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Return Enhancement through Risk Management

R-Squared PRISM

Excel Interface

USER GUIDE 2014

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Return Enhancement through Risk Management 1

CONTENTS

GETTING STARTED .......................................................................................................................................................... 3

Logon ............................................................................................................................................................................ 3

Database ...................................................................................................................................................................... 3

Reports Functions ....................................................................................................................................................... 3

RISK REPORTS .................................................................................................................................................................. 4

Risk Model .................................................................................................................................................................... 4

Portfolio and Benchmark .......................................................................................................................................... 4

Analysis ........................................................................................................................................................................ 5

Portfolio and Benchmark Return ............................................................................................................................. 5

Stock Data Items ........................................................................................................................................................ 5

Macro-economic Exposures ....................................................................................................................................... 5

Parent ........................................................................................................................................................................... 5

Select Risk Reports .................................................................................................................................................... 6

Risk Summary .......................................................................................................................................................... 6

Macro-economic Exposures ................................................................................................................................... 7

Risk by Factors ........................................................................................................................................................ 7

Risk by Holdings ...................................................................................................................................................... 7

Risk by Benchmark ................................................................................................................................................. 8

Independent Bets ................................................................................................................................................... 8

Betas ......................................................................................................................................................................... 8

Factor Correlation .................................................................................................................................................. 8

Factor Covariance .................................................................................................................................................. 8

Stock Covariance .................................................................................................................................................... 8

Portfolio Holdings ................................................................................................................................................... 8

PRISM EXCEL USER GUIDE

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Missing Stocks .......................................................................................................................................................... 9

Report Formatting .................................................................................................................................................. 9

PERFORMANCE .............................................................................................................................................................. 10

Risk Model .................................................................................................................................................................. 10

Portfolio and Benchmark ........................................................................................................................................ 10

Analysis ...................................................................................................................................................................... 11

Interest Rate File ..................................................................................................................................................... 11

Start Date and End Date ......................................................................................................................................... 11

Period ......................................................................................................................................................................... 11

MORE FUNCTIONALITY ................................................................................................................................................. 12

Load Data ................................................................................................................................................................... 12

Autoloader ................................................................................................................................................................. 12

Data Formats ............................................................................................................................................................. 12

Currency Identifiers ............................................................................................................................................. 13

Portfolios ................................................................................................................................................................... 13

Risk Models ................................................................................................................................................................ 13

Users ........................................................................................................................................................................... 13

Admin Operations ................................................................................................................................................. 13

Library ........................................................................................................................................................................ 14

Settings ...................................................................................................................................................................... 14

Glossary ...................................................................................................................................................................... 14

Frequently Asked Questions ................................................................................................................................... 14

Batch .......................................................................................................................................................................... 14

GLOSSARY ...................................................................................................................................................................... 16

OVERVIEW .................................................................................................................................................................. 16

PORTFOLIO RISK ANALYSES ..................................................................................................................................... 18

PERFORMANCE ANALYSIS ......................................................................................................................................... 29

GENERAL .................................................................................................................................................................... 32

FREQUENTLY ASKED QUESTIONS ................................................................................................................................ 33

INDEX .............................................................................................................................................................................. 44

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GETTING STARTED

Logon

With Excel open, click on the PRISM command at the right hand end of the Command bar. The logon dialogue box will appear. If your user name and password are valid, and the PRISM licence is valid, you will be asked to select which database you want to use. If you subscribe to only one database, then only that database will appear. Highlight the database you want and then click Go. If you subscribe to multiple databases you can switch between them once you have logged on by clicking on Logon Details then selecting the database you want to switch to. The PRISM toolbar will now appear below the main Excel toolbar. Once you have logged on, you remain logged on until you exist PRISM by clicking on Logon Details then on Logon and then Quit, or alternatively by clicking Logoff.

Database

Typically each Risk Model that you subscribe to will be placed into a separate database. This is to avoid any confusion over model specific data items such as the R-squared.

Reports Functions

You will see in the far left hand of the PRISM toolbar that PRISM has three main function modes:

Risk Reports for generating ex-ante risk reports,

Performance for generating reports of past performance and

More Functionality, which allows you to carry out various operations such as loading data, deleting and renaming portfolios and so on.

Select the function mode you want to use.

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RISK REPORTS

In order to run a risk report, you first need to tell PRISM which risk model you want to use and which portfolio and benchmark.

Risk Model

Each risk model is defined by the dates for which updates are available. After selecting the version of the risk model you want to use, select the date for which you want to generate your risk report. All available dates are displayed in the drop-down box to the right of the model name.

Portfolio and Benchmark

PRISM does not distinguish portfolios from benchmarks. This means that you can analyse the risk profile of any portfolio relative to any benchmark or any other portfolio. Similarly, you can compare benchmarks with each other. Each portfolio and benchmark is defined by the dates for which holdings have been loaded into PRISM. After selecting the portfolio and benchmark you want to use, select the portfolio and benchmark dates for which you want to generate your risk report. All available dates are displayed in the drop-down box to the right of the portfolio name and the benchmark name respectively. Note that portfolio, benchmark and risk model must all be in the same base currency. If you want to generate risk reports for portfolios in absolute space, in other words not benchmarked to an index or other portfolio, simply select [ CASH ] as your benchmark.

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Analysis

Moving to the right across the toolbar, the Analysis section allows you to select, from the drop down menu:

Portfolio to analyse the portfolio in isolation,

Benchmark to analyse the benchmark in isolation or

Relative to analyse the portfolio relative to the benchmark.

Portfolio and Benchmark Return

This section also invites you to tell PRISM what Expected Returns to use for the portfolio and benchmark, with the defaults of 12% and 10% respectively. The figures entered here determine the calibration of implied returns in the Reverse Optimisation results within the risk reports.

Stock Data Items

Select Stock data items from list. Stock data items are displayed in the Portfolio Holdings,

Holdings Risk and Benchmark Risk Reports. Select required items from the drop-down menu for

inclusion in this report. Any hierarchical data items have summary sections shown in the main

report.

Macro-economic Exposures

Select macro-economic variables from list. PRISM stores Macro-economic variables in the same

way as it does holdings. This permits measurement of the exposure, or beta, to each macro-

economic variable, of the portfolio, benchmark and portfolio relative to benchmark as well as of

individual holdings, to selected variables. The results can be viewed in reports of Risk by

Holdings, Risk by Benchmark, Stock Betas to factors and Stock Covariances.

Parent

Parent allows you treat two (or more) issues of one company as the same issue, for example, if your portfolio holds an ADR and the underlying, or if one is held in your portfolio or the other is held in the benchmark. This function avoids overestimating total risk that results from treating them as unrelated entities. When Parent is selected, PRISM chooses the asset with the largest stock specific risk and treats that at the holding for all securities designated as related to it, with its weight given as the sum the weights of all related holdings in the portfolio and benchmark respectively.

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To decide which holdings are related, PRISM uses S&P's Parent ID data item, so that selecting Parent from the drop-down menu instructs PRISM to treat stocks with the same Parent ID this way.

Select Risk Reports

Select the risk reports you want to generate. Once selected, the name of each risk report will be highlighted in the PRISM toolbar. De-select reports by clicking on the name of each in turn. Note that all risk numbers shown are annualised values.

Risk Summary

Risk Summary provides an overview of the risk profile of the portfolio and benchmark if applicable. Summary statistics in this report include, for portfolio, benchmark and portfolio relative to benchmark, the items shown here:

Current Portfolio Value and Portfolio Minimum Value fields will have values in them if

stock prices or holding values are input to PRISM, otherwise they will be blank.

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Macro-economic Exposures

Highlighting Exposures allows you to select Macro-economic variables from the drop-down menu. See Macro-economic exposures.

Risk by Factors

Factor Risk The Factor Risk report gives information about the characteristics of each risk

factor and quantifies its impact on portfolio and relative risk and return. It also

includes information on the return implied by the portfolio and relative holdings,

given the portfolio and benchmark expected returns input earlier, which default to

12% and 10% respectively. Items included in the Factor Risk report include:

Factor Contribution

The Factor Contribution report shows each of the contributions to portfolio risk (or

portfolio relative to benchmark risk) from the portfolio’s exposure (or relative

exposure) to each factor. This set of contributions will include the risk arising

from the exposure to the factor itself, as well as the contributions arising from the

factor’s covariance with each other factor, taking into account the exposures to

each of the factors

Risk by Holdings

Holdings Risk The Holdings Risk report shows, for each holding in the portfolio and benchmark,

the portfolio, or portfolio relative contribution to risk due to its exposure to the

model’s risk factors and its stock-specific risk. Items included in the Holdings Risk

report include:

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Factor Contribution This Factor Contribution report shows, for each holding in the portfolio and benchmark, how the stock’s contribution to the overall factor risk in the portfolio arises from the stock’s exposures to the various factors in the risk model, and their covariance with each other.

