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 downside risk, risks taken by financial institutions ...
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 t ...
for a given
probability distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...
, so is similar to
Value at Risk
Value at risk (VaR) is a measure of the risk of loss of investment/capital. 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 us ...
(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
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathema ...
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
Liquidity risk is a financial risk that for a certain period of time a given financial asset, security or commodity cannot be traded quickly enough in the market without impacting the market price.
Types
Market liquidity – An asset cannot be ...
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 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 ...
, and
TaR in this case is referred to as
Age at Risk (AaR).
References
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See also
*
Age at risk
Financial risk
Insurance