## **Learning Outcomes**

After reading this article, you will be able to explain the main concepts of portfolio theory for the ACCA FM exam. You will understand the risk–return trade-off, describe how diversification reduces risk, and identify what makes an optimal portfolio. You will learn to interpret risk using standard deviation and beta, and distinguish between systematic and unsystematic risk.

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

For ACCA Financial Management (FM), you are required to understand the principles of risk and return when constructing an investment portfolio. Specifically, you should know how:

- Investors assess the risk and return of both individual investments and portfolios
- Diversification reduces overall risk, including the distinction between systematic and unsystematic risk
- Efficient portfolios are constructed by balancing risk and expected return
- The Capital Asset Pricing Model (CAPM) relates portfolio risk to required returns

## **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 TWO actions are most likely to reduce unsystematic risk in an investment portfolio?
   a) Spreading investment across sectors
   b) Investing in risk-free government bonds only
   c) Increasing investment in a single company
   d) Choosing shares with high betas

2. What is an optimal portfolio according to portfolio theory?

3. Briefly explain the difference between systematic and unsystematic risk.

4. True or false? Increasing the number of different assets in a portfolio can reduce the total risk, but cannot eliminate all types of risk.

## **Introduction**

Portfolio theory is central to financial management. Rather than looking at investments in isolation, portfolio theory considers how diverse assets combine to affect overall risk and expected return. This is essential for understanding the behaviour of investors and for project appraisal using models like CAPM in the ACCA FM syllabus.

A portfolio is simply a group of investments. Returns from different assets will rarely move exactly together, so combining them can smooth out returns and reduce risk. The way assets interact is key to finding an optimal portfolio.

> **Key Term: portfolio**
> A collection of different investments held by an investor, allowing risk and return to be considered collectively rather than individually.

## RISK AND RETURN: THE BASICS

All investments involve risk—the possibility of actual returns differing from expected returns. Portfolio theory provides a structured way to measure, combine and manage risk.

### Measuring Return

Return is the actual or expected income from an investment, including dividends, interest or capital gains.

### Measuring Risk

Risk is typically measured as the variability of returns. The two main measures are:

- **Standard deviation (σ):** Measures total risk—the higher the standard deviation, the more unpredictable the returns.
- **Beta (β):** Measures systematic risk—how much an investment's return moves relative to the market.

> **Key Term: standard deviation**
> A statistical measure of the dispersion or spread of a set of numbers; in finance, it measures the volatility of investment returns.
>
> **Key Term: beta**
> A measure of an asset’s systematic risk, showing how much its return tends to move relative to the overall market.

## THE RISK–RETURN TRADE-OFF

Investors must balance risk and return. Higher expected returns usually require taking more risk. Portfolio theory helps to show how much return is needed to compensate for a given level of risk.

Plotting investments on a risk-return graph, most rational investors prefer points toward the top left—high expected return with low risk.

## DIVERSIFICATION: REDUCING RISK

Combining investments with different risk characteristics can reduce the total risk of a portfolio. This process is called diversification.

### Types of Risk

> **Key Term: systematic risk**
> The portion of overall risk that affects all investments in the market and cannot be eliminated by diversification (also known as market risk).
>
> **Key Term: unsystematic risk**
> The portion of total risk that is unique to a specific company or industry and can be reduced or eliminated through diversification.

Systematic risk is unavoidable and arises from market-wide factors such as economic recessions or interest rate changes.

Unsystematic risk is unique to specific firms or industries (e.g., a company-specific scandal, a new competitor) and can be reduced by holding a diversified portfolio.

### The Effect of Diversification

By holding several different investments, unsystematic risk is largely eliminated. However, systematic risk remains—this is the risk that cannot be diversified away and is measured by beta.

## OPTIMAL PORTFOLIOS AND THE EFFICIENT FRONTIER

An optimal portfolio gives the highest possible expected return for a given level of risk—no achievable portfolio offers a better risk-return combination.

The **efficient frontier** is a line on the risk–return graph representing all such optimal portfolios. Portfolios below this line are sub-optimal as the investor could get more return for the same risk or less risk for the same return.

> **Key Term: efficient frontier**
> The set of investment portfolios that offer the highest expected return for each level of risk.

Portfolios above the efficient frontier are unattainable with existing assets.

## PORTFOLIO RISK: THE ROLE OF CORRELATION

Risk reduction through diversification depends on how returns on assets move in relation to each other.

- If returns are **perfectly positively correlated** (assets always move together), no risk reduction is possible.
- If returns are **negatively correlated** (move in opposite directions), maximum risk reduction is achieved.

In practice, most assets are not perfectly correlated, so diversification benefits are usually available.

> **Key Term: correlation**
> A statistical measure of how two variables move in relation to each other; in portfolios, how the returns of two investments move together.

## SYSTEMATIC RISK, PORTFOLIOS AND CAPM

Only systematic risk matters for well-diversified investors, as unsystematic risk can be diversified away. Investors require compensation for bearing systematic risk, measured by beta.

The **Capital Asset Pricing Model (CAPM)** relates an asset’s required return to its beta. Portfolios with higher betas should offer higher expected returns since they are more sensitive to overall market risk.

> **Key Term: Capital Asset Pricing Model (CAPM)**
> A model used to determine the expected return on an asset based on its systematic risk, measured by beta, relative to the market.

### **Worked Example 1.1**

**Aisha has invested half her funds in a construction company (high risk) and half in a utility company (low risk, little correlation with construction). Explain the combined risk and possible return of Aisha’s portfolio.**

> **Answer:**
> Combining a risky asset with a less risky one—especially if their returns do not closely move together—can lower overall portfolio risk. If the utility company’s performance doesn’t depend on the same factors as construction, losses in one are less likely to coincide with losses in the other, so Aisha’s portfolio is less risky than investing only in the construction company.

### **Worked Example 1.2**

**Kei invests in five unrelated companies: retail, transport, banking, media and pharmaceuticals. What risks remain in Kei’s portfolio?**

> **Answer:**
> Kei’s portfolio will have minimal unsystematic risk, because poor results in one company are likely to be offset by better outcomes elsewhere. However, systematic risk such as a stock market downturn or major economic event will still affect all investments.

## LIMITATIONS OF DIVERSIFICATION

Diversification cannot eliminate all risk. Systematic risk—market-wide events such as economic crises or global shocks—always remains. For this reason, the expected return on a diversified portfolio reflects only the systematic risk, as shown in the CAPM.

### **Exam Warning**

> **Don’t confuse portfolio standard deviation (total risk) with beta (systematic risk only). Exam questions may test which risk is relevant for expected returns.**

## **Summary**

Portfolio theory shows that investors can reduce risk without sacrificing return by holding a diversified mix of assets. Only systematic (market) risk cannot be diversified away. An optimal portfolio sits on the efficient frontier, giving the best risk-return combination possible.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- The importance of risk and return in portfolio management
- The risk–return trade-off and measurement of risk using standard deviation and beta
- Systematic (market) and unsystematic (unique) risk and their implications
- The benefits of diversification in reducing portfolio risk
- The efficient frontier and characteristics of optimal portfolios
- Correlation and its impact on portfolio risk reduction
- How CAPM links systematic risk with required return

## **Key Terms and Concepts**

- portfolio
- standard deviation
- beta
- systematic risk
- unsystematic risk
- efficient frontier
- correlation
- Capital Asset Pricing Model (CAPM)

Portfolio theory - Optimal portfolios and risk–return trade-off