Risk by Benchmark

The Risk by Benchmark report shows, for each holding in the portfolio and benchmark, the portfolio or relative contribution to risk due to its exposure to the benchmark and its residual, or non-beta-related, risk. Items included in the Risk by Benchmark report include:

Independent Bets

The Independent Bets report, identifies combinations of portfolio exposures that are

statistically independent by applying Principal Components Analysis and adding economic

interpretation to the resulting statistically independent eigenvectors.

Betas

The Betas report shows the beta of each stock in the portfolio and benchmark to each

model risk factor.

Factor Correlation

This report displays the correlation matrix of the model’s risk factors.

Factor Covariance

This report displays the covariance matrix of the model’s risk factors.

Stock Covariance

This report displays the covariance matrix of stocks held in the portfolio and benchmark.

Portfolio Holdings

Portfolio Holdings displays portfolio and benchmark holdings, together with selected Stock Data Items.

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Missing Stocks

The user may have stocks in his or her portfolios that aren't in the universe of the risk model in question. Missing stocks have their weights set to zero when running a risk analysis and all other stocks are reweighted so that the total weight of the portfolio remains 100%. The Warnings tab identifies these stocks and reports showing individual holdings (the Holdings Risk and Benchmark Risk reports) show both the reweighted and original holdings.

Report Formatting

If you click the little arrow at the bottom right of the Go button section, it displays a few controls to help with report manipulation.

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PERFORMANCE

Performance allows you to analyse, over multiple periods, the returns from your portfolio relative to a benchmark or in absolute terms. It also allows you to attribute returns to the risk factors in the model you are using. In order to carry out a performance analysis, you first need:

Portfolio holdings for each date you wish your analysis to cover.

Benchmark holdings for each date you wish your analysis to cover.

Portfolio Net Asset Values for each date you wish your analysis to cover.

Benchmark Net Asset Values for each date you wish your analysis to cover.

Interest rates for each date you wish your analysis to cover. If you do not specify interest rates, PRISM will assume a risk-free rate of zero

In order to run a performance report, you first need to tell PRISM which risk model you want to use and which portfolio and benchmark.

Risk Model

Each risk model is defined by the dates for which updates are available. After selecting the version of the risk model you want to use, select the dates for which you want to generate your performance report.

Portfolio and Benchmark

PRISM does not distinguish portfolios from benchmarks. This means that you can analyse the performance of any portfolio relative to any benchmark or any other portfolio. Similarly, you can compare benchmarks with each other. Each portfolio and benchmark is defined by the dates for which holdings have been loaded into PRISM. After selecting the portfolio and benchmark you want to use, select the portfolio and benchmark dates for which you want to generate your performance report.

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Analysis

Moving to the right across the toolbar, the Analysis section allows you to select, from the drop down menu:

Portfolio to analyse the portfolio in isolation,

Benchmark to analyse the benchmark in isolation or

Relative to analyse the portfolio relative to the benchmark.

Interest Rate File

Moving to the right across the toolbar, you are now invited to specify a set of interest rates to incorporate in your analysis. PRISM will allow you to select from the series of interest rates that have already been loaded into it. For valid results, interest rate dates must correspond to the dates for which the analysis is being carried out.

Start Date and End Date

Just below Interest Rates selection, you are invited to select the start and end dates for the analysis. The dates that you see in the drop-down menu are the dates for which model updates exist. You are not confined to these dates for the intervals of your analysis, as you can see when you select Period.

Period

PRISM lets you carry out your Performance analysis for intervals that suit you, even though they may not correspond to the dates on which the model was updated. Choose from Weekly or Four-weekly intervals for your analysis. For dates that do not correspond to a model date, PRISM will select the most recent model date for each Performance date.

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MORE FUNCTIONALITY

This is where you can load data, check databases, delete and rename portfolios and benchmarks and manage PRISM User information.

Load Data

In Load Data, you are invited to browse to select the input file you want to load into PRISM. You can load multiple files simultaneously, simply by selecting them from your hard drive. When you have selected the files you want to load, click Load and PRISM will load the data. You can view progress in the window that appears to the right of the browse section.

Autoloader

To facilitate the automated loading of data, R-Squared Risk Management provides an autoloader service. This runs on your PRISM server and monitors a given folder on the server. Any file that is copied to that folder is automatically loaded into PRISM. The results of each load are saved to a log file which you can view via a link on the Load Data dialog. If you have multiple database, subfolders with the database names will determine the location of the file.

Data Formats

In Library, you will find sample PRISM input files to help you easily to compile your own Portfolios, Benchmarks, Portfolio and Benchmark NAVs and interest rate series. Input data files should be saved as comma separated values files (.csv) and closed before loading.

PRISM recognises SEDOLS, and CUSIPs, with or without check digits. ISINs and Bloomberg tickers will be supported in the near future. Since SEDOLS and CUSIPs change over time and indeed are reused, R-Squared Risk Management maintains an unique identifier for every issue throughout time. This RSQID is how R-Squared risk and other asset data is loaded into PRISM and it may be displayed in portfolio result sets as a data item. PRISM supports a generic identifier field called Stock ID. This may be used in reports and during data loading. When used in a report, PRISM will display a stock's CUSIP if it has

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one, then its SEDOL if there is no CUSIP. Its RSQID will be shown if the stock has neither. Note that for European models, the order of preference is reversed: SEDOL then CUSIP. During data loading it is more efficient to load by CUSIP or SEDOL if you can, by setting the field heading to CUSIP or SEDOL. PRISM will accept currency IDs in this case. If you are loading up a mix of identifiers, then set the heading to Stock ID and PRISM will determine what each stock value actually is.

Currency Identifiers

PRISM recognises ISO currency codes. Note that, when carrying out PRISM analyses, the portfolio and benchmark base currencies must match that of the model for which they are to be used.

Portfolios

Portfolios allows you to rename and delete portfolios and benchmarks. Renaming a portfolio will rename it for all dates that apply to it in PRISM.

Risk Models

Risk Models shows information about the risk model you are currently using, including current and past versions of the model, dates for which each version was updated and its base currency.

Users

In order to log on to PRISM, a user needs an account. Accounts are created by PRISM Administrators and require a unique User Name, Password and an email address. PRISM generates a random password for a new user and sends it to their email address. Users allows you to maintain and update your user details, including changing or resetting your current password.

Admin Operations

Admin operations allows PRISM Administrators to manage Users.

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Library

Library takes you to the folder where you will find useful items such as:

Sample PRISM input files to help you easily to compile your own Portfolios, Benchmarks, Portfolio and Benchmark NAVs and interest rate series. A sample Batch input file to help you run multiple reports from a single set of instructions. For more help on using Batch, click on the Toggle Help button next to the Go button in the Batch command file.

Settings

Settings allows you to change the colours that appear in PRISM reports.

Glossary

Takes you to a glossary of terms used in PRISM.

Frequently Asked Questions

Find answers to questions you may have about Loading Data, finding and understanding risk statistics and some helpful tips on how to interpret your results.

Batch

PRISM Batch uses an intuitive Excel interface to allow you to run multiple reports with a single command. To open Batch, select More Functionality and then Library. Click on the Batch file as you would any Excel file to open it.

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To create a Batch command: 1. Enter your PRISM User Name and Password 2. Enter the Name of the Database you want to use. You will find this at the right hand end of

the PRISM Command Menu ribbon, just under the Logon command. 3. Enter the name of the Risk Model and its date. You will find these near the left hand end of

the PRISM Command Menu ribbon. 4. Enter the Risk Model Date. You will see an example of the correct date format for Batch to

the right of the input matrix. Now you are ready to define your reports. 1. In the column, under Portfolio, Portfolio Date, Benchmark and Benchmark Date, enter the

names and dates of the portfolios and benchmarks you want to run risk reports for. If your portfolio does not have a benchmark, then enter [ CASH ] for the Benchmark name and leave the date field blank.

