What is Value At Risk
Value at Risk (VaR) measures the potential loss from a position, portfolio, desk, or bank. VaR refers to the greatest loss an investment can incur at a given confidence level over a specific time horizon. Although other risk measures exist, this is the most popular and straightforward approach.
![Value at Risk](https://thewhisperingvoid.com/wp-content/uploads/2024/04/a-thought-provoking-illustration-of-a-finance-expe-zsQFQOPNQaew24VfCScung-oQmNg96oR5qBCDWSQ-6nTQ-1024x576.jpeg)
A Short Example
At a 95% confidence level, an equity derivatives hedge fund estimates its Value at Risk for one day to be $500,000. This means that the fund expects to lose over $500,000 on one out of every 20 days.
Dive Deep to Understand Value At Risk
VaR calculations frequently assume a normal distribution of returns throughout the interest horizon. VaR calculations require inputs on portfolio mix, time horizon, and distribution characteristics. The last group of parameters includes average growth rate, standard deviations (volatilities), and correlations. If the time horizon is limited, the growth rate can be ignored as it has a minor impact on the overall calculation.
VaR is estimated using a simple formula for basic portfolios and simulations for more complex portfolios, assuming normality. Portfolios can be classified as basic or sophisticated based on whether they contain derivatives. If your portfolio solely contains linear instruments, normal distributions and standard deviations can be calculated analytically. If the time horizon is small, derivatives can be represented using a delta position in the underlying.
Simulations can be basic yet time-consuming. Use standard Monte Carlo methods to simulate several realisations of all underlyings until the time horizon. Calculate the portfolio’s worth per realisation. This will provide a distribution of portfolio values over the time frame. Consider the tail of the distribution: the left-hand 5% tail for 95% confidence, the 1% tail for 99% confidence, and so on.
When working with normal distributions, switching between confidence levels is simple. Refer to the table below for the standardised normal distribution. The square-root rule can be used to transition across time horizons as long as the increase is minimal. The VaR scales with the square root of the time horizon, assuming that the portfolio return is normally distributed.
Pro’s of VAR
Using historical data instead of a parameterized model allows for simulation without relying on the normal-distribution assumption. VaR is a valuable concept in practice for the following reasons.
- VaR is easily calculated for individual instruments, entire portfolios, or at any level right up to an entire bank or fund.
- You can adjust the time horizon depending on your trading style. If you hedge every day you may want a one-day horizon, if you buy and hold for many months, then a longer horizon would be relevant.
- It can be broken down into components, so you can examine different classes of risk, or you can look at the marginal risk of adding new positions to your book.
- VaR can be used to constrain positions of individual traders or entire hedge funds.
- It is easily understood, by management, by investors, by people who are perhaps not that technically sophisticated.
Con’s of VAR
Of course, there are also valid criticisms as well.
- It does not tell you what the loss will be beyond the VaR value.
- VaR is concerned with typical market conditions, not the extreme events.
- It uses historical data, “like driving a car by looking in the rear-view mirror only”.
- Within the time horizon positions could change dramatically (due to normal trading or due to hedging or expiration of derivatives)
Degree of confidence | Number of standard deviations from the mean |
99% | 2.326342 |
98% | 2.053748 |
97% | 1.88079 |
96% | 1.750686 |
95% | 1.644853 |
90% | 1.281551 |
Traditional VaR is often criticised for failing to meet key commonsense criteria. According to Artzner et al. (1997), risk measures must meet specific requirements to be coherent. VaR, as described above, is not coherent.
Other risk-measurement approaches, including as stress testing and volatility stressing, should be utilised with VaR. This is especially important for portfolios with derivatives.
Related Readings
- Put-Call Parity: All You Need To Know
- Modelling Approaches in Quantitative Finance: All You Need To Know
- Central Limit Theorem In Finance: Power Your Portfolio Now
- What is Risk In Finance?