EVERYTHING EVERYWHERE - Northfield

EVERYTHING EVERYWHERE

The Multi-Asset Class Risk Model

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FEB-3-2015

The Multi-Asset Class Risk Model

Table of Contents

INTRODUCTION .............................................................................................................................3

THE GLOBAL EVERYTHING EVERYWHERE RISK MODEL RATIONALE......................................................3

LAYOUT OF THE EE MODEL DESCRIPTION.........................................................................................3
The single country equity risk models: consistent sub-sets of the Global model .........4

SECTION 1 – AN OVERVIEW OF THE EE MODEL .................................................................................5
EE model - Global equity risk model foundations ............................................................5
The global equity risk model structure ..............................................................................5
Fixed income in an equity risk framework ........................................................................6
Fixed Income securities are split, elements analyzed then re-combined........................6

SECTION 2 – THE GLOBAL EQUITY RISK MODEL ..............................................................................6
The risk factors used and why they were chosen .............................................................6
Complete linkage cluster analysis......................................................................................8
The factor estimation universe...........................................................................................8
The global equity risk model structure ..............................................................................9
Value / Growth factor specification ..................................................................................10
Factor variance and covariance calculations exponentially weighted ..........................11
Factor variance estimation ...............................................................................................12
Estimating the stock betas to the factors.........................................................................14
The hybrid risk model structure applied to the Global Equity risk model ....................15
Asset specific risk adjustment using the Parkinson volatility estimator .......................16
60 monthly returns used to estimate the risk model: ............................................................. 16
Dealing with short data histories ............................................................................................. 16
The single country models’ specific use of the factors ..................................................17
Testing the Northfield Global Equity Risk Model............................................................17
Summary conclusion on the global equity risk model...................................................18

SECTION 3 – FIXED INCOME .........................................................................................................19
Fixed income securities in a global equity risk model framework ................................19
Interest Rate Risk...............................................................................................................20
Interest rate/term structure exposures .................................................................................... 20
“Shift, twist & butterfly” definitions........................................................................................ 21
Fixed income risk factor exposures or “Betas” ..............................................................21
Fixed income – 450,000 bonds & 57 currencies & yield curves .....................................22
Fixed income - Real and inferred yield curves ................................................................22
An example: Inferring the Thai Baht yield curve.............................................................22
Creating the “Global Yield Curve” ...................................................................................23
Scaling the stock factor exposures to the “Global Yield Curve” ...................................23
Scaling the Global Yield Curve factors to local curve factor volatilities........................23

CREDIT RISK ...............................................................................................................................24
Credit spreads....................................................................................................................26

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The Multi-Asset Class Risk Model

Fixed income prepayment, optionality, basis risk The option adjusted spread ..........27
Credit exposures for government bonds........................................................................27
What to do if government bonds’ credit exposures are undesired ...............................29
FIXED INCOME DATA AND COVERAGE.............................................................................................29
FIXED INCOME PRICING SOURCES ..................................................................................................29
DEALING WITH MISSING FIXED INCOME SECURITIES ........................................................................29
FIXED INCOME: INSTRUMENT SPECIFIC DETAILS..............................................................................30
Floating Rate Bonds ..........................................................................................................30
Index Linked Bonds ...........................................................................................................31
Mortgage-backed securities .............................................................................................31
Convertible securities........................................................................................................32
Government Bond Futures Among Other Derivatives ...................................................32
MATRIX PRICING AND OTHER PRICING RELATED ISSUES ...................................................................33
Which curve is used? ........................................................................................................33
Matrix pricing ....................................................................................................................33
THE EE MODEL SUMMARY CONCLUSION........................................................................................33
REGIONS ....................................................................................................................................34
SECTOR AND REGION MARKET CAPITALIZATION ............................................................................36
INDUSTRY SECTORS ....................................................................................................................38
SPECIAL SYMBOLS ......................................................................................................................38
Currency codes available in the Northfield risk models.................................................39
Country equity indices available in the Northfield risk models .....................................40
APPENDIX A: BOND MODELING IN THE EE RISK MODEL: TEST RESULTS .........................................41
Testing Conclusion............................................................................................................45
APPENDIX B: DERIVATIVES:..........................................................................................................46
WHY NORTHFIELD IS RIGHT FOR YOU ............................................................................................72
Powerful, Integrated, Consistent & Comparable Risk Models .......................................72
Open models: open systems. No Black Boxes! ..............................................................72
Global, Regional, Country & Asset Coverage .................................................................72
Sophisticated, flexible, robust, open analytical systems ...............................................72
Partners ..............................................................................................................................72
Innovation ..........................................................................................................................72
Excellent training, support and solutions........................................................................72

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Introduction The purpose of a risk model for investment portfolios is to analyze and
forecast the risk of portfolios consisting of equities, bonds and, potentially,
other securities, relative to their benchmarks. Further, the EE risk model’s
risk forecast for individual securities should be both defendable and intuitive,
even though this is not the main purpose of the model.

The Global The Northfield Everything Everywhere (EE) model, described herein, was
Everything developed in response to managers’ need for a straightforward, robust
Everywhere risk framework in which to analyze and control the risk of global balanced
model rationale portfolios. The EE model gives managers the tools to monitor and control
positions in individual global equity securities, fixed income securities,
currencies and some indices. The model describes securities’ risk
characteristics with estimated exposure to intuitive real world systematic risk

factors.

Layout of the EE This description of the EE risk model is in three sections. Section one gives
model a broad overview of the process by which the EE risk model is created.
Section two describes the specifics of the Global Equity risk model. Section
description three describes in detail the way in which Fixed Income securities are
treated in this sophisticated integrated hybrid model structure.

The goal in building this risk model was to produce a structure that
successfully reduces the risk characteristics of a diversified portfolio of
securities to a limited set of exposures to intuitive, easy to understand, yet
economically meaningful set of factors.

This logic of course extends further. The objective is to produce the “best
performing” model for global balanced portfolios. This is not necessarily the
best model for each individual industry, country or region. In fact, it probably
won’t be because there may be / are effects at the industry or country level
that are simply diversified away at the global level.

Importantly, “best performing” means that the model is intended to produce
the “best” forecasts of risk for diversified portfolios. This objective is not to
perfectly “explain” history. Clearly, the more factors used, the more
historical variance can be explained. However, such effects are not always
pervasive through time and across markets. To manage and forecast risk —
a relatively simple, broad and pervasive set of factors have proven to be
highly effective, intuitive and easy to use.

If the aim had been to produce the most accurate possible model of risk and
return for each security, then the models would be quite different in
character and number. Specifically, there would probably be a different risk
model for each security – which would hardly make the task of
understanding the overall portfolio risk easier, but would rather, make it
harder!

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There were three basic styles of risk models commonly used; the
fundamental or cross-sectional, the macro-economic or time series, and the
pure statistical. Each style has its own strengths and weaknesses. Northfield
has developed a new “hybrid” style that combines time-series and statistical
techniques that produces a model with significant advantages over the
traditional model structures.

The Northfield family of risk models helps managers to monitor and control
market specific equity portfolios. Along with the Everything Everywhere
equity and fixed income risk model, Northfield currently offers a global equity
only risk model and country \ region specific models for Asia, Australia,
Brazil, Canada, China, Europe, Japan, Switzerland, the United Kingdom
and the United States. These models are all fully compatible with the
Northfield Open Optimizer.

The single country The Northfield single market models are logically consistent subsets of the
equity risk models: Global model, grounded in the same modern portfolio theory, that also use a
consistent sub-sets limited set of intuitive factors and measure risk exposure with a high degree
of the Global model of accuracy. Each single market model is re-estimated based on the local
relevant stock universe, they are not “start from scratch” fundamental
models of their respective equity markets. They increase the accuracy of the
Global model when applied to a specific market by eliminating extraneous
data from the estimation process. Continuous research has improved the
single market models further.

This document describes the Northfield Everything Everywhere global equity
and fixed income risk model. Broadly, it falls into the time series class of risk
model, although the fixed income securities are also analyzed cross-
sectionally. The model is intuitive, grounded in modern portfolio theory, it
uses a limited number of real world / observable factors and measures risk
exposure with a high degree of accuracy. It helps managers to measure and
monitor portfolio risk and control positions in global equities, currencies and
bonds. The EE risk model database includes over 61,000 equities, over
550,000 fixed income securities, 1.3 million municipal bonds, 1 million
mortgage back pools and approximately 90,000 mutual funds and ETFs and
300,000 CMOs and asset backed securities from 68 developed and
emerging market countries, involving 57 currencies. The model is fully
compatible with the Northfield Open Optimizer.

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Section 1 – An The EE equity and fixed income risk model is a sophisticated blend of a pure
overview of the equity risk model and a fixed income risk model. The obvious complication
about this multi asset class risk model is that the assets have substantially
EE model different characteristics. Most obviously, equities do not have a maturity
date – whereas most fixed income instruments are issued with a maturity
date (when the money borrowed is expected to be repaid). The
characteristics of equities are therefore less structurally sensitive to time
than are fixed income securities. How are these to be reconciled in one
model? In addition, since the model covers convertible and other bonds with
embedded options, clearly a major analytical challenge is faced.

Equities are typically the most volatile asset class in a global balanced
portfolio. Various forms of convertible bonds follow, with “normal” coupon
bonds being the least volatile asset class.

EE model - Global Northfield created and has offered a Global equity risk model since 1995.
equity risk model Given that equities are the most volatile asset class and that the model has
worked well, this formed an excellent foundation for the EE model. The
foundations challenge then was to create a fixed income risk model that could be
blended with the existing equity risk model.

The global equity The Everything Everywhere risk model is based upon the Northfield Global
risk model structure Risk Model that measures every equity security's exposure to its region, its
sector, global interest rates, oil prices etc. It also takes into account the
portfolio's exposure to currency bets relative to its home currency. There are
93 factors in total including currencies. Each security, however, is only
exposed to 13 factors: region, sector, interest rates, oil prices, currency,
value / growth, market development, company size and 5 “statistical
factors,” and denomination currency. The specification of these factors will
be discussed in greater detail below.

Equities are analyzed first, then fixed income securities’ sensitivity to interest
rates are estimated and finally fixed income exposure to credit risk are
estimated using the same factors that are used to analyze equities. The logic
supporting this approach is that economically, credit risk and equity risk have
much in common. The techniques used to analyze bonds and equities are
quite different, yet the results are delivered in a consistent structure that
allows portfolios of complex instruments to be analyzed in a straightforward
and intuitive manner.

The Global equity risk model uses an analysis of the sensitivity of individual
equities to well known and understood common sources of risk or factors.
The analysis is done in a time series regression framework and results in an
intuitive model of risk that uses a limited number of exogenous, real world
and statistical factors to capture and describe the risk of individual equities
and portfolios of equities relative to a benchmark. The Global equity risk
model has been in use for years generating consistent forecasts of risk for
global portfolios.

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Fixed income in an The fixed income model framework builds on, and is totally consistent with,
equity risk the global equity model. This combination addresses all of the significant
framework sources of both equity and fixed income risk in a balanced portfolio.

Fixed Income Fixed income securities are decomposed into “atomic” sources of risk –
securities are split, specifically these are interest rate risk, currency risk and credit risk
elements analyzed components. Three interest rate specific factors were added to the existing
then re-combined equity factor model structure, to capture three types of term structure shape
change. These three factors correspond to “shift”, “twist” and “butterfly”
movements of the yield curve.

Both the credit and currency risk “atomics” of fixed income securities are
handled using the familiar factors used in the equity model. This mechanism
welds the equity and fixed income elements together in a unique, intuitive,
clear and powerful yet parsimonious Global model. Please see the final
section for specific details on the creation of the fixed income risk model.

The result of all this effort is a risk model that is specifically designed to
forecast and control the risk of Global “balanced” portfolios of bonds and
equities while still using as few risk factors as possible.

Section 2 – The The model currently includes over 61,000 equity securities in 68 countries.
Global Equity Returns, capitalization and other data are obtained from Thompson Reuters.
Risk Model A benefit of the Northfield approach is that the data required, interest rates,
oil prices, the FX rates of the currency with the USD (or other base currency),
a value / growth index, and a size index are readily available even in emerging
markets. As the model has limited reliance on detailed financial statement
data, it can be updated rapidly and is less susceptible to the vagaries of
accounting data. New information on market conditions is typically available a
few days after the month end.