2. Enter Portfolio, Benchmark or Relative in the next field according to the type of report you want to run.

3. If you would like your Risk Summary report to show the portfolio’s VaR, enter VaR in the next field, followed by percentage the confidence level you want, for example 95 or 99; and the Period, such as Daily, Weekly and so on. A list of available periods for VaR computations is given to the right of the input matrix.

4. Enter any value under the names of the reports you want to generate. A simple Yes will do. If you don’t want that report, leave that field blank.

5. Under Excel File Name, type in the exact address where you would like the output file to be saved.

Toggle Help at any time to see helpful tips on completing the Batch command, Now you are ready to press Go to run your Batched reports. You will see information about any missing stocks in the Warnings tab of your risk report.

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GLOSSARY

OVERVIEW

RELATIVE vs ABSOLUTE ANALYSES

Risk and Performance analyses can be carried out on a portfolio relative to a benchmark, or in

absolute terms (which is actually equivalent to doing it relative to base currency cash). In this

Glossary, reference is made throughout to Relative risk and Relative returns and performance.

PORTFOLIO RISK DECOMPOSITION

PRISM offers four different ways of analysing the risk structure of a portfolio, either in absolute

terms or relative to a benchmark. These are referred to below as Risk by Factors, Risk by

Holdings, Risk by Benchmark and Independent Bets.

Risk by Factors

A portfolio’s risk structure can be analysed using the risk model itself. This analysis gives

the size of the various factor bets, and of the overall stock specific risk. In most

portfolios, some factor exposures help to diversify the overall risk, and these will

therefore have negative contributions to portfolio risk.

The most important use of this analysis is to identify the major factor bets in a portfolio,

and the direction of these bets, which is given by the portfolio beta to each factor. It

also shows what proportion of the portfolio’s risk is factor-related, and how much is stock

specific. The factor-related proportion is sometimes called the portfolio R-squared.

Risk by Holdings

A portfolio’s risk structure can also be analysed in terms of the contributions to risk from

each individual holding. This analysis identifies which holdings are contributing the most

to the overall portfolio risk, and indeed, which might be diversifying the risk. It gives the

contributions to factor risk and stock specific risk from each holding, and also derives

implied returns for each stock that would make the portfolio efficient.

The most important use of this analysis is to identify which current holdings might be out

of line with the portfolio manager’s views. If a stock’s implied return is much higher that

the manager expects it to achieve, the holding size needs to be reduced; similarly, if it is

much lower that the manager’s range of expectation, it should be increased. This

analysis usually suggests a few obvious pair trades which would have the effect of making

the portfolio reflect the manager’s views more efficiently.

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Risk by Benchmark

Most managers are interested in how their portfolio is likely to behave in comparison to

its benchmark, and the portfolio beta relative to the benchmark is the most interesting

risk characteristic after the portfolio tracking error itself.

In this analysis, the portfolio’s risk structure is given in terms of systematic (benchmark-

related) and residual (benchmark-independent) risk. The contribution to portfolio risk

from each holding is given in terms of its systematic and residual components, as well as

the beta of each stock to the benchmark.

The Risk by Benchmark analysis is effectively viewing the portfolio through the lens of a

single-factor model, in which the benchmark (often the market itself) is the factor,

although the residual risks in this case are still correlated with each other.

The most important use of this analysis is to see which holdings are contributing the most

to the portfolio’s beta to the benchmark.

Independent Bets

The Risk by Factors analysis shows how big the various risk model factor bets are in the

portfolio, taking into account the fact that most of these factors are correlated with each

other. An interesting question managers sometimes ask is: How many truly independent

bets are there in a portfolio? This analysis provides the answer.

Some of a portfolio’s independent bets are immediately obvious. For example, the

portfolio stock specific risk is independent of the rest of the portfolio risk, and each of

the statistical factor bets (which are usually very small) are also, by construction,

independent of everything else. So the interesting part of the question boils down to how

many truly independent bets are there among the factor risk contributions to the overall

portfolio?

This analysis decomposes the portfolio’s risk into a set of orthogonal principal

components, which are given together with their percentage contributions to the overall

risk. Apart from the obvious special cases mentioned above, each of these principal

components will be some combination of the risk model factors, with both long and short

positions.

The most important use of this analysis is to identify how many significant independent

bets there really are in the portfolio, to see how big they are in relation to each other,

and to see what factors are contributing to the biggest independent bets.

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PORTFOLIO RISK ANALYSES

RISK SUMMARY

Portfolio Risk

Forecast portfolio volatility estimated at each point in time from the portfolio weights

and the risk model.

Benchmark Risk

Forecast benchmark volatility estimated at each point in time from the benchmark

weights and the risk model.

Tracking Error

Forecast portfolio tracking error, or volatility of the portfolio relative to the benchmark,

estimated at each point in time from the portfolio and benchmark weights and the risk

model.

Portfolio R-Squared

The percentage of portfolio risk that is explained by the Risk Model.

Benchmark R-Squared

The percentage of benchmark risk that is explained by the Risk Model.

Relative R-Squared

The percentage of portfolio tracking error, or portfolio risk relative to the benchmark

that is explained by the Risk Model.

Factor Variance / Risk

This shows the contribution to total risk from exposure to all the factors in the risk

model, including the active factors, time series factors and statistical factors.

Stock Specific Variance / Risk

This shows the contribution to total risk from idiosyncratic stock specific risk. This is the

risk in the portfolio or benchmark that cannot be attributed to factors.

Beta to Benchmark

This is the sensitivity of the portfolio to the benchmark, estimated as the covariance of

the portfolio with the benchmark, divided by the variance of the benchmark.

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Systematic Variance / Risk

This shows the contribution to total risk from the portfolio’s exposure to the benchmark.

It is a function of the portfolio’s beta to the benchmark.

Residual Variance / Risk

This shows the contribution to total risk from sources that are independent of returns to

the benchmark.

Diversification Ratio

This is a measure of diversification. It is calculated as a weighted average of each

holding’s total risk, weighted by its proportional holding size, and divided by the portfolio

or benchmark’s total risk. It is not calculated for the relative case.

Portfolio Active Share (%)

This is the sum of all the Overweight positions in the portfolio relative to the Benchmark

holdings.

Portfolio Deadweight (%)

This is 100% minus the Portfolio Active Share.

Portfolio - number of holdings

The number of portfolio holdings.

Benchmark - number of holdings

The number of benchmark holdings.

Relative - number of holdings

The combined number of holdings in the portfolio and benchmark.

RISK DECOMPOSITION by RISK MODEL

Beta to Factor

This shows the exposure of the portfolio to each factor in relative space; in other words,

it is the difference between the portfolio beta to that factor and the benchmark beta to

that factor. A relative beta of zero indicates that the portfolio has no directional

exposure to that factor, relative to the benchmark. A positive beta indicates a bet that

that factor will do well, while a negative beta represents a bet against the factor. The

beta also gives the amount by which the portfolio needs to be hedged in order to

neutralise its exposure to that factor.

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Factor Risk

This is the annualised volatility of the factor returns.

Correlation

This shows the correlation of each factor to the overall portfolio.

Factor Variance Contribution

This shows the contribution to relative risk from the portfolio’s exposure to a factor due

to the volatility of that factor.

Factor Covariance Contribution

This shows the contribution to relative risk from the portfolio’s exposure to a factor due

to the covariance of that factor with all other factors.

Total Factor Contribution

The Factor Variance Contribution and the Factor Covariance Contribution sum to give the

Total Factor Contribution.

Total Variance Contribution

This is the sum of the Total Factor Contributions plus the Stock Specific Variance.

Portfolio Relative Variance

This is the sum of Total Variance Contributions from each factor and from the

stock specific risk. The square root of the Portfolio Relative Variance is the

Portfolio Tracking Error.

% Factor Variance Contribution

100 times the Factor Variance Contribution divided by Total Variance.

% Factor Covariance Contribution

100 times the Factor Covariance Contribution divided by the Total Variance.

% Risk and Return

This is the percentage contribution to risk. It is 100 times the Total Variance Contribution

for each factor divided by the Portfolio Relative Variance. In an efficient portfolio,

where risk is traded off uniformly against expected return, this will also be the

percentage contribution to return.

