Risk-adjusted performance - Portfolio effects and diversific...

Learning Outcomes

After reading this article, you will understand how portfolio effects and diversification reduce overall portfolio risk compared to holding individual investments. You will learn to explain the impact of correlation on diversification, calculate portfolio risk and return, and evaluate the benefits of diversification for investors and financial managers. By the end, you should be able to apply risk-adjusted performance assessment to real-world scenarios in line with ACCA AFM requirements.

ACCA Advanced Financial Management (AFM) Syllabus

For ACCA Advanced Financial Management (AFM), you are required to understand how risk-adjusted assessment of performance is affected by portfolio effects and diversification. Focus your revision on the following syllabus areas:

• The relationship between risk and return in investment evaluation
• The role and impact of diversification in reducing portfolio risk
• Calculation and interpretation of portfolio risk and return
• The effect of correlation on diversified portfolios
• Application of risk measurement and portfolio concepts to advanced financial management decisions

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 explains why diversification reduces portfolio risk? a) It increases the average return.
   b) It lowers systematic risk.
   c) It offsets unsystematic risk by combining assets with imperfect correlation.
   d) It eliminates all risk in the portfolio.
2. When two assets have a correlation coefficient of +1, the risk of their combined portfolio will be:
   a) Lower than for either asset individually.
   b) The same as the weighted average of their risks.
   c) Zero.
   d) Negative.
3. True or false? Systematic risk can be eliminated through diversification.
4. Briefly explain how the correlation coefficient determines the effectiveness of diversification in a portfolio.
5. Calculate the expected return of a portfolio with 60% in Asset A (expected return 10%) and 40% in Asset B (expected return 7%).

Introduction

Risk-adjusted performance is at the centre of investment appraisal and portfolio management. Investors seek to maximize return for a given level of risk, and financial managers must understand how individual investments combine to determine the overall risk and return of the portfolio. Diversification allows investors to reduce the impact of unpredictable outcomes associated with individual investments—provided those investments are not perfectly correlated. This article explains the principles of risk reduction through diversification, including quantitative measurement of portfolio effects, and the real-world benefits and limitations this offers.

Key Term: diversification
The investment strategy of holding a range of different assets to reduce overall risk by offsetting negative movements in some with positive movements in others.

THE CONCEPT OF PORTFOLIO RISK AND RETURN

Portfolio theory focuses on how the risk and return of various individual investments combine to form the overall profile of a portfolio.

• Expected return of a portfolio is the weighted average of returns of each asset, based on their proportional holdings.
• Portfolio risk, measured as variance or standard deviation of returns, is generally less than the weighted average risk of the individual holdings, unless all assets are perfectly positively correlated.

This risk reduction effect is the main rationale for diversification.

Calculating Portfolio Return

The expected return of a portfolio ($E(R_p)$) is calculated as:

$E(R_p) = w_1 E(R_1) + w_2 E(R_2) + ... + w_n E(R_n)$

where $w$ represents weight and $E(R)$ expected return.

Measuring Portfolio Risk

The risk of a two-asset portfolio combines variances and their covariance:

$\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2 \sigma_1 \sigma_2 \rho_{1,2}$

• $σ$ denotes standard deviation (risk) of each asset
• $\rho_{1,2}$ is the correlation coefficient between asset 1 and 2

A lower or negative correlation reduces portfolio risk more effectively.

Key Term: correlation coefficient
A statistical measure ($\rho$) ranging from -1 to +1 indicating the extent to which the returns on two assets move together.

DIVERSIFICATION IN ACTION

The effectiveness of diversification depends on the relationships among asset returns.

Types of Risk

Key Term: systematic risk
The portion of total investment risk arising from market-wide factors, which cannot be diversified away.

Key Term: unsystematic risk
The portion of total risk unique to a company or industry, which can be reduced by diversification.

• Unsystematic risk (unique, specific risk) is reduced or eliminated in well-diversified portfolios.
• Systematic risk (market risk) remains, as it affects all investments.