The risk factors Northfield’s approach to global and indeed single market modeling is
used and why they straightforward and transparent. The nature of the model’s factors and the
estimation methods are readily understood. This is of key importance since
were chosen risk is more than just a statistical estimate of volatility. Risk is “what I don’t
know that can hurt me.”

The goal is to create a model that is intuitive, grounded in theory, uses a
limited number of factors and at the same time measures risk exposures as
accurately as possible. To accomplish this goal, any reliance on financial
statement ratios was minimized as accounting standards vary greatly across
countries. The variation in international standards makes it hard or impossible
to compare some accounting information from one country with the same
item from another country. Some models try to get around this problem by
measuring accounting ratios relative to country averages, but this often leads
to unintuitive results.

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The global and single country / region equity risk model specification
combines fundamental, macro-economic and statistical factors. While
benefiting from the clarity and intuition associated with the well known and
understood fundamental and macroeconomic factors, it makes innovative
use of principal components or “statistical factor” analysis of the residual
returns. This approach offers portfolio managers new insights into their
portfolios’ characteristics.

Generally portfolio managers are fully aware of their portfolios’ fundamental
characteristics. Therefore the risk model must do more, than merely state
with greater precision what portfolio managers already know. The statistical
factors are used to identify systematic sources of risk that may be transient
in nature and hence not easily incorporated in any model on a permanent
basis. Conditions in financial markets change through time and these
statistical factors automatically adapt the model to those changing conditions,
without sacrificing the stability and intuitive appeal of a pre-specified model.

Clearly, the choice of factors is one of the most important parts of estimating
a multiple factor risk model. While early academic research in the area of
global equity returns indicated that the local market index is the strongest
predictor of performance1, more recent research points to the dominance of
regional markets and global sector effects. Country / Region and Sector
indices were used to develop this model.

The first risk factor is a scheme of six broad industrial super-sectors. Sector
indices are used to account for the globalization of today's product and
security markets. As these markets become more integrated, the stock of
General Motors can be expected to respond to the same factors as the stock
of the Bavarian Motor Works.

The next class of risk factor is the scheme of five broad country / regions.
Region indices are used to account for the high correlation between specific
country product and security markets. As these markets become more
integrated, the French market may be expected to respond to the same
factors as the stock of the German market.

The decision to cluster countries into regions and industries into sectors was
taken based on test results that showed that while having more countries
and industrial sectors provided more explanatory power historically, portfolio
risk prediction was actually better with fewer sectors. This effect is
attributed to the fact that as each industrial sector is more narrowly defined,
its behavior is less consistent through time. Future portfolio behavior is
therefore less related to past observations. Broad industrial sector schemes
of up to 42 groups were tested. In the end 5 country / region and 6 industry
clusters were selected.

1 See D. Lessard, "World, Country and Industry Relationships in Equity Returns," Financial Analysts Journal,
January/February 1976.

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Complete linkage The choice of clusters was made on the basis of “complete linkage” cluster
cluster analysis analysis, correlation matrix analysis, and intuition. Cluster analysis is a
multivariate procedure for detecting natural groupings in data. This variant of
the method minimizes the maximum distance between the most distant
pairs in the clusters, and it tends to produce compact, globular clusters.

The Northfield Global model then includes the estimated influence of three
macroeconomic factors: interest rates (expressed as returns on the global
bond market index), oil prices and the exchange rate between the local
currency and the US dollar. While the importance of the relationship between
moves in interest rates and energy costs and moves in the financial markets
is self-evident, there is also considerable empirical evidence of these effects

in the finance literature. The local/US$ exchange rate is used to represent
currency as it is easily measured and testing did not suggest that more
elaborate formulations, such as trade-weighted baskets of external

currencies, provided better risk predictions.

Market development was included as a measure of investor confidence. The
model also includes two fundamental variables; size (capitalization) and value
/ growth. Again the empirical finance literature provides numerous studies of
the importance of size as a factor in equity security returns. A composite
value / growth factor was chosen as an indicative measure of the orientation
of the portfolio toward “growth” or “value”. The composite has two parts: 1)
The Dividend yield which has the advantage of being unambiguous and not
subject to ‘restatement’ or differences in accounting standards across
countries. 2) The correlation to idiosyncratic variety which has also been
shown in the academic literature and by Northfield research to be a powerful
indicator. Combining the two has created a novel, powerful and useful new
factor.

Finally any systematic source of return that has not been identified by these
readily observable real world factors is revealed by the principle components
or “statistical factor” analysis.

The factor The universe of stocks with which factors are estimated is filtered to remove
estimation universe small and probably illiquid firms. This procedure is applied to the Global
model, and we note here for completeness, the US Single country model
and the equity portion of the Everything Everywhere model.

Companies with a market capitalization value less than $100 million for
Global (and less than $250 million for US fundamental and single country
models) are excluded from the universe of securities used to estimate
sector, region, dividend yield, size etc. factor returns. These small firms will
still be included in the risk model, but will no longer play a part in the factor
estimation and thus in the covariance matrix.

Northfield research suggests that removing small and probably illiquid firms
from the estimation universe improves the stability of the factor

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relationships. This procedure has always been used in the US Fundamental
Model.

The global equity The Northfield Global Risk Model measures every security's exposure to its
risk model structure region and sector, global interest rates and oil prices etc. It also takes into
account the portfolio's exposure to currency bets relative to its home
currency. There are 90 factors in total, including currency dummy variables.
Importantly, however, each security is exposed to only 13 factors which are:

1. Region 8. Company size
2. Sector 9. “Statistical factor” 1
3. Interest rates 10. “Statistical factor” 2
4. Oil prices 11. “Statistical factor” 3
5. Currency 12. “Statistical factor” 4
6. Value / growth 13. “Statistical factor” 5
7. Market development

Mathematically, the model's form is:

Rit = Inti + β1i SectRetst + β2i RegRetct + β3i BRt + β4i Oilt + β5i FXc +
β6i ValGrowt + β7i MktDevt + β8i Sizet + β9i BF1t…+ β13i BF5t + εti

where:

Rit = the return for company i in period t, calculated in the base
Inti = currency consistent with the data file’s currency.
SectRetst =
RegRetct = the intercept
BRt =
Oilt = the return for the sector s index (s = the sector for company i)
FXc = in period t
ValGrowt =
the return for the region c index that the company i’s country
MktDevt = belongs to in period t

the return on the Citigroup World Government Bond Index (a
proxy for global interest rates) in period t

the % change in oil prices in USD terms in period t

return on currency c; β5i is a dummy variable with value 1 or 0
A two part factor.
1) Dividend yield in period t (The difference between the return
of an index consisting of the top decile by dividend yield of our
universe of stocks and the return of an index of all stocks
paying no dividend)
2) a response coefficient to the cross sectional dispersion of
stock returns within a market. This is described in greater
detail below.

market development in period t (The difference between an
index of returns of companies in developed countries and an
index of returns of companies in emerging countries)

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Sizet = company size in period t (The difference between a return
index of the 10% of the companies with the largest
capitalization and a return index of the 10% of the companies
with the smallest capitalization)

BF1t –BF5t= A series of principal components of “statistical factors”
estimated on the residuals of the rest of the model using
principal components analysis.

εti = the error term for company i in period t

Value / Growth The value/growth factor has two parts: the dividend yield (spread) factor and
factor specification the correlation of stocks to “idiosyncratic variety”. The latter part of the
factor is an innovative way of applying academic research to determine value
and momentum effects in securities markets.

The dividend yield (spread) factor time series is defined as:

Dt = Dht – D0t
Where

Dt = the return for the Dividend Yield factor for month T
Dht =
the average return of stocks in the highest 10% of dividend
yield of the estimation universe during month T

D0t = the average return of stocks with zero dividend yield in the
estimation universe during month T

The logic here is that stocks that tend to do well when high yielding stocks
(value) are doing better than low yielding stocks (growth) produce positive
coefficients.

The correlation to the cross-sectional standard deviation of stock alphas
during each period is introduced as a further measure of a stock’s value /
growth qualities. The standard deviation of stock alpha is called
“idiosyncratic variety”.

Jt = (Standard Deviation (Akt))
Akt = Rkt – (Rft + Bk * Rmt)

Where
Jt = idiosyncratic variety during month T
Akt = alpha on stock K during period T (under CAPM)
Rkt = return on stock K during period T
Rft = risk free rate of return during period T
Bk = beta of stock K
Rmt = return on the market portfolio during period T

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Stocks with “value” characteristics tend to do well when idiosyncratic variety
is low, and stocks with “growth” or momentum characteristics tend to do
well when idiosyncratic variety is high.

Two time series are now available to represent the potential return
differences relating to the “value/growth” property. Unfortunately they are,
at this point, in different units and structured in opposite directions! In the
“Dividend Yield” factor time series, high numbers are associated with
“value” doing better than “growth”. In the “Idiosyncratic Variety” factor
time series, high numbers are associated with “growth” doing better than
“value”.

In order to combine these two series in a single factor, they must be
transformed into similar units. This is accomplished by standardizing each
time series. This gives each time series a mean of zero and a standard
deviation of one.

Et = Dt – (Average [t= 1 to n] Dt) / Standard Deviation [t= 1 to n] Dt
Ft = Jt – (Average [t= 1 to n] Jt) / Standard Deviation [t= 1 to n] Jt

Where
Et = standardized Dividend Yield factor return during month T
Ft = standardized Idiosyncratic Variety factor return during month T
n = number of months in the time series

Clearly, it is important that the direction of the effect be the same in both
series, or they would tend to counter-act each other. Simply reversing the
sign on the Idiosyncratic Variety time series sets its values in the same
direction as the dividend yield spread part of the factor.

Gt = -Ft
Where
Gt = the reversed value for the Idiosyncratic Variety during month T
The two factor time series are combined by simply taking the average
Vt = (Et + Gt) / 2
Where
Vt = return to the “Value/Growth” factor during month T
Armed with the Vt factor return time series, the normal estimation regression
is run for each stock to obtain the factor exposure. High exposures imply a
“value” orientation and low exposures imply a “growth” orientation.

Factor variance and All factor models are based on observations of the past covariance among
covariance securities over some series of past time periods (e.g. past 60 months). The
calculations usefulness of history as a guide to the future is clearly a function of the rate
of evolution of the market, its participants and a host of other factors. The
exponentially faster the rate of evolution or change in market participants, the less useful
weighted

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data from the distant past is as a guide to the future. This effect has a direct
effect on the way historic data should be used for factor variance and
covariance forecast calculations.

Northfield risk models are estimated by exponentially weighting the
observed data. The recent data is given greater emphasis. The function e-nr
is used where n is the serial number of the observation (1st observation is
the latest and n is from 1 to 60 in most cases) and r is the decay rate.
Northfield research finds that an appropriate decay rate is 0.02 for all models
except the China model, which has decay rate of 0.04, and Pacific Rim
model, which has a decay rate of 0.03.

Factor variance Efficient market theory suggests that mean alphas (returns net of market
estimation risk) to a particular factor should be close to zero over time. However, in a
bubble or trending market, a particular factor may exhibit a high mean return,
with low variance around the mean for a substantial period of time.

The failure of normal theoretical assumptions to hold is an additional source
of uncertainty that the traditional factor return variance calculation does not
capture. An improved factor return variance measurement is required to
capture this source of risk.
Variances in all Northfield time series risk models are estimated from the
average of the squared value of the factor returns over the same period.
This is equivalent to assuming that the mean is zero in the usual formula.
Empirically, most factor returns do have a mean close to zero, so the change
will not be noticeable. However, when a factor return is consistently large
and of one sign (i.e. positive returns to the internet factor during tech
bubble), this procedure will inherently bias the factor variance values
upwards to provide a warning of the unusual factor behavior. The two
contrasting examples below show the difference the change can make when
a trend is apparent. More of this issue can be found in.

http://www.northinfo.com/Documents/65.pdf

Note: The traditional variance computation with which the squared
differences from the mean of a time series (last 60 months) of factor returns
are measured is not used.