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Marginal Variance Contribution

This is the increase in Variance Contribution that would result from a 1% increase in the

exposure to that factor (i.e. in the beta to that factor).

Marginal Covariance Contribution

This is the increase in Covariance Contribution that would result from a 1% increase in the

exposure to that factor.

Marginal Contribution to Risk

This is the increase in factor Contribution to Risk that would result from a 1% increase in

the exposure to that factor.

Relative Factor Beta

The relative factor beta is the difference between the beta of the factor to the portfolio,

and the beta of the factor to the benchmark. The beta of a factor to the portfolio (or

benchmark) is calculated as the covariance of the factor and the portfolio (or

benchmark), divided by the variance of the portfolio (or benchmark). Equivalently, it is

the Factor Risk times the Correlation with the portfolio, divided by the portfolio risk.

Implied Factor Risk Premium

This is derived from the Relative Factor Beta times the Target Relative Return. It is the

return you would expect from that factor, given the Target Portfolio Relative Return, if

the portfolio was efficient relative to the benchmark.

For example, a factor with a Relative Beta of 0.31 would need an expected relative

return of 0.62% in order for an efficient portfolio to achieve an overall Target Relative

Return of 2.0%.

The magnitude of the Implied Risk Premium should correspond directly to your views on

the factor. If it is larger than can be justified by your views on that factor, then reducing

the portfolio’s exposure should be considered. Conversely, if the Implied Risk Premium is

less than you think warranted by your views, an increase in the portfolio’s exposure may

be called for.

Target Relative Return

The default value of the Target Relative Return is 2.0% in relative space (assuming

a 12.0% return for the portfolio and a 10.0% return for the benchmark). The

default can be edited in the PRISM web interface or you can simply multiply the

result given by the default setting, for example if you wanted to set the portfolio

return to 3.0% you would simply multiply the numbers in this column by 1.50.

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Contribution to Return

This is 100 times the portfolio beta to the factor, times the Implied Risk Premium,

divided by the Target Relative Return. For efficient portfolios, this will be the same as

the % Risk and Return.

RISK DECOMPOSITION by HOLDINGS

Original Weights

The portfolio data input to PRISM, which may include stocks that are not covered by the

risk model.

Portfolio/ Relative Holdings

The Original Weights, scaled to sum to 100%, excluding those not covered by the model.

Stock Risk

This is the volatility of the returns to a stock. Note that this is derived from the risk

model, and is calculated from the stock’s betas to each factor, the factor covariance

matrix and the stock’s specific risk. It may differ from the historical time series volatility

of the stock’s returns for a number of reasons.

If the analysis has been conducted relative to a benchmark or reference portfolio, then

this is the risk of the stock in relative returns, in other words, the volatility of the returns

to the stock minus the returns to the benchmark.

Stock Correlation

This is the correlation of the stock returns with the portfolio returns.

Factor Contribution

This is the contribution of the stock to portfolio risk due to the stock’s exposure to the

risk model factors.

Stock-specific Contribution

This is the contribution of the stock to portfolio risk due to the stock’s specific risk.

Total Variance Contribution

This is the sum of the Factor Contributions and Stock-specific Contribution.

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Portfolio Relative Variance

This is the sum of Total Variance Contributions for each stock. The square root of

the Portfolio Relative Variance is the Portfolio Tracking Error.

% Factor Contribution

100 times the Factor Contribution divided by the Total Variance. The percentage Factor

Contributions for each stock sum to give the Portfolio Factor Contribution.

% Stock-specific Contribution

100 times the Stock-specific Contribution divided by the Total Variance. The Stock-

specific Contributions for each stock sum to give the Portfolio Stock-specific

Contribution.

% Risk and Return

This is the percentage contribution of each stock to the overall relative risk. This is 100

times the Total Variance Contribution for that stock divided by the Portfolio Relative

Variance. In an efficient portfolio, where risk is traded off uniformly against expected

return, this will also be the percentage contribution to return.

Marginal Factor Contribution

This is the increase in the stock’s Factor Contribution that would result from increasing

the holding in that stock by 1%.

Marginal Stock-specific Contribution

This is the increase in the stock’s Specific Risk Contribution that would result from

increasing the holding in that stock by 1%.

Marginal Contribution to Risk

This is the increase in the stock’s total Contribution to Risk that would result from

increasing the holding in that stock by 1%.

Marginal Contributions can be misleading if used incorrectly: an increase of 1% in the

holding of one stock always implies a reduction of 1% in another, so the values should not

be looked at in isolation. A helpful way to think about Marginal Contributions is in terms

of the net effect of pairs of trades.

Relative Beta

Relative Beta is the difference between the beta of the stock to the portfolio, and the

beta of the stock to the benchmark.

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The beta of a stock to the portfolio (or benchmark) is calculated as the covariance of the

stock and the portfolio (or benchmark), divided by the variance of the portfolio (or

benchmark). Equivalently, it is the Stock Risk times the Correlation with the portfolio,

divided by the portfolio risk.

Implied Return

This is the Relative Beta times the Target Relative Return. It is the return you would

expect from the stock, given the Target Portfolio Relative Return, if the portfolio was

efficient relative to the benchmark. For example, a stock with a Relative Beta of 0.46

would need an expected relative return of 0.92% in order for an efficient portfolio to

achieve an overall Target Relative Return of 2.0%; and a stock with a Relative Beta of

1.02 would need an expected relative return of 3.06% in order for an efficient portfolio to

achieve an overall Target Relative Return of 3.0%

The magnitude of the Implied Return should (ideally) correspond directly to your views on

the stock. If it is larger than can be justified by your views on the stock, then reducing

the holding size should be considered. Conversely, if the stock’s Implied Return is less

than you think warranted by your views, an increase in the holding size may be called for.


The default value of the Target Relative Return is 2.0% (12.0% for the portfolio and

10.0% for the benchmark). The default target relative return can be edited in the

PRISM Excel Command Bar or you can simply multiply up. For example, if you

wanted to set the portfolio return to 2.5% you would simply multiply the numbers

in this column by 1.25.

Implied Alpha

At the portfolio level this is the Target Relative Return times the percentage Stock-

specific Contribution to risk. The remaining part of the Target Relative Return will

therefore be the factor-related return.

The contribution to Portfolio Implied Alpha from each holding is the stock’s percentage

contribution to portfolio stock specific risk times the portfolio Implied Alpha. By dividing

this contribution by the holding size, we can back out the Implied Alpha for each stock.

This stock Implied Alpha is the pure alpha, sometimes called the idiosyncratic return of the stock, in that it is, by construction, independent of all the risk model factor effects.

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Contribution to Relative Return

This is the % Risk and Return times the Target Relative Return. The magnitude of a

holding’s Contribution to Relative Implied Return will, in an efficient portfolio, equal the

Contribution to Portfolio Risk.

One way of defining portfolio efficiency is that each unit of risk is compensated for by a

unit of expected return, so in an efficient portfolio, the contribution to portfolio risk

should equal the holding’s contribution to portfolio return.

RISK DECOMPOSITION by BENCHMARK

In this form of portfolio risk decomposition, we are analysing the portfolio risk structure in

terms of risk that is benchmark-related, called systematic risk, and risk that is benchmark-

independent, known as residual risk. Note that this residual risk, unlike stock specific risk, will

not be uncorrelated between stocks.

Beta to Benchmark

This is the beta of the stock to the benchmark. It is calculated as the covariance of the

stock and the benchmark, divided by the variance of the benchmark.

Residual Risk

This is the volatility of the stock that is not due to its beta to the benchmark, or in other

words, the volatility that is independent of the benchmark.

Systematic Variance

This is the stock’s contribution to the Portfolio Systematic Variance. It is calculated as

the square of the beta to benchmark multiplied by the benchmark variance.

Residual Variance

This is the stock’s contribution to the portfolio residual variance. It includes the

contribution from the stock’s own residual variance, as well as from its covariance with

the residual risk of all the other holdings in the portfolio.

Total Variance

This is simply the sum of Systematic Variance and Residual Variance contributions for

each stock.

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% Risk and Return

This is 100 times the stock’s contribution to Total Variance divided by the Portfolio

Relative Variance.

Marginal Contribution to Systematic Risk

This is the increase in a holding’s contribution to Systematic Risk that would result from a

1% increase in the holding size.

Marginal Contribution to Residual Risk

This is the increase in a holding’s contribution to Residual Risk that would result from a

1% increase in the holding size.

