This document discusses Value at Risk (VaR) and how it can be used by client advisors, sales/brokerage teams, and senior management to assess portfolio risks. VaR measures the maximum potential loss of a portfolio over a time period, given a probability. It allows risks across different asset types to be measured together. The document outlines how VaR is calculated using historical volatility and correlation data to project a range of possible future portfolio values. It also discusses how options are incorporated into VaR using measures like delta, gamma, and theta to account for non-normal return distributions. The overall aim is to inform readers about risk measurement and how VaR can help mitigate risks for clients.

1. VALUE AT RISK
A CONTRIBUTION TO OPTIMISE
AAT AND S/B SERVICES TO CLIENTS
Internal only
“The first rule of trading - there are probably many first rules - is don’t get caught in a situation in which
you can lose a great deal of money for reason you don’t understand.”
Bruce Kovner, Harvard, ex-trader at Commodities Corporation
“You have to be willing to make mistake, there is nothing wrong with it. Making your best judgment,
being wrong, making your next best judgment, being wrong, making your third best judgment, and then
doubling your money. It’s because investing and trading are self-correcting processes.”
Michael Marcus, ex-trader at Commodities Corporation
“You can lose one time out of two, if you know how to lose. Actually you can even lose seven out of ten
and still become a very rich man.”
Bernard Baruch, famous American financier
Jean-Marc Bloch
AAT-IAA London
Global Senior Technical Analyst
Direct 44 171 568 8084

2. 2
INTRODUCTION
As a former technical trader in currencies and bond futures, I have tried to understand how to
best interpret a market view by combining fundamental analysis, technical analysis and risk
management. Knowing and setting in advance which maximum amount of capital one is willing
to lose is a great advantage.
As a technical analyst on the sales staff at Bloomberg Financial Markets, I have trained on
many occasions treasurers and portfolio managers on how they can fully manage their risk:
• track volatilities and correlations
• run customised reports on portfolio Value-at-Risk (for private banking)
• combine these quantitative tools with state-of-the art technical analysis.
Further to previous documents on Technical Research and Risk-management (available upon
request), I would like to present in a simple way what Value-At-Risk means and how it can be
used by AAT and S/B to the benefit of clients money.
Elaborating on risk-management and IAA research is key for understanding and using:
• Internal high quality IAA research format
• Integration of technical analysis in that format to validate ideas
• Delivery of appropriate and timely stock recommendation to Clients
• Conversion of the research into valid strategies for Clients, via both Advisors and S/B
• External business delivery and follow-up from Advisors and S/B to better servicing clients
As defined during team meetings in London with head AAT and IAA, we aim at creating a
process of getting research / recommendation into clients portfolio. There is an underlying
dynamic to it.
Prior to this process begins, it is of prime importance to know and to monitor clients risk profile
to deliver the most adequate and timely investment ideas.
For instance, when it is time to consider using derivatives for a client, understanding the nature
of uncertainty and the nature of risk and their evolving states is crucial, prior to defining an
option scenario analysis. In other words, risk comes before reward in any investment decision.
I have compiledthree articles dealing with quantitative and risk-management tools available on
Bloomberg, and one of my articles on technical analysis. They respectively cover:
• Risk-Management: Improving your odds in the crapshoot, with H. Markowitz, Nobel Prize
• Equity Market Risk to manage a portfolio risks
• Value at Risk for derivatives and the use of delta-gamma method
• Technical Analysis with the use of Relative Strength Index: - to validate trading ideas
- to observe markets volatilities.
They outline additional in-depth analysis and give real examples.
I believe all the concepts here are easy to use by Client Advisors and S/B for any given client.

