Allocation Research Toolkit (“ART”)Allocation Research Toolkit (ART) Northfield Information Services 4 Boston Chicago London Tokyo Northfield Information Service’s Allocation

Table of Contents

Allocation Research Toolkit (“ART”)

Boston London Tokyo 2 Atlantic Avenue 2-6 Boundary Row Shiroyama Trust Tower Boston, MA 02110 London, SE1 8HP 4-3-1 Toranomon 617.451.2222 44.20.3714.4130 Minato-ku Tokyo 105-6027 81.3.5403.4655

www.northinfo.com

FEB-3-2014

Allocation Research Toolkit (ART)

Northfield Information Services Boston Chicago London Tokyo www.northinfo.com 2

Table of Contents Northfield’s Allocation Research Toolkit ..................................................................................... 4

Documentation and Advice ......................................................................................................... 4

Client-Server Architecture ........................................................................................................... 4

The Database ............................................................................................................................. 5

The Browser ......................................................................................................................................... 5 Style Analysis in the Browser................................................................................................................ 6 The Sector Ranking Window ................................................................................................................ 7 Base Currencies ................................................................................................................................... 8

Private Data Series and Composite Funds ................................................................................. 8

Daily and Quarterly Data ...................................................................................................................... 8 Asset Allocation: The Analytical Hierarchy Process ................................................................... 9

Individual Investors ............................................................................................................................... 9 Institutional Investors .......................................................................................................................... 10

Portfolio Optimization ............................................................................................................... 11

Group constraints ............................................................................................................................... 12 What Expected Returns should you use? ........................................................................................... 13 Optimization Reports .......................................................................................................................... 14

Feasible Region (graph) .................................................................................................................. 14 Optimization Summary Table (Not Shown) ..................................................................................... 15 Asset Weight Graph ........................................................................................................................ 15 Downside Risk (table) (Not Shown) ................................................................................................ 16 Single Year vs. Multiple Year Returns (graph) ................................................................................ 16 Return Distribution, Single Year (graph) ......................................................................................... 17 Annualized Return Distribution for Multiple Years (Not Shown) ...................................................... 17 Value Distribution, Single Year (Not Shown) .................................................................................. 17 Value Distribution, Multiple Years (Not Shown) .............................................................................. 17

Reports on Individual Efficient Portfolios: ........................................................................................... 17 Optimal Selection Summary (graph) ............................................................................................... 17 Optimal vs. Initial Weights (Not Shown) .......................................................................................... 18 Wealth Accumulation Table (Not Shown) ....................................................................................... 18 Wealth Accumulation (Not Shown) ................................................................................................ 18 Annualized Return Distribution for Multiple Years (graph) .............................................................. 18 Probability of Achieving Minimum Desired Return .......................................................................... 19 Cumulative Return Distribution for Multiple Years .......................................................................... 20 Implied Returns (table) .................................................................................................................... 20

Optimizing Relative to a Liability ......................................................................................................... 20 Historical Simulation ................................................................................................................. 21



Tactical Asset Allocation ..................................................................................................................... 22 Asset Class Information Coefficient .................................................................................................... 22 Cross Sectional Information Coefficient .............................................................................................. 23 Predicted vs. Realized Risk Graph ..................................................................................................... 24 The Tactical Weight Report ................................................................................................................ 25

Style Analysis ........................................................................................................................... 25

Confidence Estimates ......................................................................................................................... 25 Style History Table .............................................................................................................................. 25 Style History Graph ............................................................................................................................. 26 Style Box ............................................................................................................................................. 26 CUSUM ............................................................................................................................................... 27

Statistical Analysis .................................................................................................................... 28

Univariate regression table ................................................................................................................. 28 The univariate regression graph ......................................................................................................... 28 The multiple regression report ............................................................................................................ 29



Northfield Information Service’s Allocation Research Toolkit, (“ART”), is a flexible analytical system for analyzing and producing optimal portfolios using returns based analysis of asset classes, mutual funds, separately managed accounts, hedge funds or the user’s own database. Northfield designed ART to satisfy a wide variety of requirements for a variety of users: institutional money managers, plan sponsors, consultants, bank trust departments, and personal account managers.