Marginal Contributions can be misleading if used incorrectly: an increase of 1% in one

holding always implies a reduction of 1% in another. A helpful way to think about Marginal

Contributions is therefore in terms of pairs trades.

Implied Return

This is the return you would expect from the stock, given the Target Portfolio Relative

Return, if the portfolio was efficient relative to the benchmark.


The default value of the Target Relative Return is 2.0% (12.0% for the portfolio and

10.0% for the benchmark).

Contribution to Relative Return

This is the % Risk and Return times the Target Relative Return. The magnitude of the

Contribution to Relative Implied Return, will, in an efficient portfolio, equal the

Contribution to Portfolio Risk.

Implied Alpha

In this Risk Decomposition by Benchmark case, this is the stock return that can be

attributed to benchmark-independent, or residual, effects. It is calculated by

subtracting the benchmark-related, or systematic, return of the stock from its Implied

Return. The benchmark-related return is, of course, simply the stock’s beta to

benchmark times the benchmark return.

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Contribution to Relative Alpha

At the stock level, this is the Implied Alpha multiplied by the Relative Weight. At the portfolio level, it is the weighted sum of stock-level Implied Alphas. This is the return that can be expected from benchmark-independent, or residual, risk. In this Risk Decomposition by Benchmark case, we will have:-

Portfolio Return = Beta to benchmark * Benchmark return + Portfolio Alpha

The Risk Decomposition by Holdings and Risk Decomposition by Benchmark analyses

both look at the risk structure of a portfolio in terms of the contributions to portfolio risk

from each individual holding. They will, of course, both give the same results for the risk

contribution from each holding and its Implied Return.

In the Holdings case, the overall contribution is divided into a factor-related contribution

and a stock specific contribution. In the benchmark case, the same overall contribution

from a stock holding will be divided into a systematic (benchmark-related) part, and a

residual (benchmark-independent) part.

Because the two divisions are different, the split of the Implied Return for each stock will

also be different, leading to a different Implied Alpha in the Holdings case (stock

specific) than in the Benchmark case (residual). Note that one is a factor-independent

alpha, whereas the other is a benchmark-independent alpha.

INDEPENDENT BETS

The Risk Decomposition by Risk Model described above will tell us how much risk is coming from

the portfolio’s exposure to each of the risk model factors, but these are not usually independent

of each other. An interesting question to ask is how many truly independent bets there are in a

portfolio, and, perhaps more importantly, how big they are in relation to each other.

In this analysis, we first create a portfolio-beta-weighted extended factor covariance matrix.

The matrix is extended in the sense that we add one extra row and column to the standard

factor covariance matrix; the diagonal term for this extension is simply the portfolio stock

specific variance, and all the off-diagonal elements are zero (since the stock specific risk is, by

construction, independent of all the factors). Note that the sum of the terms in this extended

matrix equals the Portfolio Variance or Tracking Variance.

We then run a Principal Components Analysis on this matrix, and derive the resulting

eigenvectors and eigenvalues, which are then shown in the report. Each of the eigenvectors

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will be some long-short combination of the risk model factors, except the one that is the

Portfolio Stock-specific Variance; the corresponding eigenvalues are converted into percentage

contributions to the overall portfolio risk.

Notice that the Portfolio Stock Specific risk will always be the sole constituent of one of the

eigenvectors, since, as we know, it is independent of all the risk model factors. Notice also that

each of the Statistical factors will likewise appear as the sole constituent of one of the

eigenvectors, since again, by construction, each of these is independent of all the other factors.

In a pure ‘stock-picker’s’ portfolio, in which most of the factor exposures are close to the

benchmark exposures (i.e. ‘neutral’ with respect to the benchmark), and most of the Tracking

Error is therefore Stock Specific risk, we would expect to find that the biggest single

independent bet is, indeed, the Stock Specific risk, or, looked at a slightly different way, a bet

on the manager’s stock-picking ability!

However, in most cases the single biggest independent bet will be some combination of the risk

model factors. For example, imagine a manager following a Small Cap, High Value strategy, in

which she is trying to remain neutral on Sector exposures relative to some benchmark. In such a

case, we would expect the single biggest independent bet to be dominated by the Small Cap

and Value factors. Although it is usually fairly easy to interpret these combinations, there will

be occasions when it is more difficult.

The most important result, however, is probably the percentage contributions of each of the

first few independent bets to the overall portfolio risk.

Relative Beta to Factor

This is the relative beta of the portfolio to each factor.

% Contribution to Variance

This is the percentage contribution of each factor to the portfolio’s relative risk. This can

also be thought of as 100 times the Total Factor Contribution for that factor divided by

the Relative Variance.

% Risk and Return

This is the percentage contribution to risk. It is 100 times the Total Variance Contribution

for each factor divided by the Portfolio Relative Variance.

PC Contributions to Risk

This gives the Principal Components Analysis of the risk structure of the portfolio,

showing a sequence of independent bets in descending order of importance.

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Frequently, one of the largest independent contributors is the Portfolio’s Stock Specific risk. For

each independent bet, its percentage contribution to the overall portfolio risk is shown, as well

as the weights of its various constituents.

PERFORMANCE ANALYSIS

Portfolio Net Asset Value (NAV)

Input by the User.

Benchmark Net Asset Value (NAV)

Input by the User.

Interest Rates

Input by the User. These should be annualised rates of return.

Number of Net Asset Values (NAVs)

This simply counts the number of Portfolio NAVs over time.

Portfolio Returns

The log return of the Portfolio NAV for one period.

Benchmark Returns

The log return of the Benchmark NAV for one period.

Relative Returns

The Portfolio Return less the Benchmark Return.

Cash Returns

The log return to cash for the period.

Number of Returns

This simply counts the number of Portfolio Returns over time.

Portfolio Index

Portfolio performance expressed as an index starting at 100.

Benchmark Index

Benchmark performance expressed as an index starting at 100.

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Relative Index

Relative performance expressed as an index starting at 100.

Interest Rate Index

Cash performance expressed as an index starting at 100.

Number of Index Values

This simply counts the number of Portfolio Index Values over time.

RISK FORECASTS

Beta to Benchmark

This is estimated at each point in time over the historic performance analysis period from the

risk model and the portfolio and benchmark weights.

Ex Ante Portfolio Risk (p.a.)

Forecast annualised portfolio volatility estimated at each point in time over the historic

performance analysis period.

Ex Ante Benchmark Risk (p.a.)

Forecast annualised benchmark volatility estimated at each point in time over the historic

performance analysis period.

Ex Ante Tracking Error (p.a)

Forecast annualised portfolio tracking error, or risk of the portfolio relative to the benchmark,

estimated at each point in time over the historic performance analysis period.

OBSERVED RISK TESTS

Ex Post Portfolio Risk (1 year)

Observed portfolio volatility over the previous year of returns.

Ex Post Benchmark Risk (1 year)

Observed benchmark volatility over the previous year of returns.

Ex Post Tracking Error (1 year)

Observed portfolio tracking error, or volatility of the portfolio relative to the benchmark over

the previous year of returns.

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Ex Post Portfolio Risk (Cumulative)

Observed portfolio volatility for the cumulative period analysed, beginning after the first year.

Ex Post Benchmark Risk (Cumulative)

Observed benchmark volatility for the period analysed, beginning after the first year.

Ex Post Tracking Error (Cumulative)

Observed portfolio tracking error, or volatility of the portfolio relative to the benchmark for the

cumulative period analysed, beginning after the first year.

BENCHMARK RISK-ADJUSTED RETURNS

Benchmark-related Return

This is the return that is due to the portfolio’s beta to the benchmark, calculated as the

portfolio beta relative to the benchmark times the benchmark return.

Portfolio Alpha

This is the Portfolio Return minus the Benchmark-related return.

Benchmark-related Index

Benchmark-related returns expressed as an index.

Portfolio Alpha Index

Portfolio alpha expressed as an index.

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GENERAL

Factor Groups

RSQRM models employ a process known as Step-wise Multiple Regression to derive stock betas to

risk factors. Risk factors are arranged in a hierarchy so that types of common factors are

grouped together into Factor Groups or Factor Blocs. For example, Currency factors usually form

one bloc, Style factors another, Country and Industry factors two others and Statistical factors

yet another.

