Frequently Asked Questions - Market Risk
Market Risk
This section gives a more detailed breakdown of the functionality that
is available in the market risk section of the website. It attempts to explain the different types of
position that may be entered, the risk metrics that may be used to analyse the positions and the basic
hedging functionality that is available to better understand the risk to which the user is exposed. It is
not intended as an introduction to risk analysis. However if the explanations are not clear, or are in fact
missing for something that you feel is necessary, please let us know and we will update the section.
Asynchronous Risk Aggregation: ARA
This is a risk metric that ignores the positive impacts of
offsetting positions at a given aggregation level. On the principal that when things go wrong, they all go wrong together, it
takes the most extreme day of a portfolio at a risk sector level, and then sums those extreme moves. This is generally
a big number. The lower you go on a risk sector level, the bigger it gets. Its purpose is to let risk managers know when
things are going totally wrong. Given normal fat tailed (non local lepto...) distributions VaR and other confidence interval type
metrics will always be hit more often than (not very statistically) expected. Thin tailed assets (platy..) that used to
be fat are the killer
to this analysis. BDaO, used over a much longer time scale than
VaR, ES or EC, gives a more depressing description of what happens when it all goes wrong together. It does not have a
secure statistical basis, but on the assumption that what has happened before, will happen again, this is what happens
to you if it all happens tomorrow. It may be positive.
Burg Divergence
The Burg divergence is used to study the evolution of the covariance matrix of the portfolio. When one constructs a portfolio,
one of the key measures that is used is the expected volatility of the portfolio. If one looks through the portfolio to its
individual components, this is effectively represented as the co-variance matrix of the portfolio. There is no attempt here
to deny the manifest benefit of diversification. However what starts off as a diversified portfolio may lose that diversification over time.
Whilst this may not be apparent in either the performance or the volatility at an aggregate portfolio level, changes in the underlying
co-variance matrix may be observed by increases in the Burg Divergence.
CFD: Cash for Difference Contract
A cash for difference contract (CFD) is a financial derivative that allows users to
gain exposure to financial instruments without having to actually buy the underlying instrument. In effect,
it is a purely a contract between the client and a broker. The terms of the contract imply that the difference
between the current price of an instrument and the price at which the contract was struck, the execution price,
will be paid to whosoever is in profit, client or broker, in the underlying currency of the financial instrument.
In addition, there is the size of the position, which is in effect a multiplier on the sum that is to be paid.
An example is a CFD on the Dax index. If a client goes long the Dax at an execution price of 5900, in a size of
10/pt and the price of the Dax drops to 5850, the client will owe the broker 500. This is determined, from the
clients perspective by the calculation (5850 - 5950) * 10. The currency will be in Euros because the base currency
of the Dax index is in Euros. A further wrinkle on this scenario is that it is possible to have CFD's on futures
contracts. In this case there will be an additional multiplier that relates to the size of the contract. For the
example shown above, the Dax future contract as traded on the Eurex exchange has a unit size of 25/pt. That is,
the amount owing or owed on every 1/pt CFD on the DAX futures contract will change by 25 for every point
that the Dax futures contract moves from the execution price. RiskSystem maintains a database of the appropriate
multiplier (risk factor) for CFD contracts which is automatically loaded when and particular intrument type is
selected. However it is not infallible. If you think that the default risk factor with which you have been supplied is
wrong, please adjust as you think appropriate and please let us know.