At the heart of ART is the same fast optimization engine that was built to drive Northfield’s Open Optimizer, a portfolio optimizer that builds portfolios using a number of factor models for domestic and global equity and fixed income securities and derivatives. This engine, having been built to handle a broad array of investment problems, is one of the sources of ART’s distinctive range of abilities. ART bears, in addition, an attractive and easy-to-use interface, and is capable of generating a wide variety of reports, many of them presentation-quality graphic images. It comes with an enormous database, updated monthly, containing return series for U.S. mutual funds, global asset class indices, institutional money managers, hedge funds and more.

ART’s functions can be classed under four broad headings:

1. Asset Allocation 2. Optimization 3. Historical Simulation (Back-testing) 4. Style Analysis

ART comes with complete documentation and context-sensitive on-line help. Northfield’s personnel are prepared to provide customized tutorials in the use of the product using web-assisted (WebEx) support. The database for ART is maintained on the Northfield Server, and in most cases, the user only has the client application, using the Internet for access to the server. For those who need to access ART remotely without Internet connection, the server application is available, and the data can be periodically updated. Besides these capabilities, ART can save for reuse all of the inputs to an asset allocation problem. For example, the user can save the list of assets in the portfolio, the constraints, and the summary statistics, and mix and match them in various ways. One application of this might be in a firm that uses the same combination of assets in all its clients’ portfolios, but customizes constraints and risk tolerance to each client’s requirements.

Northfield’s Allocation

Research Toolkit

Documentation and Advice

Client-Server Architecture



The Browser allows the user to select funds for inclusion in a portfolio. It is split into three separate scrolling sections:

1. The sector selection window. 2. The funds in a sector window. 3. The fund data and transformation window.

The Browser allows the user to select funds from over 14,000 different asset classes. The data includes at least 400 well (and some not so well) known indexes (such as the S&P 500, MSCI EAFE and Lehman Aggregate Bond) The funds and indices are grouped into a number of sectors; the user can display and choose funds from one sector, selected sectors or all of the following sectors:1

1. Currency 2. Index: Short Term US and Non US 3. Index: Non US Bonds 4. Index: Non US Bonds, Currency Hedged 5. Index: Non US Equities 6. Index: FTSE 7. Index: US Bonds 8. Index: US Equity 9. Index: Alternative and Hedge Fund Indices 10. Aggressive Growth 11. Balanced 12. Convertible Bonds 13. Equity Income Funds 14. Global Bond Funds 15. Global Equity Funds 16. Growth and Income Funds 17. Growth Funds 18. High Quality (Investment Grade Corporate) Bonds 19. High Quality Municipal Bonds 20. High Yield (Junk) Bonds 21. High Yield Municipal Bonds 22. International Bonds 23. International Equity Funds 24. Money Market Taxable 25. Money Market Tax-free 26. Money Market: Government 27. Mortgage Backed Securities 28. Option Income 29. Precious Metal 1 The listed sectors are for the base subscription. For additional fee, Mobius separately managed account and Hedgefund.net’s hedge fund data are available and grouped by appropriate sectors.

The Database

The Browser



30. Single State Municipal Bonds 31. Small Capitalization Stocks 32. Specialty (Industry) Funds 33. U.S. Government Bonds 34. Utility Funds 35. User Defined Sectors (using client private data series)

The Browser is used to select funds for inclusion in the portfolio by selecting, in the left Browser Window, any of the sectors listed above, selecting the desired fund (or index) from the middle window, and dragging it and dropping it onto the Main Table. In order to expedite the fund selection process, the user can check a number of different funds, and copy and paste them into the Main Table as a group.

