Have you ever wondered how do portfolio managers compare the risk associated with two different asset classes? Or how do they calculate the risk of a portfolio comprising of different asset classes? For example, risk of a fixed income security is measured by Duration and Convexity whereas the risk of an equity share is measured by Standard Deviation and Variance. This is where the role of Value at Risk (VAR) comes into play. Its one of the most widely accepted measure of market risk for all the portfolio managers. Now let us delve deeper into the concept of Value at Risk and see how it is calculated.

## What is Value at Risk (VAR)

VAR is a probability-based measure of loss potential. It is an estimate of the minimum loss that is expected to be exceeded in a specified time period with a given level of probability. Let’s explain this in an easier manner.

You just have to remember three things when it comes to Value at Risk (VAR)-

- Minimum Loss
- Specified Time Period
- Probability of exceeding that loss

For example, a __3%__ VAR of __$50__ over the next __1 week__ would mean that a minimum loss that would occur within the next 1 week is $50 and the probability of this loss is 3%. Just to make the things clearer, we can also restate the above statement as, there is 97% chance that our loss will not exceed $50 within the next 1 week.

Value at Risk (VAR) can also be stated as a percentage of the portfolio i.e. a specific percentage of the portfolio is the VAR of the portfolio. For example, if its 5% VAR of 2% over the next 1 day and the portfolio value is $10,000, then it is equivalent to 5% VAR of $200 (2% of $10,000) over the next 1 day.

## Methods of Calculating Value at Risk (VaR)-

There are 3 main methods of calculating VAR. They are as follows-

**1. Analytical VAR-** This method uses the expected return and the standard deviation of the stocks in computing the VAR assuming that the returns of the subject asset/portfolio exhibits a ‘Normal Distribution’. Basically, a level of confidence is selected, and the Z value is matched according to the selected probability. For this purpose, one-tailed Z table is referred, as we are just concerned with the negative side of the distribution.

For example, if the portfolio value is $20,000 and if 1-month average return and standard deviation is 10% and 15% respectively. Daily VAR at 5% level of significance can be calculated as-

VAR= [R_{p }– (z) (σ)] V_{p} => VAR = [0.1 – (1.65) (0.15)] 20000 => -$3000 (rounded) => 15% of the Portfolio.

Where,

R_{p} = Return of the portfolio.

Z= Z value for 5% level of confidence in one tailed test.

σ = Standard Deviation of the portfolio.

V_{p}= Value of the portfolio

This can be explained with the help of the following self-explanatory graph.

Thus, there is a 5% chance that a minimum loss of 15% of the portfolio (i.e. $3000) will occur within the next 1 month. In other words, we are 95% confident that the loss will not exceed $3000 within the next 1 month.

**2. Historical VAR-** This is probably the easiest way to calculate VAR. All you have to do is collect the information regarding the historical returns of the asset, arrange all the historical returns in ascending order and then choose the percentile of the observations according to level of confidence required. The periodicity of the returns will define the time period of VAR.

For Example, to compute the 5% monthly VAR, we look at the 5^{th} percentile of the monthly return distribution.

**3. Monte Carlo VAR-** In this method, a software generates the distribution of the returns on a security/portfolio. This is done according to the inputs provided by the analyst regarding the historical return and standard deviation of the security. This method runs a lot of simulations to capture all the possibilities of the movement of the security.

A limitation of this method is that it uses a lot of assumptions. For example, for a portfolio of 100 stocks, we have to input the standard deviation of all the stocks along with the correlations among all of them to calculate the standard deviation of the portfolio. Nearly 5,000 correlations are required for this. So, we can say that this method is as good as its inputs.

## Advantages of Value at Risk (VAR)-

**1. Comparability-** It is a versatile measure and can be used to measure the market risk of asset classes exhibiting different risk characteristics. The question asked in the beginning of the article is answered here. Bonds and Equity differ a lot in their risk characteristics, still Value at risk (VAR) for both can be compared after calculating them separately.

Kindly note that VAR of different securities is not additive i.e. you cannot calculate the VAR of two different assets and add them up to get the VAR of a combined portfolio because when two or more securities are combined, their standard deviation decreases due to diversification.

**2. Risk Budgeting Process-** It is often used in the risk budgeting process of fund management firms where the upper management allocates VAR across the divisions and the manager’s goal is to maximize the return given the allocated VAR. This helps the firm to compare the performance of different divisions according to the allocated VAR.

**3. Acceptability-** One of the biggest advantages of VAR is its acceptability among the regulatory authorities. A fund management company has a lot of restrictions and reporting obligations imposed by the regulatory authorities and VAR can be used for these filings.

**4. Easy to Interpret-** As VAR is measured in terms of currency or as a percentage, it is easily understood by the analysts and can simply be applied to their analysis.

Calculation of VAR is also a part of many financial software. You just have to set a few parameters and the software does the rest for you (like in Bloomberg). You don’t have to be a statistical expert to calculate it.

There are also disadvantages of Value at Risk (VAR) like it does not tell you the expected loss if the loss goes beyond the minimum threshold. Even the risk of liquidity is not considered directly, it just focuses on the market risk. And sometimes, it is also difficult to estimate the inputs used for calculating VAR.

## CONCLUSION

Value at Risk (VAR) is an important risk measure used by the portfolio managers across the globe. Its ease of understanding and wide acceptance by the regulatory authorities makes it even more favorable for the fund management companies to adopt. Though its advantages clearly weigh more than the disadvantages, however one should consider its limitations while using it.

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