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Time-at-risk
Time at Risk (TaR) is a time-based risk measure designed for corporate finance practice. TaR represents certain quantile for a given probability distribution, so is similar to Value at Risk (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(= ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, such as banks and insurance companies, acceptable to the regulator (economics), regulator. In recent years attention has turned to coherent risk measure, convex and coherent risk measurement. Mathematically A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns. The common notation for a risk measure associated with a random variable X is \rho(X). A risk measure \rho: \mathcal \to \mathbb \cup \ should have certain properties: ; Normalized : \rho(0) = 0 ; Translative : \mathrm\; a \in \mathbb \; \mathrm \; Z \in \mathcal ,\;\mathrm\; \rho(Z + a) = \rho(Z) - a ; Monotone : \mathrm\; Z_1,Z_2 \in \mathcal \;\mathrm\; Z_1 \leq Z_2 ,\; \mathrm \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 than the number of groups created. Common quantiles have special names, such as '' quartiles'' (four groups), '' deciles'' (ten groups), and '' percentiles'' (100 groups). 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. -quantiles are values that partition a finite set of values into subsets of (nearly) equal sizes. There are partitions of the -quantiles, one for each integer satisfying . In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given portfolio, time horizon, and probability ''p'', the ''p'' VaR can be defined informally as the maximum possible loss during that time after excluding all worse outcomes whose combined probability is at most ''p''. This assumes mark-to-market pricing, and no trading in the portfolio. For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by $1 million or more over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 sold due to lack of liquidity in the market – essentially a sub-set of market risk. This can be accounted for by: * Widening bid–ask spread * Making explicit liquidity reserves * Lengthening holding period for value at risk (VaR) calculations Funding liquidity – Risk that liabilities: * Cannot be met when they fall due * Can only be met at an uneconomic price * Can be name-specific or systemic Causes Liquidity risk arises from situations in which a party interested in trading an asset cannot do it because nobody in the market wants to trade for that asset. Liquidity risk becomes particularly important to parties who are about to hold or currently hold an asset, since it affects their ability to trade. Manifestation of liquidity r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 risk to individuals who are spending down savings is that they will live longer than expected, and thus exhaust their savings, dying in poverty or burdening relatives. This is also referred to as "outliving one's savings" or "outliving one's assets". Individuals Individuals often underestimate longevity risk. In the United States, most retirees do not expect to live past 85, but this is in fact the median conditional life expectancy for men at 65 (half of 65-year-old men will live to 85 or older, and more women will). Low interest rates and declining returns exacerbating longevity risk The collapse in returns on government bonds is taking place against the backdrop of a protracted fall in returns for other core assets such as blue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Risk
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. Modern portfolio theory initiated by Harry Markowitz in 1952 under his thesis titled "Portfolio Selection" is the discipline and study which pertains to managing market and financial risk. In modern portfolio theory, the variance (or standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...) of a portfolio is used as the definition of risk. Types According to Bender and Panz (2021), financial risks can be sorted into five different categories. In their study, they apply an algorith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