The Browser has the ability to activate the use of the Style Button. This initiates a Style Analysis using the Style Groups that are assigned (and re assignable by the user) to each asset class sector. This option, as implemented in the Browser, uses the most recent five years of returns data (or from fund inception if newer) to estimate the style weights, tracking error (the annualized standard deviation of active return), and alpha (the annualized mean active return) for each fund in the chosen sectors. This will help you select funds that are likely to have the required exposure and performance. Below is a screen shot of the Browser’s style analysis. This for Equity Growth funds, which use the Russell Style Group, which includes the Russell 1000 Value (R1V), Russell 1000 Growth, Russell 2000 Growth, and Russell 2000 Value indices.

In addition to the Browser’s style analysis, a more detailed style analysis is described on pages 23-25 herein.

Style Analysis in the Browser



The Sector Ranking Window ranks funds within a chosen group of sectors for any historical time period by selecting from a choice of the following time periods and statistical measures:

Time Periods: 1. Quarterly 2. Yearly 3. Three Years 4. Five Years (the default) 5. Ten Years 6. User Defined Time Periods

Statistical Measures: 1. Return 2. Standard deviation of return 3. Sharpe Ratio (the default) 4. Skewness 5. Negative half std deviation 6. % of losing months 7. Range of monthly returns

The sector-ranking window allows the user to view plots showing the distributions of values across each characteristic (average return, return/risk, etc.) over a number of different intervals: last quarter, last year, last three years, last five years, and last ten years, or a user defined time period.

The Sector Ranking Window is shown below:

The Sector Ranking Window



Each fund has a base currency. Most of the existing funds and indices (although not all) have the US Dollar as the base currency. For private data it is possible to specify a base currency other than the US dollar. This makes it possible to perform all of the analyses by specifying any of the following currencies as an alternate base currency: Argentine Austral Australian $ Austrian Shilling Belgian Franc Brazilian Real Canadian $ Chilean Peso Colombian Peso Danish Krone Dutch Guilder Euro Finnish Markka French Franc

German Mark Greek Drachma Hong Kong $ Indonesian Rupiah Irish Punt Italian Lira Japanese Yen Luxembourg Franc Malaysian Ringgit Mexican Peso New Zealand $ Norwegian Krone Peru Sol

Philippine Peso Singaporean $ So African Rand So Korean Won Spanish Peseta Swedish Krona Swiss Franc Taiwan Dollar Thai Baht UK Pound Venezuelan Bolivar

The user can add a CSV file for private or proprietary data series. Any new sectors are added to the left side of the Browser Window. It is also possible to create composite funds that consist of several funds with fixed weights. Composite funds can be used to model currency hedging (full and partial) or as a model portfolio (liability) for asset allocation studies. Composite funds can also be used to construct a market proxy for estimating a fund’s beta using the Capital Asset Pricing Model. Because some time series are only available with quarterly frequency, and because some time series are available with daily frequency, ART allows users to import data with quarterly or daily frequency as well as the normal monthly frequency. When combining funds of different frequency in a portfolio or other analysis, the program converts all of the funds to the lowest frequency (monthly or quarterly). Although the ART database currently only includes monthly data, daily series are planned for some of the more popular series, such as the S&P large, mid and small and style (growth and value) indices.2

2 Additionally, we include the NCREIF index, which has quarterly returns available at www.ncreif.org. This index is in our alternative and hedge fund index sector.

Base Currencies

Private Data Series and

Composite Funds

Daily and Quarterly Data

http://www.ncreif.org/



Northfield believes that the Analytical Hierarch Process (AHP) is appropriate for the asset allocation decisions.3,4,5 Northfield has adapted the AHP to help guide the asset allocation process for both individual and institutional investors. Northfield has developed the AHP and created at least two sample processes that can be modified to fit any organization’s decisions criteria and the asset classes and their proxies that it prefers. Benefits of the AHP include:

1. There is no simple way to determine what risk tolerance is appropriate for an individual investor. It may be more reasonable to estimate the appropriate risk tolerance by inference from a portfolio deemed suitable by a decision support system such as the analytic hierarchy process.

2. The AHP allows introduction of qualitative judgments that are hard to express in terms of risk and return as required by Modern Portfolio Theory.

