## **Learning Outcomes**

After reading this article, you will be able to explain how the CAPM determines required return and systematic risk, define and interpret alpha, identify pricing errors in the CAPM framework, and critically evaluate the model’s limitations. You will also be able to apply and discuss these concepts in the context of ACCA Financial Management (FM) exam questions.

## **ACCA Financial Management (FM) Syllabus**

For ACCA Financial Management (FM), you are required to understand the application and critical evaluation of the Capital Asset Pricing Model, especially in relation to project and company valuation. In particular, focus on:

- The relationship between systematic and unsystematic risk
- The use of CAPM to estimate a required (risk-adjusted) return
- The interpretation of alpha and its connection to pricing errors
- The practical and theoretical limitations of the CAPM in real-world business and investment appraisal
- Use of CAPM-derived discount rates in project evaluation

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. What does a positive alpha indicate about a security according to the CAPM?
2. Which type of risk does the CAPM consider relevant when calculating expected returns?
3. Name two practical limitations of applying the CAPM in investment appraisal.
4. Explain how pricing errors can arise when using CAPM to estimate required returns.

## **Introduction**

The Capital Asset Pricing Model (CAPM) is widely used to estimate the required return on equity, both for evaluating company value and for setting project discount rates. Although it is a core tool in financial management, real-world deviations can occur—most notably in the form of 'alpha' or pricing errors, and from limitations in the model’s assumptions. Understanding how and why these deviations arise—and their limits—is essential for critical ACCA FM exam responses.

## The CAPM: Determining Required Return

CAPM estimates the expected return for an asset based on its sensitivity to systematic (market) risk.

The CAPM formula is:
$$E(r) = R_f + \beta (E(r_m) - R_f)$$
Where:

- $E(r)$ = expected (required) return on the asset
- $R_f$ = risk-free rate
- $\beta$ = beta coefficient (systematic risk relative to the market)
- $E(r_m)$ = expected market return

> **Key Term: systematic risk**
> The risk arising from general market fluctuations, which cannot be diversified away and to which all securities are exposed.
>
> **Key Term: beta**
> A measure of a security’s sensitivity to movements in the overall market; beta greater than 1 indicates higher volatility than the market, and less than 1 indicates lower volatility.

The CAPM assumes investors are only rewarded for bearing systematic risk. Unsystematic (diversifiable) risk is not priced, as it can be mitigated through diversification.

### CAPM and the Security Market Line

The Security Market Line (SML) is a graphical representation of the CAPM, showing the relationship between required return and beta. According to the model, all correctly priced assets should plot on the SML. If a security’s actual return differs from that predicted by the SML, it may indicate mispricing or other risks.

## Alpha and Pricing Errors in CAPM

While the CAPM predicts that all assets should line up on the SML, market realities often differ. The degree to which a security’s observed average return diverges from the CAPM’s predicted return is known as alpha.

> **Key Term: alpha**
> The difference between a security’s actual return and its expected return as predicted by the CAPM, representing abnormal performance or mispricing.

An asset with a positive alpha has delivered returns above the CAPM benchmark—suggesting it is undervalued, while a negative alpha suggests overvaluation relative to its risk.

### **Worked Example 1.1**

A company’s share has a beta of 1.3. The risk-free rate is 3%, and the expected market return is 9%. The actual average annual return over several years was 12%. What is the security’s alpha using CAPM?

> **Answer:**
> Required return = \$3\% + 1.3 \times (9\% - 3\%) = 3\% + 1.3 \times 6\% = 3\% + 7.8\% = 10.8\%$
> Calculated alpha = Actual return – CAPM return = \$12\% - 10.8\% = 1.2\%$
> A positive alpha (1.2%) indicates the share has outperformed the risk predicted by the model; this could be temporary, or reflect a CAPM mispricing.

## Sources of Alpha: Interpreting Deviations

Alpha can arise for several reasons:

- Temporary mispricing or market inefficiencies
- Unique, unsystematic risks that have not been diversified away (e.g., company-specific news)
- Limitations in estimating beta or the equity risk premium
- Omissions of other risk factors not captured by beta (e.g., size or value anomalies)

Consistent positive alpha suggests either persistent market inefficiency or that the model is missing relevant risks.

## CAPM Limitations: Theory vs. Reality

Although the CAPM is a fundamentally important model, its application in practice is subject to several limitations.

> **Key Term: pricing error**
> The observed difference between the actual return and the return predicted by the CAPM, measured by alpha.

Limitations include:

- **Assumption of perfect markets:** CAPM assumes no taxes, no transaction costs, and rational investors with full access to information. In the real world, these conditions rarely apply.
- **Beta estimation:** Beta is usually estimated using historical returns, which may not predict future risk exposure accurately.
- **Single risk factor:** CAPM only accounts for systematic (market) risk; other relevant risks (e.g., company size, value, momentum) may be ignored.
- **Well-diversified investors:** Not all investors may hold fully diversified portfolios, so some might care about unsystematic risk.
- **Difficulties estimating the equity risk premium:** The premium is often based on historical data, which may not reflect future market conditions.

### **Worked Example 1.2**

Suppose a construction firm’s shares have a beta of 1.8. The CAPM predicts a required return of 14%, but the shares generate only a 10% return over three years. What is likely happening?

> **Answer:**
> The negative alpha (\$10\% - 14\% = -4\%$) suggests the shares underperformed the required return for their risk. This could be due to poor company performance not captured by beta, or it may reflect temporary mispricing or that the company faces additional non-market risks.

### **Exam Warning**

> Always distinguish between systematic risk (measured by beta, relevant for required return under CAPM) and alpha, which measures actual return deviations—this is often tested in exam calculations and interpretations.

## Using CAPM and Alpha in Decision-Making

Alpha and CAPM are especially relevant for:

- Appraising individual projects or securities: A persistent alpha may indicate a pricing error.
- Valuing a company or new project: Use proxy betas from comparable businesses, but adjust for differences in gearing and business risk.
- Evaluating management performance: Alpha is sometimes used to assess whether a fund manager has truly added value.

> **Revision Tip**
> In your revision, practice distinguishing between market anomalies and short-term return deviations—temporary alphas are common, but only persistent or systematic alphas challenge the CAPM’s adequacy.

## **Summary**

CAPM provides a framework for determining required returns based on systematic risk (beta). Alpha measures the difference between actual and predicted returns, indicating assets that are over- or under-priced within the CAPM model. In practice, pricing errors and model limitations are common, and exam answers must recognize both CAPM’s strengths and its practical flaws.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- The CAPM formula and its components
- The concept of systematic risk and beta
- Definition and significance of alpha (pricing error)
- Causes of pricing errors and their interpretation
- The main limitations of the CAPM in real-life situations
- Implications for project appraisal and investment decisions

## **Key Terms and Concepts**

- systematic risk
- beta
- alpha
- pricing error

CAPM and required return - Alpha, pricing errors, and limitations