# Time at risk

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Time at Risk (TaR) is a time-based risk measure designed for corporate finance practice.

In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator. In recent years attention has turned towards convex and coherent risk measurement.

## Contents

TaR represents certain quantile for a given probability distribution, so is similar to Value at Risk (VaR). [1] However, TaR measures risk amount as time(time until an adverse event) rather than value (loss amount).

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 less quantile than the number of groups created. Thus quartiles are the three cut points that will divide a dataset into four equal-sized groups. Common quantiles have special names: for instance quartile, decile. The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.

## Definition and examples

Mathematical definition of TaR is same as that of VaR. [2]

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 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, and TaR in this case is referred to as Age at Risk (AaR).

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.

## Related Research Articles

Insurance is a means of protection from financial loss. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss.

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Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose, given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses.

Adverse selection is a term commonly used in economics, insurance, and risk management that describes a situation where market participation is affected by asymmetric information. When buyers and sellers have different information, it is known as a state of asymmetric information. Traders with better private information about the quality of a product will selectively participate in trades which benefit them the most, at the expense of the other trader. A textbook example is Akerlof's market for lemons.

Market risk is the risk of losses in positions arising from movements in market prices.:

A credit risk is the risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial. In an efficient market, higher levels of credit risk will be associated with higher borrowing costs. Because of this, measures of borrowing costs such as yield spreads can be used to infer credit risk levels based on assessments by market participants.

In finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system, that can be contained therein without harming the entire system. It can be defined as "financial system instability, potentially catastrophic, caused or exacerbated by idiosyncratic events or conditions in financial intermediaries". It refers to the risks imposed by interlinkages and interdependencies in a system or market, where the failure of a single entity or cluster of entities can cause a cascading failure, which could potentially bankrupt or bring down the entire system or market. It is also sometimes erroneously referred to as "systematic 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.

Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial loss and uncertainty about its extent.

In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance.

In accounting, liquidity is a measure of the ability of a debtor to pay their debts as and when they fall due. It is usually expressed as a ratio or a percentage of current liabilities. Liquidity is the ability to pay short-term obligations.

Initially pioneered by financial institutions during the 1970s as interest rates became increasingly volatile, asset and liability management is the practice of managing risks that arise due to mismatches between the assets and liabilities.

A flight-to-quality, or flight-to-safety, is a financial market phenomenon occurring when investors sell what they perceive to be higher-risk investments and purchase safer investments, such as US treasuries or gold. This is considered a sign of fear in the marketplace, as investors seek less risk in exchange for lower profits.

In financial economics, a liquidity crisis refers to an acute shortage of liquidity. Liquidity may refer to market liquidity, funding liquidity, or accounting liquidity. Additionally, some economists define a market to be liquid if it can absorb "liquidity trades" without large changes in price. This shortage of liquidity could reflect a fall in asset prices below their long run fundamental price, deterioration in external financing conditions, reduction in the number of market participants, or simply difficulty in trading assets.

Consumption smoothing is the economic concept used to express the desire of people to have a stable path of consumption. People desire to translate their consumption from periods of high income to periods of low income to obtain more stability and predictability. There exists many states of the world, which means there are many possible outcomes that can occur throughout an individual's life. Therefore, to reduce the uncertainty that occurs, people choose to give up some consumption today to prevent against an adverse outcome in the future.

Bond insurance is a type of insurance whereby an insurance company guarantees scheduled payments of interest and principal on a bond or other security in the event of a payment default by the issuer of the bond or security. As compensation for its insurance, the insurer is paid a premium by the issuer or owner of the security to be insured. Bond insurance is a form of "credit enhancement" that generally results in the rating of the insured security being the higher of (i) the claims-paying rating of the insurer and (ii) the rating the bond would have without insurance.

The interbank lending market is a market in which banks extend loans to one another for a specified term. Most interbank loans are for maturities of one week or less, the majority being overnight. Such loans are made at the interbank rate. A sharp decline in transaction volume in this market was a major contributing factor to the collapse of several financial institutions during the financial crisis of 2007.

Age at Risk (AaR) is a time-based risk measure designed to measure longevity risk in actuarial models.

The Liquidity-at-Risk is a quantity to measure financial risks and is the maximum net liquidity drain relative to the expected liquidity position which should not be exceeded at a given confidence level. The LaR is analog to the Value-at-Risk (VaR) where a quantile of the EBIT-distribution is considered, however it does take stochastic cash flows into account.

## References

1. Jorion, Philippe (2007). Value at risk : the new benchmark for managing financial risk (3. ed.). New York [u.a.]: McGraw-Hill. ISBN   978-0-07-146495-6.
2. Embrechts, Alexander J. McNeil, Rüdiger Frey, Paul (2005). Quantitative risk management : concepts, techniques and tools. Princeton, N.J.: Princeton University Press. ISBN   978-0-691-12255-7.