Value at risk (VaR)

Definition

Value at risk (VaR) is a statistical measure used in finance to estimate the potential loss that an investment portfolio, trading position, or a group of financial instruments may face over a specified time horizon for a given confidence interval.

What is value at risk?

VaR is typically expressed over a specific time period, such as one day or one month. It is associated with a confidence level, often expressed as a percentage (e.g., 95% or 99%). A 95% VaR means there is a 5% chance that losses could exceed the estimated value. For example, if a portfolio has a one-day 95% VaR of $100,000, this means that there is a 5% chance that the portfolio could lose more than $100,000 in one day under normal market conditions.

VaR accounts for the diversification effect within a portfolio. A diversified portfolio with assets that do not move in perfect correlation will generally have a lower VaR.

However, VaR also has some limitations. It does not provide information about the magnitude of losses beyond the VaR threshold. It also assumes that asset returns follow a normal distribution, which may not hold in extreme market conditions.

VaR is a widely used risk management tool in the financial industry and is often required by regulatory authorities for institutions like banks and investment firms. Furthermore, it’s an important tool in risk management, helping financial institutions and investors understand and quantify the level of risk associated with their portfolios.

Marginal value at risk

Marginal value at risk (MVaR) measures the additional risk a new investment or asset brings to a portfolio. It quantifies how the overall value at risk of a portfolio changes with the inclusion of this new asset. MVaR helps in understanding the risk contribution, aiding in portfolio optimisation and risk management.

By assessing MVaR, investors can make informed decisions about which assets to add or remove to maintain their desired risk level while maximising potential returns. It is a key tool for identifying the impact of individual assets on the portfolio’s total risk profile.

Example of value at risk

A financial analyst at a hedge fund is tasked with assessing the potential risk of a portfolio of stocks. Using value at risk (VaR) analysis, the analyst calculates that there is a 5% chance that the portfolio could lose more than £100,000 over the next trading day. This means that under normal market conditions, the maximum loss the portfolio could incur within one day is estimated to be £100,000, with a 5% probability of exceeding this amount.

Based on this VaR assessment, the hedge fund’s risk management team can make informed decisions about adjusting the portfolio’s composition or implementing hedging strategies to reduce the potential downside risk within acceptable levels.