more risk than necessary.
Portfolios that fall on the efficient frontier are considered "optimal". If a portfolio is below this frontier, it means there is a better combination of risk and return that could be achieved. Any portfolio above it would be impossible based on current market conditions.
To build an efficient portfolio, investors combine assets that behave differently under varying market conditions, reducing overall risk through diversification. The efficient frontier is usually shown as a curve, with risk (measured as standard deviation) on the horizontal axis and expected return on the vertical axis.
To build an efficient portfolio, investors combine assets that behave differently under varying market conditions, reducing overall risk through diversification. The efficient frontier is usually shown as a curve, with risk (measured as standard deviation) on the horizontal axis and expected return on the vertical axis.
CAPM and the SML
DEFINITION
The Security Market Line (SML) is a visual tool used in finance to represent the relationship between an asset's risk and its expected return. It comes from CAPM and shows how much return investors should expect for taking on a specific level of risk.
On the SML graph:
- The horizontal axis represents the risk (measured by beta).
- The vertical axis represents the expected return.
- The line starts at the risk-free rate, which is the return from a completely risk-free investment, often considered to be government bonds.
- As risk increases, the expected return also increases in line with the slope of the SML.
Having a return above the SML indicates a security is undervalued, since it offers a greater return than its risk level. If it falls below the line, it is seen as overvalued because the return does not justify the risk. The SML is useful for comparing individual securities and deciding whether they are priced fairly in the market.
Limitations and criticisms of CAPM
The CAPM model has been criticised for oversimplifying reality. One major limitation is that it only considers a single factor - market risk - when in practice, asset returns are influenced by multiple factors. Other limitations are outlined below.
1. Unrealistic assumptions
CAPM relies on several unrealistic assumptions. It assumes that all investors have the same expectations about risk and return, which is rarely true in practice. It also assumes markets are perfectly efficient, meaning that all information is instantly reflected in stock prices, which does not always happen.
Another assumption is that investors can borrow or lend unlimited amounts at a risk-free rate, ignoring real-world constraints like borrowing limits and varying interest rates. These simplifications can make CAPM less useful in complex, real-world investing.
Another assumption is that investors can borrow or lend unlimited amounts at a risk-free rate, ignoring real-world constraints like borrowing limits and varying interest rates. These simplifications can make CAPM less useful in complex, real-world investing.
Estimating the market risk premium in CAPM can be difficult. The risk premium represents the additional return expected from investing in the stock market versus a risk-free asset. There is no consensus on what the "correct" risk premium should be, and it can vary significantly depending on the time period or data used.
Plus, historical returns may not always be a good predictor of future performance, which introduces uncertainty. This makes using CAPM tricky, as an inaccurate risk premium leads to unreliable expected return estimates.
Plus, historical returns may not always be a good predictor of future performance, which introduces uncertainty. This makes using CAPM tricky, as an inaccurate risk premium leads to unreliable expected return estimates.
3. Instability of beta over time
CAPM uses beta to measure a stock's sensitivity to market movements, but beta can be unstable. It is based on historical data, and a stock's beta might change over time due to shifts in the company's business model, industry conditions, or broader economic changes.
As a result, a beta value calculated today might not reflect future market behaviour. This instability weakens CAPM’s effectiveness because the model assumes that beta remains constant when, in reality, it can fluctuate and lead to miscalculated expected returns.
As a result, a beta value calculated today might not reflect future market behaviour. This instability weakens CAPM’s effectiveness because the model assumes that beta remains constant when, in reality, it can fluctuate and lead to miscalculated expected returns.
4. Empirical evidence against CAPM
Empirical evidence often challenges the predictions of CAPM. Studies have shown that factors other than market risk, like size and value, also affect stock returns. For example, small-cap stocks tend to outperform large-cap stocks, which CAPM does not account for.
CAPM further struggles to explain anomalies like the momentum effect, where stocks that have performed well recently continue to do well in the short term. These discrepancies between theory and reality suggest that CAPM may not be sufficient for explaining asset returns across various market conditions.
