## **Learning Outcomes**

After reading this article, you will be able to explain the principles of portfolio theory as required for ACCA FM. You will understand the concept of the efficient frontier, interpret the meaning of dominance between investment portfolios, assess how diversification affects risk, and apply these ideas to make better investment decisions based on the risk–return relationship.

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

For ACCA Financial Management (FM), you are required to understand and apply portfolio theory concepts as part of risk and return analysis. Specifically, this article covers:

- The relationship between risk and return for individual investments and portfolios
- How diversification affects portfolio risk
- The construction and interpretation of the efficient frontier
- The concept of dominance between portfolios and the process of eliminating dominated options
- Selection of portfolios considering investor risk preferences
- The relevance of these concepts to the cost of capital and investment appraisal

## **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 meant by the term "efficient portfolio"?
2. Portfolio X offers an expected return of 8% with a risk (standard deviation) of 10%. Portfolio Y offers an expected return of 8% with a risk of 13%. Which portfolio dominates?
3. True or false? Diversification can eliminate all types of investment risk.
4. Briefly explain how the efficient frontier helps in selecting an appropriate investment portfolio.
5. Why are portfolios lying below the efficient frontier considered suboptimal?

## **Introduction**

The risk–return relationship is a core principle in financial management. Investors need to balance their desire for higher returns with the appetite for risk. Portfolio theory provides a structured approach for combining investments to reduce risk without sacrificing returns.

You should understand how portfolios are constructed, why diversification works, and how to use the efficient frontier to identify the best possible combinations of investments. A strong understanding of these ideas is essential for making and evaluating investment decisions in the ACCA FM exam.

> **Key Term: portfolio**
> A collection of different investments held together, such as shares, bonds, or other assets, to spread and manage risk.
>
> **Key Term: risk (standard deviation)**
> A numerical measure of how much the returns on an investment or portfolio fluctuate around the average (expected) return.
>
> **Key Term: return**
> The gain or loss from an investment, typically expressed as a percentage of the initial amount invested.

## **PORTFOLIO THEORY AND DIVERSIFICATION**

Portfolio theory explores how combining different investments affects the overall risk and return faced by investors.

When you hold several assets together in a portfolio, the combined risk is usually lower than simply averaging the risk of each investment. This effect comes from imperfect correlations—assets do not all move in the same direction at the same time.

> **Key Term: diversification**
> The process of spreading investments across different assets or sectors in order to reduce risk.

By combining assets whose returns do not move perfectly together, you can lower the overall variability of returns—this is the main advantage of diversification.

### Risk Types in Portfolio Theory

Total risk in a portfolio can be separated into:

- **Systematic (market) risk:**
  Influences all assets, cannot be diversified away.
- **Unsystematic (specific) risk:**
  Is unique to an asset and can be reduced or eliminated by holding a diversified portfolio.

> **Key Term: systematic risk**
> The part of total risk that affects all assets and cannot be eliminated by diversification.
>
> **Key Term: unsystematic risk**
> The risk unique to a particular asset or company, which can be largely removed through diversification.

As the number of different investments increases, unsystematic risk falls, but systematic risk remains.

### The Risk–Return Trade-Off

Investors expect to receive higher returns if they are willing to accept higher risk. The challenge is to find the best balance—maximising return for every level of risk taken.

> **Key Term: risk–return trade-off**
> The fundamental relationship in finance that higher returns are available only by accepting higher levels of risk.

## **THE EFFICIENT FRONTIER**

The efficient frontier is a graphical representation of the best possible portfolios that can be constructed from a set of investments. Portfolios on this frontier give the highest expected return for each level of risk.

### Constructing the Efficient Frontier

If you plot portfolios on a graph, with risk (standard deviation) on the x-axis and expected return on the y-axis, you will usually find that:

- Some portfolios have higher risk and higher return.
- Others have lower risk but also lower return.
- Some portfolios are "dominated," meaning another portfolio gives a higher or equal expected return at a lower or equal level of risk.

The **efficient frontier** is the set of portfolios that are not dominated by any others. Portfolios below or to the right of this curve are suboptimal for investors.

> **Key Term: efficient frontier**
> The curve showing the set of portfolios offering the highest expected return for each possible level of risk.

## **PORTFOLIO DOMINANCE**

A portfolio ‘dominates’ another if, for the same or less risk, it offers a higher return, or for the same or higher return, it has less risk. Rational investors will not choose dominated portfolios.

> **Key Term: dominance (in portfolio selection)**
> When one portfolio has higher return and/or lower risk than another, making the dominated portfolio a suboptimal choice.

Dominated portfolios can be eliminated from consideration, leaving only efficient options for investors.

### **Worked Example 1.1**

An investor is considering three portfolios:

- **Portfolio A:** Expected return 6%, risk 8%
- **Portfolio B:** Expected return 8%, risk 10%
- **Portfolio C:** Expected return 7%, risk 12%

Which portfolios are on the efficient frontier?

> **Answer:**
> Portfolio B dominates Portfolio C because it offers higher expected return (8% vs 7%) at lower risk (10% vs 12%). Portfolio A is not dominated—though it provides a lower return, it also has the lowest risk. Portfolios A and B make up part of the efficient frontier.

### **Worked Example 1.2**

Suppose Portfolio D has an expected return of 7% and risk of 10%, while Portfolio E has an expected return of 7% and risk of 13%. Which dominates?

> **Answer:**
> Portfolio D dominates Portfolio E. Both have the same expected return, but Portfolio D has lower risk. Portfolio E should not be chosen by a rational investor.

## **CHOOSING BETWEEN EFFICIENT PORTFOLIOS**

Once dominated portfolios are excluded, investors must select a portfolio from the efficient frontier. The choice depends on individual risk tolerance:

- Risk-averse investors prefer portfolios near the lower-risk, lower-return end.
- Risk-tolerant investors pick higher-risk, higher-return portfolios.

There is no single "best" efficient portfolio; the best choice depends on attitude to risk.

> **Key Term: risk aversion**
> The preference to avoid risk, choosing lower-risk portfolios even if it means accepting lower expected returns.

## **WHY THE EFFICIENT FRONTIER MATTERS**

The efficient frontier guides investors in selecting the most effective combination of investments. It simplifies choices by removing inferior options and clarifies the relationship between risk and return.

For financial managers, these principles underpin corporate investment, capital budgeting, and the use of models like the capital asset pricing model (CAPM).

### **Exam Warning**

> Do not assume diversification can eliminate all investment risk. Only unsystematic risk is reduced; systematic risk always remains, even with a large portfolio.

## **Summary**

Efficient portfolio selection means focusing on the risk–return combination, using diversification to reduce unsystematic risk, and only considering portfolios on the efficient frontier. Dominated portfolios should be ignored. Final selection depends on risk preference.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the concepts of diversification, systematic and unsystematic risk
- Define and interpret the efficient frontier on a risk–return graph
- Identify dominated and efficient portfolios
- Explain dominance and the elimination of suboptimal portfolios
- Understand investor choice along the efficient frontier based on risk appetite

## **Key Terms and Concepts**

- portfolio
- risk (standard deviation)
- return
- diversification
- systematic risk
- unsystematic risk
- risk–return trade-off
- efficient frontier
- dominance (in portfolio selection)
- risk aversion

Portfolio theory - Efficient frontier and dominance