## **Learning Outcomes**

This article explains the purpose and application of risk identification and measurement in financial management, with a particular focus on Value at Risk (VaR) and stress testing. You will learn the key concepts, methods for quantifying potential losses, and practical considerations for interpreting risk metrics. After reading this, you should be able to apply VaR and stress tests to real business scenarios, evaluate their limitations, and understand their relevance for ACCA AFM exam questions.

## **ACCA Advanced Financial Management (AFM) Syllabus**

For ACCA Advanced Financial Management (AFM), you are required to understand the importance of risk measurement techniques within treasury and risk management activities. In particular, you should be prepared to:

- Explain the purpose of risk identification and assessment in financial strategy and treasury management.
- Apply and interpret Value at Risk (VaR) as a measure of potential financial loss.
- Evaluate the use and significance of stress testing and scenario analysis for risk management.
- Assess the limitations and practical considerations in using VaR and stress tests in exam situations.

## **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 does Value at Risk (VaR) specifically estimate in a financial context?
2. Which risk assessment technique helps identify the impact of extreme but plausible market events on a portfolio?
3. True or false? VaR can guarantee maximum loss will not exceed its calculated value.
4. Briefly distinguish between stress testing and scenario analysis.

## **Introduction**

Accurately identifying and measuring financial risk is essential for effective treasury management and investment decision-making. Leading techniques, such as Value at Risk (VaR) and stress testing, provide quantitative understanding of potential losses and allow management to test robustness to adverse events. These tools help financial managers communicate risk with clarity, assess capital adequacy, and satisfy regulatory and stakeholder requirements. Understanding both their application and limitations is critical for success in the ACCA AFM exam.

## **IDENTIFYING AND MEASURING RISK**

The first step in risk management is identifying exposures to market changes, such as fluctuations in interest rates, currencies, or asset prices. Subsequently, risk must be measured—transforming uncertain outcomes into quantifiable figures that guide decision-making.

### Value at Risk (VaR) Explained

Value at Risk, commonly known as VaR, is a statistical measure used to estimate the maximum potential loss on an investment or portfolio over a specified time horizon, at a given confidence level, under normal market conditions.

> **Key Term: Value at Risk (VaR)**
> A statistical estimate of the maximum expected loss on a portfolio over a defined period and confidence level, assuming normal market conditions.

For example, a daily VaR of \$5 million at 99% confidence means there is only a 1% chance the loss will exceed \$5 million in a single day.

#### Interpreting VaR

VaR is widely reported in financial institutions and by regulators as a standard risk metric. It answers the question: "How much could we lose, with X% confidence, over a specific period?" However, VaR does **not** indicate the worst-case loss, nor does it measure the likelihood or scale of losses beyond the VaR threshold.

> **Key Term: confidence level**
> The probability that a loss will not exceed the VaR amount over the chosen time period.

### Calculation Methods for VaR

VaR can be estimated using several techniques. The three most common are:

- **Historical simulation:** Uses actual historical market changes to model possible losses.
- **Variance-covariance (parametric) approach:** Assumes normally distributed returns and uses the portfolio's mean and standard deviation.
- **Monte Carlo simulation:** Simulates a large number of random scenarios to determine the distribution of possible outcomes.

The core steps involve setting a holding period (e.g., 1 day, 10 days), choosing a confidence level (commonly 95% or 99%), and then determining the loss threshold that separates the most extreme outcomes.

> **Key Term: holding period**
> The time interval over which VaR is calculated, defining the risk assessment horizon.

### **Worked Example 1.1**

A bank holds a portfolio expected to have a mean return of \$0 with a standard deviation of \$2 million over a 1-day period. Calculate the 99% one-day VaR assuming normal distribution.

> **Answer:**  
> At 99% confidence, the z-score is approximately -2.33. VaR = |z| × standard deviation = 2.33 × \$2 million = \$4.66 million. Thus, there is a 1% probability the loss will exceed \$4.66 million in one day.

### Stress Testing and Scenario Analysis

VaR provides useful information under normal conditions but does not capture losses in extreme or unusual situations. Stress testing and scenario analysis are supplementary techniques designed to address this limitation by evaluating the impact of rare, severe events or adverse market movements.

> **Key Term: stress testing**
> A risk management process that measures a portfolio's potential losses under extreme, hypothetical market conditions.
>
> **Key Term: scenario analysis**
> An approach to estimating the effect of specific historical events or projected adverse scenarios on financial performance.

Stress tests might include shocks to interest rates, rapid shifts in exchange rates, or major asset price declines. Scenario analysis could involve replaying market conditions from previous crises to assess potential exposure.

### **Worked Example 1.2**

An investment manager wants to check how a bond portfolio would be affected if interest rates suddenly rise by 2%. Historical VaR shows a daily risk of \$1.2m, but the scenario analysis reveals a potential loss of \$4m under the assumed rate shock. Why is this information important?

> **Answer:**  
> VaR measures loss under typical daily volatility, but scenario analysis uncovers vulnerability to rare, extreme market changes not reflected in normal VaR. This highlights portfolio risk that would otherwise be missed.

### Interpreting and Using VaR and Stress Tests

VaR and stress testing assist in risk communication, capital allocation, and regulatory compliance. However, they require critical interpretation:

- VaR is not additive across business units or risk types without careful modelling.
- VaR relies on assumptions of market normality; actual extreme losses may be far higher.
- Stress tests help identify exposure to "tail risk"—rare but catastrophic losses.

### **Exam Warning**

> Relying solely on VaR can lead to underestimating true exposure, especially during periods of market upheaval. Always consider additional measures like stress testing in your exam answers.

### **Revision Tip**

> In calculations, state your assumptions about distribution and confidence levels. When discussing results, explain both strengths and limitations.

## **Summary**

Effective risk measurement requires a combination of tools. Value at Risk provides a standardized, quantitative measure of expected losses under normal market conditions, helping set risk limits and inform decisions. Stress testing and scenario analysis complement VaR by exposing vulnerabilities to unlikely but severe events. Becoming proficient in both techniques, and understanding their limitations, is essential for ACCA AFM.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Define Value at Risk (VaR) and explain its key features and interpretation
- Describe the main methods for calculating VaR and the purpose of the confidence level
- Identify the role and process of stress testing and scenario analysis
- Recognize the limitations of VaR and the need for supplementary risk measures
- Apply and interpret VaR and stress test outputs in practical case scenarios

## **Key Terms and Concepts**

- Value at Risk (VaR)
- confidence level
- holding period
- stress testing
- scenario analysis

Risk identification and measurement - Value at Risk and stress testing