The principle is shown using returns data for the Inflation Factor (Northfield
US Macroeconomic Model) and US Fundamental Model Tech Sector from
January 1995 through December 1999. The Inflation factor does indeed
have a mean quite close to zero over the sample period and the two factor
variance estimates are very close. Examples of such stark contrast were not
found in the global or single country model factors.

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The Multi-Asset Class Risk Model Mont hly ret urn Cumulat ive ret urn

I nf la t ion f a ct or r e t ur nsm onthly and cum ulative

10
8
6
4
2
0

-2
-4
-6
-8
- 10

Sep- 94
Apr- 95
Oct- 95
May- 96
Dec- 96
Jun- 97
Jan- 98
Jul- 98
Feb- 99
Aug- 99
Mar- 00
Oct- 00

Da te

Traditional calculation Annual Factor Variance
“New” calculation 81.516
81.517
Factor Mean
-0.01

However, in the second example, of the US Tech sector, the result is quite
different. The mean is far from zero and the factor variance estimated is
correspondingly significantly higher when the average of the squared returns
is used, rather than the average of the squared differences from the mean.

S&P 500 tech stock returns Cumulative return Monthly return
Da te 35
900 25
800 15
700 5
600 -5
500 -15
400 -25
300 -35
200
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0
cumulative
monthly

Sep-94
Apr-95
Oct-95
May-96
Dec-96
Jun-97
Jan-98
Jul-98
Feb-99
Aug-99
Mar-00
Oct-00

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The Multi-Asset Class Risk Model Annual Factor Variance
700.44
Traditional calculation 876.24
“New” calculation
Factor Mean 3.83

Estimating the stock Calculating the sensitivities of securities to the selected factors is a crucial
betas to the factors process in risk model construction. The coefficients in the Northfield single
country risk model have been estimated using a weighted generalized least

squares (WLS) stepwise procedure. This has the benefit of dampening the
effect of outliers on the results, while retaining clarity.

Weighted generalized least squares (WLS) differs from the popularly used
Ordinary Least Squares Regression (OLS) in that in WLS each observation is
weighted differently. For the purposes of these models, the observations
were scaled by the inverse of the residual. This procedure ensures that
unusual events do not have an unduly high influence on the results.

Stepwise regression consists of regressing the dependent variable on one
independent variable, capturing the residuals, and regressing those on the
remaining independent variable(s). The technique is useful when
multicollinearity (highly-correlated independent variables) is potentially a
problem. Where multicolinearity does occur, traditional multiple regression
produces coefficients are unstable over time. Sector and market indices are
often correlated; stepwise procedures address this problem.

This procedure first extracts the effects of the sectors and regions, then
estimates the sensitivities to interest rates and oil prices and finally
determines the sensitivity to market development, company size and
dividend yield. The sequence for the regressions is as follows:

1) Regress company returns on the sector index, capturing the residuals.
2) Regress the returns on the sector index, weighing each observation

proportionately to the residual of the previous regression, then capturing
the residuals.
3) Regress the residuals obtained from the last regression on the region
index, capturing the residuals.
4) Regress the residual returns on the region index, weighing each
observation proportionately to the residual of the previous regression,
then capturing the residuals.
5) Run a multiple regression with the residuals of the previous regressions
as the dependent variable, and the Citigroup World Government Bond
Index and the oil prices as the independent variables.

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6) Run a multiple regression with the residuals acquired in step # 5 as the
dependent variable and market development, company size and dividend
yield factors as the independent variables.

7) Run a principal components analysis of the remaining residual returns to
investigate the possible existence of other factors. Use any significant
principal components as additional factors.

The hybrid risk The introduction of "hybrid" modeling in our line of Single Market models has
model structure proven very useful and been extremely well received. The hybrid risk model
structure is now applied to the Global model
applied to the
Global Equity risk In the Northfield hybrid model, the usual observable-factor model is built with
whatever known factors are most appropriate to the observed market data.
model By re-examining the residuals to estimate the temporary “statistical factors”,
the hybrid model addresses one of the key limitations of traditional risk
models - the fact that they cannot “learn” or adapt as markets change. The
application of a principal components analysis on the residuals from the main
observable factor model allows automatic adaptation to changes in the set of
factors that is influencing market behavior at a particular moment in time.

An implicit assumption of any factor model is that the factors specified
account for all the sources of correlation between securities. Unfortunately,
factor models can only be built from past data. As such, the model will
provide an imperfect representation of future correlations as conditions
change, potentially or often even, resulting in an omitted variable bias. This
can be addressed by performing a principal components analysis on the
residuals from the observable factor model. To be clear, the principle
components are only run on that part of the securities’ returns not explained
by the model's factors. Using the output from this analysis, temporary
factors can be added to the model. These new factors can quantify the
existence of whatever new or transient forces are influencing the market
currently.

The hybrid model structure makes the Northfield risk models adaptive to
market changes in a way that traditional observable-factor models are not.
Yet unlike pure "statistical factor" models wherein the principal components
analysis is used to explain all of the security correlation, Northfield’s hybrid
models have a fully specified (and clearly understandable) observable-factor
structure. Given that the expected value of the variance explained by the
temporary factors is greater than zero, the use of temporary factors in this
fashion adapts Northfield models very quickly to new influences in the
market.

It should be noted that the economic meaning of the statistical factors varies
through time and from market to market. Although it may not be able to give
them detailed economic interpretations, this is still a much better approach

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to risk assessment than mislabeling such risks as being company specific
(which would occur in the absence of this approach).

Asset specific risk In principle, whatever is left over from the principle components analysis is
adjustment using truly stock specific. The danger is that despite best efforts the model may
now under-represent the asset specific or residual risk. Clearly, this is
the Parkinson undesirable.
volatility estimator

In the presence of uneven or high intra-month volatility, serial correlation or
heteroskedasticity in returns, the Parkinson method of estimating volatility
produces superior results. The approach has been used successfully in the
US Fundamental Model for many years and has been tested and adopted for

use in the global and single country risk models.

The Parkinson method uses the highest / lowest observed asset prices over
each time period to infer total volatility. This is distinct from traditional
approaches that typically use month end data and effectively ignore intra
month values. The Parkinson method has the benefit, therefore, that it does
not ignore volatility related information from prices, simply because the
prices / returns occurred intra month as opposed to the month end. This
information is incorporated into the factor models as an adjustment to the
asset specific risk in those cases where the Parkinson method estimates a
higher total volatility than the initial risk model estimate.
The basics of the Parkinson method can be found in: Parkinson, Michael;
“The Extreme Value Method for Estimating the Variance of The Rate of
Return;” Journal of Business; 1980; v 53(1); 61-66.

60 monthly returns In normal circumstances, 60 months of returns are analyzed for each stock.
used to estimate the The question immediately arises, then how to handle new or changed
companies for which there is little or no history of returns.
risk model:

Dealing with short For companies with shorter return histories, the missing returns are proxied
data histories by the return of an equal weighted index of all stocks in the same sector and
country as the subject security. The asset specific risk of the subject security
is statistically adjusted to overcome the volatility muting caused by the
substitution of index return data.

The volatility of the stock is increased in relation to the amount of history that
is actually available. For example, if just 3 months of real returns were
available and 57 months of sector history had to be used, the volatility of that
series would be increased by the proportion of the real observed stock to the
spliced on sector returns. In this example, the adjustment would multiply
the residual by Sqrt (60/3) = Sqrt(20) = 4.47

In other words, in the early months after an IPO, the model will significantly
inflate the asset specific risk of the stock as compared to the residual values
arising from the regression.

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The single country The order in which the sector and region effect is estimated is reversed in
models’ specific use the Northfield single country models. By extracting the “region” effect first,
(in this case the region usually just being a single country) the “region” factor
of the factors becomes equivalent to a CAPM beta. Then, instead of using a world bond
index (in US dollars) as a global interest rate proxy, the local government
bond index (in local currency) is used for a single country model. Lastly for a
single country model, the market development factor becomes meaningless,
and is dropped.

Testing the The global equity risk model was thoroughly tested by comparing realized
Northfield Global and estimated risk numbers. Two statistics have been used to measure the
Equity Risk Model effectiveness of the new specification both over the past five years, and over

the life of the model history.

The correlation of realized and estimated tracking error and absolute risk of
the portfolio for each month is measured and the average taken across time
periods. The correlation values represent the cross-sectional correlation
between forecasted values of the risk, and the realized values of the risk
over the subsequent 12 months. These values measure the ability of the
model to discriminate low-risk portfolios from high-risk portfolios. High
numbers, close to one, are good. Values close to zero suggest that the
model is useless. Values below zero indicate that the model is consistently
wrong. The test results show high values for most of the test periods.

In addition to correlations the bias of estimated and realized risk numbers is
also observed. For each portfolio in each month a bias number is calculated
by dividing the estimated risk number by realized risk number to determine
by how much forecast risk was overestimated or, indeed, underestimated.

On average, 30 portfolios were created for each month. An average across
time is calculated over the two sample periods. A value of one indicates that
the model is exactly right on average, while values above one suggest our
forecasts were too high on average. Values below one suggest our values
are too low on average. Since underestimating risk is more dangerous to the
investor than overestimating, Northfield models are calibrated to be a little
high on average (say 1.10-1.20). In practice, the desirable amount of bias will
be larger in countries like the US where the cross-sectional dispersion of
returns is larger (the average level of correlation between stocks is lower),
and less in countries where cross-sectional dispersion of stock returns is
lower (correlations between stock returns are higher). The five-year test
periods include the unusual conditions of the internet/tech bubble period, so
it is not surprising that the models were a little low on average in the case of
the 5-year figures.

The tables and graphs below show a comparison between the performance
of the current model specification and the performance of the Global model
as previously specified up to early 2004.

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Global

“Old” Specification Enhanced

Correlation Bias Correlation Bias

13 yr 5yr 13 yr 5yr 13 yr 5yr 13 yr 5yr

Tracking Error 0.65 0.68 1.05 1.02 Tracking Error 0.73 0.73 1.11 1.03

Portfolio 0.49 0.44 1.2 0.9 Portfolio 0.55 0.45 1.15 0.96

Correlations - Global

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

0

JDeucn--9900
JJDDeeuuccnn----99992112
JJDDeeuuccnn----99993443
JJJDDDeeeuuucccnnn------999999657765
JDeucn--9988
JJDDeeuuccnn----09900990
JDeucn--0011
JDeucn--0022

TrkErrOld TrkErrNew

Summary Results from the Northfield global equity risk model are intuitive and
conclusion on the straightforward to interpret. This is the result of the model specification and
global equity risk the refinements that have been introduced over the years.

model Any one security will be exposed to just 13 of the 90 factors or variables now
used in the risk model.

The full factor structure includes five regions, six super-sectors (with each
security participating in one region and one sector), two macroeconomic
factors: the Citigroup World Government Bond Index and Oil Prices in US
dollars, the developed versus emerging markets (investor confidence),
company size, and value / growth and finally the five “statistical factors” or
principle components that are designed to capture any systematic sources of
risk missed by the pre-specified factors.

The risk model provably forecasts risk with a high degree of accuracy, while
retaining its intuitive appeal and ease of use and interpretation.

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The Northfield family of Single Market Models is the result of years of
rigorous research, testing, and field experience. They were designed with
several goals in mind: transparency, flexibility, completeness, comparability
and ease of interpretation. These models are powerful tools, which, when
used appropriately, can add significant value and understanding to the
investment process.

Section 3 – Fixed The fixed income model framework builds on, and is totally consistent with,
Income the global equity model. This combination addresses all of the significant
sources of both equity and fixed income risk in a balanced portfolio. Fixed
income securities are decomposed into “atomic” sources of risk –
specifically these are interest rate risk, currency risk and credit risk. Three

interest rate specific factors were added to the existing equity factor model
structure, to capture three types of term structure shape change. These

three factors correspond to “shift” (change in interest rates), “twist”
(change in the slope of the yield curve) and “butterfly” (change in the
curvature of the yield curve) movements of the yield curve. Both the credit

and currency risk “atomics” of fixed income securities are handled using the
familiar factors used in the equity model. This mechanism welds the equity
and fixed income elements together in a unique, intuitive, clear and powerful

yet parsimonious Global model.

