Value at Risk

Value at Risk (VaR) measures the maximum potential financial loss over a set period. It's a key financial metric for investment decisions, quantifying worst-case scenarios. In stock markets, VaR estimates expected losses for a stock or portfolio based on investor confidence and market sentiment. Key elements include potential loss amount, time frame, and probability.

Also, this concept attaches a confidence level or probability of incurring loss as a percentage value. Investors widely use value at risk to understand and manage the downside risk associated with their investments.

Let us understand this concept in detail, learn how to calculate VaR, and also see some of its limitations.

What is Value at Risk (VaR)?

Value at risk is a tool used to assess the potential loss in the value of an investment. This loss is calculated:

• Over a certain period
  and
• At a given confidence level

For example:

• Say you invested in a mutual fund scheme and calculated its value at risk
• You found that you can lose Rs. 10,000 over the next month
• There is a 95% chance of incurring this loss (confidence level)
• In other words, we can also infer that:
  • There is a 95% chance that you will not incur a loss of more than Rs. 10,000

Value at risk can also be considered a safety net. It helps you understand the worst-case scenario for your investments.

Know what asset classes are and how they behave in a typical market

Understanding value at risk with an example

Say there's a mutual fund that invests in a mix of large-cap stocks listed on the Bombay Stock Exchange (BSE). Over the past year, it has shown that on any given day, it moves up or down about 1% from its average return. This volatility is represented by the standard deviation.

Now, let’s assume that we want to calculate the VaR at a 95% confidence level for this mutual fund over a single day. Consider the following data:

• Average daily return (mean): 0.1%
• The standard deviation of daily returns (volatility): 1.2%

Using the formula for VaR (discussed later) at a 95% confidence level, this mutual fund has a VaR of approximately 2.068%. This means there's a 5% chance that on any given day, the fund could lose more than 2.068% of its value.

Elements of value at risk

The VaR is composed of several elements that collectively provide a framework for managing risk in investment portfolios. Let’s have a look at them:

• Time horizon
  • VaR is calculated over a specific time period, such as one day, one week, or one month.
  • The choice of time horizon depends on the:
    • Investment horizon
      and
    • Frequency of monitoring risk
• Confidence level
  • This represents the level of certainty associated with the VaR estimate.
  • Common confidence levels include 90%, 95%, and 99% .
• Return period (also known as the holding period)
  • It specifies the time over which potential losses are evaluated.
  • For example:
    • A one-day VaR estimates potential losses over the next trading day.
    • On the other hand, a one-month VaR estimates losses over the next month.
• Market data
  • VaR calculations rely on historical or simulated market data to estimate the distribution of possible returns.
  • Some common types of market data include:
    • Historical price movements
    • Volatility
    • Correlations between assets

Advantages of value at risk

Value at risk is a widely used financial metric due to the several benefits it offers to investors, such as its easy-to-understand nature, standard measure, universal acceptability, and more. Let’s study them in detail:

Easy to understand

VaR provides a clear and concise measure of potential losses. It translates complex risk metrics into easily interpretable figures. This simplicity helps in effective communication and decision-making among investors.

Applicability

VaR applies to various asset classes, including:

• Stocks
• Bonds
• Commodities, and
• Derivatives

This universal applicability allows for comprehensive risk assessment across diversified investment portfolios.

Universal

VaR provides a universal framework for assessing risk. It offers consistent risk management practices across different:

• Financial markets
  and
• Regulatory environments

This standardisation enhances transparency and comparability in risk reporting and regulatory compliance.

Formula of value at risk

The formula for value at risk depends on the method used to calculate it. Primarily, VaR is calculated using three main methods. Let’s check their respective formulas:

• Parametric (Variance-Covariance) Method: -1 x (percentile loss) x (portfolio value)
• Historical Simulation Method: -1 x (Z-score) x standard deviation of returns) x (portfolio value)
• Monte Carlo Simulation Method: -1 x (percentile loss) x (portfolio value)

How to calculate value at risk?

Among the several methods, the historical method is one of the popular ways of calculating the value at risk. Let us understand its working through a hypothetical example:

• Say you want to calculate the VaR for a mutual fund scheme
• This portfolio consists of Indian stocks
• The time horizon is one month
• The confidence level is 95%

Now, you will follow these steps:

Step I: Collect historical returns data

• Gather historical daily returns data for the mutual fund scheme's portfolio, focusing on Indian stocks
• You can obtain this data from financial databases, such as:
  • Mutual fund fact sheets
    or
  •  Market indices such as:
    • The S&P BSE Sensex
    • NIFTY 50

Step II: Sort returns

• Sort the daily returns data from worst to best
• Basically, arrange them in ascending order

Step III: Determine percentile

• Decide on the confidence level
• In this example, we are using a 95% confidence level
• This implies we are aiming to capture the "worst-case scenario" that occurs with a probability of 5%
• Conversely, there's a 95% probability that the actual loss will not exceed the VaR estimate.