3. The AHP output avoids the problem that estimation error causes in traditional optimization, resulting in concentrated portfolios that do not perform as well out of sample as a more diversified portfolio.

To develop a portfolio suitable for an individual investor, the technique poses a number of questions that define an investor’s ability to handle and willingness to assume risk. We include with ART a sample project that creates model portfolios for an individual investor that uses a number of well-known indices to establish a model portfolio based on answers to 12 questions related to the investor’s objectives, income, investments and risk profile.

3 Thomas Saaty, Multicriteria Decision Making, RWS Publications 4 Paul Bolster, Emery Trahan and Vahan Janjigian, “Determining Investor Suitability Using the Analytic Hierarchy Process,” Financial Analysts Journal 51, July-August 1995 5 Paul Bolster and Sandy Warrick, “Suitability and Optimality in the Asset Allocation Process,” http://208.15.47.66/Papers/NorthfieldResearchDocs/19990901_ahp.pdf

Asset Allocation: The Analytical

Hierarchy Process

Individual Investors



The AHP process is fully customizable, with users able to specify:

1. The tabbed windows that group the questions into separate categories 2. Each question’s text description. 3. The weight given to each question. 4. The text for each response level (normally five) for each question. 5. The funds or indices that are proxies for each asset class 6. The “suitability rating” (1 is highly suitable, 9 is highly unsuitable,

intermediate values represent different levels of suitability) for every combination of question, asset class and response levels.

Using the model specified, the AHP suggests a portfolio that is likely to provide a suitable asset allocation for that investor. This portfolio can then be used in the portfolio optimization process. The results of the AHP calculation can then be moved into the main table using two different methods.

1. The AHP portfolio can be used as a model portfolio (benchmark or liability) so that a suitable mutual fund portfolio can have the desired active return and risk relative to the AHP asset allocation, which is normally constructed using passively managed indices.

2. The AHP asset class proxies and weights can be used as the funds in the main table. This method is used to ensure that the risk and return of AHP model portfolios are suitable for hypothetical investors. This is done using the “Send to MT” icon in the screen shot below.

For Institutional Investors, we use the “Manager Selection” model that directly rates asset managers. We expect that consultants, sponsors and investment advisors will develop their own questionnaire based on their own

Institutional Investors



manager evaluation criteria. This model allows three different ways to input the rating data:

1. The panel view that allows for users to rate each fund using radio buttons. This is usually the fastest way to input the ratings.

2. The table view 3. The aggregate manager table which uses rows to hold each fund’s and

columns to hold each question. This allows for quick comparisons between managers.

To aid users develop their own models, we provide two samples that are based on published techniques for fund or manager selection. The first is a fund selection technique developed by Saraoglu and Detzler.6

We also provide a 16 question (organized in four groups) example based on the questions and weightings that are proposed in EnnisKnupp’s “An Expert System for Evaluating Investment Managers”.7 The user sets up an asset allocation problem in the Main Table Window. This contains a spreadsheet whose rows carry information about individual asset classes, and a section of input boxes where global information is specified. The user enters an asset class into the spreadsheet by typing in its identifying code or, more usually, dragging the fund from the database and dropping it into the table. As stored in the database, each asset class has a time series of returns, assignment to one or two sectors (Growth, Growth and Income, etc.), 6 Hakan Saraoglu and Miranda Lam Detzler, “A Sensible Mutual Fund Selection Model,” Financial Analyst’s Journal, May/June 2002 Volume 58 Number 3 7 http://www.ennisknupp.com/

Portfolio Optimization

http://www.ennisknupp.com/



identifying codes (ticker, SEDOL), and current yield. ART calculates the summary statistics, such as average monthly return, standard deviation of average return, and correlations with other asset classes. There can be up to 150 asset classes in an asset allocation problem. Two types of constraints can be used in optimization, either separately or in combination:

1. Individual constraints on the separate series are used to constrain the weights on the asset classes, as shown below. For example, t-bills, high yield bonds and foreign bonds can be constrained to 10% maximum weight for each asset class, while each equity fund is constrained to 30%, as shown below.