Component Value at Risk: C-VaR
The C-VaR of an instrument is a measure of the impact of an individual position on the
overall risk of the portfolio. Whilst the individual VaRs of the instruments has importance, in a portfolio, it is only the impact of that risk on
the risk of the portfolio that has primary importance. at RiskSystem C-VaR is also used in Reduced Set Hedging to reduce the calculation time of a
hedge portfolio
Current Portfolio
The current portfolio gives a detailed view of all the position data that is currently
held by a client on the RiskSystem databases. It effectively replicates the information that was supplied by
the user when the position was entered. If is does not, it would be very much appreciated if you could contact
us ASAP as that constitutes a proper problem. As well as the basic position information it also gives Market (Mkt)
and Risk information. The market column reflects an indicative market price for the asset to which the user is
exposed. It is not in any way real-time, but under most conditions (excluding week-ends and holidays) it should not
be more than 24 hours stale. This reflects the ethos of RiskSystem that it is a risk site, not a pricing site. If the
actual price is seriously relevant, then hopefully the system has allowed you to avoid the bullet, but chances are
that you are not too worried about the expectation of bad times, more likely the realisation. However, its value is in
allowing the user to see if the price that we are using is in the general vicinity of the price of the asset to which
they are exposed. Please note that many FSB/CFD providers scale up asset prices (EUR/USD scaling from a market price
of 1.3111 to 13111 for example) in oder to make the contract price more understandable. So long as the applied risk
factor (in this case 10,000) is correct, there should be no need for concern. The risk figure is that calculated
using your current risk metric preference and base currency preference. The defaults are Value at Risk and USD, however
these are easily changed in the Risk Analysis/Preference/Risk Analysis page.
The positions may be deleted by hitting the delete button associated with each position.
The position may be edited by hitting the edit button. In this case the position will be deleted from the database
and the position details will be moved into the upper half of the screen. After you have edited the details as you require,
hit the update portfolio button to save the details to the database. If you use a particular asset on a general basis, and
you have an aversion to the dropdown menus, instead of deleting a position when you are not exposed to that asset, edit
it with a position size of zero. In this case when you next gain exposure, just use the edit function to reflect the
exposure.
Economic Capital: ES
Economic Capital (ES) is a risk metric that attempts to determine possible extreme changes in the
value of a portfolio from a historical simulation of the performance of the portfolio. On the basis of it happened before so it
can happen again, it gives a (vaguely) statistical metric of potentially extreme price changes in the value of the users
portfolio. As such, it uses the preferences that the user has selected for the VaR risk metric.
Economic capital is a difficult area to model, however within the restricted area of exchange traded instruments
for which this site is intended for use, the EC model reflects standard academic prejudices. Please be aware however
that unless you use an appropriate OutSample Window period (1 year recommended), the risk number will be low.
Expected Shortfall: ES
Expected Shortfall (ES) is a risk metric that attempts to determine possible extreme changes in the
value of a portfolio from a historical simulation of the performance of the portfolio. On the basis of it happened before so it
can happen again, it gives a (vaguely) statistical metric of potentially extreme price changes in the value of the users
portfolio. As such, it uses the preferences that the user has selected for the VaR risk metric.
In contrast to VaR however it averages over the moves on the days that the portfolio made or lost more than the VaR number
to come up with a larger number. Irrespective of using a (very) small number of datapoints on which to hang your metric
it has the very cool property of being a coherent risk metric.
Forward Instruments
Forward instruments are those whose settlement date is greater than three days (a somewhat
arbitrary number it may be admitted) of the execution date. The options available are FSB and CFD. Notwithstanding the
fact that FSB and CFD contracts are extant from their execution date, oftentimes the contract has an expiry date that
is short (months or less). This is reflected in the fact that selecting a forward instrument type will mean that an expiry
date option will be given to the user. The default expiry date is one month from the entry of the position, but may be adjusted
by the user. This is relevant because after the expiry date, the risk of that position will be held at zero.
FSB: Financial Spread Bet Contract
A financial spread bet contract (FSB) is a financial derivative that allows users to
gain exposure to financial instruments without having to actually buy the underlying instrument. In effect,
it is a purely a contract between the client and a broker. The terms of the contract imply that the difference
between the current price of an instrument and the price at which the contract was struck, the execution price,
will be paid to whosoever is in profit, client or broker, in the base currency of the client account.
In addition, there is the size of the position, which is in effect a multiplier on the sum that is to be paid.
