# Value at Risk (VAR)

A measurement technique that estimates the risk of an investment

# What is Value at Risk (VAR)?

Value at Risk (VAR) is a measurement technique that estimates the risk of an investment. In other words, VAR is a statistical technique that measures the amount of potential loss that could happen in a portfolio of investment over a period of time. Value at Risk gives the probability of losing more than a given amount on a given portfolio over a period of time.

### Advantages of Value at Risk (VAR)

#### 1. Easy to understand

Value at Risk is a single number that indicates the extent of risk in a given portfolio. Value at Risk is either measured in price unites or in form of percentage. This makes the interpretation and understanding of VAR easier.

#### 2. Applicability

Value at Risk is applicable to all the assets in various portfolios. Value at Risk is applicable to bonds, shares, derivatives, currencies or any other asset with a price. Thus, VAR can be easily used by different banks and financial institutions to measure the profitability and risk of different assets, and allocate risk based on VAR.

#### 3. Universal

As the Value at Risk figure is used by everyone it can be considered as a standard in buying, selling or recommending assets.

### Limitations of Value at Risk

#### 1. Large portfolios

Calculation of Value at Risk for a portfolio not only requires one to calculate the risk and return of the asset but also the correlations between them. Thus, the greater the number or diversity of assets in a portfolio, calculating VAR will be difficult.

#### 2. The difference in methods

The different approaches in calculating VAR can lead to different results with the same portfolio.

#### 3. Assumptions

Calculation of VAR requires one to make assumptions as inputs. If assumptions are not good or are wrong, the VAR figure will also be wrong.

### Key Elements of Value at Risk

1. Specified amount of loss in value or percentage
2. Time period over which the risk is assessed
3. Confidence interval

### Example VAR Assessment Question

If we have a 95% confidence interval, what is the maximum loss that can occur from this investment over a period of one month?

### Methods Used for Calculating VAR

#### 1. Historical Method

It is the simplest method for calculating Value at Risk. In the historical method, market data for the last 250 days is taken to calculate the percentage change for each risk factor on each day. Each percentage change is then calculated with current market value to present 250 scenarios for future value. For each of the scenarios, the portfolio is valued using full non-linear pricing models. The third worst day selected is assumed to be 99% VAR.

Where:

vi is number of variables on day i

m is the number of days for which historical data is taken

#### 2. Parametric Method

It is also known as the variance-covariance method. This method assumes a normal distribution in returns. In other words, under this method, two factors are to be estimated, an expected return and a standard deviation. This method is best suited to risk measurement problems where the distributions are known and reliably estimated. This method is unreliable when the sample size is small.

Let loss be ‘l’ for a portfolio ‘p’ with ‘n’ number of instruments.

#### 3. Monte Carlo Method

Under this method, Value at Risk is calculated by randomly creating a number of scenarios for future rates using non-linear pricing models to estimate the change in the value of each scenario, and then calculating the VAR according to the worst losses. The method is suitable to a great range of risk measurement problems, especially when dealing with complicated factors. This method assumes that there is a known probability distribution for risk factors.

### Marginal Value at Risk (MVAR)

It is the amount of additional risk that is added due to a new investment in the portfolio. MVAR helps fund managers to understand the change in a portfolio due to subtraction or addition of a particular investment. An investment may individually have a high Value at Risk, but if it is negatively correlated with the portfolio, it may contribute a much lower amount of VAR to the portfolio than its original amount.

### Incremental Value at Risk

It is the amount of uncertainty added to a portfolio or subtracted from a portfolio due to buying or selling of an investment. Incremental VAR is calculated by taking into consideration the portfolio’s standard deviation and rate of return and the individual investment’s rate of return and the portfolio share.

### Conditional Value at Risk (CVAR)

It is also known as the expected shortfall, average value at risk, tail VAR, mean excess loss or mean shortfall. CVAR is an extension of VAR. CVAR helps to calculate the average of the losses that occur beyond the Value at Risk point in a distribution. The smaller the CVAR, the better it is.