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U.S. SHORT TERM

Equity Risk Model

IDENTIFY ANALYZE QUANTIFY

NORTHFIELD

Oct-22-2012

U.S. Short Term Equity Risk Model

Table of Contents

INTRODUCTION .............................................................................................................................2 Forecasting Short-Term Risk ..............................................................................................2 Statistical Factor Model ......................................................................................................2 PROCESS OVERVIEW......................................................................................................................3 Estimating the Statistical Factor Model .............................................................................3 Incorporating Option Implied Volatility .............................................................................4 THE DATA ....................................................................................................................................6 New Constituents ................................................................................................................6 SUMMARY ....................................................................................................................................6

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U.S. Short Term Equity Risk Model

Introduction

The Northfield U.S. Short Term Equity Risk Model is designed to help investment professionals having short-term holding periods monitor and control the risks in their investments. Used in conjunction with Northfield's Open Optimizer, it allows users to incorporate risk forecasts into portfolio construction and management.

Forecasting Short- Risk control for short-term trading is different than it is for traditional Term Risk management. Typical holding periods for positions are measured in hours as

opposed to months or years. Fast response to short-horizon market events and news is also critical. Accordingly, the periodicity of the data used for the model is daily, and not weekly or monthly as in most commercially available equity risk models. High frequency data has several undesirable statistical properties. Short-term return distributions are affected by serial correlation 1 and heteroscedasticity, with noise in the data often dominating regime shifts. As a result, estimating return volatility becomes more difficult. We have devised a novel solution to this problem. The U.S. Short Term Model uses forward-looking variance estimates derived from option-implied volatilities. While option-implied volatility doesn't typically equate to realized volatility, relative (to historic) implied volatility levels better predict volatility changes than recent sample volatility. Option traders integrate information quickly.

Statistical Factor The U.S. Short Term Model is a so-called statistical factor model. In such Model models the factors are not specified as being directly connected with any

observable real-world phenomena, but rather both the factors and the sensitivities of a security to those factors are inferred from the security behaviors themselves. The primary benefit of such models is that the factor structure, determined directly from data, evolves over time to fit new conditions.

Since the factor definitions are newly derived from each new sample of data, the user has no guarantee that the sixth factor derived from today's data set has any relation to the sixth factor derived from last month's data. For active managers, the lack of definition may be problematic, as one or more factors may be correlated with the manager's stock selection criteria. In such a case, efforts to control risk by managing factor exposures would limit the ability to expose the portfolio to characteristics that the manager believes to be desirable. This is not a problem, however, for hedging trading desks or index funds, where we only care about `being like' our index, without regard to exactly what the criteria for similarity are.

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See, for example, Roll, Richard. "A Simple Measure of the Effective Bid-Ask Spread in an Efficient Market." Journal of Finance 39 (September 1984): 1,127-1,139. Negative serial correlation is found between daily closing prices. Also see Fama. Eugene F. "The Behavior of Stock Market Prices." Journal of Business 38 (January 1965):34-105.

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U.S. Short Term Equity Risk Model

Process Overview

Estimating the The use of a statistical factor model is somewhat controversial. Critics argue Statistical Factor that, without any tie to real-world phenomena, such models are susceptible Model to transitory noise in the data. In our model, a large set of weighted

observations, both in number of securities and periods, over a relatively short sample window mitigates the impact of non-pervasive effects. Pervasive transitory effects, however, are the very features one seeks to capture in a short term model. From daily returns over the past 230 trading days for all securities in the model's universe having a complete history (~ 5000 securities), we find the twenty largest sources of comovement. To prevent volatile companies from having undue influence, return series are first normalized to unit magnitude. Weighting companies by square root of market cap balances size and quantity. To emphasize the common behavior in recent returns and pick up changes in a company's sensitivity, observation weights decay with time e-0.01 per trading day so the oldest period has one-tenth the weight of the newest. The statistical method employed to find these twenty common sources is Principal Components Analysis. PCA captures the most explanatory directions to reduce data dimension. (Investment professionals are no doubt familiar with market beta as a reduction of stock returns into a single dimension, the direction of the market.) Using PCA, the 5000 initial directions the scaled and weighted return series for 5000 stocks are distilled into twenty. With the twenty components set, security exposures are inferred via Bayesian estimation. Priors are centered at the median exposure of each industry. Bayesian regression increases the accuracy of individual forecasts over standard regression and, by softening extremes, vastly improves the out-of-sample performance of optimized portfolios.