2. Group constraints. For example, all equity funds can be assigned to the group ‘Eq’, which has a 40% minimum and 70% maximum constraint, as shown below.

Other global inputs are:

1. Tax rates, both for income and for capital gains. ART computes the net after-tax return by subtracting the income tax applied to the yield and the capital gains tax to the total return minus the yield.

2. The risk free rate of return 3. Time horizon of the user 4. Target annual return, used to compute target semi-variance when the

semivariance option is used to compute risk. Target annual return is also used as the return for which portfolio return probabilities are estimated.

Group constraints



5. Time period over which ART should calculate historical summary statistics,

6. RAP, the risk acceptance parameter. The RAP balances the client’s return and risk: it is the amount of extra return needed to compensate for an increment of risk as measured by portfolio variance. As the RAP increases, the optimum portfolio moves further to the right on the efficient frontier.

All the Main Table inputs can be stored in a CSV file for reuse in this or other projects. This use of multiple files permits the user, for example, to keep using the same asset classes but different summary statistics representing different economic scenarios, or the same asset classes but different constraints, corresponding to different clients. ART offers both mean-variance and mean-semi-variance optimization. Nevertheless, Northfield strongly recommends use of mean-variance optimization, since the use of statistically estimated semi-variance assumes that the sample skew represents the expected skew, which is generally not the case for asset class returns. Although only one portfolio can be optimal for a given RAP, ART generates information on up to 99 (11 is the default) efficient portfolios across a range of RAP values centered on the input RAP. ART allows the user to specify a trading cost for each asset as a percentage of value of that asset, and will optimize the asset allocation while taking into consideration the costs of altering the initial portfolio. Thus, a user can implement an “overlay” strategy with an arbitrary portion of the total portfolio set aside for tactical asset allocation employing index futures. The user can now calculate the asset allocation employing both the underlying asset classes and futures while accounting for their differing transaction costs. Northfield strongly recommends taking ART’s original summary statistics only as an initial estimate, and suggests that users override the return values that ART calculates from the time series. As investment advisors know well, historic returns for an asset class, even when estimated over a very long period, may not be reasonable estimates of future returns. To reinforce this concept, ART uses three columns to hold the historically estimated and input returns:

1. Historic returns are estimated for the period between the starting and ending dates.

2. Input returns are the client’s current expectation for the return of the fund over the investment horizon. This column is initialized as the historic returns of funds whose input return is zero, which is the case for funds that are added to the portfolio.

3. Expected Returns are the Bayesian adjusted input returns.

What Expected Returns should you

use?



Northfield has adapted the a Bayesian adjustment feature in response to users’ queries concerning how they might optimize a portfolio when they were uncertain of their inputs and feared that small perturbations in the inputs would lead to radically different portfolios.8,9,10,11 The Bayesian adjustment is enabled by clicking on a check box in the Main Table Window to adjust the input returns for the uncertainty in their forecasts. The underlying notion is that any forecast return (even if it is just a projection of past returns) is not a point forecast, but a forecast of the expected value of an unknown distribution. ART takes the standard deviation itself as a measure of the uncertainty in the forecast, and to a degree that is based on the uncertainty, pulls the forecast expected returns in toward one another. The concept is best illustrated by an extreme example: if you have forecast different returns for several asset classes, but are completely lacking in confidence in your forecasts, what should you do? The solution would be to build your portfolio by equally weighting the assets. The Bayesian adjustment tends to flatten the efficient frontier and thereby to allay this concern. There are eighteen reports that ART can produce to describe a single run of its asset allocation optimizer. These can be printed, exported or pasted directly from ART in an attractive format for presentation directly to clients. This graph plots 2500 randomly selected feasible portfolios, and uses two shades, one to represent the feasible portfolios subject to the constraints, and the other to show all other (unconstrained) feasible portfolios. This allows one to see at a glance what one is giving up by imposing constraints on the asset allocation optimization. The graph also shows the positions of the initial portfolio (red circle labeled “i”) and each asset class (magenta circles labeled F1 through F9 for nine funds).