An example is a FSB on the S&P index for a client whose base currency is Euros. If a client goes long the S&P at an execution price of 1210, in a size of
10/pt and the price of the S&P drops to 1200, the client will owe the broker 100. This is determined, from the
clients perspective by the calculation (5850 - 5950) * 10. The currency will be in Euros because the base currency
of the client is in Euros. A further wrinkle on this scenario is that it is possible to have FSB's on futures
contracts. In this case there will be an additional multiplier that relates to the size of the contract. For the
example shown above, the S&P future contract as traded on the Globex exchange has a unit size of $5/pt. That is,
the amount owing or owed on every 1/pt FSB on the S&P futures contract will change by 5 for every point
that the S&P futures contract moves from the execution price. FSB's give the client access to financial instruments
in different currencies from their base currency without having exposure to the underlying foreing exchange rate. This
may or may not be a good thing, but from a client perspective it may simplify their view of their exposure.
RiskSystem maintains a database of the appropriate
multiplier (risk factor) for FSB contracts which is automatically loaded when and particular intrument type is
selected.However it is not infallible. If you think that the default risk factor with which you have been supplied is
wrong, please adjust as you think appropriate and please let us know.
Future Instruments
Futures are exchange traded derivative instruments, similar to CFD's, that allow the client
exposure to an underlying financial instrument, or basket of financial instruments. Selecting a Future instrument will
cause the system to suggest an expiry date option to the user.The default expiry date is one month from the entry of the position, but may be adjusted
by the user. This is relevant because after the expiry date, the risk of that position will be held at zero. There are
a number of instrument type options for the Future based on the fact that for some underlying financial instruments
there is more than one liquid futures contract. An example is the S&P index where there is a mini contract with an size
of $5/pt and a larger contract with a size of $50/pt. RiskSystem maintains a database of these risk factors,
however it is not infalliable. If you think that the default risk factor with which you have been supplied is
wrong, please adjust as you think appropriate and please let us know.
Gross Exposure
Gross Exposure is a risk metric that reflects the underlying financial cost of a
position. It effectively represents the cost of all positions under the condition that all underlying asset prices go to
zero. RiskSystem allows users to modify this by offering options of range of changes in underlying asset price ranging
from 100% (Default) to 5%. In addition it allows the user to determine if they want to include the impact of potentially (possibly)
offsetting long and short positions. The sum of absolutes choice (default) assumes all changes in value are positive and
sums the constituent values. This is akin to Gross Exposure in standard equity portfolio literature. The sum of actual
allows the offsets of positive and negative values. This is akin to Net Exposure in standard equity portfolio literature.
Guaranteed Stop/Limit Orders: GSO/GLO
These instruments are commonly used in on-line trading as a risk managment tool. They work by
guaranteeing the holder the ability to buy or sell a given amount of underlying at a fixed price at any time in the future. In calm markets
this is not particularly valuable, but in very volatile / gapping markets this can be of extreme value. The fact that they are in effect, infinitely
long lived options that are very difficult to price, they are almost always mispriced, generally on the cheap side. They are modelled in
RiskSystem as barriers, either blow (Stop) or above (Limit) on the underlying price of an asset. Please note that the use of double sided
VaR as a risk metric is not consistent with a single sided GSO/GLO. As such, from a risk perspective, the order may be modelled for risk purposes
as a two sided option.
Hedge Option
The Hedge Option buttons allow a user to specify in great detail the exact External instruments
that may be used in the Risk Anlysis Hedging functionality. Selecting a risk sector effectively selects all the instruments in this
risk sector. As such, only L5 risk sectors may be selected in order to limit potential calculation times. If the risk sector from which you
wish to select hedging instruments is not in the current list, go to the Preferences - Risk Sector page for the specific asset class
in which you have an interest and click the button associated with the risk sector you wish to see. When you re-load the asset class
risk exposure sheet, the new risk sector will be in the list.
Kullback-Leibler Divergence
The Kullback-Leibler divergence is a measure of the distance between two multivariate normal probability distributions.