Within factor blocs, stocks are regressed simultaneously against individual factors (hence:

Multiple Regression), while factor blocs are regressed sequentially (or Step-wise), according to

their position within the risk factor hierarchy.

Risk factor hierarchies are specific to each model and are described in Risk Model Factsheets.

Statistical Factors

Statistical factors are risk factors that are defined by the historical returns of the stocks in the

relevant universe – in contrast to pre-defined risk factors, which are determined during the

design of the risk model. Statistical factors make use of the fact that both the stock betas and

the factor covariance matrix (and, hence, the residual risks) can be estimated from stock

returns data by factor analysis or Principal Components Analysis.

In this method, the historic stock returns for the whole universe of stocks are first converted

into a historic covariance matrix over some look-back period. This covariance matrix (or, in

some cases, the corresponding correlation matrix) is then transformed into a series of

orthogonal, statistical factors.

This type of model will, by construction, have the best possible fit with the in-sample data,

although this is, of course, no guarantee that it will necessarily have the best fit in subsequent

out-of-sample data.

The limitation of statistical factors is that it is often hard to give them any kind of intuitive

economic meaning. Moreover, the results often vary considerably over different data sets and

different time periods, leading to a worrying instability in the model.

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FREQUENTLY ASKED QUESTIONS

How do I load a portfolio into PRISM? In Excel, create a sheet with the portfolio holdings and save it as a .csv file. Sample input files can be found under More Functionality / Library in the PRISM Command Menu. In PRISM, go to More Functions, then Load Data. PRISM prompts you to Browse, Select and Load the portfolio. How do I load a benchmark into PRISM? PRISM does not distinguish between portfolios and benchmarks at the loading stage, although it lets you do so when you carry out a risk analysis or a performance analysis. In Excel, create a sheet with the benchmark holdings. Sample input files can be found under More Functionality / Library in the PRISM Command Menu. In PRISM, go to More Functions, then Load Data. PRISM prompts you to Browse, Select and Load the portfolio. In PRISM, go to More Functions, then Load Data. PRISM prompts you to Browse, Select and Load the portfolio. How do I load interest rates into PRISM? In Excel, create a sheet with the portfolio holdings. Sample input files can be found under More Functionality / Library in the PRISM Command Menu. In PRISM, go to More Functions, then Load Data. PRISM prompts you to Browse, Select and Load the portfolio. How do I load portfolio and benchmark Net Asset Values (NAVs) into PRISM? In Excel, create a sheet with the portfolio holdings. Sample input files can be found under More Functionality / Library in the PRISM Command Menu. In PRISM, go to More Functions, then Load Data. PRISM prompts you to Browse, Select and Load the portfolio.

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Which stock identifiers does PRISM recognise? PRISM recognises 7-digit SEDOLS, Cusips, ISINs, Bloomberg tickers and of course, RSQ stock identifiers. Note that, as most commercial stock identifiers can change over time, the name of the stock they refer to is specific to the date of the model being used. RSQ stock identifiers are unique and do not change over time. Where can I see the volatility of my portfolio? This is displayed in Cell B13 of the Summary page of the risk analysis. Where can I see the tracking error of my portfolio? This is displayed in Cell D13 of the Summary page of the risk analysis. It is also in Column D of the Totals row of the Factor Risk page and Column G of the Totals row of the Holdings Risk page. Where can I see the beta of my portfolio to its benchmark? This is displayed in Cell D14 of the Summary page of the risk analysis. Where can I see the Diversification Ratio? This is displayed in Cell B24 of the Summary page of the risk analysis. Where can I see the Marginal Contribution to Risk of my portfolio relative to its benchmark? Marginal Factor Contribution to Risk is displayed in Column N of the of the Factor Risk page of the risk analysis. Marginal Holdings Contribution to Risk is displayed in Column Q of the of the Holdings Risk page of the risk analysis. How can I see what my portfolio’s exposures to macro-economic variables are? In Risk Reports, select Macro-economic Exposures. Now you will notice that the option Macro-economic Factors is no longer greyed out. From the drop-down menu, highlight the Macro-economic variables you are interested in. Now run the risk report, the Betas page of which will show you the beta of your portfolio and each of its component stocks, to each Macro-economic variable selected.

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You can also see the relationship between each Macro-economic variable and the model's risk factors by including each variable as a holding in the portfolio. The Betas report will display the beta of each variable to each of the model's risk factors. Another way to do this is to create a portfolio that comprises equally-weighted Macro-economic variables as its holdings. This can then be analysed as a stand-alone portfolio or as a benchmark to a real portfolio. Where can I see the portfolio’s beta to each model risk factor? The Betas report shows this information. Where can I see the contribution to portfolio risk of each model risk factor? This is displayed in Column K of the Factor Risk page of the risk analysis. Where can I see how volatile each model risk factor is? This is displayed in Column C of the Factor Risk page of the risk analysis. Where can I see the contributions to portfolio risk of factor groups? This is displayed just above the Totals rows of Column K of the Factor Risk page of the risk analysis. Where can I see how much of each factor’s risk contribution is due to the variance of the factor and its covariance with other factors? This is displayed in Columns I and J of the Factor Risk page of the risk analysis. Where can I see the contributions to risk of individual holdings? This is displayed in Column N of the Holdings Risk page of the risk analysis. Where can I see how volatile each holding is? This is displayed in Column G of the Holdings Risk page of the risk analysis.

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Where can I see how much of each holding’s risk contribution is due to its exposure to the model’s risk factors? This is displayed in Columns I and L of the Holdings Risk page of the risk analysis. Where can I see how much of each holding’s risk contribution is due to its stock-specific effects? This is displayed in Columns J and M of the Holdings Risk page of the risk analysis. Where can I see each holding’s beta to the benchmark? This is displayed in Column F of the Benchmark Risk page of the risk analysis. Where can I see how much of each holding’s risk contribution is due to its exposure to the benchmark? This is displayed in Columns I and L of the Benchmark Risk page of the risk analysis. Where can I see how much of each holding’s risk contribution is due to its non-benchmark-related effects?

This is displayed in Columns J and M of the Benchmark Risk page of the risk analysis. How can I see the betas of each holding to each model risk factor? This is displayed in the Betas page of the risk analysis. How can I see stock data items for each holding? In Risk Reports, select Portfolio Holdings. Now you will notice that the option Stock Data Items is no longer greyed out. From the drop-down menu, highlight the items you are interested in. Now run the risk report, which will show you for each holding in your portfolio and benchmark, the stock data items you selected. Can I compare two portfolios with each other? Yes. Because your portfolios and benchmarks were loaded into PRISM in exactly the same way, you can compare two portfolios, simply by nominating one portfolio as Portfolio and another as Benchmark. Can I compare two benchmarks with each other?

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Yes. Because your portfolios and benchmarks were loaded into PRISM in exactly the same way, you can compare two benchmarks, simply by nominating one as Portfolio and another as Benchmark. How do I carry out Reverse Optimisation using PRISM? There are two types of Reverse Optimisation: by risk factor and by individual holdings. To Reverse Optimise by Risk Factor, simply generate a Risk Factor report and you'll find the reverse optimisation results in columns O, P and Q. To Reverse Optimise by Holdings, simply generate a Holdings Risk report and you'll find the reverse optimisation results in columns R, S, T and U. In the PRISM Glossary, you will find help in interpreting each column. My target portfolio return is not 12% per annum and my target benchmark return is not 10% per annum. How can I change these so that PRISM shows the right Implied Risk Premiums, Implied Returns and Contributions to Returns for my portfolio and benchmark? There are two ways to do this. The first is, when you are setting the parameters for your risk reports or performance reports, to change from the default options when you run your risk reports. This is done simply by editing the 12 or the 10 as applicable. PRISM will adjust its calculations accordingly. The second way is, after the risk report has been generated, to manually adjust the results as required. For example, if your target portfolio return is 9% instead of 12%, simply multiply the results in columns P and Q of the Factor Risk report and columns S and U of the Holdings Risk report by 0.75 (9/12). The adjustment for the benchmark return follows the same logic: for example, if your target benchmark return is 5% instead of 10%, simply halve the results in columns P and Q of the Factor Risk report and columns S and U of the Holdings Risk report. My portfolio dates do not correspond exactly to the risk model dates. Does this matter for Performance Analysis? No, you can still generate a Performance Analysis. PRISM will choose the most recent model date for each portfolio and benchmark date.

