Evaluate the three value-at-risk (VaR) approaches used to measure market risk

Assignment Brief

Module Title: Risk 1: Credit and Market Risks

PART A - No appendix allowed for this part.

Evaluate the three value-at-risk (VaR) approaches used to measure market risk. You should use real world numerical example to illustrate:

1. VaR as a measure of market risk.
2. The limitations of VaR and the techniques developed to address these limitations (such as Extreme Shortfall, Conditional VaR, Back Testing and Extreme Value Theory)

Within the risk management framework introduced in week 1, critically discuss the issues associated with measuring and managing credit and counterparty credit risk in financial institutions. You should present an understanding of the regulatory aspects of credit and counterparty credit risk within the discussion.

PART B - Group Presentation during Week 12 and Reflective Statement

1. Prepare and present a group presentation (during week 12) on any contemporary issues in credit/counterparty credit/market risks management. Further, you are required to submit the original presented slides for your group as an appendix to the assignment.
2. Write an individual reflective statement on the group presentation (indicative length 500 words) setting out why your group chose the topic, what you gained from engaging with the presentation and what you think you have learned as a result of the presentation. You should submit as appendix all documents that specifically highlight your contribution to the presentation such as any notes, readings, contributions you have made to the group presentation.

Sample Answer

Evaluating Value-at-Risk (VaR) Approaches to Measuring Market Risk

Value-at-Risk (VaR) is a widely used statistical measure that estimates the potential loss in value of a portfolio over a defined period for a given confidence level. It is a fundamental tool in the risk management framework of financial institutions for measuring market risk, the risk of loss from movements in market prices. VaR allows institutions to quantify risk, allocate capital, and comply with regulatory standards such as Basel III.

VaR as a Measure of Market Risk

There are three primary VaR approaches: Historical Simulation, Variance-Covariance (Parametric VaR), and Monte Carlo Simulation.

(a) Historical Simulation

This method uses historical market data to calculate potential losses. The changes in market variables (e.g., equity prices, interest rates) over a past period are applied to the current portfolio. VaR is derived by ranking historical losses and selecting the appropriate percentile.

Example: Suppose a portfolio worth $10 million uses 250 days of historical returns. If the 5th percentile daily loss is $300,000, the 1-day 95% VaR is $300,000. This implies there is a 5% chance of losing more than $300,000 in a day.

(b) Variance-Covariance (Parametric VaR)

Assumes returns are normally distributed and calculates VaR using the portfolio’s standard deviation (σ) and mean (μ).

Value-at-Risk (VaR) Formula

VaR = Zₐ × σ × √t

Where:

• Zₐ: Z-score for the confidence level (e.g., 1.65 for 95%)

• σ: Standard deviation of portfolio returns

• t: Time horizon in days

Example

Suppose a portfolio has a daily return standard deviation (σ) of 1%, and the portfolio value is $10,000,000.

For a 1-day VaR at 95% confidence level (Zₐ = 1.65):

VaR = 1.65 × 0.01 × 10,000,000 = $165,000

This means there is a 5% chance the portfolio could lose more than $165,000 in one day.

(c) Monte Carlo Simulation

This approach uses stochastic modelling to simulate thousands of possible future price scenarios based on assumed statistical distributions. VaR is calculated from the simulated distribution of returns.

Example: A Monte Carlo model simulates 10,000 future scenarios. After ranking simulated losses, the 5th percentile is $200,000. Thus, the 1-day 95% VaR is $200,000.

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