What is monotonicity in coherent risk measure?

What is monotonicity in coherent risk measure?

A measure of risk is said coherent if it is monotone, sub-‐additive, positive homogeneous and translation invariant. Monotonicity means that, if Z1 and Z2 are two losses and Z1 is smaller than Z2, then the value of the risk measure in Z2 is greater than the value of the risk measure in Z1.

Which risk measures are coherent?

A functional → is said to be coherent risk measure for if it satisfies the following properties:

• Normalized.
• Monotonicity.
• Sub-additivity.
• Positive homogeneity.
• Translation invariance.
• Convex risk measures.
• Value at risk.
• Average value at risk.

What is financial risk measures?

Risk measures are statistical measures that are historical predictors of investment risk and volatility, and they are also major components in modern portfolio theory (MPT). MPT is a standard financial and academic methodology for assessing the performance of a stock or a stock fund as compared to its benchmark index.

What is the best risk measure?

A comparison of standard measures. Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR).

Is VaR a coherent risk measure?

In other words, VaR is not a “coherent” measure of risk. This problem is caused by the fact that VaR is a quantile on the distribution of profit and loss and not an expectation, so that the shape of the tail before and after the VaR probability need not have any bearing on the actual VaR number.

Is volatility a coherent risk measure?

The standard deviation is always coherent. Notice that standard deviation, in finance, is often called volatility. The proofs are exactly as those we consider here below for the standard deviation.

Does higher standard deviation mean more risk?

In investing, standard deviation is used as an indicator of market volatility and thus of risk. The higher the standard deviation, the riskier the investment.

What is risk measurement techniques?

The process involves identifying and analyzing the amount of risk involved in an investment, and either accepting that risk or mitigating it. Some common measures of risk include standard deviation, beta, value at risk (VaR), and conditional value at risk (CVaR).

What are the 3 types of risks?

There are different types of risks that a firm might face and needs to overcome. Widely, risks can be classified into three types: Business Risk, Non-Business Risk, and Financial Risk.

Is volatility a good measure of risk?

Volatility gives certain information about the dispersion of returns around the mean, but gives equal weight to positive and negative deviations. Moreover, it completely leaves out extreme risk probabilities. Volatility is thus a very incomplete measure of risk.

Is VaR a spectral risk measure?

A spectral risk measure (SRM) is a risk measure that is calculated as a weighted average of outcomes, the weights of which depend on the user’s risk aversion. Unlike value at risk (VaR), for example, it is an example of a ‘coherent risk measure’ as described in the field of mathematical finance.

Why is VaR not considered a coherent measure of risk?