Time at Risk (TaR) is a time-based
risk measure
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as ban ...
designed for corporate finance practice.
TaR represents certain
quantile
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile ...
for a given probability distribution, so is similar to
Value at Risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by ...
(VaR).
However, TaR measures risk amount as time(time until an adverse event) rather than value (loss amount).
Definition and examples
Mathematical definition of TaR is same as
that of VaR.
However, value-based random variable is replaced with time-based one, and given time-horizon is replaced with given finance structure.
Examples comparing VaR and TaR are as below.
*“An insurance company's 90% VaR is 10 million dollars for 1-year insurance risk.”
: This means it is 90% probability that insurance claim payout would be below 10 million dollars; so if the insurer has accumulated 10 million dollars in cash, it would be 90% safe.
*“An insurance company's 90% TaR is 3 years for liquidity risk under current finance structure.”
: This means it is 90% probability that net liquid assets(= liquid assets - volatile liabilities) would not be run out within 3 years; so for 3 years, the insurer under current finance structure would be 90% safe.
For
confidence level
In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as ...
α,
* VaR can be interpreted as “Required minimum capital to sustain loss”
* TaR can be interpreted as “Maximum period of time that an adverse event would not occur or would be prevented (ie. safe against the event)”
Thus for same α, lower VaR means lower risk and higher TaR means lower risk.
Applications
TaR is a simple measure for whom are familiar with VaR, so is easy to communicate by. TaR also can be used for supplementary purpose to VaR analysis.
Applying TaR in financial models, practitioners can analyze sources of risks and take remedial actions in corporate finance planning;
not only for liquidity risk mentioned above, but also for any risks that demands time-based analysis.
When TaR is applied to a household's financial planning it can measure
longevity risk
A longevity risk is any potential risk attached to the increasing life expectancy of pensioners and policy holders, which can eventually result in higher pay-out ratios than expected for many pension funds and insurance companies.
One important r ...
, and
TaR in this case is referred to as
Age at Risk (AaR).
References
{{Reflist
See also
*
Age at risk
Financial risk
Insurance