In the specific case here, it is metric that looks at the change from the ex-ante portfolio to the realised portfolio. It takes into
account both drift and co-vartiance and as such may be thoguth of as a weighted combination of the Mahalanobis distance and the Burg
divergence. It is widely used in information theory and signal processing to determine how badly a signal has been degraded. It's use in
a portfolio is to determine how rae from its initial specification a portfolio has moved.
Ledoit Shrinkage
Ledoit Shrinkage is based on the assumption that the sample covariance matrix, i.e the covariance matrix
constructed by those points in the overall timeseries that are used, is a bad approximator of the "real" covariance matrix. The principal
objection is that the sample covariance matrix is very volatile so that the assumption that it resembles the real covariance matrix is
unlikely to be a good one. In the place of the sample covariance matrix it uses a process that "shrinks" the values of co-efficients
that is considers outliers, closer to values that it considers central. As a result, the shrunk covariance matrix should exhibit more stability
than the sample covariance matrix over time. This may be a good thing.
Mahalanobis Distance
Mahalanobis distance is the matrix equivalent of the Sharpe ratio, and curiously enough, it has been around for much longer. Effectively
it looks at the difference between the ex-post and ex-ante drift of the components of the portfolio, but modified by the inverse of the
ex-ante covariance matrix. As such it is a measure of the current portfolio performance compared to the its historical performance. It has
a particularly useful property that the probability distribution of the distance is Chi-Squared and so a statistical likelihood may
be estimated for all realisations of the parameter.
Option Instruments
RiskSystem provides option functionality based on the Black model for Equities,
Commodities and Futures or the Garman - Kohlhagn model for Foreign Exchange options. For those
who are used to the Black-Scholes model (or even Black-Scholes-Merton model) apologies. Given that this is a risk
system and not a pricing system, exact accuracy in pricing is not a key priority. In addition, whilst getting funding
rates is fairly trivial, though not necessarily personal funding rates, getting dividend rates (for equities/indices)
or storage/repo rates for commodities is not. As such, the Black model takes no rates. The user has to enter an expiry date
and a strike rate. The strike rate should be in the same units of the underlying time series. To observe the
time series units for a given instrument, please use the Time Series Analysis functionality. The Garman-Kohlhagen model
uses the appropriate / interpolated LIBOR rates out to one year and then the compounded one-year rate for longer maturity options.The implied volatility
that is used is 120% of the realised one year volatility of the underlying instrument. It is not perfect but it reflects
the general observation that implied volatility is greater than realised (how else would option traders make money?).
If this is a problem and you feel that your risk is greatly misconstrued by this approximation, please let us know.
We would be delighted to discuss with you an implementation of a more accurate solution.
Passive Hedging
Passive Hedging is the simplest type of risk control. It attempts to detemine the
most efficient manner of reducing risk in the portfolio utilising a user-defined set of hedging instruments. There are no
other contraints, other the the type and number of hedging instruments available, and no information is
given on expected drift or volatility of the hedging instruments. The analysis may use either a multi-variate least squares
optimiser or it is possible to optimise over a specific risk metric. Please note however, in the case that the risk metric
is not coherent, there is a non-zero probability that the suggested hedge portfolio is not a global minimum.
Portfolio
RiskSystem gives its users the functionality to have their positions in
more than one portfolio. Whilst there is a large amount of functionality that allows the user to slice and dice
their risk by asset class and risk sector, it may not suit those who have strategies with different time scales,
or strategies which the user would like to keep separate. The user can create up to ten different portfolios
into which they may place individual positions. All positions in all portfolios are aggregated into the Main portfolio.
If you do not like the name 'Main', this can be edited, but all positions will still be aggregated into that
portfolio. If you delete a portfolio, this will be removed from the system. Any positions that are in a deleted portfolio
will be moved to the Main portfolio.