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WHAT IS VALUE AT RISK?
Value at Risk (VaR) measures the maximum potential loss on a single or group of securities
over a selected period, given a specified probability. Once a probability, i.e., the degree of
confidence, has been established, VaR represents the securities’ statistical maximum loss.
For example, if a Portfolio’s VaR is calculated to be $1.5MM, given a horizon of one week and a
probability of 3%, there is a 3% chance that at that horizon date, the Portfolio’s value will be $1.5MM or
more below its current value. Therefore, VaR focuses on the potential occurrence of losses, which are
statistically unlikely but not inconceivable.
One of the primary benefits of VaR analysis as opposed to other risk assessment tools is that it can
measure the systematic price risk across all types of markets and then distill them down to a
single number. This allows those who manage or oversee portfolio containing, for example, both equity
securities and equity options to examine the price risk in all positions simultaneously since the same
methodologies are used across all markets.
HOW TO USE VaR IN THE MARKETS
A wide range of market participants and regulators as a risk assessment tool uses VaR.
1) Client Advisors: VaR can help investment/client advisors to assess potential individual portfolio
volatility. If a client’s philosophy and objective are to seek steady capital growth through a stable
portfolio, the advisor must be alert to strategies that could lead to excessive volatility.
VaR can help determine if the fund is being fairly compensated in terms of expected return for its price
risk.
2) Sales / Brokerage: equity, fixed income, currency and derivatives sales/traders use VaR to assess
the price risk of inventories. Unlike portfolio managers or client advisors, traders often use a one
or two-day horizon since a client average holding period can be very short.
(VaR is a particularly helpful tool for proprietary traders who deal in a range of securities since it can
measure risk across markets and factors in correlation.)
3) Senior management: Management needs to monitor the risk across a large number of
portfolios and trading accounts on a monthly or weekly basis. VaR allows them to calculate a
number that captures the price risk in a straightforward, easy to understand manner.
Obviously, we are concerned with 1) and 2) where questions and issues might remain.
This internal document aim at informing us of what risk is and how it can be mitigated.
There is a market vendor issue there, since all the risk tools I am mentioning are usable only via the
Bloomberg. However, technical analysis is not. I realise that the number of Bloomberg terminals is quite
sufficient. So their use can be leveraged.

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HOW TO CALCULATE VaR
Different methodologies have been advanced, each with its own strengths and weaknesses:
• Structured Monte Carlo
• Historical simulation
• Fixed scenarios
• Variance/Covariance (detailed in J.P. Morgan Riskmetrics® Document)
This methodology has been implemented on Bloomberg.
For portfolios with normally distributed returns, i.e. no explicit or embedded options, VaR uses
historical volatilities to project a range of possible future values for each security and incorporates
historical correlation to factor in the benefits of diversification. Therefore, VaR relies on the premise that
prior volatility and correlation data can be used to forecast a range of possible values for a
group of securities as of some specified horizon date.
This relationship is shown in figure 1 below.
Figure 1
For a portfolio with normally distributed future values, this range can be depicted as a bell-shaped
curve, defined by the probability, which represents the boundary of a range of future value that results in
“large” losses. In other words, the VaR represents the point on the curve some designated number
of standard deviations away from the mean. The lower the probability, the higher the VaR, because
the user is demanding a greater degree of certainty (fear) of losses occurring. Figure 2 below shows this
function:
Figure 2
Probability of
Occurance
5%
3% Value at risk
A B
Lower Unchanged Higher
Portfolio value Portfolio Value Portfolio Value
VALUE OF PORTFOLIO AT HORIZON
The horizon value of the portfolio at A, which corresponds to 3% probability, is less than the horizon value at point B, which corresponds
to 5% probability. The VAR is the difference between the unchanged or original value and the horizon value.
Portfolio
Value
Historical Volatility
PVAR Range of possible
FUNCTION future portfolio values
Historical correlation
Now Time

