Capital Asset Pricing Model, Assumptions, Importance

Capital Asset Pricing Model (CAPM) is a model that describes the relationship between expected return and risk of investing in a security. It shows that the expected return on a security is equal to the risk-free return plus a risk premium, which is based on the beta of that security. Below is an illustration of the CAPM concept.

CAPM Formula and Calculation

Ra = Rrf + [Ba*(Rm – Rrf)]

Where:

Ra = Expected return on a security
Rrf = Risk-free rate
Ba = Beta of the security
Rm = Expected return of the market

Note: “Risk Premium” = (Rm – Rrf)

CAPM formula is used to calculate the expected return on investable asset. It is based on the premise that investors have assumptions of systematic risk (also known as market risk or non-diversifiable risk) and need to be compensated for it in the form of a risk premium – an amount of market return greater than the risk-free rate. By investing in a security, investors want a higher return for taking on additional risk.

• Expected Return 

The “Ra” notation above represents the expected return of a capital asset over time, given all of the other variables in the equation.  The expected return is a long-term assumption about how an investment will play out over its entire life.

• Risk-Free Rate 

The “Rrf” notation is for the risk-free rate, which is typically equal to the yield on a 10-year US government bond.  The risk-free rate should correspond to the country where the investment is being made, and the maturity of the bond should match the time horizon of the investment.  Professional convention, however, is to typically use the 10-year rate no matter what, because it’s the most heavily quoted and most liquid bond.

The beta (denoted as “Ba” in the CAPM formula) is a measure of a stock’s risk (volatility of returns) reflected by measuring the fluctuation of its price changes relative to the overall market. In other words, it is the stock’s sensitivity to market risk. For instance, if a company’s beta is equal to 1.5 the security has 150% of the volatility of returns of the market average. However, if the beta is equal to 1, the expected return on a security is equal to the average market return.  A beta of -1 means security has a perfect negative correlation with the market.

• Market Risk Premium

From the above components of CAPM we can simplify the formula to reduce “expected return of the market minus the risk-free rate” to be simply the “market risk premium”.  The market risk premium represents the additional return over and above the risk-free rate, which is required to compensate investors for investing in a riskier asset class. Put another way, the more volatile a market or an asset class is, the higher the market risk premium will be.

CAPM Assumptions:

1. Risk-Free Asset

CAPM assumes the existence of a risk-free asset, meaning an asset that has a guaranteed return with no risk of financial loss. Investors can borrow or lend unlimited amounts at the risk-free rate.

2. Single-Period Model

CAPM is a single-period model, assuming that investors have identical investment horizons typically over a single time period. This simplification disregards the effects of multi-period investment strategies and lifecycle investment considerations.

3. Markets are Perfectly Competitive and Efficient

The model assumes that all securities are perfectly divisible and that markets are frictionless—no transaction costs, taxes, or restrictions on short selling exist. It also assumes all information is available to all investors simultaneously and accurately, leading to securities always being fairly priced (market efficiency).

4. Homogeneous Expectations

All investors have the same expectations regarding the volatilities, correlations, and expected returns of investment portfolios. This assumption simplifies the analysis by ensuring that all investors agree on the risk and return of all securities.

5. Investors are Rational and Risk-Averse

CAPM assumes that investors are rational, meaning they will always choose more wealth over less and prefer more return for less risk. Investors are risk-averse, meaning they need to be compensated for taking on additional risk, and will always choose the portfolio with the highest expected utility.

6. Investors Hold Diversified Portfolios

The model presupposes that all investors hold diversified portfolios that approximate the market portfolio. This “market portfolio” contains all assets in the market, with each asset weighted by its market capitalization. The diversification effectively eliminates unsystematic risk (specific to individual securities).

7. Only Systematic Risk Matters

CAPM contends that the only risk priced by the market is systematic risk, as represented by the beta (β) of a security. Systematic risk is inherent to the entire market and cannot be eliminated through diversification. Unsystematic risk, which is specific to individual securities or industries, is assumed to be diversified away.

8. Unlimited Borrowing and Lending

Investors can borrow and lend unlimited amounts at the risk-free rate. This assumption is crucial for the construction of the Capital Market Line (CML), where all investors will choose a combination of the risk-free asset and the market portfolio.

CAPM Importance:

1. Risk-Return Tradeoff Understanding

CAPM provides a clear and quantifiable relationship between the expected return of a security and its risk, as measured by beta (β). This model highlights the linear relationship where the expected return on a security is equal to the risk-free rate plus the risk premium. This risk premium is determined by the security’s sensitivity to market movements (beta) and the market’s overall risk premium.

2. Portfolio Diversification

CAPM underscores the benefits of diversification, focusing only on the systematic risk of a security or a portfolio (i.e., risk that cannot be diversified away). It suggests that the only type of risk for which investors should receive an expected return is the risk that cannot be eliminated through diversification. This principle guides investors on how to effectively diversify their portfolios to minimize unsystematic risk.

3. Security Valuation

The model is widely used for asset pricing – helping to determine what an investment should be worth based on its risk. It’s particularly useful in the valuation of stocks, where the expected return as determined by CAPM is used as the discount rate for valuing a company’s future cash flows in the discounted cash flow (DCF) analysis.

4. Performance Evaluation

CAPM helps in evaluating the performance of portfolios or individual securities by providing a benchmark return that should be achieved given the level of risk assumed. If the actual returns exceed the CAPM return, the investment is considered to have generated positive alpha, indicating superior performance adjusted for risk.

5. Cost of Capital

Businesses use CAPM to estimate their cost of equity. This is crucial for making decisions about capital structure, such as determining the appropriate mix of debt and equity financing. The cost of equity calculated through CAPM is used to assess the weighted average cost of capital (WACC), a key factor in capital budgeting decisions and corporate finance.

6. Strategic Decision Making

Companies can apply the insights from CAPM for strategic decisions such as expansion, mergers, acquisitions, and other investment opportunities. By understanding the required return for taking on additional risk, managers can make more informed decisions that align with shareholder value maximization.

7. Regulatory Use

Regulators may use CAPM to set required rates of return for utility companies or to assess the fairness of returns given the risk levels of regulated firms, ensuring that these companies do not charge excessive prices or take on excessive risk at the expense of consumers.

8. Investment Strategy

Investment advisors and financial planners use CAPM to tailor investment strategies according to individual risk profiles, helping clients achieve optimal returns for their specific levels of risk tolerance.

9. Educational Framework

In academia, CAPM is a standard teaching tool that introduces students to the concepts of systematic risk, risk-return tradeoff, and market efficiency, forming the backbone of many finance courses.