RiskMetrics
Encyclopedia
The RiskMetrics variance
model
(also known as exponential smoother) 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 1998, as client demand for the group's risk management
expertise exceeded the firm's internal risk management resources, RiskMetrics Group was spun off from J.P. Morgan. The technical document was revised in 1996. In 2001, it was revised again in Return to RiskMetrics. In 2006, a new method for modeling risk factor returns was introduced (RM2006). On 25 January 2008, RiskMetrics Group listed on the New York Stock Exchange . In June 2010, RiskMetrics was acquired by MSCI.
and volatility
. By generating future scenarios for each risk factor, we can infer changes in portfolio value and reprice the portfolio for different "states of the world".
of portfolio value, as described by Harry Markowitz
. While comparatively easy to calculate, standard deviation is not an ideal risk measure since it penalizes profits as well as losses.
as the risk measure of choice among investment banks looking to be able to measure their portfolio risk for the benefit of banking regulators. VaR is a downside risk measure, meaning that it typically focuses on losses.
, also known variously as expected tail loss, XLoss, conditional VaR, or CVaR.
An important property of incremental risk is subadditivity. That is, the sum of the incremental risks of the positions in a portfolio equals the total risk of the portfolio. This property has important applications in the allocation of risk to different units, where the goal is to keep the sum of the risks equal to the total risk.
Since there are three risk measures covered by RiskMetrics, there are three incremental risk measures: Incremental VaR (IVaR), Incremental Expected Shortfall (IES), and Incremental Standard Deviation (ISD).
Incremental statistics also have applications to portfolio optimization. A portfolio with minimum risk will have incremental risk equal to zero for all positions. Conversely, if the incremental risk is zero for all positions, the portfolio is guaranteed to have minimum risk only if the risk measure is subadditive.
satisfies the following four properties:
1. Subadditivity
A risk measure is subadditive if for any portfolios A and B, the risk of A+B is never greater than the risk of A plus the risk of B. In other words, the risk of the sum of subportfolios is smaller than or equal to the sum of their individual risks.
Standard deviation and expected shortfall are subadditive, while VaR is not.
Subadditivity is required in connection with aggregation of risks across desks, business units, accounts, or subsidiary companies. This property is important when different business units calculate their risks independently and we want to get an idea of the total risk involved. Subadditivity could also be a matter of concern for regulators, where firms might be motivated to break up into affiliates to satisfy capital requirements.
2. Translation invariance
Adding cash to the portfolio decreases its risk by the same amount.
3. Positive homogeneity of degree 1
If we double the size of every position in a portfolio, the risk of the portfolio will be twice as large.
4. Monotonicity
If losses in portfolio A are larger than losses in portfolio B for all possible risk factor return scenarios, then the risk of portfolio A is higher than the risk of portfolio B.
There are various ways to quantify the error of some estimates. One approach is to estimate a confidence interval of the risk measurement.
can be observed. The covariance matrix can be used to compute portfolio variance. RiskMetrics assumes that the market is driven by risk factors with observable covariance. The risk factors are represented by time series of prices or levels of stocks, currencies, commodities, and interest rates. Instruments are evaluated from these risk factors via various pricing models. The portfolio itself is assumed to be some linear combination of these instruments.
This method has the advantage of simplicity, but as a model, it is slow to adapt to changing market conditions. It also suffers from simulation error, as the number of simulations is limited by the historical period (typically between 250 and 500 business days).
simulation generates random market scenarios drawn from that multivariate normal distribution. For each scenario, the profit (loss) of the portfolio is computed. This collection of profit (loss) scenarios provides a sampling of the profit (loss) distribution from which one can compute the risk measures of choice.
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
model
Statistical model
A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...
(also known as exponential smoother) was first established in 1989, when Sir Dennis Weatherstone
Dennis Weatherstone
Sir Dennis Weatherstone KBE was the former CEO and Chairman of J. P. Morgan & Co.. He attended the Northwest Polytechnic...
, the new chairman of J.P. Morgan
J.P. Morgan & Co.
