Portfolio theory - Beta estimation and interpretation

Learning Outcomes

After reading this article, you will be able to explain how beta measures systematic risk within portfolio theory, describe the process of estimating and interpreting beta, and apply beta in investment appraisal using the Capital Asset Pricing Model (CAPM). You will distinguish between systematic and unsystematic risk and know how to use betas for project discount rates in the ACCA FM exam context.

ACCA Financial Management (FM) Syllabus

For ACCA Financial Management (FM), you are required to understand portfolio theory, the measurement of risk, and their applications for project appraisal. Focus your revision on:

• The distinction between systematic and unsystematic risk
• The role of beta in measuring systematic risk within a portfolio
• Methods for estimating and interpreting beta
• The use of proxy betas and the impact of capital structure on beta
• The application of CAPM in calculating a risk-adjusted discount rate for investment projects

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. Which of the following best describes beta in the context of portfolio theory?
   1. A measure of total investment risk
   2. A measure of systematic risk relative to the market
   3. A company's gearing ratio
   4. The expected return on a risk-free asset

2. What is the difference between systematic and unsystematic risk?

3. Briefly explain how you would estimate the beta for a project that is completely different from a company’s current business.

4. True or false? The beta of a company is always the same as the beta of its industry.

Introduction

Portfolio theory explains how risk and return are linked in investing. Diversification allows investors to reduce the impact of certain risks, but not all types of risk can be eliminated. Beta is the key measure used to quantify how sensitive an asset or project is to market-wide risk (systematic risk). Understanding how to estimate, interpret, and apply beta is essential for investment appraisal and for using the Capital Asset Pricing Model (CAPM) in the ACCA Financial Management exam.

Key Term: Systematic risk
The portion of total risk that is due to economy-wide factors and cannot be eliminated through holding a diversified portfolio. Also known as market risk.

Key Term: Unsystematic risk
The portion of total risk unique to a particular company or industry, which can be reduced or eliminated through diversification.

Key Term: Beta (β)
A measure of an asset’s sensitivity to systematic risk, showing how much its returns vary relative to movements in the overall market.

Key Term: Asset beta (βₐ)
The measure of systematic risk for a business’s core activities, excluding the financial effects of debt financing (gearing or debt).

Key Term: Equity beta (βₑ)
The measure of systematic risk for a company’s equity holders, including both business and financial (gearing) risk.

Portfolio Risk and the Role of Beta

A portfolio made up of many investments achieves diversification. While this reduces the impact of company-specific events (unsystematic risk), risks that affect the entire market—such as economic downturns or political instability—cannot be avoided. Beta measures how much a share or project’s returns move in response to changes in the broader market.

A share with a beta of 1 will move in line with the market; greater than 1 means more sensitive; less than 1 means less sensitive; a negative beta moves opposite to the market.

Systematic vs. Unsystematic Risk

Total risk of an investment = Systematic risk + Unsystematic risk.

Diversification can only reduce unsystematic risk. Therefore, investors are only rewarded for bearing systematic risk. In pricing assets, the market cares only about systematic risk, which is captured by beta.

Worked Example 1.1

Suppose L Co manufactures both raincoats and sunglasses. If one summer is rainy, sunglasses sales fall and raincoat sales rise, but the company’s overall profits are stable. Explain what risk types are being managed and which remain.

Answer:
By producing both raincoats and sunglasses, L Co reduces unsystematic risk through diversification (company-specific ups and downs). However, if the entire market is in recession and consumer spending falls, both product lines could be affected—reflecting unavoidable systematic risk.

Estimating Beta

Beta is typically estimated using regression analysis. A company’s historic share returns are compared against market returns. The resulting beta tells us how much the company's equity moves for each unit of market movement. However, the past may not perfectly predict the future, and changes in business or financial structure can alter beta.

Key Term: Proxy beta
An estimated beta for a project or division based on similar listed companies in the same industry, used when direct historical data is not available.