Fixed income By their nature, fixed income securities must be treated somewhat
securities in a differently to equities. There were several issues to be addressed in order to
global equity risk extend the Everything Everywhere factor structure as originally adopted from
model framework the Global Equity Model to cover Fixed Income.

The major sources of risk with fixed income instruments are:
- interest rate risk
- credit risk
- currency risk
- “forward” equity risk with convertibles
- “prepayment” risk with mortgage- or asset-backed securities
- effect of embedded put, call and sinking fund provisions

To approach each of these sources of risk there were a variety of well known
and broadly accepted methods from which to choose. In some cases,
however, none of the accepted methods were deemed appropriate. In these
cases we developed our own, enhanced, methodology – specifically for
pricing convertible bonds, and for rapidly pricing large numbers of mortgage-
backed securities.

In this section we describe how we approached the largest sources of risk,
and the methods chosen.

For example there were two clear choices of how to model interest rate
dependent securities:

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Option 1. The approach used in EE is to link the fixed income and equity
models together via the components of credit risk. In this way, we link the
two models tightly together and allow the user to view aggregate bets
across asset classes. This is one of the core objectives of the model.

The Northfield approach is to decompose fixed income securities into
“atomic” risk factors:

• Interest Rate Risk
• Currency Risk
• Credit Risk

The vector of risk exposures of each individual bond is comprised of two
pieces. The first piece consists of interest rate sensitivities. The second
piece consists of risk sensitivities equal to effective duration times the
sensitivities of the credit synthetic which is described later.

By doing this, we capture:

• Interest rate sensitivities to the three familiar factors with which
practitioners are conversant and comfortable.

• Option risk which is explicitly included during the interest rate sensitivity
estimation process.

• Credit risk is captured as a duration-weighted exposure to the appropriate
credit synthetic, further described below.

• Currency exposure - explicitly included as a dummy variable in the model.

Option 2. Estimate sensitivities for each country to changes in, say, fifteen
different maturity points on the term structure, then, sensitivities to perhaps
19 credit spread changes, sensitivities to possibly 65 industry spread
changes, and also sensitivities to various volatility surfaces and so forth. This
would capture, in a very complete and robust fashion, the risks present in
fixed income instruments.

This approach would be completely disconnected from the equity approach,
except very loosely via the covariance matrix. Further, this approach would
result in some 5000 factors, therefore, catastrophically failing the parsimony
(limited number of factors) test, and was rejected.

Interest Rate Risk The interest rate related risk of fixed income securities is estimated from
Interest rate/term their sensitivity to changes in three interest rate term structure factors. The
structure exposures three factors describe changes in the shape of the term structure of interest
rates (changes in the shape of the yield curve) as familiar to bond managers:
a simple parallel shift component, a steepening / flattening twist component,
and a third term expressing changes in the wings or the curvature that is
typically called “butterfly” (S/T/B).

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“Shift, twist & The three Treasury Factors (TFs) are:
butterfly” definitions
• TF1 or “Shift” – This is effectively a measure of the risk of a parallel shift
in the global average yield curve. Exposure to this factor is comparable to
duration, adjusted to reflect that rate volatility is lesser or greater in some
countries than in the world on average. The larger a security or portfolio’s
absolute coefficient is to the factor, the more sensitive the security or
portfolio is to interest rate changes. If a portfolio has a more negative
sensitivity to TF1 than its benchmark, then, rising rates will hurt the
portfolio more than the benchmark and falling rates would be relatively,
more beneficial.

• TF2 or “Twist” – is a measure of change of steepness of the yield curve,
as measured in the direction of increasing maturity (i.e. long rates minus
short rates). The more negative the security or portfolio’s coefficient is to
the factor, the more sensitive it is, relative to the benchmark, to increasing
steepness or increasing long term rates and decreasing short term rates.

• TF3 or “Butterfly” – is a measure of the change in curvature of the term
structure. Net of the second factor, typical yield curves have a peak at
intermediate maturities relative to shorter and longer maturity. The level of
this peak may increase or decrease through time. The more negative the
security or portfolio’s coefficient is to the factor, the more sensitive it is,
relative to the benchmark, to increased convexity, or if less negative
(positive relative exposure) the security or portfolio will benefit from a
flattening curve.

The security factor exposures are estimated by re-pricing each bond under
incremental changes of the parameters we use to express shift, twist, and
butterfly. Assuming a log normal diffusion of interest rates for our binomial
tree pricing approach, the curve shape defining equation coefficients are
changed iteratively and the bond re-priced. The price change relative to the
base price under the original (no change in shape) scenario is then captured.

Mathematically, the sensitivity is an approximation of 1/P dP/dy. We
increment the yield curve by a finite but small amount (typically a minute part
of a basis point) and re-price the security, giving us the change in price for a
small yet finite change in yield. As the change in yield is so extremely small
this provides us with a good approximation to the first derivative of price with
respect to yield.

Fixed income risk The term-structure exposures are estimated by pricing the bond under four
factor exposures or scenarios, corresponding to the base case (no change) and each change in
the shape of the term-structure of interest rates; a shift, twist, and butterfly
“Betas” movement. The instruments are priced using a binomial tree. This allows the
effect of embedded call, put and sinking fund structures to be included
explicitly.

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Fixed income – EE currently incorporates some 450,000 fixed-income securities issued in
450,000 bonds & 57 fifty-seven currencies. Consequently, now it uses the same number of real
or implied treasury yield curves as there are currencies. This structure
currencies & yield provides for more accurate valuation of fixed income securities and thus
curves enhanced risk estimation for fixed income portfolios. In early versions of the
model each bond was priced according to changes in the curve from the
largest bond market in the region. While quite satisfactory for global balance
portfolio risk analysis and construction, more accuracy was required for
single region fixed income only portfolios. The structure described achieves
this goal.

Fixed income - Real The yield curve term structure used for EE is founded on the yield curves of
and inferred yield five major currencies that also have large fixed income markets: The US
curves dollar, the British pound, the Japanese yen, the Swiss franc and the Euro.
Each yield curve is constructed using the current prices and parameters of
existing government bonds issued in the currency. Remotely historical yield
curve structures are constructed using yield data from the US Treasury, the
Bank of England, Bank of Japan, Bank of Switzerland and the European
Central Bank respectively.

Yield curves for securities issued in currencies other than the five major or
“core” currencies are inferred from the five core currency curves. The non-
core curves are inferred by forming a new curve constructed from the yield
curves of the five major currency curves weighted by the inverse of their
exchange rate volatility with the currency under consideration. This is a
simple and unambiguous rule by which all the non-core curves are
constructed.

An example: Here is an outline of the process used to infer or construct a Thai Baht (THB)
Inferring the Thai curve.

Baht yield curve 1. Estimate the volatility of the exchange rate of the Thai Baht with the
major currencies: USD/THB, GBP/THB, JPY/THB, CHF/THB, EUR/THB

2. Rank the currencies by the inverse of the relative volatility of their
exchange rate with the Thai Baht.

3. Create a new curve from the five core curves weighted by the
inverse of the exchange rate relative volatilities calculated above.

This approach assumes that if term structures of two different currencies are
similar to each other, the exchange rate volatility on these will be low. If
there is minimal volatility between the two currencies (e.g. USD and THB)
this would imply that the Thai Baht yield curve is very similarly or even
identically shaped as the US curve, differing by a spread. The spread is
captured as an element of risk as is calculated for the Option Adjusted
Spread for each fixed income security.

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Armed with real or inferred yield curves for each currency in the model, each
fixed income or convertible security can be priced and risk parameters
estimated using currency appropriate curves.

Creating the An important point to note: The EE model uses a “Global Yield Curve” to
“Global Yield report the forecast volatility of the “shift” “twist” and “butterfly” factors.
This “Global Curve” is itself inferred or constructed from the five major
Curve” currency yield curves weighted by the outstanding dollar value of
government or “treasury” securities traded in each currency.

Scaling the stock The three Global Yield Curve factors are a pivot for the calculation of risk
factor exposures to parameters for both the individual security risk exposures as well as the
factors of the yield curves based in all of the fifty-seven currencies. A further
the “Global Yield adjustment is needed to uplift the factor exposures for a non-US fixed
Curve” income security. Each fixed income security’s factor exposures are scaled by
the ratio of the volatility of the respective factor from the respective
currency's yield curve and the same factor from the Global Yield Curve.

Scaling the Global For example if a particular US bond has an exposure to term structure factor
Yield Curve factors 2 (“Twist” or Curvature) of 0.03 and the volatility of the same factor in the
to local curve factor USD denominated yield curve is 1.25 more volatile than the same factor in
the Global Yield Curve then the reported exposure in the EE data file will be
volatilities 0.0375 (0.03 * 1.25). This ensures that the variance of the factor from each
currency's yield curve is recognized in the risk equation. It also retains the
convenience and simplicity of the EE model structure by using just one term
structure - the Global Yield Curve to represent interest rate risk for fixed
income securities.

To run through the whole process in steps:

• A government yield curve is calculated or inferred and calibrated for each
major market. Coefficients for expressing this curve as a function
involving the three interest rate coefficients (S/T/B) are calculated.

• The option adjusted spread (OAS) is estimated for each bond.
• Price each bond using the relevant curve in a binomial tree.
• Then increment each coefficient in turn by a little bit and again price the

bond to get the sensitivity of the bond to changes in each of these three
coefficients.
This analysis is performed for the entire fixed income universe. Northfield
estimates all security sensitivities prior to the model’s distribution. Only the
security exposures, factor variances, and factor correlations are distributed.
As a result, the final model when used in conjunction with the Open
Optimizer analytical system represents a very easy to use and rapid system
with minimal IT requirements for the client.

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Credit Risk Northfield's strategy is to model credit risk as a function of the "equity"
factors in the model. The intuition is that equity analysts and credit analysts
focus on the same basic characteristics of the firm. Clearly, some credit
analysts just focus on the probability of downgrade / upgrade. However,

logically the agencies ratings are in turn focusing on the same features as
equity analysts - the risk of future cash flows of the firm.

Traditional risk models separate equity and fixed in terms of different factors,
and perhaps join them back together through a potentially huge covariance
matrix. In our model, the two asset classes are unified. In this framework
the credit risk of a bond (the equity-like portion of the bond) is modeled as a
set of exposures to the equity factors in the model. Equity and fixed income

instrument risks are expressed by exposures to the same factors. This is
one of the unique advantages of the Northfield model.

Our main approach to corporate credit builds on the fundamental economics
driving the financial sustainability of a debt issuer. It is based on the
common intuition that the more assets and more stable they are, and less
debt, the more creditworthy a debtor is. In essence, these three
fundamental factors determine the financial capacity of the borrower to meet
its obligations in the future.

A rigorous theoretical framework that captures the above intuition views a
firm as a pair of options. First, stockholders hold an implicit call option which
the bondholders are short, which has a strike price equal to the level of the
firm debt and where the underlying is the total of the firm’s assets. The put-
call parity further implies that for the de facto owners of the portfolio
consisting of the firm’s assets, and a short position in the firm debt [i.e. the
Stockholders], there is a corresponding put option, the exercise of which is
essentially the event of default. The idea of using this implicit firm option has
existed in prior work in this area notably by Merton, and Leland & Toft, to
infer probability of default.

We derive a solution of corporate bond’s credit factor exposures which are
directly related to the factor exposures of the associated company’s stock.
The relation has the form:

Factor Exposure Bond = -(E/B) * (delta put/delta call) * Factor Exposure
Of the Stock of the Bond Issuer

Where E is the market capitalization of the firm, B is the market value of the
firm’s debt, and the put and call are calculated with respect of the time
horizon of the particular bond tranche. Instead of using the maturity of the
bond as the expiry date of the options, we use the effective duration, which
takes into consideration the aggregate effect of embedded redemption
events, and coupons. The implicit assumption regarding the time of default
"exercise", is that if a firm defaults, it will default on all of its debt, which is
consistent with conventional bond indentures.

