Value at risk

Value at risk (VaR) is a risk measure that summarizes in a single number the overall risk (value at risk) in a portfolio of financial assets. This value is a function of two parameters: the time horizon (number of days) and the confidence level. As such, it is represented by the loss corresponding to relevant percentile of the distribution of the change in the value of the underlying portfolio over a respective period. If N and X denote the number of days in the period and the confidence level, respectively, then the percentile order is the (100-x)^th. So if N= 10 and X=99, value-at-risk (VaR) is the first percentile of the distribution of changes in the value of the underlying portfolio over the next ten days.

Notwithstanding its wide-spread use and application in many areas,  VaR has a certain weakness: it doesn’t produce consistent results across different return distributions. A more accurate measure that can overcome this shortcoming is known as the expected shortfall or (C-VaR).

Capital at risk

Capital at risk (CaR) is a measure of risk that reflects the probability that the return of initial capital (principal) invested would be doubtful up to a certain degree. If the performance of an investment lies within specified limits, repayment of initial capital invested can be made as per contractual terms. Otherwise, the provider of the capital (invested amount) could lose some or all of the initial capital invested. Generally speaking, capital at risk is defined as the amount of capital that is set aside by an individual or entity as a means by which certain types of risk can be covered.

In the specific context of credit risk, capital at risk (CaR) is measured as a function of the probability distribution of economic loss. The probability distribution of economic loss is, in turn, a function of the distributions and correlations of certain factors: potential replacement cost, default and recovery.

Capital at risk should not be confused with capital risk or risk capital. Capital risk represents the risk arising from the partial or total investment amount that is invested and is exposed to risk of loss. For example, if an individual has initially invested $5,000 in stocks. This initial investment is the capital invested or paid in. Therefore, the capital risk here is $5,000, irrespective of the current market value of these stocks at a certain point in time (that might be greater or smaller than the original capital invested.

Risk capital, on the other hand, refers to amounts of money allocated to high-risk venues (e.g., speculative activity, high-risk, high-reward investments). However, and in general contexts, all types of monetary and non-monetary assets that are exposed to potential losses in value are classified as risk capital.

In short

Capital at risk (CaR) conceptually and practically differs from value at risk (VaR). Though both CaR and VaR are popular financial risk assessment and risk management tools, CaR is essentially the amount of capital that is set aside to cover and absorb future potential losses. For example, an insurance firm is required to maintain a surplus amount of cash, out of the premiums it receives, in case it has to pay for losses and expenses that exceed the premiums received. The amount of this surplus is corresponds to capital at risk.  It represents the amount of capital at risk that insurance firms must set aside based on the number of estimated claims and the amount of actual premiums.

VaR, on the other hand, is a metric applied to account for a potential worst-case investment scenario over a particular time frame. For example, if an entity has a 95% one-day VaR of $10,000, this would be interpreted as a 5% chance that its minimum loss will be $10,000 in a single day (the defined time frame). In other words, VaR reflects is a worst-case scenario. From a different perspective, this VaR means it can be 95% confident that its losses will not exceed $10,000 in a single day.