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Does PRISM have a Batch function to allow me to run multiple reports from a single command? Yes, it does. In the PRISM Command Menu, go to More Functionality / Library. There you will find a sample Batch input file. For specific help on using Batch, click on the Toggle Help button next to the Go button in the Batch command file. What are Factor Groups? RSQ models employ a process known as Step-wise Multiple Regression to derive stock betas to risk factors. Risk factors are arranged in a hierarchy so that types of common factors are grouped together into Factor Groups or Factor Blocs. For example, Currency factors usually form one bloc, Style factors another, Country and Industry factors two others and Statistical factors yet another. Within factor blocs, stocks are regressed simultaneously against individual factors (hence: Multiple Regression), while factor blocs are regressed sequentially (or Step-wise), according to their position within the risk factor hierarchy. Risk factor hierarchies are specific to each model and are described in Risk Model Factsheets. What are Statistical Factors? Statistical factors are risk factors that are defined by the historical returns of the stocks in the relevant universe – in contrast to pre-defined risk factors, which are determined during the design of the risk model. Statistical factors make use of the fact that both the stock betas and the factor covariance matrix (and, hence, the residual risks) can be estimated from stock returns data by factor analysis or Principal Components Analysis. In this method, the historic stock returns for the whole universe of stocks are first converted into a historic covariance matrix over some look-back period. This covariance matrix (or, in some cases, the corresponding correlation matrix) is then transformed into a series of orthogonal, statistical factors. This type of model will, by construction, have the best possible fit with the in-sample data, although this is, of course, no guarantee that it will necessarily have the best fit in subsequent out-of-sample data. The limitation of statistical factors is that it is often hard to give them any kind of intuitive economic meaning. Moreover, the results often vary considerably over different data sets and different time periods, leading to a worrying instability in the model.

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Does Factor Risk include contributions to risk from Statistical Factors? Yes. You can see how much risk is due to Statistical factors at the bottom of your Factor Risk report. Why do the Factor Risk and the Stock Risk not add up to Total Risk? Factor Risk, Stock Risk and Total Risk are all given by standard deviations. Standard deviations are not additive; but as they are the square root of variances, which are additive, you can derive the Total Risk by squaring each of the Factor Risk and the Stock Risk and taking the square root of the sum of the two. This way they do add up. Why do the Systematic Risk and the Residual Risk not add up to the Total Risk? Systematic Risk, Residual Risk and Total Risk are all given by standard deviations. Standard deviations are not additive; but as they are the square root of variances, which are additive, you can derive the Total Risk by squaring each of the Systematic Risk and the Residual Risk and taking the square root of the sum of the two. This way they do add up. What is the difference between Factor Risk and Systematic Risk? Factor Risk is the collective term for risk that is attributable to the model's risk factors, while Systematic Risk describes that part of risk that is due to its exposure to its benchmark. What is the difference between Stock-specific Risk and Residual Risk? Stock Risk describes risk that is not attributable to the model's risk factors, while Residual Risk describes that part of risk that is not explained by its exposure to its benchmark. Why do individual Factor Risks not add up to Factor Risk in the total row of the Factor Risk page? Individual Factor Risks and Total Risk are all given by standard deviations. Standard deviations are not additive; but as they are the square root of variances, which are additive, you can derive the Total Risk by squaring each of the Factor Risks and taking the square root of the sum of Factor Risks. This way they do add up.

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Why do individual Holdings Risks not add up to Portfolio Risk in the total row of the Holdings Risk page? Individual Holdings Risks and Total Risk are all given by standard deviations. Standard deviations are not additive; but as they are the square root of variances, which are additive, you can derive the Total Risk by squaring each of the Holdings Risks and taking the square root of the sum of Factor Risks. This way they do add up. Some stocks have been listed for only a short time. Are these Short History Stocks treated differently to stocks with full trading histories? Yes. The actual treatment depends on the amount of historical return data that is available. For example, stocks with very few return observations may be given the risk factor betas of the average of their peers in terms of their currency of denomination, industry group or country of listing. Only full-history stocks have betas to statistical factors. I thought Cash is risk-less, yet the analysis is showing me that it is contributing to portfolio risk. Why? In absolute terms, cash is indeed risk-less, but relative to a benchmark that is invested in risky assets, it does carry risk. How do I use the Independent Bets analysis? The aim of the Independent Bets analysis is to capture the benefit of Principal Components Analysis while benefitting from the intuitive interpretation afforded by pre-specified risk factors. When you inspect the Independent Bets analysis, you will notice that Row 4 tells you how much of the portfolio’s risk is attributable to each Independent Bet, with PC1 representing the largest share, PC2 the next largest and so on. Typically the first three factors explain about 75% of the risk of a portfolio, but this can vary. For each PC factor with a significant share of portfolio risk, sort the data in descending order, so you can see which pre-specified factors contribute most to its effect, and, at the bottom of the matrix, which are softening the contribution of the PC factor. You can gain further insight from the Betas page of the analysis by sorting, for each of the pre-specified factors, as identified by the Independent Bets analysis as the most interesting, from highest to lowest to see which stocks are having the greatest impact.

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Some of the holdings in my portfolio are showing negative contributions to risk. What does this mean? A negative contribution to risk from a risk factor or a portfolio holding means that that risk factor or holding is helping to diversify, or lower the risk of your portfolio. Increasing the portfolio's exposure to the risk factor or its holding in the stock will, other things being equal, reduce the risk of the portfolio. Reducing the portfolio's exposure to the risk factor or its holding in the stock will, other things being equal, increase the risk of the portfolio. Why does so much of my portfolio’s risk come from stocks that are not held in the portfolio? Stocks that are not held in a portfolio but which are held in the benchmark can contribute to the risk of the portfolio relative to the benchmark. One way to think of this is that, from the perspective of the benchmark, a portfolio weight of zero is equivalent to a negative relative position, which is a source of relative risk. Zero holdings do not contribute to the risk of the portfolio in absolute terms. Why does my portfolio have exposure to currencies that are not even held in the portfolio? Individual stocks, and therefore portfolios that hold them, can have exposures, or betas to currencies other than those in which they are denominated. This exposure is usually a function of the nature of their businesses. Think of Nestlé, a Swiss stock denominated in Swiss Francs, that in fact derives very little of its profits from within Switzerland. Currency exposures are estimated using time-series analysis, which is driven directly by the market's estimation of the sensitivity of the stock to each currency. If this sensitivity passes the risk model's test for statistical significance, it will be manifest as the stock's beta to that currency, regardless of its currency of denomination. The beta, or exposure, of the portfolio to a currency, or to any other risk factor, is the weighted sum of the betas to the risk factor of the holdings in the portfolio. Why is there such a big difference between the portfolio’s exposure to industry groups and its holdings in those groups? The exposure of the portfolio to each industry group risk factor is a function of the beta of each stock in the portfolio to the industry group risk factor, as well as its weight in the portfolio. Because the value of each stock beta is not necessarily 1.0 (because stock returns are driven by other things, such as leverage), exposure is quite likely to be different to holding weights.

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Industry group exposures are estimated using time-series analysis, which is driven directly by the market's estimation of the sensitivity of the stock to each industry group. If this sensitivity passes the risk model's test for statistical significance, it will be manifest as the stock's beta to that industry group, regardless of its industry classification. The beta, or exposure, of the portfolio to an industry group, or to any other risk factor, is the weighted sum of the betas to the risk factor of the holdings in the portfolio. Why is there such a big difference between the portfolio’s exposure to countries and regions and its holdings in those countries and regions? The exposure of the portfolio to each country or region risk factor is a function of the beta of each stock in the portfolio to the country or region risk factor, as well as its weight in the portfolio. Because the value of each stock beta is not necessarily 1.0 (because stock returns are driven by other things, such as leverage), exposure is quite likely to be different to holding weights. Country or region exposures are estimated using time-series analysis, which is driven directly by the market's estimation of the sensitivity of the stock to each country or region. If this sensitivity passes the risk model's test for statistical significance, then it will be manifest as the stock's beta to that country or region, regardless of its country of listing. The beta, or exposure, of the portfolio to a currency, or to any other risk factor, is the weighted sum of the betas to the risk factor of the holdings in the portfolio. Do concentrated portfolios have a higher stock-specific component of risk than more diversified portfolios? It seems intuitive that very concentrated portfolios should have higher stock-specific risk but this isn't necessarily the case. It depends more on which stocks. One way to think about this is to imagine a single factor model, where, say, the market is the factor. If the risk of the stocks is mostly explained by their beta to the market, then the stock-specific risk will be small. On the other hand, if the stocks' betas explain relatively little, then the stock-specific risk will be high. This principle extrapolates to multi-factor models. More important is whether the portfolio is long-short (or benchmarked) or long-only relative to cash. In the former case the risk is generally lower but much of the factor risk is offset by the long-short (or the over-weight/ under-weight). In the absolute case the risk is generally higher but factor risk is not offset so the stock-specific component is lower.