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The derivation exits with the same intuition with which it starts. First, it
states that, everything else the same, the closer the firm is to default
(deeper into junk status) the higher the delta of the put will be relative to the
delta of the call. Given that option gamma is the same for puts as for calls
the approach to junk status will tend to proportionately increase the ratio of
two deltas more than it will decrease the ratio E/B per unit of decline in the
firm asset value. That will make the bond’s factor exposures more similar to
that of the stock and this reflects the empirical evidence that junk bonds
behave like equities.

Another implication from the bond-from-equity exposure relation transpires.
If two debt issues from the same issuer have the same maturities and
duration characteristics they will also have the same factor exposures. Since
an identical relationship is applied to stock specific component of risk to
calculate the bond specific risk, the two debt issues will have identical total
risk.

The particular implementation of these calculations has been achieved by
European put and call pricing. Provided that in practice the "default" is
exercisable as an "American" type of option event, we find an upward biased
estimate of the firm asset volatility implied by the price of the default put
option that is reflected in option adjusted credit spreads (please see credit
spreads section for the methodology of OAS calculation).

An obvious input that goes into the firm’s sustainability factor exposure
calculations is the capital structure of the firm. When this information is not
available for a bond's issuer, we utilize a bucketing technique, which consists
of grouping bonds by region, sector and credit rating, and calculating median
bond factor exposure and specific risk form the constituents that carry all the
requisite information for the firm sustainability calculations. Subsequently, all
bond constituents that do not possess the requisite input information
associate with those average risk parameters for their bucket.

Besides grouping bonds based on sector, region, and rating, we specialize
some of the categories into sub-buckets. For sovereign issues rated AAA,
denominated in the national currency, and denominated in the five major
currencies - GBP, USD, EUR, CHF and JPY we have separate buckets. For
"covered" bonds from the English-Speaking and Continental Europe region
rated A and above we also have separate buckets.

The buckets formed by financial companies play a special role in the current
modeling of sovereign debt credit, that are not in the specialized sovereign
buckets mentioned previously. The current credit framework for sovereign
entities is intertwined with the aggregate credit outlook of financial
institutions (a group dominated by banks) from the same countries. The
rationale for this is that the fortunes of fixed income obligations from
governments and banks from such countries are inextricably connected. This
is easier seen for countries that cannot monetize their debt at will. If a

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government is unable to meet its fiscal obligations, it directly affects its
ability to ascertain the stability of its banking system. In reflection, should the
banking system have a prevailing difficulty with credit, it undermines the
country economy as a whole and dries up government revenues. A similar
argument can also be applied to governments that can monetize debt at will
the details of which are given in the Northfield Newsletter from December
2011. This overall argument leads to the conclusion that a government with
a rating of e.g. BB should justifiably inherit the average risk characteristics of
the group of banks from the same country and with the same credit rating.

In cases where we do not have sufficient data to calculate the average risk
characteristics of a bucket (and hence its constituents), we resort to an
alternative methodology. It involves the time series of Option Adjusted
Spread changes as a carrier of information about changes in the credit
standing of a particular issuer. The volatility of credit spreads is modeled as
a function of the volatility of the factors that define the spread. The time
series of median credit spreads for each bucket allows a time series of credit
spread absolute changes to be calculated and regressed against the factor
returns for the "equity" factors in the model like oil prices, dividend yield etc.
This results in a set of "Credit Spread Synthetic Securities" of unit duration,
with exposures to the "equity" factors. The factor exposures of the synthetic
securities are the result of the time series regression of credit spread
absolute changes for the appropriate bucket as the dependent variable and
our equity factor returns as the independent variables. The specific risk of
the unit duration credit security is the residual of this regression. To derive
the actual credit exposures and asset specific risk of a bond under the
alternative credit risk approach, we multiply the unit-duration credit synthetic
vector of factor exposures and specific risk applicable to a bond's bucket by
the effective duration of the bond.

Credit spreads The initial intention was to use published yield spread data rather than
compute our own. However, it is almost always unclear from the published
spreads whether the constituent securities are callable, or put-able, and if so
in what proportion. In addition, the duration breakdown of the constituent
securities is not, typically, disclosed. One duration number for a portfolio is
insufficient.

To surmount these issues in the model, credit spreads are estimated
explicitly. The exact procedure for Option Adjusted Spread (OAS) time series
calculation is as follows. The OAS is calculated for each individual bond
issue in the universe each month. While calculating OAS, each bond is
priced via a binomial lattice to capture embedded options’ effect on each
bond’s risk characteristics. The option adjusted spread of each bond within a
bucket becomes part of the group of OAS from which the median spread for
a bucket is determined, that is used later to determine the credit synthetic
securities credit exposure.

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The Northfield process fully accounts for the options embedded in each
security controls the constituents and thus avoids duration bias. As a result
of this process, the Northfield credit spreads are "cleaner" than the usual
published series. To the extent that historical data is sparse or unavailable,
we resort to published yield series, where available. In the event that this
option is also unavailable, a proxy from the largest regional market with an
adjusted series is used.

Fixed Income pricing data is of inferior quality compared to stock price data.
However, for risk modeling purposes, any error in pricing only inflicts a
tertiary effect on the final results: the sensitivities of a given bond issue to
the various term structure movements are affected only marginally by errors

in pricing.

Fixed income Risks such as Prepayment Risk, Option (Call or Put) Risk, and Basis Risk are
prepayment, implicitly incorporated into the exposures of the security during the pricing
optionality, basis process. When generating the exposures to term-structure shape changes,
risk. The option the bond is iteratively re-priced under four effective scenarios (no change,
adjusted spread shift, twist, and butterfly). With each price calculation the effect of
embedded options, prepayments and basis risk is taken into account. Thus,
there is no need to account for this elsewhere in the model and so the
clutter of additional factors that would be required to model these effects
explicitly is avoided.

Credit exposures The argument for including or not including the Credit Risk components for
for government government bonds follows: Are all governments seen to be equally likely to
bonds pay their obligations? For instance, the US has defaulted in the past, while
the UK never has. Is the US equally credit worthy? How do they both
compare to Australia, Brazil, Chile and Denmark, for example? Most
investors would regard the US to be "safe" while that may not be true of
some of the others.

Our current approach divides sovereign bonds into several categories. Each
gets a different treatment in the EE model.
Category 1
Bonds that form the five risk free yield curves applicable to the five major
currencies in the model - USD, CHF, GBP, EUR, JPY. These bonds must be:
- AAA rated
- "On the run" (Highly Liquid, and coupon close to most recent issue of that
maturity)

These bonds have no credit risk exposures and no asset specific risk. In
terms of countries, this group would include the US, UK, Japan, Switzerland
and the AAA rated issuers of Euro.

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Category 2
Bond that are:
- AAA rated
- "Off the run" (not current coupon so less liquid, and not part of the yield
curve)
- Issued as national currency debt in USD, GBP, JPY, EUR, and CHF

In terms of countries, this group would include the US, UK, Japan,
Switzerland and the AAA rated issuers of Euro.

These bonds have small equity factor risk exposures derived from the OAS
spread history. In this regard, it should be noted that OAS spreads represent
both credit risk and illiquidity.

In this category, bonds have no asset specific risk. The reason is that the
respective sovereign governments can invoke debt monetization at will, if
contemporaneous government revenues are insufficient to meet debt
redemption amounts, thus precluding the potential of an actual default.

Category 3
Bond that are:
- AAA rated
- Issued as national currency debt but NOT in USD, GBP, JPY, EUR, and CHF

These bonds have credit risk exposures derived from the median OAS
history of the financial companies of the same rating and region. Please see
description of next category for the rationale of this association.

In this category, bonds have no asset specific risk. The reason is that the
respective sovereign governments can invoke debt monetization at will, if
contemporaneous government revenues are insufficient to meet debt
redemption amounts, thus precluding the potential of an actual default.

Category 4
All other government bonds.

The EE model has always categorized government bonds as being part of the
financial sector. The rationale for this is that governments are the effective
guarantors of banks, and that government bond debt is the largest single
asset of essentially every bank. The health of government finances and the
health of the banking system within a given country are joined at the hip.

As mentioned previously, in these cases, the equity exposures for credit risk
for a government bond are the average credit exposures of comparably rated
financial institutions in that country. So if the government debt of country X
is rated "A", we use the average factor exposures of "A" rated financial sector
companies in that country or region. It should be noted, that to the extent
that corporate borrowers are characterized with statistical factors, so are the
bonds of the related government.

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The Multi-Asset Class Risk Model

What to do if One of the principle features of the Northfield philosophy and systems is
government bonds’ their openness. This means that the user is able to go into the database and
change the data supplied if desired. So in the case of Gilts, should the user
credit exposures feel that they are truly default risk free, their credit exposures may be set to
are undesired zero. Equally, there may be other governments' securities for which you feel
the Northfield estimate of credit risk exposure is inadequate, in which case
you may just as easily raise them.

Fixed income The fixed income part of the model includes government, and corporate
data and bonds, index linked and convertible bonds from all the major and virtually all
coverage developing markets. We work constantly with our data suppliers to improve
coverage.

Included on request basis (otherwise the local user database becomes
unmanageably large) are securitized instruments and municipal bonds.

Modeled on request basis are financial derivatives and funds of unknown
constituents.

Securitized instruments, municipal bonds, derivatives, and funds can be
respectively downloaded and modeled through Northfield’s delivery system
EENIAC (Everything Everywhere, Northfield Information Access Console).

Fixed income Thomson-Reuters and FTID are currently the primary source for all data used
pricing sources in estimating the EE Model.

Dealing with It is part of reality that data coverage for fixed income securities from each
missing fixed and every vendor is generally poorer, less integrated, and less transparent
than that for equities. Many users have started to realize over time that
income global coverage of fixed income securities, from any risk model vendor is not
securities perfect. As a result we have devoted some effort to making a
straightforward process and step-by-step guide to creating proxy securities.

There are at least two situations where you may need to create a proxy
bond.
1. Our data vendors do not cover the bond completely, or at all.
2. The bond is excluded from our model because it is issued “outside’ the

model. For example, the Cayman Islands are not included in the model.
One might proxy the regional exposure of these as Region 2 (US, UK
etc).

Northfield provides an online service (EENIAC) for taking the terms and
conditions for omitted bonds and producing the factor sensitivities. These
can then be appended to the model data file. (Note: there is a function to
allow this appending within the FactSet platform for risk analysis and within
Risk in P.A.)

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The Multi-Asset Class Risk Model

Fixed Income: The general approach to modeling fixed income security risk has been clearly
Instrument laid out above. The focus is now on some specific instruments’
characteristics. The main source of risk for Government bonds linked to an
specific details interest rate index is basis risk. In the context of a balanced portfolio, this risk

is going to be swamped by other sources of equity and bond risk and can
therefore be safely approximated, for the moment, as local cash.

Floating Rate Bonds Clearly, this is not quite so true for Corporate Floating Rate bonds where the
credit spread issue remains.

For floating rate instruments, we calculate interest rate sensitivities in the
normal fashion and they often turn to be rather minute. This is to be
expected because if coupon payments are synchronous with rate changes
and there is no magnitude difference between the two then interest rate
sensitivities would be zero. Since there are some timing differences
between coupons and reference index resets, and there is some basis
associated with the coupon over the index there are some trace bond return
sensitivities to yield curve movements.

Regarding credit factor sensitivities, we have to introduce the concept of
spread duration. Usually, coupon's don't get adjusted because of the credit
standing of an issuer has changed. This lack of adjustment in terms of
coupon bps means that there should be an adjustment in the current value,
which is the other name of duration. This duration is due to changes in the
credit spread and as such it is customary to call it spread duration. This is
the correct duration measure to scale the regular EE OAS changes
regression coefficients, to eventually derive the credit factor exposures of
the bond. We use a simple but effective way to derive the spread duration.
We assume the bond is non-floating, calculate its duration and use this
number as our spread duration.