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U.S. Short Term Equity Risk Model

Incorporating We believe that we can do better still. There has been much research in the Option Implied field of estimating future volatility from historical volatility and from that Volatility implied by prices observed in the exchange-traded options on stocks. Many

investors believe that the implied volatility is a better forecast of future volatility than historical volatility 2 since it contains opinions of option-traders on future events such as mergers, lawsuits, elections, EPA action, and so forth, which historical volatility cannot contain. Likewise, it is immune to past disturbances that are not currently relevant. For example, the high volatility surrounding the FDA's approval of a new drug last March is not necessarily relevant to the decision of how risky the security is in the immediate future. The implied volatility can also rapidly react to new information, whereas historical volatility may take several days since it is calculated over a window (most commonly 30 days). For all of these reasons, we have included in our model the information available from the option market.

Remarkably, the added information is not limited to optionable securities. By looking cross-sectionally at the optionable securities, we can infer marketpervasive effects (i.e. those affecting even non-optionable securities) 3 . The process is as follows: We first build a statistical factor model without considering options. During every estimation period, we keep track of the mean ratio between the implied and historical volatility for each optionable security 4. We can then construct a forecast conditioned on the current implied volatility. By projecting these forecasts on the optionable securities' factor exposures and stock-specific risks, we attribute effects common across securities to the factors and capture changes in stock-specific risk levels. What remains falls stock-by-stock to the stock-specific risks of the optionable securities. Thus, systematic changes affect all securities, and stock-specific phenomena are correctly attributed to individual companies.

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See Ederington, Louis and Guan, Wei. "Is Implied Volatility an Informationally Efficient and Effective Predictor of Future Volatility?" Working Paper, January 12, 1998. e.g. During times of crisis, stock-specific effects disappear and correlation across assets goes to 1. Also the levels of VIX and RVXK

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5 U.S. Short Term Equity Risk Model

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 30.0% 40.0% 50.0% 60.0% 70.0%

10.0%

20.0%

The model reacts to market events nearly spontaneously.

The model instantly picked up the regime shift of Oct 2008:

0.0%

Avg Pairwise Correlation of S&P500 Constituents According to Model

Forecast Volatility of S&P500

This chart shows the model's ability to catch the spikes in correlation during Aug 2007 and Oct 2008:

02/03/2003 05/06/2003 08/06/2003 11/05/2003 02/09/2004 05/11/2004 08/12/2004 11/15/2004 02/16/2005 05/19/2005 08/19/2005 11/18/2005 02/23/2006 05/25/2006 08/25/2006 11/27/2006 03/02/2007 06/04/2007 09/04/2007 12/04/2007 03/07/2008 06/09/2008 09/09/2008 12/09/2008 03/13/2009

02/03/2003 05/02/2003 07/31/2003 10/28/2003 01/28/2004 04/27/2004 07/27/2004 10/25/2004 01/25/2005 04/25/2005 07/22/2005 10/19/2005 01/19/2006 04/19/2006 07/18/2006 10/13/2006 01/16/2007 04/16/2007 07/13/2007 10/10/2007 01/09/2008 04/09/2008 07/08/2008 10/03/2008 01/02/2009 04/02/2009

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U.S. Short Term Equity Risk Model

The Data

The model covers a universe of over 5000 securities and is re-estimated daily. Data reflecting the prior day's close is available by 5AM EST. Data is completely open and accessible. It is stored in comma separated text files and easily to integrate with existing systems.

New Constituents Since the estimation is Bayesian, missing data poses no difficulties. Without

any return history, companies are assumed to have the median exposure and 95th percentile stock-specific risk of companies in the same industry. As information (returns) becomes available, the estimate balances the prior and the information based on the quantity and quality of information, just as it does for companies having a complete return history. The Northfield U.S. Short Term Model is an extremely sophisticated quantitative tool aimed at allowing U.S. equity managers to measure and control their exposure in a rapidly reacting model. Developed through rigorous research, it is a powerful tool in portfolio management. Our staff is committed to making certain that our clients are fully satisfied with this product.

Summary

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