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**Market risk** is the risk of losses in positions arising from movements in market prices.:^{ [1] }

- Risk management
- Measuring the potential loss amount due to market risk
- Regulatory views
- Use in annual reports of U.S. corporations
- See also
- References
- External links

*Equity risk*, the risk that stock or stock indices (e.g. Euro Stoxx 50, etc. ) prices or their implied volatility will change.*Interest rate risk*, the risk that interest rates (e.g. Libor, Euribor, etc.) or their implied volatility will change.*Currency risk*, the risk that foreign exchange rates (e.g. EUR/USD, EUR/GBP, etc.) or their implied volatility will change.*Commodity risk*, the risk that commodity prices (e.g. corn, crude oil) or their implied volatility will change.*Margining risk*results from uncertain future cash outflows due to margin calls covering adverse value changes of a given position.*Shape risk**Holding period risk**Basis risk*

**Equity risk** is "the financial risk involved in holding equity in a particular investment". Equity risk often refers to equity in companies through the purchase of stocks, and does not commonly refer to the risk in paying into real estate or building equity in properties.

The **stock** of a corporation is all of the shares into which ownership of the corporation is divided. In American English, the shares are commonly known as "stocks." A single share of the stock represents fractional ownership of the corporation in proportion to the total number of shares. This typically entitles the stockholder to that fraction of the company's earnings, proceeds from liquidation of assets, or voting power, often dividing these up in proportion to the amount of money each stockholder has invested. Not all stock is necessarily equal, as certain classes of stock may be issued for example without voting rights, with enhanced voting rights, or with a certain priority to receive profits or liquidation proceeds before or after other classes of shareholders.

The **EURO STOXX 50** is a stock index of Eurozone stocks designed by STOXX, an index provider owned by Deutsche Börse Group. According to STOXX, its goal is "to provide a blue-chip representation of Supersector leaders in the Eurozone". It is made up of fifty of the largest and most liquid stocks. The index futures and options on the EURO STOXX 50, traded on Eurex, are among the most liquid such products in Europe and the world.

All businesses take risks based on two factors: the probability an adverse circumstance will come about and the cost of such adverse circumstance. Risk management is the study of how to control risks and balance the possibility of gains.

**Risk management** is the identification, evaluation, and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor, and control the probability or impact of unfortunate events or to maximize the realization of opportunities.

As with other forms of risk, the potential loss amount due to market risk may be measured in a number of ways or conventions. Traditionally, one convention is to use value at risk (VaR). The conventions of using VaR are well established and accepted in the short-term risk management practice.

**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.

However, VaR contains a number of limiting assumptions that constrain its accuracy. The first assumption is that the composition of the portfolio measured remains unchanged over the specified period. Over short time horizons, this limiting assumption is often regarded as reasonable. However, over longer time horizons, many of the positions in the portfolio may have been changed. The VaR of the unchanged portfolio is no longer relevant. Other problematic issues with VaR is that it is not sub-additive, and therefore not a coherent risk measure.^{ [2] } As a result, other suggestions for measuring market risk is Conditional Value-at-Risk (CVaR) that is coherent for general loss distributions, including discrete distributions and is sub-additive.^{ [3] }

The variance covariance and historical simulation approach to calculating VaR assumes that historical correlations are stable and will not change in the future or breakdown under times of market stress. However these assumptions are inappropriate as during periods of high volatility and market turbulence, historical correlations tend to break down. Intuitively, this is evident during a financial crisis where all industry sectors experience a significant increase in correlations, as opposed to an upwards trending market. This phenomenon is also known as asymmetric correlations or asymmetric dependence. Rather than using Historical Simulation, Monte-Carlo simulations with well-specified multivariate models are an excellent alternative. For example, to improve the estimation of the variance covariance matrix, one can generate a forecast of asset distributions via Monte-Carlo simulation based upon the Gaussian copula and well-specified marginals.^{ [4] } Allowing the modeling process to allow for empirical characteristics in stock returns such as auto-regression, asymmetric volatility, skewness, and kurtosis is important. Not accounting for these attributes lead to severe estimation error in the correlation and variance covariance that have negative biases (as much as 70% of the true values).^{ [5] } Estimation of VaR or CVaR for large portfolios of assets using the variance covariance matrix may be inappropriate if the underlying returns distributions exhibit asymmetric dependence. In such scenarios, vine copulas that allow for asymmetric dependence (e.g., Clayton, Rotated Gumbel) across portfolios of assets are most appropriate in the calculation of tail risk using VaR or CVaR.^{ [6] }

**Historical simulation** in finance's value at risk (VaR) analysis is a procedure for predicting the value at risk by 'simulating' or constructing the cumulative distribution function (CDF) of assets returns over time. Unlike parametric VaR models, historical simulation does not assume a particular distribution of the asset returns. Also, it is relatively easy to implement. However, there are a couple of shortcomings of historical simulation. Historical simulation applies equal weight to all returns of the whole period; this is inconsistent with the diminishing predictability of data that are further away from the present.

