Get to Know Value at Risk (VaR): How to Calculate It?

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In Derivative Strategies on the virtues and disadvantages of Value at Risk, published in 1997, Nicholas Nassim Taleb and Philippe Jorian engaged in a fierce debate that stunned the financial, risk management, and Value at Risk (VaR) industries. Jorian, who comes from an academic background, is the only person who has written a textbook on value at risk. Taleb, a brilliant orator, writer, and unorthodox trader, questioned everything Jorian stated in his capacity as a dealer.

What is VaR, or Value at Risk?

Let’s start with the meaning of value at risk. Value at risk quantifies the risk associated with stock and portfolio investments. It provides a likely estimate of investment loss for a specific period, such as a month, based on certain market circumstances. VAR is a tool investors use to calculate the number of assets needed to offset potential losses. It is a statistical method for calculating the amount of financial risk present in a portfolio of equities over a predetermined time.

It helps calculate the overall risk of individual portfolios. If the assets’ 99% daily VAR is ₹100, then there would be 99 days out of 100 where the everyday loss is less than ₹100. You may calculate the Value at Risk for a portfolio of one or more assets. It will gather the most accurate data.

VaR Formulas and Techniques

Historical Approach

One of the simple methods used by most traders to determine Value at Risk, or VaR, is the historical approach. This approach involves calculating the “risk factor” for each day based on the “previous 250 days of market data”. The present market’s worth is then considered along with each percentage change.

It displays the 250 potential outcomes that will affect the value in the future. The investor calculates the portfolio for each scenario using complete or non-linear pricing models. Nonetheless, the worst possible day would fall into the 99% VaR bracket.

The historical technique’s value at risk calculation formula is:

Value at Risk = vm (vi / v(i – 1))

Here, Vi is the abbreviation for the number of variables on day ‘i’. Further, m is the number of days from which the historical data is taken.

Parametric Approach

The normal distribution of returns is used by the variance-covariance approach, commonly known as the parametric method. The investor employs the expected return and standard deviation, two important variables, in this strategy. Yet, with the problems with risk assessment, investors have found that this approach works best. For instance, it applies to issues where the anticipated value is accurate and the investor is aware of the dividends.

Check the value at risk calculation formula for this strategy below, where “l” stands for loss, “p” stands for a portfolio, and “n” stands for the number of instruments.

VaR Parametric Method Formula

lp= l1+ l2+ l3 +…..+ ln

σ2p = σ21+σ22+σ23 + ….+ σ2n+ ρ1,2,3,…nσ1σ2σ3σn

Where:

σ2p – Standard Deviation of the loss on portfolio

σ21 – loss form instrument 1

Ρ1,2,3,…n – Correlation between losses 1 to n

Monte Carlo Technique

The Monte Carlo Method is another widely used technique. Using this approach, the VaR (Value at Risk) increases through a selection of random scenarios. Yet, the investor has built up this series to reflect future rates. Non-linear pricing models are used by the investor to determine how much the value of each scenario is expected to fluctuate. The Value of Risk is then calculated based on the worst losses. Yet, a wide variety of issues involving risk measures can be solved using this approach.

Here are the advantages of VaR.

• Accessibility
Assessing the risk is an effortless operation since agencies or investors can grasp the whole risk of the venture from a single numerical answer.
• Common Usage
It is a frequently used instrument to assess the risk components of portfolios. It may thus be trusted and used for cross-verification through comparison. It is a recognised statistic representing risks, so investors may use it while purchasing, promoting, or selling an asset.
• Relevance
The computation may be used for various asset types, including bonds, derivatives, currencies, shares, etc. As a result, major investment businesses or financial institutions can use the VaR report to distribute money when evaluating the risks associated with various asset classes.
• Structured
The report establishes a structured methodology to inform the investor or analyst about the risks associated with various investments in a comprehensible and organised way,. As a result, risk management and financial monitoring are now comparatively easier tasks.

Let’s now learn about the downsides as well.

• Application
Certain techniques, such as Monte Carlo simulation, can be costly and difficult to explain in an application context. However, the computation only takes a few of the worst-case possibilities into account. In order to assess the instances VaR tends to overlook, firms do stress tests.
• Variable Results
Different computation techniques might produce different results. As a result, it is never certain whether such analysis is accurate.
• Security
It is possible for an event to happen or not based on the likelihood of that event being realised as a result of this computation. Investors are given a false feeling of security by chance, which may really work against them.
• Portfolio Analysis
Each asset type must be assessed independently while determining the risk of a large portfolio. The difficulty of determining VaR increases with the number of key asset types in the portfolio. Together with the risk-return equation, other factors, such as asset correlation, must be taken into account.

Final Take

Value at Risk, often known as VaR, gives investors the best understanding of the greatest predicted loss they would incur over the course of an investment. The VaR calculates every possible outcome, including the worst-case scenario. We have examined the techniques for calculating VaR in this post. Despite the fact that all of these techniques are helpful, you must take their respective time frames into account.