Portfolio / Position Analysis: Hedge
The Hedge option allows the user to identify, an asset, or a portfolio of assets,
which in combination with those of the user portfolio and with appropriate weights, minimise the volatility of the
combined portfolio of assets. From an analysis perspective it allows the user to determine the amount of their
risk that is generic risk and how much is idiosyncratic risk. In order to achieve equality amongst all the underlying
instruments, all instruemnts are considered to be Financial Spread Bets. This has the impact of removing foreign
exchange effects from the analysis. For a more complete hedging functionality, please use the Risk Control Hedging
Functionality. Hedge instruments may be selected from three options. Internal means that only assets currently in the
portfolio will be considered. External maeans only those that are in Risk sectors that have been selected using the
Hedge buttons will be considered. Both means what it says.
The Hedge P/F size option allows the user to specify the size of the hedge portfolio.
The default option is 1. In this case the functionality determines the hedge size for each asset in the selected hedging
assets and diplays them, ranking from the best hedge to the worst. In this case best hedge is defined as that which reduces the
VaR of the portfolio by the greatest amount, column A+Pf Risk. The Size column indicated the size of the position in the asset
(in FSB terms) that minimised to volatility of the combined portfolio. Please be aware that in the risk analysis section,
the hedge routine operates under a minimised volatility criterion. Thus, if there is very little hedging potential in a
given asset the VaR of the resultant combination portfolio may be increased from that of the original portfolio.
Selecting a Hedge P/F size greater then 1 means that the functionality will be looking for
the combination of assets which along with those in the portfolio will have the lowest volatility. The outputs show the appropriate
size (in FSB terms) of the constituents of the most efficient hedging portfolio. The risk of the hedging portfolio is shown in the
column marked A Risk. The risk of the combination of the Use portfolio and the hedge portfolio is given in the column markets A+Pf Risk.
Please note that only the mose efficient hedge portfolio out of all the possible combinations will be displayed.
Portfolio / Position Analysis: Vol, VaR, Skew , Kurtosis
This takes all the positions that have been selected using the USE option buttons and calculates the
selected risk metric for each position. The parameterisation of these estimates will be consistent with those used for the
Value at Risk and the other confidence interval metrics.
Risk Sector
Risk Sectors are at the heart of the system. All risks in all asset classes, may
be broken down into individual risk sectors. Currently there are five levels of risk sector. Level 1 (L1) divides into the
four main asset classes: Equities, Commodities, Foreign Exchange and Fixed Income. L2 risk sectors are the major
geographic blocks: ASia/Pacific, Europe, Americas, Middle East and Africa. L3 risk sectors are subdivisions within the
L2 sectors. For example Central Asia is a sub-division of Asia/Pacific. The L4 risk sectors are the individual countries
within any given L3 sector. Following the example above, the L4 risk sectors associated the Central Asia are China and
Hong Kong. Below the country level are the L5 sectors that divide equities into Stocks and Indices etc. The use
of risk sectors allow a user to determine the level at whivh they observe their risk, from country to asset class and
also to determine risk sectors from which they would like to select hedge portfolios.
RS Hedge
The determination of a set of hedge positions for a given portfolio can become a very time
consuming process. In RiskSystem the user has the ability to use all the positions in their portfolio as possible hedge instruments or external instruments,
or a cfombination of both sets. As such it is very possible that the list of target assets may have hundreds of different assets and if one was
looking for a hedge portfolio or four instruments then an estimate of the number of possible hedge portfolios is the approximately the number of target assets
raised to the power of the number of hedge assets. Thus for a two hundred asset portfolio, attempting to find a four asset hedge portfolio would require
approximately 200^4 (1.6 billion) separate estimations. Even using very fast computers this will not be completed in a short time.
In order to counter this effect the Reduced Set (RS) hedge process is introduced. In this approach, only the assets with the
highest (absolute) component VaR (see above) are considered as target assets. This greatly reduces the number of target assets, but as they are of more relevance to the
risk of the portfolio, there is not a significant loss of generality in attempting to detemine the appropriate hedge portfolio.
Sector Analysis
Sector Analysis allows the user to analyse the makeup of their portfolio in terms
of statistical relationships with other assets in other asset classes.