In addition, care has to be taken regarding the intervening cash flow, embedded options, changes in floating rate interest rates of the financial positions in the portfolio. They cannot be ignored if their impact can be large.

The Basel Committee did set revised Minimum capital requirements for market risk in January 2016. These revisions will address deficiencies relating to;

- Boundary between the trading book and banking book
- Internal models approach for market risk
- The standardised approach for market risk
- Use of Value at risk v/s Expected shortfall to measure of risk under stress
- The risk of market illiquidity

In the United States, a section on market risk is mandated by the SEC ^{ [7] } in all annual reports submitted on Form 10-K. The company must detail how its own results may depend directly on financial markets. This is designed to show, for example, an investor who believes he is investing in a normal milk company, that the company is in fact also carrying out non-dairy activities such as investing in complex derivatives or foreign exchange futures.

**Financial economics** is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on *both sides* of a trade". Its concern is thus the interrelation of financial variables, such as prices, interest rates and shares, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital.

In finance, the **capital asset pricing model** (**CAPM**) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.

**Harry Max Markowitz** is an American economist, and a recipient of the 1989 John von Neumann Theory Prize and the 1990 Nobel Memorial Prize in Economic Sciences.

**Modern portfolio theory** (**MPT**), or **mean-variance analysis**, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. It uses the variance of asset prices as a proxy for risk.

In finance, the **beta** of an investment indicates whether the investment is more or less volatile than the market as a whole.

In probability theory and statistics, a **copula** is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform. Copulas are used to describe the dependence between random variables. Their name comes from the Latin for "link" or "tie", similar but unrelated to grammatical copulas in linguistics. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio-optimization applications.

**Financial modeling** is the task of building an abstract representation of a real world financial situation. This is a mathematical model designed to represent the performance of a financial asset or portfolio of a business, project, or any other investment.

**Financial risk modeling** is the use of formal econometric techniques to determine the aggregate risk in a financial portfolio. Risk modeling is one of many subtasks within the broader area of financial modeling.

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.

The following outline is provided as an overview of and topical guide to finance:

The **RiskMetrics** variance model was first established in 1989, when Sir Dennis Weatherstone, the new chairman of J.P. Morgan, asked for a daily report measuring and explaining the risks of his firm. Nearly four years later in 1992, J.P. Morgan launched the RiskMetrics methodology to the marketplace, making the substantive research and analysis that satisfied Sir Dennis Weatherstone's request freely available to all market participants.

In finance, **volatility** is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.

In finance, **model risk** is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, model risk is more and more prevalent in activities other than financial securities valuation, such as assigning consumer credit scores, real-time probability prediction of fraudulent credit card transactions, and computing the probability of air flight passenger being a terrorist. Rebonato in 2002 defines model risk as "the risk of occurrence of a significant difference between the mark-to-model value of a complex and/or illiquid instrument, and the price at which the same instrument is revealed to have traded in the market".

**News analysis** refers to the measurement of the various qualitative and quantitative attributes of textual news stories. Some of these attributes are: sentiment, relevance, and novelty. Expressing news stories as numbers and metadata permits the manipulation of everyday information in a mathematical and statistical way.

**Credit valuation adjustment** (**CVA**) is the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the market value of counterparty credit risk. This price depends on counterparty credit spreads as well as on the market risk factors that drive derivatives’ values and, therefore, exposure. CVA is one of a family of related valuation adjustments, collectively xVA; for further context here see Financial economics #Derivative pricing.

**Portfolio optimization** is the process of selecting the best portfolio, out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk. Factors being considered may range from tangible to intangible.

**Mathematical finance**, also known as **quantitative finance**, is a field of applied mathematics, concerned with mathematical modeling of financial markets. Generally, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock. The fundamental theorem of arbitrage-free pricing is one of the key theorems in mathematical finance, while the Black–Scholes equation and formula are amongst the key results.

**Financial correlations** measure the relationship between the changes of two or more financial variables over time. For example, the prices of equity stocks and fixed interest bonds often move in opposite directions: when investors sell stocks, they often use the proceeds to buy bonds and vice versa. In this case, stock and bond prices are negatively correlated.