J.P. Morgan & Co. was a commercial and investment banking institution based in the United States founded by J. Pierpont Morgan and commonly known as the House of Morgan or simply Morgan. Today, J.P...
, 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
Marketplace
A marketplace is the space, actual, virtual or metaphorical, in which a market operates. The term is also used in a trademark law context to denote the actual consumer environment, ie. the 'real world' in which products and services are provided and consumed.-Marketplaces and street markets:A...
, making the substantive research and analysis that satisfied Sir Dennis Weatherstone's request freely available to all market participants.
In 1998, as client demand for the group's risk management
Risk management
Risk management is the identification, assessment, and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor, and control the probability and/or impact of unfortunate events or to maximize the realization of opportunities...
expertise exceeded the firm's internal risk management resources, RiskMetrics Group was spun off from J.P. Morgan. The technical document was revised in 1996. In 2001, it was revised again in Return to RiskMetrics. In 2006, a new method for modeling risk factor returns was introduced (RM2006). On 25 January 2008, RiskMetrics Group listed on the New York Stock Exchange . In June 2010, RiskMetrics was acquired by MSCI.
Risk measurement process
Portfolio risk measurement can be broken down into steps. The first is modeling the market that drives changes in the portfolio's value. The market model must be sufficiently specified so that the portfolio can be revalued using information from the market model. The risk measurements are then extracted from the probability distribution of the changes in portfolio value. The change in value of the portfolio is typically referred to by portfolio managers as profit and loss, or P&L.Risk factors
Risk management systems are based on models that describe potential changes in the factors affecting portfolio value. These risk factors are the building blocks for all pricing functions. In general, the factors driving the prices of financial securities are equity prices, foreign exchange rates, commodity prices, interest rates, correlationCorrelation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
and volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
. By generating future scenarios for each risk factor, we can infer changes in portfolio value and reprice the portfolio for different "states of the world".
Standard deviation
The first widely used portfolio risk measure was the standard deviationStandard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
of portfolio value, as described by Harry Markowitz
Harry Markowitz
Harry Max Markowitz is an American economist and a recipient of the John von Neumann Theory Prize and the Nobel Memorial Prize in Economic Sciences....
. While comparatively easy to calculate, standard deviation is not an ideal risk measure since it penalizes profits as well as losses.
Value at risk
The 1994 tech doc popularized VaRVar
Var, VAR, VAr, VaR or var can mean:VAR* Varna Airport IATA airport code* Vacuum arc remelting, a process for production of steel and special alloys...
as the risk measure of choice among investment banks looking to be able to measure their portfolio risk for the benefit of banking regulators. VaR is a downside risk measure, meaning that it typically focuses on losses.
Expected shortfall
A third commonly used risk measure is expected shortfallExpected shortfall
Expected shortfall is a risk measure, a concept used in finance to evaluate the market risk or credit risk of a portfolio. It is an alternative to value at risk that is more sensitive to the shape of the loss distribution in the tail of the distribution...
, also known variously as expected tail loss, XLoss, conditional VaR, or CVaR.
Marginal VaR
The Marginal VaR of a position with respect to a portfolio can be thought of as the amount of risk that the position is adding to the portfolio. It can be formally defined as the difference between the VaR of the total portfolio and the VaR of the portfolio without the position.Incremental risk
Incremental risk statistics provide information regarding the sensitivity of portfolio risk to changes in the position holding sizes in the portfolio.An important property of incremental risk is subadditivity. That is, the sum of the incremental risks of the positions in a portfolio equals the total risk of the portfolio. This property has important applications in the allocation of risk to different units, where the goal is to keep the sum of the risks equal to the total risk.
Since there are three risk measures covered by RiskMetrics, there are three incremental risk measures: Incremental VaR (IVaR), Incremental Expected Shortfall (IES), and Incremental Standard Deviation (ISD).
Incremental statistics also have applications to portfolio optimization. A portfolio with minimum risk will have incremental risk equal to zero for all positions. Conversely, if the incremental risk is zero for all positions, the portfolio is guaranteed to have minimum risk only if the risk measure is subadditive.
