What is VaR (Value at Risk)?

VaR (Value at Risk) is a fairly comment metric that institutions such as commercial banks and hedge funds use to calculate their risk. What type of risk? More specifically, it calculates how much you can lose on an investment.

A dictionary definition of VaR would be, "a statistic that quantifies the extent of possible financial losses within a firm, portfolio, or position over a specific time frame." For example, a "3% one-month VaR of 2%" means that the portfolio has a 3% chance of declining in value by 2% over the next month.

Because the markets are very random and no one can exactly predict the future, we can say that the outcome of our portfolio will land in a bell-shaped distribution depending on the random events that happen in the future.

If you want to know how much you might lose in your portfolio over the next month, you can just use a confidence interval. If you remember that bell-shaped curve from statistics, you can have a 95% confidence interval where you say, "I am 95% confident that my outcome will be above this number." See the example below...

In this example, we are 95% confident that our return will be above $42m. However, in 5% of cases, our return will be below $42m. This $42m figure is our VaR and is used to estimate the greatest loss on a statistical probability.

Calculating VaR

There are multiple ways to compute VaR. One such way is the Historical Method. In the Historical Method, one collects historical price data for the asset or portfolio over a specified period and then calculates the returns for each period, such as daily returns. These returns are ranked from worst to best, and the VaR is determined by selecting the return at the desired confidence level, such as the 5th percentile for a 95% confidence level. This approach assumes that historical market behavior is indicative of future risks, without making any assumptions about the distribution of returns.

An additional way you can calculate VaR is by using the Parametric Method. The Parametric Method, also known as the variance-covariance method, calculates VaR by assuming a specific statistical distribution of returns, typically a normal distribution. This method involves calculating the mean and standard deviation of historical returns for the asset or portfolio. With these parameters, and assuming a normal distribution, one chooses a confidence level (e.g., 95% or 99%) and uses the corresponding z-score to calculate VaR, just like the example shown above.

A third way to calculate VaR is the Monte Carlo Method. The Monte Carlo Method involves taking your portfolio and simulating potential scenarios many many times, randomly changing the different inputs. By simulating an abundance of scenarios, the user is able to calculate the distribution of potential outcomes and thereby compute VaR. The more situations you simulate, the more accurate the model. It is akin to flipping a coin over and over again. If you flip it 10 times and you get 7 heads and 3 tails, it would be a mistake to assume that the probability of flipping heads is 70% and tails 30%. However, if you flip the coin millions of times, you will be able to more accurately find the true distribution of 50/50.

CVaR (Conditional Value at Risk)

An extension off of VaR is the metric CVaR or Conditional Value at Risk. CVaR, also known as expected shortfall, essentially aims to answer the question, "in those 5% of situations where my return is below VaR, how much am I going to lose?"

To calculate CVaR you basically take the weighted average of the losses in the tail of the distribution below the VaR. For example, for the VaR above of $42m you might find that the CVaR or average losses in extreme situations is $35m.

CVaR is very useful as it helps one focus on the expected loss (what might go wrong) versus the loss limit (where extensive losses might begin). VaR (although not perfect) is an essential part of many risk management strategies and helps financial firms protect themselves from potential blow ups.