An **X-Value Adjustment** is a generic term referring collectively to a number of different “Valuation Adjustments” in relation to derivative instruments held by banks. The purpose of these is twofold: primarily to hedge for possible losses due to counterparty default; but also, to determine the amount of capital required under Basel III. For a discussion as to the impact of xVA on the bank's overall balance sheet, return on equity, and dividend policy, see: XVA has, in many institutions, led to the creation of specialized desks. Note that the various XVA require careful and correct aggregation without double counting.

- ↑ Bank for International Settlements: A glossary of terms used in payments and settlement systems There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most commonly used types of market risk are om Wikipedia, the free encyclopedia Jump to navigation Jump to search Categories of Financial risk Solidus-Constantius Gallus-thessalonica RIC 149.jpg Credit risk Concentration risk Market risk Interest rate risk Currency risk Equity risk Commodity risk Liquidity risk Refinancing risk Operational risk Country risk Legal risk Model risk Political risk Valuation risk Reputational risk Volatility risk Settlement risk Profit risk Systemic risk v t e Bank regulation and standards Bank for International Settlements Basel Accords (Basel I, Basel II, Basel III, Basel IV) Financial Stability Board Background Banking (Regulation) Monetary policy Central bank Risk Risk management Regulatory capital Tier 1 Tier 2 Pillar 1: Regulatory capital Credit risk Standardized IRB Approach F-IRB A-IRB PD LGD EAD Operational risk Basic Standardized AMA Market risk Duration Value at risk Pillar 2: Supervisory review Economic capital Liquidity risk Legal risk Pillar 3: Market disclosure Disclosure Business and Economics Portal v t e Market risk is the risk of losses in positions arising from movements in market prices.[1] There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most commonly used types of market risk are[2]: Equity risk, the risk that stock or stock indices (e.g. Euro Stoxx 50, etc. ) prices or their implied volatility will change. Interest rate risk, the risk that interest rates (e.g. Libor, Euribor, etc.) or their implied volatility will change. Currency risk, the risk that foreign exchange rates (e.g. EUR/USD, EUR/GBP, etc.) or their implied volatility will change. Commodity risk, the risk that commodity prices (e.g. corn, crude oil) or their implied volatility will change. Margining risk results from uncertain future cash outflows due to margin calls covering adverse value changes of a given position. Shape risk Holding period risk Basis risk Contents 1 Risk management 2 Measuring the potential loss amount due to market risk 3 Regulatory views 4 Use in annual reports of U.S. corporations 5 See also 6 References 7 External links Risk management All businesses take risks based on two factors: the probability an adverse circumstance will come about and the cost of such adverse circumstance. Risk management is the study of how to control risks and balance the possibility of gains. Measuring the potential loss amount due to market risk As with other forms of risk, the potential loss amount due to market risk may be measured in a number of ways or conventions. Traditionally, one convention is to use value at risk (VaR). The conventions of using VaR are well established and accepted in the short-term risk management practice. However, VaR contains a number of limiting assumptions that constrain its accuracy. The first assumption is that the composition of the portfolio measured remains unchanged over the specified period. Over short time horizons, this limiting assumption is often regarded as reasonable. However, over longer time horizons, many of the positions in the portfolio may have been changed. The VaR of the unchanged portfolio is no longer relevant. Other problematic issues with VaR is that it is not sub-additive, and therefore not a coherent risk measure.[3] As a result, other suggestions for measuring market risk is Conditional Value-at-Risk (CVaR) that is coherent for general loss distributions, including discrete distributions and is sub-additive.[4] The variance covariance and historical simulation approach to calculating VaR assumes that historical correlations are stable and will not change in the future or breakdown under times of market stress. However these assumptions are inappropriate as during periods of high volatility and market turbulence, historical correlations tend to break down. Intuitively, this is evident during a financial crisis where all industry sectors experience a significant increase in correlations, as opposed to an upwards trending market. This phenomenon is also known as asymmetric correlations or asymmetric dependence. Rather than using Historical Simulation, Monte-Carlo simulations with well-specified multivariate models are an excellent alternative. For example, to improve the estimation of the variance covariance matrix, one can generate a forecast of asset distributions via Monte-Carlo simulation based upon the Gaussian copula and well-specified marginals.