Value at Risk (VaR) is defined as the amount which, over a predefined amount of time, losses won't be exceeded with a specified confidence. As such, VaR represents a worst-case scenario at a particular confidence level (e.g. 95%) over a specific time period (e.g. 1 month or 1 year). It is perhaps most relevant when one is particularly concerned with cashflows, but it does not include the time value of money, as there is no discount rate applied to each period's cashflows. VaR is very often used at banks and insurance companies to give some feel for the riskiness of an investment strategy.
VaR is very easy to calculate using Monte Carlo simulation on a cashflow model (for example, the NPV of a Capital Investment model) by calculating the percentile of a specific output (e.g. the 95 or 99 percentile of the potential losses over a 1 year period).
The links to the NPV of a Capital Investment software specific models are provided here:
You set up a cell to sum the cashflows over the period of interest, name it as an output, and run a simulation. If this is done with the above model, adding up the Net Incomes for the first six years, the result looks like the figure below.
The 5th percentile of this distribution is -$173,179. In other words, we are 95% confident of losing no more than $173k in the next six years.
You set up a cell to sum the cashflows over the period of interest, name it as an output, and run a simulation. If this is done with the above model, adding up the Net Incomes for the first six years, the result will have a distribution where the 5th percentile is -$152,413. In other words, we are 95% confident of losing no more than $152k in the next six years.
There are many other ways than VaR to look at financial risk. For example:
- Probability of failing to make the hurdle rate of return (see NPV theory)
- Probability of losing money (the area in the above graph to the left of zero = 71.7%)
- Probability of negative cash flow in any period
- Probability of bankruptcy
- Basel II and credit risk
- Modeling credit risk with a Markov Chain model
Each measure takes a slightly different look at the same cash-flow distributions. The choice of measure or measures of risk one produces should be those that best match the decision processes that management is using.
CVaR
The Conditional Value at Risk (CVaR) is similar to the VaR, and it also represents a worst-case scenario at a particular confidence level (e.g. 95%) over a specific time period (e.g. 1 month or 1 year). However, the CVaR is not the value of the percentile, but it is the mean of all values above the 95 percentile.
A Markov Chain model to estimate the credit risk of a bond portfolio shows the calculations and use of the VaR and CVaR.
