CAPM and required return - Security Market Line and expected...

Learning Outcomes

After reading this article, you will be able to explain how the Capital Asset Pricing Model (CAPM) determines required return, interpret the Security Market Line (SML), and distinguish between systematic and unsystematic risk. You will also practice applying CAPM to calculate an expected return using beta and understand its implications for project appraisal and equity valuation in the ACCA FM exam.

ACCA Financial Management (FM) Syllabus

For ACCA Financial Management (FM), you are required to understand how required return is found using CAPM and the Security Market Line. This article addresses:

• The relationship between risk and return in capital markets
• The distinction between systematic and unsystematic risk
• The use of beta as a measure of systematic risk
• The Security Market Line and its relevance to expected return
• How CAPM is used to estimate a required return for shares and projects
• The practical interpretation and exam application of the SML

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 is measured by the slope of the Security Market Line (SML) in CAPM?
   1. Risk-free rate
   2. Market risk premium
   3. Asset beta
   4. Company gearing

2. True or false? Systematic risk is the portion of risk in a share's return that can be diversified away by holding more shares.

3. A share has a beta of 1.3, the risk-free rate is 4%, and the expected market return is 10%. What is its required return?

4. Briefly explain the meaning of the Security Market Line (SML) and its relevance in investment appraisal.

Introduction

Understanding the relationship between risk and return is fundamental to financial decision-making. The Capital Asset Pricing Model (CAPM) offers a method to calculate the return required by equity investors, taking account of the level of risk compared to the overall market. The Security Market Line (SML) illustrates this relationship and is central to evaluating shares, portfolios, or new projects for the ACCA FM exam.

Key Term: Capital Asset Pricing Model (CAPM)
A model that estimates an investment's required return by quantifying the relationship between systematic risk (beta) and expected market returns relative to the risk-free rate.

Key Term: Security Market Line (SML)
The straight line in CAPM that plots required return against beta, showing how required return increases linearly with risk.

SYSTEMATIC AND UNSYSTEMATIC RISK

Investors face risks from individual companies and from overall market movements. Not all these risks are treated equally in pricing.

• Systematic risk refers to the risk caused by economy-wide factors, such as economic recession or changes in interest rates, which affect almost all securities.
• Unsystematic risk relates to firm-specific factors, such as management decisions or factory fires, which can be diversified away.

A diversified investor is rewarded only for systematic risk.

Key Term: Systematic risk
Risk related to market-wide factors that cannot be eliminated by diversifying a portfolio; measured by beta.

Key Term: Unsystematic risk
The risk specific to an individual company or sector, which can be nearly eliminated through diversification.

THE ROLE OF BETA IN CAPM

CAPM uses the concept of beta (β) to measure a security's sensitivity to market movements. Beta quantifies how much an asset's return changes in response to the market's changes.

• Beta of 1: matches market risk
• Beta < 1: less volatile than market
• Beta > 1: more volatile than market
• Beta = 0: risk-free investment (no reaction to market)

Key Term: Beta
A measure of an investment’s systematic risk, representing how much its return moves relative to overall market returns.

THE SECURITY MARKET LINE (SML)

The SML is a graphical representation of the CAPM formula. On a graph, beta is on the horizontal axis, and required return is on the vertical axis. The SML starts at the risk-free rate (beta = 0) and rises linearly according to the market risk premium.

CAPM Formula:
Required return = Risk-free rate + β × (Market return – Risk-free rate)

This tells us:

• Any investment’s required return lies on the SML according to its beta
• Investors are compensated only for systematic risk, not unsystematic risk
• Shares with higher beta require higher returns from investors

Key Term: Market risk premium
The additional return expected by investors for taking on average market risk rather than a risk-free investment; calculated as (expected market return – risk-free rate).

Worked Example 1.1

Suppose the risk-free rate is 3%, the expected market return is 8%, and Share X has a beta of 1.4.

Question: What is the required return for Share X according to the SML?

Answer:
Required return = 3% + 1.4 × (8% – 3%)
Required return = 3% + 1.4 × 5% = 3% + 7% = 10%

Worked Example 1.2

Share Y has a beta of 0.7. The market risk premium is 6%. The risk-free rate is 2%.

Question: What is the expected return for Share Y?

Answer:
Required return = 2% + 0.7 × 6% = 2% + 4.2% = 6.2%

USING CAPM AND SML FOR INVESTMENT APPRAISAL

When assessing an investment or a project, compare its estimated return to the required return found using CAPM:

• If expected return ≥ required return (on the SML), the project is acceptable as it offers enough compensation for its risk.
• If expected return < required return, the risk is not compensated, so the project should be rejected.

This helps ensure that the return matches the systematic risk faced by shareholders.

Worked Example 1.3

A project has a beta of 1.1, the risk-free rate is 5%, and the market return is 11%. The project’s expected return is 12%.

Question: Should the company accept the project?

Answer:
Required return = 5% + 1.1 × (11% – 5%)
Required return = 5% + 1.1 × 6% = 5% + 6.6% = 11.6%
As the project’s expected return (12%) exceeds the required (11.6%), it should be accepted.

Exam Warning

Be careful: Beta reflects only systematic risk. CAPM does not reward or price unsystematic risk, so only risks that cannot be diversified away are considered.

INTERPRETING THE SML

The SML helps in visualising whether an investment is priced fairly:

• An investment above the SML (offering more return than required by its beta) is considered underpriced or offering abnormal profit (arbitrage opportunity).
• An investment below the SML is overpriced for its risk and should be avoided.

All securities in an efficient market should lie on the SML.

Revision Tip

When calculating required return, always use decimals (e.g., 0.08 for 8%) in the CAPM formula and keep calculations clear. Remember: market risk premium is (market return – risk-free rate).

Summary

CAPM is used to determine the required return on shares given their systematic risk, measured by beta. The Security Market Line visualises how required return increases with beta. Only systematic risk is priced—diversifying a portfolio removes unsystematic risk. For investment appraisal, always compare a project's expected return to the required return found using CAPM.

Key Point Checklist

This article has covered the following key knowledge points:

• Explain the difference between systematic and unsystematic risk
• Use beta as a measure of systematic risk in CAPM
• Calculate required return using the Security Market Line (SML)
• Interpret what it means for an investment to lie above, below, or on the SML
• Apply CAPM to project appraisal, ensuring risk-adjusted required return is met

Key Terms and Concepts

• Capital Asset Pricing Model (CAPM)
• Security Market Line (SML)
• Systematic risk
• Unsystematic risk
• Beta
• Market risk premium