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How do I hedge unintended factor exposures? It depends on what the unintended factor exposure is. If it is a Currency, or a market/country factor, you could hedge the exposure directly using a currency forward or a market ETF or future (always assuming you’re allowed to go short if the unintended exposure is long). If there is no tradable instrument that matches the unintended factor exposure directly, your only recourse is to find stocks whose exposure to the unintended factor will help to damp down the exposure. This could be done by eye, or by optimisation. Or if you don’t want to add any additional stocks to the portfolio, you could try optimising the existing set of holdings while putting a constraint on to damp down the unintended exposure. My Performance Analysis says there is no contribution to return from statistical factors, even though my risk report said they contributed to risk. Why? The objective of Performance Analysis is to quantify the contribution to return of each deliberate exposure in your portfolio. Statistical Factors capture unintended risk for which the risk model nevertheless was able to identify a systematic component. As this risk is unintended, it is included in the non-factor-related return. Some risk factors contribute much more (or less) to performance than they did to risk. What is going on? Factor risk is a function of historical returns to the factor over the model look-back period, analysed using a mean-variance methodology. This assumes that the investment horizon will resemble the model look-back period in terms of factor volatility and that stock returns are approximately log-normally distributed. There are a number of possible explanations for differences in contribution to ex-ante risk and ex-post return:

The portfolio composition changed significantly during the performance analysis period.

The factor volatility observed in the performance analysis period is higher or lower than that observed in the model look-back period.

Factor returns in the performance analysis period exhibited trending that violates the assumption of log-normality.

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INDEX % Contribution to Variance, 28 % Risk and Return, 20, 26, 28

Stock, 23 Admin Operations, 13 ADR, 5 Analysis, 11

by Portfolio, Benchmark, Relative, 5 Performance, 29, 43 Relative v Absolute, 16

Autoloader, 12 Base currency, 13 Batch, 14, 38 Benchmark, 4, 10 Benchmark Risk-adjusted Returns, 31 Benchmark-independent. See Residual Benchmark-related. See Systematic Beta, 8, 17

Factor, 21, 35, 36 Relative, 23 to Benchmark, 18, 25, 30, 34, 36 to Factor, 19, 28

Cash, 40 Comma Separated Values Files, 12 Compare Two Benchmarks, 36 Compare Two Portfolios, 36 Contribution to Relative Alpha, 27 Contribution to Relative Return, 25, 26 Contribution to Return, 7, 22, 43 Correlation

Factor, 20 Stock, 22

Correlation Matrix

Factor, 8 Covariance

Factor Contribution, 35 Covariance Contribution

Factor, 20 Covariance Matrix, 27

Factor, 8 Stock, 8

CSV. See Comma Separated Values Files Data Formats, 12 Database, 3 Diversification Ratio, 19, 34 Efficient Portfolio, 22, 25 Eigenvectors, 27 Expected Returns, 5 Exposure

Country and Region, 42 Currency, 41 Factor, 36 Industry Group, 41 to Benchmark, 36 Unintended, 43

Factor Bets, 16 Factor Blocs. See Factor Groups Factor Contribution, 7, 8

Holding, 22 Total, 20

Factor Groups, 32, 38 Frequently Asked Questions, 14, 33 Full-history Stocks, 40 Getting Started, 3 Glossary, 14, 16 Hedge, 43 Holdings, 8 Identifiers

Currency, 13 Stock, 34

Implied Alpha, 24, 26 Implied Factor Risk Premium, 21, 37 Implied Return, 16, 24, 26, 37 Independent Bets, 8, 17, 27, 40 Index

Benchmark, 29 Benchmark-related, 31 Interest Rate, 30 Portfolio, 29 Portfolio Alpha, 31 Relative, 30

Index Values

Number of, 30 Input Files

Sample, 14 Interest Rate File, 11 Interest Rates, 29 Library, 14 Load Benchmark, 33 Load Data, 12 Load Interest Rates, 33 Load Net Asset Values, 33 Load Portfolio, 33 Logoff, 3 Logon, 3 Macro Economic Variables, 34 Macro Exposures, 5, 7

R-Squared


Marginal Contribution to Residual Risk, 26 Marginal Contribution to Risk, 21, 34

Stock, 23 Marginal Contribution to Systematic Risk, 26 Marginal Covariance Contribution to Risk, 21 Marginal Factor Contribution to Risk

Stock, 23 Marginal Stock-specific Contribution to Risk

Stock, 23 Marginal Variance Contribution to Risk, 21 More Functionality, 12 Multiple Regression, 32, 38

Stepwise, 32 NAV. See Net Asset Value Net Asset Value

Benchmark, 29 Number of, 29 Portfolio, 29

Number of Holdings

Benchmark, 19 Portfolio, 19 Relative, 19

Observed Risk Tests, 30 Original Weights, 22 Parent, 5 Password, 13 Performance Reports, 10 Period, 11 Portfolio, 4, 10, 13

Concentrated, 42 Diversified, 42

Portfolio Active Share, 19 Portfolio Alpha, 31 Portfolio Dates, 37 Portfolio Deadweight, 19 Portfolio Holdings, 22 Portfolio Holdings Report, 5 Portfolio Manager’s Views, 16 Portfolio Minimum Value, 6 Portfolio Stock-specific Variance, 28 Portfolio Value, 6 Portfolio Variance, 27 Principal Components, 17 Principal Components Analysis, 27, 32, 38 PRISM Administrator, 13 PRISM Licence, 3 Report Formatting, 9 Returns

Benchmark, 29 Benchmark-related, 31 Cash, 29

Number of, 29 Portfolio, 29 Relative, 29

Reverse Optimisation

by Benchmark. See Implied Return by Factor. See Implied Factor Risk Premium by Stock. See Implied Return

Risk

Benchmark, 18 Benchmark ex post, 30, 31 Benchmark, ex ante, 30 by Benchmark, 8, 9, 17 by Factors, 7, 16 by Holdings, 7, 16 Factor, 7, 18, 20, 39 Factor Contribution, 35, 43 Factor, Holding, 39 Holding, 7, 40 Holding, Contribution, 35, 36 Portfolio, 18, 40 Portfolio ex ante, 30 Portfolio ex post, 30, 31 Residual, 17, 19, 25, 39 Stock, 22, 39 Stock-specific, 17, 18, 28, 36, 39 Systematic, 17, 19, 39 Total, 39

Risk Contribution

Factor Groups, 35 Negative, 16, 41 Principal Components, 28 Residual, 36 Stock-specific, 22

Risk Decomposition

by Benchmark, 25 by Holdings, 22 by Risk Model, 19 Portfolo, 16

Risk Factor Hierarchy, 32 Risk Forecasts, 30 Risk Model, 4, 10 Risk Models, 13 Risk Reports, 4, 6 Risk Summary, 6, 18 R-squared, 16

Benchmark, 18 Portfolio, 18 Relative, 18

Sample Input Files. See Library Settings, 14

R-Squared


Short-history Stocks, 40 Statistical Factors, 17, 32, 38, 39, 43 Stock Data Items, 5, 36 Target Benchmark Return, 37 Target Portfolio Return, 37 Target Relative Return, 21, 24, 26 Tracking Error, 18, 20, 23, 34

ex ante, 30 ex post, 30, 31

Tracking Variance, 27 User, 13 User Name, 13 Variance

Contribution, Actual, 28 Factor, 18 Factor Contribution, 35

Portfolio, 20 Residual, 19, 25 Stock-specific, 18 Systematic, 19, 25 Total, 25

Variance Contribution

Factor, 20 Total, 20, 22

Volatility, 18, 22

Factor, 35 Holding, 35 Portfolio, 34

Warnings, 9, 15 Zero Holdings, 41

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