8 Iversen, Gudmund R. Bayesian Statistical Inference, Quantitative Applications in the Social Sciences 43,. Newbury Park: Sage Publications, Inc., 1984. 9 Jorion, Philippe. “International Portfolio Diversification with Estimation Risk,” Journal of Business, Volume 58, No. 3, July 1985 10 Jorion, Philippe, “Bayes-Stein Estimation for Portfolio Analysis”, Journal of Financial and Quantitative Analysis, Vol. 21, No. 3, Sep., 1986 11 Jorion, P., “Bayesian and CAPM Estimators of the Means: Implications for Portfolio Selection,” Journal of Banking and Finance, June 1991

Optimization Reports

Feasible Region (graph)



The Optimization Summary Table shows the return, risk, utility, efficiency and asset class weights of the initial portfolio each of the portfolios along the efficient frontier. This report represents graphically the weights on the asset classes in the portfolios on the efficient frontier, from the least risky portfolio to the most risky.

Optimization Summary Table (Not Shown)

Asset Weight Graph



The downside risk table shows, for probabilities of 5%, 10%, 50%, 90%, and 95%, the values above which returns can be expected to fall, for each of the efficient portfolios. For each efficient portfolio, this plots the expected return and the range within which the returns can be expected to fall with 68% (+1 Standard Deviation) probability, and this is plotted for both one year and the multiple-year period time horizon specified by the user.

Downside Risk (table) (Not Shown)

Single Year vs. Multiple Year Returns (graph)



This graph shows, for a single year, the ranges within which returns to each portfolio can be expected to fall with 68% probability and with 95% probability. It also shows the minimum target return that the user specified.

The Annualized Return Distribution for Multiple Years graph is the same as the Return Distribution, Single Year, except that one-year forecasts are replaced with those for the time horizon specified in the main table. The Value Distribution, Single Year graph is similar to the Return Distribution, Single Year report except that it shows the change in value of a portfolio starting at 100. This graph is the same as the preceding one, but for the time horizon specified by the user. It differs from the Annualized Return Distribution for Multiple Years graph by showing cumulative values instead of returns. In addition to providing charts and tables that define the behavior of the efficient frontier, ART also provides detailed reports on each of the efficient portfolios and the initial portfolio. This is a traditional pie chart showing the composition of the optimal portfolio, accompanied by some relevant statistics.

Return Distribution, Single Year (graph)

Annualized Return Distribution for Multiple

Years (Not Shown)

Value Distribution, Single Year (Not

Shown)

Value Distribution, Multiple Years (Not

Shown)

Reports on Individual Efficient Portfolios:

Optimal Selection Summary (graph)



The Optimal vs. Initial Weights graph is a pair of pie charts, showing the initial portfolio and the optimal portfolio side by side. The Wealth Accumulation table holds year-end values for a specified efficient portfolio, on the assumption of an initial value of 100, up to the horizon set by the user. This Wealth Accumulation graph shows the growth of a dollar invested in the initial portfolio and in the specified efficient portfolio. This shows graphically the distribution of compound annual returns out to the time horizon that the user set in the Main Table Window. It does this by plotting the expected return and bands representing one and two standard deviations either side of the expected return, for each yearly increment.

Optimal vs. Initial Weights (Not Shown)

Wealth Accumulation Table (Not Shown)

Wealth Accumulation (Not Shown)

Annualized Return Distribution for Multiple

Years (graph)



This graph shows the probability of achieving the desired (target) return for different time periods.

Probability of Achieving Minimum Desired

Return



The Cumulative Return Distribution for Multiple Years graph is similar to the Annualized Return Distribution for Multiple Years graph, except that it plots the distribution of cumulative returns instead of compound annual returns. The “implied returns” are a unique set of forecast returns for the assets for which the initial weights equal the optimal portfolio weights. The useful of implied returns in returns estimation was described by Black and Litterman.12 The implied returns assume:

1. The initial portfolio is optimal. 2. The covariance matrix represents future expectations 3. The RAP is consistent with an investor who would hold the initial

portfolio.

