Market Risk

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

*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*

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.

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.^{[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]}

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.

- Systemic risk
- Cost risk
- Demand risk
- Risk modeling
- Risk attitude
- Modern portfolio theory
- Risk return ratio

**^**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
- How hedge funds limit exposure to market risk

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