[5] Allowing the modeling process to allow for empirical characteristics in stock returns such as auto-regression, asymmetric volatility, skewness, and kurtosis is important. Not accounting for these attributes lead to severe estimation error in the correlation and variance covariance that have negative biases (as much as 70% of the true values).[6] Estimation of VaR or CVaR for large portfolios of assets using the variance covariance matrix may be inappropriate if the underlying returns distributions exhibit asymmetric dependence. In such scenarios, vine copulas that allow for asymmetric dependence (e.g., Clayton, Rotated Gumbel) across portfolios of assets are most appropriate in the calculation of tail risk using VaR or CVaR.[7] In addition, care has to be taken regarding the intervening cash flow, embedded options, changes in floating rate interest rates of the financial positions in the portfolio. They cannot be ignored if their impact can be large. Regulatory views The Basel Committee did set revised Minimum capital requirements for market risk in January 2016. These revisions will address deficiencies relating to; Boundary between the trading book and banking book Internal models approach for market risk The standardised approach for market risk Use of Value at risk v/s Expected shortfall to measure of risk under stress The risk of market illiquidity Use in annual reports of U.S. corporations In the United States, a section on market risk is mandated by the SEC[8] in all annual reports submitted on Form 10-K. The company must detail how its own results may depend directly on financial markets. This is designed to show, for example, an investor who believes he is investing in a normal milk company, that the company is in fact also carrying out non-dairy activities such as investing in complex derivatives or foreign exchange futures. See also Systemic risk Cost risk Demand risk Risk modeling Risk attitude Modern portfolio theory Risk return ratio References Bank for International Settlements: A glossary of terms used in payments and settlement systems [1] "Example Domain". www.example.com. Retrieved 2017-09-25. Artzner, P.; Delbaen, F.; Eber, J.; Heath, D. (July 1999). "Coherent measure of risk". Mathematical Finance. 9 (3): 203–228. doi:10.1111/1467-9965.00068. Rockafellar, R.; Uryasev, S. (July 2002). "Conditional value-at-risk for general loss distributions". Journal of Banking & Finance. 26 (7): 1443–1471. doi:10.1016/S0378-4266(02)00271-6. Low, R.K.Y.; Faff, R.; Aas, K. (2016). "Enhancing mean–variance portfolio selection by modeling distributional asymmetries". Journal of Economics and Business. 85: 49. doi:10.1016/j.jeconbus.2016.01.003. Fantazzinni, D. (2009). "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study". Computational Statistics & Data Analysis,. 53 (6): 2168–2188. doi:10.1016/j.csda.2008.02.002. Low, R.K.Y.; Alcock, J.; Faff, R.; Brailsford, T. (2013). "Canonical vine copulas in the context of modern portfolio management: Are they worth it?". Journal of Banking & Finance. 37 (8): 3085. doi:10.1016/j.jbankfin.2013.02.036. FAQ on the United States SEC Market Disclosure Rules Dorfman, Mark S. (1997). Introduction to Risk Management and Insurance (6th ed.). Prentice Hall. ISBN 0-13-752106-5. title=Example Domain|website=www.example.com|access-date=2017-09-25}}
- ↑ Artzner, P.; Delbaen, F.; Eber, J.; Heath, D. (July 1999). "Coherent measure of risk".
*Mathematical Finance*.**9**(3): 203–228. doi:10.1111/1467-9965.00068. - ↑ Rockafellar, R.; Uryasev, S. (July 2002). "Conditional value-at-risk for general loss distributions".
*Journal of Banking & Finance*.**26**(7): 1443–1471. doi:10.1016/S0378-4266(02)00271-6. - ↑ Low, R.K.Y.; Faff, R.; Aas, K. (2016). "Enhancing mean–variance portfolio selection by modeling distributional asymmetries".
*Journal of Economics and Business*.**85**: 49. doi:10.1016/j.jeconbus.2016.01.003. - ↑ Fantazzinni, D. (2009). "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study".
*Computational Statistics & Data Analysis*.**53**(6): 2168–2188. doi:10.1016/j.csda.2008.02.002. - ↑ Low, R.K.Y.; Alcock, J.; Faff, R.; Brailsford, T. (2013). "Canonical vine copulas in the context of modern portfolio management: Are they worth it?".
*Journal of Banking & Finance*.**37**(8): 3085. doi:10.1016/j.jbankfin.2013.02.036. - ↑ FAQ on the United States SEC Market Disclosure Rules

- Dorfman, Mark S. (1997).
*Introduction to Risk Management and Insurance (6th ed.)*. Prentice Hall. ISBN 0-13-752106-5.

- Managing market risks by forward pricing
- Bank Management and Control, Springer - Management for Professionals, 2014
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