Why is this an adequate measure? Let's think back about a floating rate
bond and how a binomial price is calculated. All cash flows on all interest
rate paths are discounted to the present moment using a risk-neutralized
expectation. In the tree there are rates going up and rates going down, so
for a floating rate instrument there are coupons going up and coupons going
down. The coupon sizes are important in the discounting to derive a price,
but their timing is much more important in the calculation of duration. The
size-weighted time pattern of cash flows (which is closely linked to duration)
along each interest rate path is certainly dominated by a large face amount,
and an average of many such patterns where interest rate go up and down
(and so do coupons) will be very close to one time pattern where interest
rate are pegged at the current levels. The latter is the same as a duration
calculated for a bond whose coupon is kept constant and at the current
coupon level.

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The Multi-Asset Class Risk Model

Index Linked Bonds Index-linked securities have both coupon payments and principal payment
linked to an inflation index, such as the RPI or CPI. As such, they can be
considered in three pieces:

1. A bullet-coupon bond
2. A series of additional coupon cash flows associated with the inflation

linked coupons. The size of future additional coupon cash flows is
dependent on the inflation assumption used, while the paid coupons are
clearly known.
3. An additional zero coupon bond of the same maturity due to the principal
payment being inflation linked, whose size is, again, a function of the
inflation assumption used.

Securities (2) and (3) above are generated based on consensus inflation
forecasts from the Economist. The security is priced and its sensitivities
estimated in the usual fashion. Note that to perform scenario analysis over
various inflation assumptions one can simply add/subtract further exposures
to generic securities representing (2) and (3) to the existing bond.

Mortgage-backed The model potentially has access to a universe of more than one and a
securities quarter million individual mortgage-backed or asset-backed instruments
through INTEX.

The usual method of pricing and hence, estimating sensitivities for bonds
discounting back through a binomial tree is, unfortunately inapplicable to
instruments that display clear path dependency, such as mortgages. The
use of Monte Carlo techniques is required, by which a large number of paths
from the tree are sampled, and the price of the security estimated along
each path. The average over all paths provides an acceptably accurate
estimate of the security value assuming that the sampling process and the
number of sampled paths are sufficient.

For this process to run sufficiently, quickly and to be applied across a very
broad universe of securities, advanced techniques are employed. Sobol
quasi-random sequences are used as part of the quasi-Monte Carlo process.
A quasi-random sequence can span a given space much more quickly,
efficiently and comprehensively than a true random process. This allows
securities to be accurately priced using only a tenth of the number of sample
paths required by full basic, Monte Carlo.

The prepayment model used is simple, but adequate given the objectives of
the EE model. Prepayments are linked to the interest rate level, spread
between coupon and current yield, and time. This captures the majority of
the facets of prepayment risk in a very tractable manner and still allows the
process to be performed rapidly. Strategic relationships with third-party
vendors that provide other sophisticated models to the industry are under
consideration, should the demand prove sufficient.

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The Multi-Asset Class Risk Model

Convertible There are various approaches to considering convertible risk proposed in the
securities academic and business literature. The majority of these involve some quite
heroic assumptions, some of which contradict the intent of our EE model.
There are two classic textbook approaches. One is to assume that interest
rates are constant and use Black-Scholes to value the option part of the
convertible. The other approach assumes two interest rates (one risky, and
one risk-free) that are constant for the life of the convertible. The price is
then calculated using a stock price diffusion process modeled with a binomial
tree.

Neither approach is appealing to practitioners. Although the “constant
interest rates” assumption is marginally acceptable for short-dated options,
many convertibles have embedded options spanning ten years or more.
Clearly, the constant interest rates assumption is truly heroic over a ten-year
horizon; it was one that simply couldn’t be accepted given that the goal is to
explicitly capture both fixed income risk and equity risk.

Our model uses an interest-rate process modeled as a binomial tree and a
stock price diffusion process, again modeled as a binomial tree, while having
the two trees combine in three dimension. One way to think about this is of
a different stock price tree for each of many possible interest rate paths. The
two trees recombine: each node branches into four future nodes.
Correlation between the stock price and a short rate is incorporated into this
structure. This 3D tree allows us to price the instrument in the same
manner as binomial trees, and also allows us to inspect at each node the
value of the option to convert, and thus incorporates this specific into the
valuation. Using the quadranomial tree in pricing provides rational
sensitivities to changes in interest rates, a tractable and not too
computationally intensive pricing model, and avoids unpalatable
assumptions.

The credit risk component of the convertible securities risks are modeled as
sensitivities to the equity factors. Some exposure to the underlying equity
issue is included as is some exposure to the appropriate unit duration credit
synthetic security that reflects the credit risk portion of the bond-like
behavior of the convert. The components of credit/equity factor risk
stemming from either potential conversion into stock or, conversely, of not
converting, are combined into one estimate using the instruments delta to
the underlying stock price.

Government Bond Northfield provides an automated service (EENIAC) to model government
Futures Among bond futures worldwide; effectively dealing with every possible deliverable
bond, correctly calculating the position using the conversion factor to the
Other Derivatives cheapest-to-deliver instrument. We also provide the ability to model a wide
array if interest-rate, credit, equity and currency derivatives. Please see the
section on Derivative Modeling.

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The Multi-Asset Class Risk Model

Matrix pricing This section clarifies the Northfield procedures used for:
and other pricing 1. Pricing in the absence of vendor price data / bad price data
2. The choice of curves used for pricing
related issues

Which curve is Although the volatility of three interest-rate factors in the model is measured,
used? securities are actually priced, option-adjusted spreads calculated, and
sensitivities determined based on many curves. The curve used for a given
security is the zero-coupon yield curve observed or inferred as described
above.

Matrix pricing In the event that a reasonable price for a security can’t be found, a matrix-
pricing process is employed.

Matrix pricing assigns an option-adjusted spread to the security based on the
median for similar securities defined by region, sector and credit rating. So,
for example, a BB industrial Asian bond would be assigned the average
option-adjusted spread of all other BB industrial Asian bonds and a price
implied given the spread used. While this may not be a perfectly accurate
price for the security, it is close enough to allow us to estimate an accurate
set of sensitivities for the bond.

The EE model This powerful and innovative tool can add much value to the investment
summary process by giving insights into the sources of systematic risk and the means
of controlling them.
conclusion

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The Multi-Asset Class Risk Model

Regions Every security falls into one of five regions, comprising a total of 68

developed and emerging countries. The country clustered regions are:

Country Country Name Country Region Region Name Developed /
Code number Code Emerging
AUSTRIA Continental Europe
*AT BELGIUM C2 R1 Continental Europe Developed
*BE FRANCE C3 R1 Continental Europe Developed
*FR GERMANY C9 R1 Continental Europe Developed
*DE ITALY C10 R1 Continental Europe Developed
*IT LUXEMBOURG C14 R1 Continental Europe Developed
*LU NETHERLANDS C32 R1 Continental Europe Developed
*NL SPAIN C18 R1 Continental Europe Developed
*ES SWITZERLAND C25 R1 Continental Europe Developed
*CH BAHRAIN C27 R1 Continental Europe Developed
*BH CYPRUS C49 R1 Continental Europe Emerging
*CY CZECH REPUBLIC C51 R1 Continental Europe Emerging
*CZ EGYPT C40 R1 Continental Europe Emerging
*EG ESTONIA C52 R1 Continental Europe Emerging
*EE GREECE C53 R1 Continental Europe Emerging
*GR HUNGARY C11 R1 Continental Europe Emerging
*HU IRAN C41 R1 Continental Europe Emerging
*IR JORDAN C55 R1 Continental Europe Emerging
*JO KUWAIT C56 R1 Continental Europe Emerging
*KW LATVIA C57 R1 Continental Europe Emerging
*LV LITHUANIA C58 R1 Continental Europe Emerging
*LT MALTA C59 R1 Continental Europe Emerging
*MT MOROCCO C60 R1 Continental Europe Emerging
*MA OMAN C61 R1 Continental Europe Emerging
*OM POLAND C62 R1 Continental Europe Emerging
*PL PORTUGAL C43 R1 Continental Europe Emerging
*PT QATAR C44 R1 Continental Europe Emerging
*QA ROMANIA C63 R1 Continental Europe Emerging
*RO RUSSIA C64 R1 Continental Europe Emerging
*RU SAUDI ARABIA C45 R1 Continental Europe Emerging
*SA SLOVAK REPUBLIC C65 R1 Continental Europe Emerging
*SK SLOVENIA C66 R1 Continental Europe Emerging
*SI TUNISIA C67 R1 Continental Europe Emerging
*TN TURKEY C68 R1 Continental Europe Emerging
*TR AUSTRALIA C47 R1 English Speaking Emerging
*AU CANADA C1 R2 English Speaking Developed
*CA IRELAND C4 R2 English Speaking Developed
*IE NEW ZEALAND C13 R2 English Speaking Developed
*NZ C19 R2 Developed

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Country Country Name Country Region Region Name Developed /
Code number Code Emerging
UNITED KINGDOM English Speaking
*GB UNITED STATES C28 R2 English Speaking Developed
*US SOUTH AFRICA C29 R2 English Speaking Developed
*ZA DENMARK C23 R2 Scandinavia Emerging
*DK FINLAND C7 R3 Scandinavia Developed
*FI ICELAND C8 R3 Scandinavia Developed
*IS NORWAY C54 R3 Scandinavia Developed
*NO SWEDEN C20 R3 Scandinavia Developed
*SE ARGENTINA C26 R3 South & Latin America Developed
*AR BRAZIL C35 R4 South & Latin America Emerging
*BR CHILE C33 R4 South & Latin America Emerging
*CL COLOMBIA C5 R4 South & Latin America Emerging
*CO MEXICO C6 R4 South & Latin America Emerging
*MX PERU C17 R4 South & Latin America Emerging
*PE VENEZUELA C36 R4 South & Latin America Emerging
*VE HONG KONG C37 R4 The Far East Emerging
*HK JAPAN C12 R5 The Far East Developed
*JP SINGAPORE C15 R5 The Far East Developed
*SG BANGLADESH C22 R5 The Far East Developed
*BD CHINA C50 R5 The Far East Emerging
*CN INDIA C39 R5 The Far East Emerging
*IN INDONESIA C38 R5 The Far East Emerging
*ID ISRAEL C34 R5 The Far East Emerging
*IL MALAYSIA C48 R5 The Far East Emerging
*MY PAKISTAN C16 R5 The Far East Emerging
*PK PHILIPPINES C42 R5 The Far East Emerging
*PH SOUTH KOREA C21 R5 The Far East Emerging
*KR SRI LANKA C24 R5 The Far East Emerging
*LK TAIWAN C46 R5 The Far East Emerging
*TW THAILAND C31 R5 The Far East Emerging
*TH C30 R5 Emerging

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The Multi-Asset Class Risk Model

Sector and The following table shows the Total Equity Market Capitalization by region
Region Market and industrial sector for each country in the Global Equity Risk Model as of
Capitalization September 30, 2012.