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Since it is not possible to track the historical volatility and correlation for every security, each security is
mapped to one or more “primitive” assets. Bloomberg tracks the volatilities and correlations of
several thousand primitive assets. These data are stored for these primitive assets and are
used to project future values for each appropriately mapped security.
For equity, the primitive asset is the country’s index for which the stock’s Beta is calculated. An individual
stock’s Beta and market value are used, in conjunction with the index’s historical volatility, to project the
range of future values for that particular stock. In the portfolio theory, the higher the diversification
in the portfolio, the lower the Beta on the stock, therefore the lower the volatility.
The currency exposure is mapped directly to the “cash” primitive asset. If all of the securities are
denominated in the portfolios base currency, there will be no impact. If some securities are
denominated in other currencies, the historical exchange rate volatility between the securities’
currency and the base currency will be incorporated. All currencies’ volatilities are measured
versus the U.S. dollar, therefore the dollar’s volatility is always zero.
OPTIONS IN VaR
Options introduce non-normal or “skewed” return distributions. The method outlined by
JP Morgan in an update to their Riskmetrics® documents recommends calculating the delta,
gamma and theta for each option in order to reveal the option’s asymmetrical return pattern.
While delta is a linear measure, gamma and theta are nonlinear and, therefore, capture the third and
fourth moments of the curve: skewness and kurtosis.
• Skewness measures the asymmetry of the distribution about the mean.
• Kurtosis measures the fatness of the tails, the likelihood of the portfolio’s value in the tails.
These measures are extremely important.
For exchange-traded options or OTC options, calculating delta, gamma and theta is
accomplished using a Modified Black-Scholes model for European style options and a binomial
price-tree for American style options.
THE IMPORTANCE OF DATA SET
Bloomberg offers three data sets:
• the full Bloomberg Data Set
• the Restricted Bloomberg Data Set
• JP Morgan’s Riskmetrics® Data Set.
The main differences among the three are the number of primitive assets and the flexibility with
which a user can weight the historical data.
Bloomberg’s full set provides more primitive assets enabling to map a greater number of
securities to more narrowly defined buckets. Therefore, securities are mapped to primitive assets
whose rating and sector characteristics more closely match their own. The historical volatilities of these
primitive assets will, therefore, tend to track those of the actual securities more accurately. This is mostly
useful on the fixed income, corporate and municipal bonds side.
The Restrictive Data Set mimics the same primitive asset classes as those of Riskmetrics but
uses Bloomberg historical price data. This data set allows determining the impact of different
pricing sources on a portfolio’s VaR.

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Bloomberg lets users select any “decay factor” from 0% to 9% while Riskmetrics® has a fixed
decay of 6%. The decay factor allows recent volatility data to be weighted more heavily than past data in
order to capture trends in volatility.
A decay factor of 0% means that no decay is used; that is, each day’s volatility data for the previous
year is equally weighted.
If any other decay factor is used, recent data is given more weighting than previous historical data. For
example, a decay factor of 5% means each day’s volatility data counts only 95% as much as the day
after. There is no “correct” decay factor.
Understanding the implications of choosing a specific decay is particularly important. Technical
analysis is helpful in differentiating trending markets to trading ranges, therefore to locate
various volatilities in the markets. I covered this in my article “Staying Ahead With Day’s End
Trade Signals” which is enclosed with this document.
CONCLUSION
As demonstrated, Value at Risk report enables us to assess the risk across a group of
securities using historical volatilities and correlations as well as options analysis. As we all
know, these concepts are crucial in today’s financial markets. So are their uses before any IAA
stock picking and any technical analysis. That is my belief.
AAT and S/B will offer additional insight into strengths and weaknesses of markets by:
• fully utilising the methodology in VaR
• tracking volatilities and correlations (Optional)
• running VaR report on a regular basis (This can be scheduled automatically.)
• using sophisticated option analytics, which allows for the modeling of nonlinear assets
By combining these tools with their expertise, AAT and S/B will:
• determine whether there is excessive market risk in the owned securities
• better monitor each client’s risk profile
• pinpoint which securities are guilty of adding undue risk
• measure risk across the entire portfolio
• deliver appropriate and timely investment or trading ideas coupled with sound money-
management guidelines.