ART’s capacity to produce optimal asset allocations for portfolios extends to an ability to optimize with respect to a liability stream, which can also be thought of as a benchmark or a model portfolio. The Main Table Window offers four different methods, all of which permit the user to specify a funding ratio:

1. The simplest is for the user to specify a discount rate. 2. Another is for the user to specify a mean discount rate and a standard

deviation that ART will use for varying the discount rate stochastically. 3. The third method is for the user to specify a time series from the database

as a model of the liability stream. For example, a long-term treasury bond can model a pension fund’s liabilities. Another example would be a 60/40 stock/bond model portfolio, which could use a compound fund that is 60% the Russell 3000 and 40% the Lehman aggregate bond index.

4. You can use the AHP output portfolio as the liability. This is particularly useful if you are using asset class proxies for the AHP portfolio and you are implementing a portfolio using mutual funds.

12 Black, F., and Robert Litterman, "Global Portfolio Optimization," Financial Analysts Journal, Sept/Oct 1992, 28-43.

Cumulative Return Distribution for Multiple

Years

Implied Returns (table)

Optimizing Relative to a Liability



ART allows the user to backtest different asset allocations and rebalancing frequencies using any time series from its database. For hypothetical asset allocations, both initial positions and changes in subsequent months are entered in a table that is like a spreadsheet, and with these proportions and its own return database, ART generates a return series for the portfolio. This shows what the performance of such a portfolio would have been over a user-defined historical period. To increase the realism of the simulation, the user can specify cash flows, month by month, and transaction costs for changes in the allocations. Results can reflect monthly, quarterly, or annual rebalancing. Resulting series can be exported to ART’s main database for reuse as new asset classes.

The historic simulation feature shows the simulated performance of an investment policy under different rebalancing policies (monthly, quarterly, yearly and never). The simulation produces the following reports:

1. Strategy Detail 2. Monthly Return Detail 3. Rolling Period Analysis 4. Return Distribution Graph 5. Simulation Summary 6. Performance Comparison Graph, shown below 7. Recent Performance Summary

Historical Simulation



ART has a unique feature: the ability to historically simulate Tactical Asset Allocation Strategies. In order to create an optimized Tactical Asset Allocation simulation, the manager needs to provide, in an external CSV file, a time series of historical expected returns for each asset in the simulation. ART simulates the tactical asset allocation process by re-estimating the covariance matrix and optimizing the portfolio at the chosen rebalancing frequency. The following parameters that control the process are constant throughout the simulation:

1. Risk estimation period (common start date or rolling periods) 2. Risk Acceptance Parameter 3. Maximum and minimum (can be negative) positions for each asset class 4. Total allowable leverage (sum of the short positions)

When you rebalance with the optimizer, the simulation will provide the following additional reports.

1. Asset Class Information Coefficient 2. Historical Cross Sectional Information Coefficient 3. Comparison of Realized and Predicted Risk 4. Tactical Weight Report

The asset class IC is the time series correlation between the predicted and realized return for each asset class. This feature shows which asset classes you can predict accurately, and which asset classes will need an improved predictive ability to be included in a TAA process.

Tactical Asset Allocation

Asset Class Information Coefficient



This graph shows the time history of the Cross Sectional Information Coefficient, which is the correlation between the predicted returns and the realized returns. If this value is positive for a month, then you probably made money with an optimized portfolio using those alphas. For effective TAA, you need the average cross sectional IC to be high relative to its standard deviation.13 This graph shows a point for the cross sectional IC for each month, and superimposes both 3-month and 12-month moving averages to help determine how may rolling 3 and 12 month periods will likely have negative returns, neglecting transaction and implementation costs.

13 The ratio of the average IC to its standard deviation is proportional to the strategy’s Information ratio, as shown by Sorensen, Qian, Schoen and Hua, “Multiple Alpha Sources and Active Management,” Journal of Portfolio Management, Winter 2004

Cross Sectional Information Coefficient



The Predicted vs. Realized Risk Graph shows the comparison between the 12-month annualized predicted volatility (standard deviation) of the portfolio with the 12-month realized volatility. This graph helps you determine if the historically estimated covariance matrix is effective when combined with the alphas that you provide.