CAPM further struggles to explain anomalies like the momentum effect, where stocks that have performed well recently continue to do well in the short term. These discrepancies between theory and reality suggest that CAPM may not be sufficient for explaining asset returns across various market conditions.
Recap of the Capital Asset Pricing Model (CAPM)
CAPM is a core part of MPT and every student of finance will need to become familiar with it. Though CAPM has a lot of limitations, it still serves as a useful and simple model for the comparison between different types of securities.
For instance, the SML can determine whether securities are fairly priced and rebalance a portfolio if it has too much risk, as compared to an industry benchmark like a large stock index. Still, CAPM should not be the only model used to determine the worth of a stock, as it can be misleading.
For instance, the SML can determine whether securities are fairly priced and rebalance a portfolio if it has too much risk, as compared to an industry benchmark like a large stock index. Still, CAPM should not be the only model used to determine the worth of a stock, as it can be misleading.
FAQ on the Capital Asset Pricing Model (CAPM)
Q: What is the Capital Asset Pricing Model (CAPM)?
The Capital Asset Pricing Model (CAPM) is a financial model used to determine the expected return on an investment based on its risk relative to the market. It accounts for the risk-free rate, the stock’s beta (a measure of its risk compared to the market), and the market risk premium (the additional return expected from taking on more risk than a risk-free investment). CAPM helps investors assess whether a stock is fairly valued by comparing its expected return to its risk.
Q: How to calculate the Capital Asset Pricing Model (CAPM)?
To calculate the expected return using the CAPM formula, follow these steps:
E(Ri) = (Rf) + (β x (RM – Rf))
Where:
• E(Ri) = Expected return of the asset
• Rf = Expected return of the asset
• β = Beta of the asset (its risk relative to the market)
• RM = Expected market return (often based on a market index like the S&P 500)
E(Ri) = (Rf) + (β x (RM – Rf))
Where:
• E(Ri) = Expected return of the asset
• Rf = Expected return of the asset
• β = Beta of the asset (its risk relative to the market)
• RM = Expected market return (often based on a market index like the S&P 500)
Q: What is the International Capital Asset Pricing Model (ICAPM)?
The International Capital Asset Pricing Model (ICAPM) extends the traditional CAPM to a global context. It considers multiple national markets and exchange rate risks, making it more suitable for cross-border investments. Investors in the ICAPM account for both global market risks and specific country risks, allowing a better understanding of expected returns when investing internationally.
Q: When should you use CAPM?
CAPM is useful when you want to estimate the expected return of an asset based on its risk compared to the overall market. It is best suited for situations where you need a simple model to compare different investments or to determine whether a stock is fairly valued based on its risk and expected return.
Q: What are the advantages of CAPM?
CAPM is easy to use and provides a clear, simple way to estimate expected returns. It offers a systematic approach to comparing risk and return, making it useful for asset valuation and portfolio management. It also emphasises the importance of market risk (beta) while ignoring company-specific risks, promoting diversification in investment strategies.
Q: What are the disadvantages of CAPM?
CAPM relies on assumptions that do not hold in real markets, such as perfect information and unlimited borrowing at a risk-free rate. It also depends heavily on beta, which can change over time and may not capture all risks. Additionally, CAPM struggles to explain anomalies like the outperformance of small-cap stocks or momentum effects.
Q: How to interpret CAPM results?
CAPM results give you an estimate of a stock’s expected return based on its market risk (beta). If the expected return is higher than what you would normally require for the level of risk, the stock might be undervalued. If it is lower, the stock could be overvalued. CAPM helps assess if an asset is priced appropriately for its risk level.
- Small-cap stocks: Shares of companies with relatively low market values, typically offering higher growth potential but carrying greater volatility and risk.
- Large-cap stocks: Shares in well-established companies with high market values, often noted for their stability and steadier, though usually slower, growth.
- Standard deviation: A statistical measure of how much a set of numbers (like share prices) can vary from their average. In finance, it’s used as a stand-in for an investment’s risk or volatility.
- Historical returns: Past performance data for a share or index.