Step IV: Identify the return value at the “5th percentile”

• Find the return value corresponding to the 5th percentile
• That’s because this value represents the VaR at a 95% confidence level
• Now, assume that return at the 5th percentile is -2%
• This means there's a 5% chance of the mutual fund scheme experiencing a loss of 2% or more over the next month
• Do note that these predictions are based on historical data

Now, let’s study all the three methods of calculating Value at Risk (VaR).

Historical method

Formula: -1 x (Z-score) x standard deviation of returns) x (portfolio value)

This method uses historical data directly to estimate VaR without assuming a specific distribution. Let’s see the calculation steps:

• Arrange historical daily returns of the portfolio from worst to best
• Choose the historical return corresponding to the desired confidence level (e.g., 5th percentile for 95% confidence)
• Apply the formula

Parametric method

Formula: -1 x (percentile loss) x (portfolio value)

The parametric method estimates VaR, assuming that returns follow a normal distribution. Follow these steps to calculate VaR using this method:

• Calculate Expected Return (μ) and Standard Deviation (σ) by using historical data
• Choose a confidence level (e.g., 95%) and find the corresponding Z-score from the standard normal distribution table (e.g., Z ≈ 1.645 for 95% confidence)
• Lastly, apply the formula

Monte Carlo method

Formula: -1 x (percentile loss) x (portfolio value)

Monte Carlo simulation generates multiple simulations of possible future scenarios based on historical data and assumptions about return distributions. Follow these steps under this method:

• Generate a large number of random scenarios based on assumed distributions for each asset in the portfolio
• For each scenario, calculate the portfolio value based on:
  • Simulated returns
    and
  • Asset correlations

• Sort simulated portfolio values and determine the value corresponding to the desired confidence level
• Lastly, apply the formula

Limitations of value at risk

Using value at risk, mutual fund investors can calculate their maximum potential losses. However, this method comes with several limitations, such as:

Large portfolio

Value at risk underestimates potential losses when it is applied to large portfolios with:

• Diverse assets
  and
• Complex risk factors
  

That’s because VaR assumes that asset returns follow a normal distribution and that correlations remain stable, which may not hold true in volatile or crisis periods.

Large portfolios have numerous assets and intricate dependencies. Thus, when applied to them, VaR underestimates potential losses due to the inability to accurately capture:

• Extreme events
• Sudden correlations shifts

Reliance on historical data

VaR calculations heavily depend on historical data. Usually, historical market conditions do not accurately reflect future market behaviour. This happens due to several factors, such as:

• Changing economic policies
• Geopolitical events
• Regulatory changes
• Market reforms

Therefore, when you rely solely on historical data for VaR analysis, you either overestimate or underestimate the risk

Assumptions

VaR calculations often assume that asset returns are:

• Uncorrelated
  or
• Have stable correlations

However, correlations between different asset classes vary over time, especially during periods of market stress. While calculating value at risk, we ignore these dynamic correlations. This ignorance results in inaccurate risk assessments. Further, it holds especially true for diversified mutual fund portfolios.

Difference in methods

There are different VaR models to calculate value at risk, such as:

• Historical VaR
• Parametric VaR
• Monte Carlo simulation

All these methods have their own assumptions and limitations. This leads to complexity, and sometimes, the interpretations also grossly differ

What to do before using value at risk

As a mutual fund investor, you can use VaR as a risk management tool. It can help you assess the likely downside risk of a mutual fund scheme’s portfolio or asset allocation. However, you must understand your risk tolerance before utilising VaR. It represents your ability to endure fluctuations in the value of your investments.

This identification ensures that the level of risk indicated by VaR aligns with your:

• Investment objectives
  and
• Risk appetite

For example:

• Say you have a low-risk tolerance and are investing for retirement
• In this case, you can:
  • Prioritise preserving capital
    and
  • Make investments that have a lower VaR

• Now assume a different scenario where you:
  • Have a higher risk tolerance
    and
  • Are investing for long-term growth

• In this situation, you are more comfortable with investments that have a higher VaR

Summary

Value at Risk (VaR) is a statistical method for calculating the potential investment losses with a set confidence level. Used by several fund managers and mutual fund investors, it acts as a safety net and helps to understand the “worst-case scenarios”.

However, this method relies heavily on historical data, which usually does not predict future market behaviour accurately. Additionally, it overlooks changing correlations between assets, and different VaR methods can even return varied results. Are you looking to invest in some of the top-performing mutual funds? The Bajaj Finserv Platform has listed 1,000+ mutual funds online. Compare them today by using the SIP calculator, step up calculator and the lumpsum calculator.

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