The Role of Correlation

• Perfect positive correlation (ρ = +1): No risk reduction.
• Zero correlation (ρ = 0): Maximum risk reduction, but some portfolio risk remains.
• Perfect negative correlation (ρ = –1): Complete diversification, portfolio risk can be eliminated (rare in practice).

Worked Example 1.1

A portfolio consists of two assets: Asset X (expected return 8%, standard deviation 12%) and Asset Y (expected return 6%, standard deviation 7%), each with 50% weighting. The correlation coefficient between X and Y is 0.2. Calculate the portfolio's expected return and standard deviation.

Answer:

• Expected return:
  $E(R_p) = (0.5 \times 8\%) + (0.5 \times 6\%) = 7\%$
• Portfolio variance: $$\sigma_p^2 = (0.5^2 \times 12^2) + (0.5^2 \times 7^2) + 2 \times 0.5 \times 0.5 \times 12 \times 7 \times 0.2 \\ = (0.25 \times 144) + (0.25 \times 49) + (0.5 \times 12 \times 7 \times 0.2) \\ = 36 + 12.25 + (0.5 \times 84 \times 0.2) \\ = 36 + 12.25 + (8.4) = 56.65$$
• Standard deviation:
  $\sigma_p = \sqrt{56.65} ≈ 7.53\%$ Portfolio risk (7.53%) is lower than the simple average (9.5%) due to diversification.

Diversification and Number of Assets

Holding more assets continues to reduce unsystematic risk, but with diminishing incremental benefit. When the portfolio is large (e.g., 20+ well-selected assets), the unsystematic portion is almost eliminated, and overall risk approaches systematic risk only.

DIVERSIFICATION BENEFITS AND LIMITATIONS

Diversification provides several important benefits:

• Reduces the impact of poor performance in any single asset
• Increases the likelihood of more stable portfolio returns
• Encourages inclusion of assets with different risk-return profiles

However, diversification is limited by:

• The presence of systematic risk, which cannot be diversified away
• Practical constraints such as high correlations during market stress or liquidity shortages
• Diminishing marginal benefit: risk reduction levels off as portfolio size increases

Worked Example 1.2

Explain what happens to portfolio risk if all holdings are perfectly positively correlated.

Answer:
If all assets are perfectly positively correlated (ρ = +1), diversification does not reduce risk: the portfolio's total risk equals the weighted average of individual risks.

PORTFOLIO IMPLICATIONS FOR FINANCIAL MANAGERS

Financial managers must recognise that shareholders can—and do—hold diversified portfolios. When evaluating projects or investments, use risk-adjusted performance measures based on systematic risk, not total (standalone) risk. The Capital Asset Pricing Model (CAPM) provides a framework for this:

• The required return reflects only market (systematic) risk, assuming investors are diversified.
• Projects should be evaluated using appropriate risk-adjusted discount rates.

Key Term: portfolio effect
The phenomenon where the overall risk of a group of assets is lower than the average risk of the individual assets, due to diversification.

Revision Tip

If asked about reducing investment risk, always differentiate between diversifiable (unsystematic) and non-diversifiable (systematic) risk. Use clear terminology in your exam answers.

Summary

Diversification allows investors to achieve lower risk than holding individual assets by combining those with low or negative correlations. Portfolio effects make risk-adjusted performance assessment central to advanced financial management and investment appraisal. While diversification significantly lowers unsystematic risk, systematic risk remains, setting a minimum bound on portfolio risk. Financial managers should evaluate investments using risk-adjusted metrics that reflect market-wide risk, not project- or asset-specific uncertainties that can be eliminated through a diversified portfolio.

Key Point Checklist

This article has covered the following key knowledge points:

• Diversification as a method for reducing portfolio risk
• The meanings of systematic and unsystematic risk
• The impact of correlation on diversification effectiveness
• How to calculate expected return and risk of a portfolio
• Why only systematic risk is relevant for risk-adjusted performance measures
• The limits of risk reduction through diversification

Key Terms and Concepts

• diversification
• correlation coefficient
• systematic risk
• unsystematic risk
• portfolio effect