To estimate the beta for a proposed project (especially in a new industry), use a proxy beta from similar businesses. This proxy beta can then be adjusted for differences in financial structure.

Worked Example 1.2

Beech Ltd, a food retailer (with a beta of 0.6), wants to invest in renewable energy, an industry where similar companies have an average equity beta of 1.3 and a typical gearing ratio (debt as a proportion of total capital) of 40%. Beech Ltd finances the project with 70% equity and 30% debt. How should Beech Ltd estimate the project’s equity beta?

Answer:
First, use the industry equity beta of 1.3 and its gearing (40%) to de-gear the beta, finding the asset beta. Then, re-gear this asset beta using Beech Ltd's capital structure (30% debt) to get the appropriate equity beta for the project. This adjusted beta should be used with the CAPM.

Interpreting Beta Values

• β = 1: Security moves in line with the market.
• β > 1: Security is more volatile than the market (riskier).
• β < 1: Security is less volatile (safer) than the market.
• β = 0: No correlation with the market (risk-free).
• β < 0: Moves opposite to the market (rare).

Effects of Gearing (Financial Gearing) on Beta

Beta is affected by gearing. Higher financial gearing increases equity beta, because debt amplifies the impact of business risk on equity holders. Asset beta reflects only business risk, while equity beta captures both business and financial risk.

The ACCA exam provides the asset beta formula:

where:

• $V_e$ = Market value of equity
• $V_d$ = Market value of debt
• $T$ = Corporate tax rate
• $\beta_e$ = Equity beta

To estimate a project-specific or ungeared (asset) beta:

• Use the proxy company’s equity beta and capital structure to calculate asset beta.
• Adjust the asset beta to your company’s proposed project capital structure (re-gear as appropriate).

Worked Example 1.3

Swan Co is planning a new hotel business. Similar companies have an equity beta of 1.5 and a typical capital structure of 60% equity, 40% debt (tax rate 25%). Swan Co will use 80% equity and 20% debt for the hotel project. Calculate the asset beta for the hotel sector and Swan Co’s project equity beta.

Answer:
Step 1: De-gear to asset beta using the proxy company:
Asset beta = $1.5 \times 0.60/(0.60 + 0.40 \times (1 - 0.25)) = 1.2$

Step 2: Re-gear to Swan Co structure:
Project equity beta = $1.2 \times (0.80 + 0.20 \times (1 - 0.25))/0.80 = 1.35$

Swan Co should use a project beta of 1.35 for CAPM calculations.

Exam Warning

If instructed to use a beta from the stock market, check whether it includes gearing effects (equity beta) and whether you need to adjust it using the asset beta formula. Using the wrong beta can result in an incorrect project discount rate and lower exam marks.

CAPM and Beta in Practice

The Capital Asset Pricing Model (CAPM) relates required return to beta:

Where:

• $E(r)$ = Expected return (cost of equity)
• $R_f$ = Risk-free rate
• $E(r_m)$ = Expected return on the market
• $\beta$ = Systematic risk of the security/project

Only systematic risk (measured by beta) is reflected in required returns, since unsystematic risk can be diversified away.

Summary

Beta quantifies how sensitive an investment is to market risk. In portfolio theory, only systematic risk matters for well-diversified investors, and the CAPM uses beta to set required returns. Estimating beta for projects may involve proxy company data and gearing adjustments using the asset beta formula. Choose and interpret the correct beta to apply the appropriate project discount rate in investment appraisal.

Key Point Checklist

This article has covered the following key knowledge points:

• Define systematic and unsystematic risk in a portfolio context
• Explain the purpose and interpretation of beta
• Describe how to estimate project beta using proxy companies
• Apply the asset beta formula to adjust for differences in gearing
• Use beta and CAPM to set a risk-adjusted required return for projects

Key Terms and Concepts

• Systematic risk
• Unsystematic risk
• Beta (β)
• Asset beta (βₐ)
• Equity beta (βₑ)
• Proxy beta