Coherent risk measures
A coherent risk measureCoherent risk measure
In the field of 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...
satisfies the following four properties:
1. Subadditivity
A risk measure is subadditive if for any portfolios A and B, the risk of A+B is never greater than the risk of A plus the risk of B. In other words, the risk of the sum of subportfolios is smaller than or equal to the sum of their individual risks.
Standard deviation and expected shortfall are subadditive, while VaR is not.
Subadditivity is required in connection with aggregation of risks across desks, business units, accounts, or subsidiary companies. This property is important when different business units calculate their risks independently and we want to get an idea of the total risk involved. Subadditivity could also be a matter of concern for regulators, where firms might be motivated to break up into affiliates to satisfy capital requirements.
2. Translation invariance
Adding cash to the portfolio decreases its risk by the same amount.
3. Positive homogeneity of degree 1
If we double the size of every position in a portfolio, the risk of the portfolio will be twice as large.
4. Monotonicity
If losses in portfolio A are larger than losses in portfolio B for all possible risk factor return scenarios, then the risk of portfolio A is higher than the risk of portfolio B.
Assessing risk measures
The estimation process of any risk measure can be wrong by a considerable margin. If from the imprecise estimate we cannot get a good understanding what the true value could be, then the estimate is virtually worthless. A good risk measurement is to supplement any estimated risk measure with some indicator of their precision, or, of the size of its error.There are various ways to quantify the error of some estimates. One approach is to estimate a confidence interval of the risk measurement.
Market models
RiskMetrics describes three models for modeling the risk factors that define financial markets.Covariance approach
The first is very similar to the mean-covariance approach of Markowitz. Markowitz assumed that asset covariance matrix can be observed. The covariance matrix can be used to compute portfolio variance. RiskMetrics assumes that the market is driven by risk factors with observable covariance. The risk factors are represented by time series of prices or levels of stocks, currencies, commodities, and interest rates. Instruments are evaluated from these risk factors via various pricing models. The portfolio itself is assumed to be some linear combination of these instruments.Historical simulation
The second market model assumes that the market only has finitely many possible changes, drawn from a risk factor return sample of a defined historical period. Typically one performs a historical simulation by sampling from past day-on-day risk factor changes, and applying them to the current level of the risk factors to obtain risk factor price scenarios. These perturbed risk factor price scenarios are used to generate a profit (loss) distribution for the portfolio.This method has the advantage of simplicity, but as a model, it is slow to adapt to changing market conditions. It also suffers from simulation error, as the number of simulations is limited by the historical period (typically between 250 and 500 business days).
Monte carlo simulation
The third market model assumes that the logarithm of the return, or, log-return, of any risk factor typically follows a normal distribution. Collectively, the log-returns of the risk factors are multivariate normal. Monte CarloMonte Carlo
Monte Carlo is an administrative area of the Principality of Monaco....
simulation generates random market scenarios drawn from that multivariate normal distribution. For each scenario, the profit (loss) of the portfolio is computed. This collection of profit (loss) scenarios provides a sampling of the profit (loss) distribution from which one can compute the risk measures of choice.
See also
- SunGardSunGardSunGard is a multinational company based in Wayne, Pennsylvania, which provides software and services to education, financial services, and public sector organizations. It was formed in 1983, as a spin-off of the computer services division of Sun Oil Company, during a period of low crude oil...
- largest financial systems company offering financial products and services - GARCH - a non-linear parametric variance estimating model
- Moody's AnalyticsMoody's AnalyticsMoody’s Analytics provides capital markets and risk management professionals with credit analysis, economic research, financial risk management software, and advisory services...
- competitor offering risk management solutions - Algorithmics - competitor offering risk management solutions
- RiskLabRiskLabRiskLab is a laboratory that conducts research in financial risk management. The first was created in 1994 at Eidgenössische Technische Hochschule Zürich in Zurich, Switzerland. In 1996, another one was created independently at the University of Toronto, this time sponsored by the private company...
- Research Institute conducting risk management
External links
- http://www.riskmetrics.com