Predicted vs. Realized Risk Graph



The Tactical Weight Report shows the weights of the portfolio after every optimization. ART has the ability to perform returns based style analysis of fund data. In order make this feature as easy to use as possible we introduce the use of Style Groups to choose a suitable set of indices for the funds you want to analyze. Furthermore, ART is able to analyze long-short managers by optionally allowing both negative weights and weights that exceed 100%.

One common criticism of Style Analysis is that it does not provide confidence limits, unlike linear regression, which reports the t-statistic for each variable. To remedy this situation, confidence limits (standard errors) are provided for the weight estimates.14 The error estimate for each style exposure is shown in the right hand column of the Fund Analysis Window.

The Style Analysis outputs a table with the style exposures, alphas and tracking error for a user specified rolling period.

14 Angelo Lobosco and Dan diBartolomeo, “Approximating the Confidence Intervals for Sharpe Style Weights,” Financial Analyst Journal, 1997

The Tactical Weight Report

Style Analysis

Confidence Estimates

Style History Table



The alphas and tracking error are calculated over the rolling period relative to the “best-fit” weights of the chosen style indices. The r2 is the portion of the fund’s variance that is explained by the best fit weights. In order to better visualize how much the style exposures varied over the time period, the Style Analysis history is also shown as a graph

Another way to see style exposure and style drift is the Style Box, which chooses four funds from a Style Group to represent a corner of a Style Box. In this case, the corners chosen represent S&P large cap vs. small cap (left vs. right) and growth vs. value (up vs. down).

Style History Graph

Style Box



CUSUM is a technique originally developed for the study of digital signals. It has been successfully adapted for use in monitoring returns of active managers.15 The method involves calculated the rolling sum of standardized active returns and then identifying the key inflection points in the time series. We can then analyze returns subsequent to the last inflection point as being the most relevant for making judgments about manager performance. ART allows the user to either choose a single fund as the benchmark or use the “best fit” benchmark determined by style analysis.

15 Thomas K. Philips, Emmanuel Yashchin and David M. Stein, "Using Statistical Process Control To Monitor Active Managers", http://www.research.ibm.com/stat/qprc/QPRC_03contr.htm

CUSUM



To aid the user in understanding more deeply the nature of the asset classes and funds, ART allows the user to perform regression analyses on the series, both univariate and multivariate regression, with the usual range of regression diagnostics, including ANOVA. Any lead or lag is can be specified, and, of course, autoregression (when a lagged time series is regressed on itself) is possible. The univariate regression table contains summaries of all univariate regressions specified in the Regression Window. The table shows the intercept and the slope coefficient for each regression, standard errors, and so forth. In the Regression Window, the user can set several series as the dependent variables, and, in a single operation, ART will regress each of these against all the listed series that can represent the independent variable. The univariate regression graph shows, one at a time, the scatterplot of the dependent variable and the independent variable and the regression line itself. Also shown is the regression equation, with the values of the coefficients. The user can step through this report, showing successively the graph with each of the dependent variables listed in the Regression Window.

Statistical Analysis

Univariate regression table

The univariate regression graph



The multiple regression report contains the standard output of a multivariate regression analysis, including the standard errors of the coefficients, R2, adjusted R2, and an ANOVA table, and, because this is for time series analysis, the Durbin-Watson statistic.

The multiple regression report

Boston London Tokyo 2 Atlantic Avenue 2-6 Boundary Row Shiroyama Trust Tower Boston, MA 02110 London, SE1 8HP 4-3-1 Toranomon 617.451.2222 44.20.3714.4130 Minato-ku Tokyo 105-6027 81.3.5403.4655

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Allocation Research Toolkit (“ART”)Allocation Research Toolkit (ART) Northfield Information Services 4 Boston Chicago London Tokyo Northfield Information Service’s Allocation