Country Code
Country Name
Number Companies
Industrial % of global
capitalization
Consumer % of global
capitalization
Technology / Health % of
global capitalization
Interest Rate Sensitive % of
global capitalization
Non Energy minerals % of
global capitalization
Energy minerals % of global
capitalization
Country % of Global
Capitalization

Continental Europe Region

*AT AUSTRIA 145 .035% .002% .001% .088% .009% .022% .157%
241 .028% .132% .022% .056% .006% .000% .245%
*BE BELGIUM 1,049 .359% .919% .505% .778% .007% .537% 3.105%
1,396 1.263% .161% .684% .866% .017% .016% 3.007%
*FR FRANCE 394 .089% .049% .011% .352% .006% .305% .812%
125 .023% .047% .017% .023% .012% .048% .171%
*DE GERMANY 302 .117% .315% .126% .197% .078% .226% 1.059%
3,096 .060% .129% .021% 1.046% .006% .049% 1.312%
*IT ITALY 447 .391% .547% .554% .435% .000% .000% 1.928%
47 .000% .001% .015% .004% .020%
*LX LUXEMBOURG 134 .005% .001% .000% .003% .000% .009%
29 .001% .002% .011% .076% .003% .003% .092%
*NL NETHERLANDS 209 .036% .003% .021% .023% .001% .088%
18 .001% .001% .000% .000% .002%
*ES SPAIN 280 .006% .011% .001% .011% .003% .033%
65 .000% .000% .013% .019% .001% .037% .069%
*SW SWITZERLAND 235 .006% .002% .000% .013% .000% .023%
206 .010% .005% .015% .054% .000% .001% .084%
*BH BAHRAIN 32 .000% .000% .000% .000% .001%
35 .001% .000% .000% .002% .003% .000% .004%
*CY CYPRUS 22 .000% .001% .000% .002% .000% .000% .003%
82 .006% .004% .000% .052% .010% .001% .065%
*CZ CZECH REPUBLIC 119 .003% .001% .001% .012% .000% .001% .018%
718 .013% .013% .004% .092% .026% .158%
*EG EGYPT 61 .007% .011% .001% .025% .001% .011% .056%
43 .026% .004% .010% .071% .279% .003% .113%
*EE ESTONIA 265 .005% .000% .000% .005% .007% .006% .017%
763 .179% .076% .104% .508% .000% 1.350% 2.497%
*GR GREECE 152 .123% .021% .033% .117% .004% .306%
47 .000% .001% .001% .002% .007% .001% .004%
*HU HUNGARY 58 .000% .001% .002% .001% .000% .005%
39 .001% .001% .000% .004% .006%
*JO JORDAN 387 .052% .038% .039% .133% .007% .276%

*KW KUWAIT

*LV LATVIA

*LT LITHUANIA

*MT MALTA

*MA MOROCCO

*OM OMAN

*PL POLAND

*PR PORTUGAL

*QA QATAR

*RO ROMANIA

*RU RUSSIA

*SA SAUDI ARABIA

*SK SLOVAK REPUBLIC

*SI SLOVENIA

*TN TUNISIA

*TK TURKEY

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The Multi-Asset Class Risk Model

Country Code
Country Name
Number Companies
Industrial % of global
capitalization
Consumer % of global
capitalization
Technology / Health % of
global capitalization
Interest Rate Sensitive % of
global capitalization
Non Energy minerals % of
global capitalization
Energy minerals % of global
capitalization
Country % of Global
Capitalization

English Speaking Region

*AU AUSTRALIA 1,955 .132% .131% .061% .699% .358% .100% 1.482%
*CA CANADA 4,567 .411% 2.402%
*IR IRELAND 226 .358% .161% .120% .796% .557% .010% .190%
*NZ NEW ZEALAND 163 .001% .074%
*GB UNITED KINGDOM 2,748 .027% .036% .019% .094% .003% .760% 5.257%
*US UNITED STATES 19,474 5.226% 52.606%
*SA SOUTH AFRICA 415 .018% .011% .007% .037% .000% .053% .689%

229 .238% 1.246% .845% 1.434% .733% .000% .207%
148 .003% .183%
11 7.844% 9.040% 14.153% 14.538% 1.805% .000% .002%
266 .102% .276%
520 .051% .130% .098% .136% .222% .008% .674%

84 Scandinavia Region .007% .023%
551 .380% 1.754%
*DK DENMARK 214 .057% .020% .094% .036% .000% .017% .283%
*FI FINLAND 67 .285% .385%
*IS ICELAND 159 .073% .009% .040% .052% .006% .562%
*NO NORWAY 159 .000% .098%
*SE SWEDEN 36 .001% .000% .001% .000% .000% .009%

1,382 .077% .010% .007% .063% .016% .178% 2.296%
3,761 .044% 3.971%
791 .183% .090% .073% .307% .012% .006% .817%
194 .001% .018%
2,694 South and Latin America Region .502% 3.728%
3,398 .297% 1.598%
*AR ARGENTINA 439 .002% .003% .009% .002% .036% .487%
*BZ BRAZIL 587 .010% .161%
*CH CHILE 947 .128% .281% .064% .515% .386% .016% .391%
*CO COLOMBIA 498 .018% .045%
*MX MEXICO 257 .045% .059% .011% .137% .014% .006% .190%
*PE PERU 1,967 .027% 1.709%
*VZ VENEZUELA 281 .014% .011% .001% .073% .001% .000% .016%
1,759 .024% .859%
1,201 .156% .174% .114% .069% .050% .154% .815%
63,389 11.34%
.007% .010% .001% .030% .049%

.001% .000% .008%

The Far East Region

*HK HONG KONG .329% .369% .478% .920% .023%
*JP JAPAN
*SG 1.342% .866% .868% .772% .079%
*BD SINGAPORE
*CN BANGLADESH .258% .090% .034% .427% .001%
*IN
*IO CHINA .002% .001% .004% .010% .000%
*IS INDIA
*MA INDONESIA .869% .344% .331% 1.506% .176%
*PK ISRAEL
*PH MALAYSIA .378% .182% .248% .415% .078%
*SK PAKISTAN
*SL PHILIPPINES .146% .083% .016% .196% .010%
*TW SOUTH KOREA
*TH SRI LANKA .027% .008% .084% .032% .000%
TAIWAN
THAILAND .122% .070% .023% .156% .004%
Totals
.007% .005% .001% .014% .000%

.026% .046% .004% .104% .005%

.375% .167% .861% .170% .108%

.003% .007% .001% .005% .000%

.189% .064% .403% .150% .028%

.168% .102% .131% .255% .004%

16.50% 16.33% 21.39% 29.25% 5.19%

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The Multi-Asset Class Risk Model

Industry Sectors Nineteen global industrial groups are condensed into six super sector

clusters that have been shown to exhibit common patterns of behavior. The
industry clusters are:

Cluster 1 Cluster 2
Industrial Consumer

Industrial Services Consumer Non-Durables
Producer Manufacturing Consumer Services
Process Industries Retail Trade
Consumer Durables Financial Services
Transportation Commercial Services
Miscellaneous Distribution Services

Cluster 3 Cluster 4
Technology and Health Interest Rate Sensitive

Health Technology Finance
Technology Services Utilities
Health Services Communications
Computer Technology
Electronic Technology Cluster 6
Energy Minerals
Cluster 5 Energy Minerals
Non-Energy Minerals
Non-Energy Minerals

Special Symbols In order to take exposure to foreign currencies into account when measuring

risk, the database includes 70 special symbols for currencies. These symbols
are treated as tickers by the optimization system.
In order to ensure that the current data files are as far as practical compatible
with historic data files, they include “dead” or legacy currencies that no
longer exist. Equally, the historic data files may include currencies that exist
now that did not exist in the past. Also, the reader will note some currencies
have both the ISO code and the legacy Northfield currency codes available,
again to ensure ease of use and continuity.
For example, the Global model history extends well back into the pre-Euro
period when currencies like the French Franc and the Italian Lira were

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represented as separate currency factors. In order to make the physical files
uniform across time, we include all the individual currencies plus the Euro in
all factor files. For those periods when a particular currency did not exist, all
security factor exposures to that currency will be zero, so there will be no
change whatsoever in the actual analysis. When all data files across time
have the same layout, processes that stretch across time such as
performance attribution and back testing are made much easier.

Currency codes Symbol Currency Symbol Currency
available in the *ARS Argentine Peso *AUD Australian Dollar
Northfield risk *ATS Austrian Schilling *BHD Bahraini Dinar
*BDT Bangladesh Taka *BEF Belgian Franc
models *BRL Brazilian Real *GBP British Pounds
*CAD Canadian Dollar *CLP Chilean Peso
*CNY China Renminbi *COP Colombian Peso
*CYP Cyprus Pound *CZK Czech Koruna
*DKK Danish Krone *EGP Egyptian Pound
*EEK Estonian Kroon *EUR Euro
*FIM Finnish Markka *FRF French Franc
*DEM German Deutschemark *GRD Greek Drachma
*HKD Hong Kong Dollar *HUF Hungarian Forint
*ISK Icelandic Krona *INR Indian Rupee
*IDR Indonesian Rupiah *IRR Iran Rial
*IEP Irish Punt *ILS Israeli Shekel
*ITL Italian Lira *JPY Japanese Yen
*JOD Jordanian Dinar *KWD Kuwait Dinar
*LVL Latvian Lats *LTL Lithuanian Litas
*LUF Luxembourg Franc *MYR Malaysian Ringgit
*MTL Maltese Lira *MXN Mexican Peso
*MAD Moroccan Dirham *NLG Netherlands Guilder
*NZD New Zealand Dollar *NOK Norwegian Krone
*NOK Norwegian Krone *OMR Oman Rial
*PKR Pakistan Rupee *PEN Peruvian New Sol
*PHP Philippines Peso *PLN Polish Zloty
*PTE Portuguese Escudo *QAR Qatari Rial
*ROL Romanian Leu *RUB Russian Rouble
*SAR Saudi Arabian Riyal *SGD Singapore Dollar
*SKK Slovakia Koruna *SIT Slovenian Tolar
*ZAR South African Rand *KRW South Korean Won
*ESP Spanish Peseta *LKR Sri Lanka Rupee
*SEK Swedish Krona *CHF Swiss Franc
*TWD Taiwan Dollar *THB Thailand Baht
*TND Tunisian Dinar *TRL Turkish Lira
*$$$ U.S. Dollar *VEB Venezuelan Bolivar

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Country equity In addition, the following country indices and their risk factor exposures have
indices available in been incorporated into the database:
the Northfield risk
Symbol Country Symbol Country
models *AR ARGENTINA *AU AUSTRALIA
*AT AUSTRIA *BH BAHRAIN
*BD BANGLADESH *BE BELGIUM
*BR BRAZIL *CA CANADA
*CL CHILE *CN CHINA
*CO COLOMBIA *CY CYPRUS
*CZ CZECH REPUBLIC *DK DENMARK
*EG EGYPT *EE ESTONIA
*FI FINLAND *FR FRANCE
*DE GERMANY *GR GREECE
*HK HONG KONG *HU HUNGARY
*IS ICELAND *IN INDIA
*ID INDONESIA *IR IRAN
*IE IRELAND *IL ISRAEL
*IT ITALY *JP JAPAN
*JO JORDAN *KW KUWAIT
*LV LATVIA *LT LITHUANIA
*LU LUXEMBOURG *MY MALAYSIA
*MT MALTA *MX MEXICO
*MA MOROCCO *NL NETHERLANDS
*NZ NEW ZEALAND *NO NORWAY
*OM OMAN *PK PAKISTAN
*PE PERU *PH PHILIPPINES
*PL POLAND *PT PORTUGAL
*QA QATAR *RO ROMANIA
*RU RUSSIA *SA SAUDI ARABIA
*SG SINGAPORE *SK SLOVAK REPUBLIC
*SI SLOVENIA *ZA SOUTH AFRICA
*KR SOUTH KOREA *ES SPAIN
*LK SRI LANKA *SE SWEDEN
*CH SWITZERLAND *TW TAIWAN
*TH THAILAND *TN TUNISIA
*TR TURKEY *GB UNITED KINGDOM
*US UNITED STATES *VE VENEZUELA

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Appendix A: The EE model's test results are presented below. They are a product from
Bond Modeling in our extensive testing on a universe of the 27 thousand most actively traded
the EE Risk Model: bonds around the world, as well as portfolios thereof, in which we
benchmarked their predicted and realized risk performance during the period
Test Results of February to June 2011. The realized (or observed) risk performance was
based on bond prices sourced from one of the largest and most respected
commercial bond data providers in the industry.

There were four tests performed. In the first test we took 50 random
portfolios of 100 bonds each and compared model predicted risk with
realized volatility over the period. Each portfolio was picked so that it is
biased towards a particular bond duration band. Given the dominant role of

interest rate sensitivity on bond risk this should be considered as the most
appropriate broad test for the model. Here is what we found:

25

20 realized standard deviation
as function of model

15 predicted in annual percent
terms

10 regression line

5

0
0 10 20 30

The predicted vs. realized variance correlation is 0.97. The R-squared of the
same relationship is 0.94.
The slope regression coefficient in the graph above is 0.87 and it has a very
high statistical significance with a t-statistic of 18.62.
As an issue of high importance, in the same regression we also found that
there is a statistically significant intercept (t-statistic = -5.13) of -2.6%. It can
be rashly interpreted as an upward bias in the model risk prediction, but we
want to assert that this is not the case. The rationale for our assertion is as
follows.