Sector Analysis - Constrained
Sector Analysis allows the user to analyse the makeup of their portfolio in terms
of statistical relationships with other assets in other asset classes, but at the same time restricting some of the assets
used in the analysis based on user defined constraints. The purpose behind this functionality is to run a global type of
analysis that only selects assets within a particular range.
Sector Component Risk
Sector component risk is a variation on the normal risk exposure in that it effectively provides
the change in the overall portfolio risk if all the positions in that risk sector were removed from the portfolio. As such it
gives a good measure of the actual diversification of the positions withinthe portfolio. Within risk metrics it has a weel defined
definition for the confidence interval metrics, VaR, Expected Shortfall and Economic Capital, and this has been generalised and
applied to the Gross Exposure and Stress Test metrics.
Spot Instruments
Spot instruments are those whose settlement date is within three days (a somewhat
arbitrary number it may be admitted) of the execution date. The instrument types that are available are Cash, FSB and
CFD. Cash refers to a direct purchase, or sale (short or not) of a financial instrument, for example, a buy of 1000 shares
in Citigroup, a US bank holding company. For FSB's and CFD's, given that these are derivative contracts, they are
generally considered to be Spot instruments.
Stress Test
Stress Test is a risk metric that reflects the financial cost of a move in the
asset price of all the assets within a given risk sector. For each asset class there are a range of stress moves
available to apply to all the assets within a given asset class. If these are not sufficient, please inform us.
In addition it allows the user to determine if they want to include the impact of potentially (possibly)
offsetting long and short positions. The sum of absolutes choice (default) assumes all changes in value are positive and
sums the (absolute) constituent values. This is akin to Gross Exposure in standard equity portfolio literature. The sum of actual
allows the offsets of positive and negative values. This is akin to Net Exposure in standard equity portfolio literature.
Use Option
The Use option buttons allow a user to specify in great detail the exact parts of the
portfolio that they want to analyse. Above this functionality the user is able to specify which portfolio and which asset
class they want to study. To get futher detail the user has the option of selecting specific risk sectors in which they
are interested at any given time. Initially only the top level Use button will be selected. The Use functionality works
on a level down principal. That is, if you have selected a high level risk sector, all of the risk sectors that are sub-sectors
will automatically be selected. Initally, the list of availale risk sectors will reflect the positions that you hold in the main
portfolio. If you wish to increase the number of risk sectors, go to the Preferences - Risk Sector page for the specific asset class
in which you have an interest and click the button associated with the risk sector you wish to see. When you re-load the asset class
risk exposure sheet, the new risk sector will be in the list. Please note that selecting or deselecting a risk sector will not impact any other
part of the risk analysis section. This simply limits the available positions for the specific analysis.
Value at Risk: VaR
Value at Risk (VaR) is a risk metric that attempts to detemine possible extreme changes in the
value of a portfolio from a historical simulation of the perfomance of the portfolio. On the basis of it happened before so it
can happen again, it gives a (vaguely) statistical metric of potentially extreme price changes in the value of the users
portfolio. For a more detailed explanation of VaR and its pros and cons, please look elsewhere, however at RiskSystem
it is considered the least worse individual risk metric. Given the range of available parameters, they will be treated
seperately however the default values are those recommended by the Bank of International Standards (BIS) in the
Basle II protocols, if that is a useful recommendation.
Von Neumann Entropy
Von Neumann introduced this quantity, also known as quantum relative entropy in an attempt to extend the classical notion
of entropy to quantised, or discrete states. As a system becomes more disorderly, its entropy is said to increase. If you
consider that the state of your portfolio at inception to be the most orderly, which can be thought of as saying that
the statistical properties of the portfolio are in line with your expectations, then as the system moves away from this
original state, from a statistical properties perspective, its Von Neumann entropy will increase. As such this functionality
may be used as a diagnostic, along with the Kullback-Leibler divergence to study the stability of the portfolio over time.