2 Note that in the version of the EE model prior to the firm sustainability credit was introduced,
when the same type of regression was performed, the slope coefficient was 0.74 with a t-
statistic of 16 and an R-squared of 0.84 - all values are somewhat lower than the current ones.
Hence, the firm sustainability credit approach introduced a moderate but marked improvement
in the ability of the model to predict risk accurately.

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There are three facts of importance to our argument. First, each of the
random portfolios on which the test was performed was biased towards a
different duration level. Second, the amount of the difference between
predicted and realized risk across portfolios is approximately constant. Third,
the predicted risk for all portfolios consists of exclusively factor risk, with
negligible specific risk, the reason being that each portfolio is comprised of
hundreds of bonds from various issuers and is fully diversified.

We would first argue that most commercially accessible bond pricing
processes are prone to have one disadvantage when it comes to estimating
volatility– an element of smoothing. Bonds, as a vast majority, are not traded
continuously as stocks, and the gaps in traded prices need to be filled. The
data provider's business is to furnish prices on a daily basis, even in the
absence of trades for a particular bond. In the absence of a model of risk
drivers, it is hard to come up with a rigorous way to fill in the gaps. The tool
at disposal generally leans towards interpolation. This is understandable - the
pricing source’s prime purpose is to come up with a price, and the common
sense thing to do is look at the neighboring values. This does not undermine
the practical accuracy of the daily price value. However, when one utilizes
such prices to estimate bond return volatility, one in essence is compounding
this smoothing effect to an ostensible level. Smoothing, of course, means
less volatility of the reported time series.

The key to understanding this issue is that we, at Northfield, are not trying to
explain the pricing source’s observed return volatility, but actually both we
and the pricing source, in different ways are trying to estimate an
unobservable variable – the “what if” continuous bond return volatility.
Many bonds are not traded every day, but we would like to know what it will
be if they did – i.e. what is the risk inherent if we try to sell this bond today.
The only way we differ is that Northfield and the pricing source try to
accomplish this estimation in different ways – we create a risk model, and
the pricing source hand collects values, interpolates where needed, and
enters values in a database.

The immediately good news for both us and the pricing source is the perfect
correlation between our estimate and theirs. Given the complete
independence of the sources and methods of data derivation, the maximum
likelihood inference is that both organizations are doing a good job.

We take this line of analysis further. If the difference between our estimate
of standard deviation and the pricing source’s estimate was risk “bias”
contributed by Northfield, then it will necessarily be factor risk error, because
we report no specific risk for those test portfolios, and so it will likely be a
different difference for the different portfolios as the different test portfolios
have different factor exposures (notably durations). But the difference is
[almost] constant across portfolios which contradicts the hypothesis that this
is factor risk. And since Northfield’s estimate has nothing but factor risk this
also contradicts the hypothesis that our estimate is the one contributing to

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The Multi-Asset Class Risk Model

the difference. Since we call in broad concepts from the financial world (EE
factors), which in essence are easier to accept as epitomizing the forces
driving risk, than the demonstrably idiosyncratic nature of a data collecting
methodology of the pricing source, it is sound statistical logic to state that
our estimate is more likely to be right. In that sense we would assert that
our estimates are right and the so called “realized” volatility has a downward
bias.

Another contributor with equal importance to this uniform difference is the
survivorship bias. Bonds that are priced over the test period are necessarily
bonds in good standing over the same period, i.e. they have not defaulted.
The ex-ante prediction of risk however, assumes that default for those bonds
is possible. In that sense the "liquid bond" group is a biased sample towards
"survivors" of the odds. This creates a divergence between the unbiased
view of the risk model, and the biased sample. Moreover, the liquid bond
group is biased towards higher credits, which potentially cannot improve
much but potentially but can go to default. This makes the sample even
more biased, enlarging the difference between model predicted and realized
bond and portfolio risk.

As a continuation of our test sequence, a variation of the 50 portfolio test
was also performed, this time with completely random broad portfolios.
Those portfolios being big samples of a population have very similar
characteristics, and the quality of the results are dominated by the
sameness. Yet, even in this setting the high correlation between realized and
predicted risk of 0.73 and regression explanation (slope of 0.6 with t-statistic
of 7.5), prove the ability of the model to discern risk within a narrow range of
risk values.

3.5

3

2.5
Realized standard

2 deviation as function of
predicted

1.5 Regression line

1

0.5

0
0246

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The Multi-Asset Class Risk Model

Another test was performed to look at credit risk in isolation. The test takes
the credit buckets from the new model, where in essence each synthetic
record is an equal-weighted portfolio of the bonds in that bucket, and
aggregates the buckets per credit rating over sectors and region. The
resulting “total” risk was only credit induced risk – currency and treasury
factor exposures were removed. Effectively, the test is based on a pool of
close to a hundred thousand bonds.

As can be intuitively expected, the volatility goes clearly from higher to lower
as we go from lower to higher credit quality, as defined by the rating
agencies. The only marked exception is the lowest rating C - it has a lower
credit volatility than the next rating up. This make sense, given that such

debtors are practically in default and for them the certainty of the debt dues
demanded dwarf any business level uncertainty from the non-performing

economic assets.

Rating Credit Volatility - Annual stdev %
AAA 0.260628455
AA 0.420209
A 1.393854161
BBB 2.060612143
BB 3.9441636
B 5.623509565
CCC 4.817308667
CC 6.447296667
C 4.323928

The last test was at the individual bond level. As we did initially for random
portfolios, we compared the realized and predicted risk of individual bonds.
The vast majority (60%) of bonds came in within 1% realized historic
standard deviation under predicted. About 90% of the bonds came within
3% realized historic standard deviation under predicted. We have to
remember the smoothing component of "observed" bond volatility revealed
by the portfolio level analysis, and the survivorship bias of liquid bonds
mentioned earlier. Undoubtedly, both play a role here and we should
necessarily explain those constant level differences between the risk model
results and the results derived from the data from the pricing source with
these two phenomena.

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The Multi-Asset Class Risk Model distribution of the
10000 difference: realized minus
9000 predicted risk
8000
7000
6000
5000
4000
3000
2000
1000
0
-20-16-12 -8 -4 0 4 8 12 16 20 24 28 32 36

Testing Conclusion The result presented here are even more impressive in view of the fact that
the model that produced them builds on the very basic economics of the
instruments, not from a statistical technique that starts off with the modeled
data (regressions, PCA, etc.) Statistical techniques often guarantee, at least
at the individual instrument level, that the breakdown in risk sources will sum
up to the modeled variable. On the other hand, working the modeled
variable up from the very fundamental characteristics of the financial
instrument offers no such guarantee, unless such methodology is the right
one. The excellent agreement between our model results and those of the
pricing source's are a credit to our sustained endeavor for harmonizing
statistical methodology and economic intuition.

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The Multi-Asset Class Risk Model

Appendix B: Derivatives: The following table lists the various derivatives covered in the EE model and how they are treated:

Instrument A. Cashflow B. Pricing C. Factor D. Specific Risk E. Composite F. Represen- G. Output Files H. Offsetting
elements Exposures tation "cash" in main
portfolio file
Currency Long side in future Futures price on long A combination Not existent due No need for A record to be 1. DataFile.csv (exposures
Futures / delivery of underlying side derived as FV of from underlying to currency composite appended to record) Yes. Given that
Forwards representation, due the master EE the price of the
currency; short side in spot; instrument is currency factor factor presence to no specific risk exposures file 2. PortFile.csv (offsetting instrument in the
a fixed obligation in listed with futures exposure of future in the model. "cash" to be added to main exposure file is the
portfolio file) futures price, an
price currency price in the holding of subject offset in zero risk
exposures file currency and security has to be
added to the main
interest factor portfolio file to
exposures from bring the
economic value of
fixed obligation in the position to its
price currency actual level
(possibly zero).
EENIAC calculates
a summary
offsetting cash
amount for all
positions requiring
this adjustment
within each
uploaded request.

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The Multi-Asset Class Risk Model

Instrument A. Cashflow B. Pricing C. Factor D. Specific Risk E. Composite F. Represen- G. Output Files H. Offsetting
elements Exposures tation "cash" in main
portfolio file

Stock Index Long side in future Futures price on long Effectively, a Yes. Proper Composite 1. A holding 1. PortFile.csv (offsetting Yes. Given that
Futures / delivery of index the price of the
Forwards constituents; short side derived as FV of combination from specific risk representation is file (extension "cash" to be added to main instrument in the
spot; instrument is underlying factor representation is needed to render hld) to be portfolio file). composite assets
side in a fixed file is the futures
obligation in price listed with futures exposure of future needed because appropriate specific placed in the 2. A holding file with a name price, an offset in
currency. price in the holding of index index risk in situations Northfield corresponding to the ID of the zero risk security
composite assets and interest factor constituents do position provided by the user has to be added to
file. exposures from have non-factor where a constituent Optimizer and extension .hld. the main portfolio
fixed obligation in explained risk. of the underlying is inputs file to bring the
economic value of
also held separately directory. the position to its
price currency. in the portfolio. actual level.
2. A record in 3. CompFile.csv - a set of EENIAC calculates
the composite records to be appended to the a summary
assets file. main composite asset file. offsetting cash
amount for all
positions requiring
this adjustment
within each
uploaded request.

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The Multi-Asset Class Risk Model

Instrument A. Cashflow B. Pricing C. Factor D. Specific Risk E. Composite F. Represen- G. Output Files H. Offsetting
elements Exposures tation "cash" in main
portfolio file

Quanto Long side in future Futures price on long Effectively, a Yes. Proper Composite 1. A holding 1. PortFile.csv (offsetting Yes. Given that
Index the price of the
Futures delivery of index side derived as FV of combination from specific risk representation is file (extension "cash" to be added to main instrument in the
constituents valued in spot adjusting for underlying factor representation is needed to render hld) to be portfolio file). exposure file is the
futures price, an
a currency different correlation between exposure of future needed because appropriate specific placed in the 2. A holding file with a name offset in zero risk
from the price local returns and holding of index index risk in situations Northfield corresponding to the ID of the security has to be
and interest factor constituents do position provided by the user added to the main
currency; short side in price currency (see exposures from have non-factor where a constituent Optimizer and extension .hld. portfolio file to
a fixed obligation in descriptive fixed obligation in explained risk. of the underlying is inputs bring the
economic value of
price currency. attachments on also held separately directory. the position to its
derivative analytics); price currency. in the portfolio. actual level.
instrument is listed 2. A record in 3. CompFile.csv - a set of EENIAC calculates
with futures price in the composite records to be appended to the a summary
the composite assets assets file. main composite asset file. offsetting cash
amount for all
file. positions requiring
this adjustment
within each
uploaded request.

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The Multi-Asset Class Risk Model

Instrument A. Cashflow B. Pricing C. Factor D. Specific Risk E. Composite F. Represen- G. Output Files H. Offsetting
elements Exposures tation "cash" in main
portfolio file

Basic Long side in a Price of instrument is Effectively, a Yes for equity For equity options 1. For 1. A holding file with a name Not needed
Options contingent claim on because options
an equity or an index derived via Black- delta-neutral sized options and not composite currency corresponding to the ID of the always have non-
of stocks or a Scholes method. position in the for currency representation is options - a position provided by the user zero economic
currency. value and can be
underlying, with options. Proper needed to render record to be and extension .hld. listed with it in a
the exposures of specific risk appropriate specific appended to datafile or a
representation is risk in situations the exposures 2. CompFile.csv - a set of composite assets
the underlying needed because where a constituent file. records to be appended to the file.
being scaled by equity and equity of the underlying is main composite asset file.
index also held separately 2. For equity
the ratio of the constituents do in the portfolio. options - a 3. DataFile.csv - exposure file
delta times the have non-factor holding file apendate where currency
explained risk. (extension hld) options are listed.
underlying price to be placed in
over the option

price.

the Northfield

Optimizer
inputs

directory, plus
a record in the

composite

assets file.

49 www.northinfo.com