Hot-To Guide to Quant Models NOMURA

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How to use them, how to build them and how to choose between them

We are often asked about choices that we make in construction of quant models for stock or asset selection. What are the pros and cons of various approaches and the consequences of adopting a particular framework? Here we offer a review of the various approaches. It is intended to help those who build quant models and also for users of quant models to help them characterise the various possible approaches with which they may be faced.

We have arranged the note around a series of questions or themes:

Rationale for why strategies work or is this just an empirical exercise?

Ranking versus exposure

Sector-Neutral versus non-sector-neutral

Univariate versus multivariate

Dynamic versus static models

Factor choice

Portfolio simulations and regressions

Data

Rebalance frequency

Choice of benchmark

Recent developments: Has back-testing gone out of fashion? How to avoid overcrowding.

Global

The How-To Guide to Quant Models

Inigo Fraser-Jenkins +44 20 7102 4658

[email protected] NI plc, London

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Rishav Dev +44 20 7102 9122


Saurabh Katiyar +44 20 7102 9135


Arjun Bhattacharya +44 207 102 9158


Maureen Hughes +44 20 7102 4659


PORTFOLIO STRATEGY Global Strategy

Market Commentary/Strategy

August 07, 2009

Nomura International plc, London

http://www.nomura.com

Global Equity Research

August 07, 2009

2 Nomura Equity Research

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August 07, 2009

Nomura Equity Research 3

1. Introduction

We are often asked about choices that we make in the construction of quant models for stock or asset selection. What are the pros and cons of various approaches and the consequences of adopting a particular framework? Here we offer a review of the various approaches. We have structured this report around a series of questions and illustrate some of the approaches at the end with examples of some of the models that we run. This note is designed both for those who build quant models and also for non-quants who want to use quant models and need to choose between them. It reflects our experience of running quant strategies over the past 10 years.

We have focused here on questions that come up in the process of trying to generate alpha. For some of these questions we have a clear preference. In other cases the answer may be dependent on how they are used and on the preferences of the user. This will not be an exhaustive list of all the choices that have to be made in the quant portfolio management process. There will be other questions relating to risk exposure, optimisation and elements of portfolio construction that are not covered here, for a discussion of such subjects please see for example From Fama-French to the ABL Framework1

Quant approaches tend to be big on back-testing. This is an important way of showing how strategies would have performed over time. There are, however, potential pitfalls and it is these that we consider in this report. The field tends to be an empirical one. Although confidence is improved in models if it is possible to provide a theoretical justification, often these appeal to behavioural finance. Having a theoretical rationale can make an approach more robust, and we lead our report with a section on that; however, at the core there will always be a need to show how an approach has worked over time. In section 12, we ask to what extent the events of August 2007 have shaken the dependence on back-testing.

We discuss the main questions and issues that we think are relevant to quant modelling in the next 11 sections. The report concludes with a review of the quant strategies that we currently run.

1 For our recent work on portfolio construction see Cheung, W. (2009), “The Transparent ABL (I): Strategy Combination, Factor Mimicking, Hedging, and Stock-Specific Bets in A Unified and Optimiser-Free Framework”, Nomura 2009 and Cheung, W. (2009), “From Fama-French to the ABL Framework”, Nomura 2009. While for recent work on risk modeling see Malhotra, R., W. Luo, A. Gupta, G. Dhavale, and X. Long (2009), “Nomura Statistical Risk Model Suite I: A First Look”, Nomura 2009.

We review quant approaches, which

is aimed at those who build quant

models and also at those who use

them

Our focus here is on the alpha

generation and factor selection process

Quants tend to be big on back-testing,

but confidence is strengthened if there

is a theoretical justification

August 07, 2009


2. Rationale for why strategies work, or is this just an empirical exercise?

The field of quant modelling, at least as practiced in the industry, has tended to be primarily an empirical exercise. The rationale for adopting strategies has usually been that it has worked over time, or worked in particular market environments; however, confidence in models is improved if there is some kind of theoretical rationale.

The Efficient Markets Hypothesis (EMH) would tell us not to waste our time building quant models. Any apparent ’anomaly‘ is just a risk factor, so we should not try to bother to beat the market. However, there has been a more fruitful attempt to rationalise the persistence of factors that many quant analysts employ, using some of the techniques from behavioural finance. Of particular interest here is the literature on investor under-reaction and investor over-reaction.

Momentum strategies have received a lot of attention in academic literature. For example, Jegadeesh and Titman (2005) survey the empirical evidence supporting the excess returns momentum strategies. They go on to show that momentum is unlikely to be explained away purely as a risk factor. They also show that neither price momentum nor earnings momentum subsumes the other; both can offer a marginal contribution in explaining the cross-section of stocks returns. Much of the original academic work on momentum was conducted on US datasets, an example of this expanded to other markets is Rouwenhorst (1998).

The general finding is that if portfolios are formed based on returns of periods for less than one month, momentum is a contrarian indicator, but for formation periods of three to 12 months, it is a positive indicator of future returns.

As to why Momentum strategies should work, the behavioural finance literature suggests possible explanations for the positive effect of momentum for periods between three and 12 months in the form of short-term under-reaction. An important example from this large body of literature is Barberis, Schleifer and Vishny (1998), who employ two effects from psychology to stock prices. They note that investors suffer from conservatism, that is they are slow to update their beliefs. Interestingly, the evidence from the psychology literature suggests that investors do update their beliefs at the right time in response to new information; however, the changes that they make are too small each time, hence, the under-reaction in the short term. The result is that if there is new information in the market, prices will respond slowly as the importance of the information becomes apparent. If this is the case, then momentum effects would be apparent in stock prices.2 Momentum as a contrarian indicator when formed on periods of one month, week or day implies there is an over-reaction to news in the very short term.

2 An alternative explanation of the effectiveness of momentum strategies by Daniel, Hirshleifer and Subramanyam (1998) is that it is attributable to a “self-attribution” bias. An example of how this model would work is that investors could form a positive view on a set of stocks, some of which go on to outperform. Where subsequent performance was in line with their a priori view investors tend to wrongly attribute too much confidence to the correctness of their view. This overconfidence leads them to drive up the stock to levels above those supported by fundamentals in the short term. On this basis, the momentum effect is actually attributable to over-reaction rather than under-reaction.

One possible reason for momentum

working suggested in the behavioural

finance literature is that investors under-

react to new information

August 07, 2009


Turning to value effects, aside from our own work on the effectiveness of value strategies there is a large body of academic literature that supports the existence of these effects. An example of empirical studies of this would be Lakonishok, Schleifer and Vishny (1994), who show how investors extrapolate the past performance of “glamour” stocks too far into the future and drive them up to high valuations; however, the high valuations are not merited given the ability of such stocks to deliver superior growth over the long run. Specifically, they calculate that investors implicitly extrapolate the recent superior growth of glamour stocks on average 10 years in the future, yet these stocks are, on average, able to sustain that growth for only two years. Eventually, the market realises the superior growth rates can no longer be sustained and there is a period of underperformance.

The behavioural explanation for this is known as the “representativeness heuristic”. This is the tendency of investors to view small sample events as typical. Specifically for stocks, this suggests that after a run of superior earnings growth, investors project the continuation of the superior growth too far into the future, hence, overvaluing the stocks. The result would be that highly valued stocks should underperform when the overvaluation in realised and lowly valued stocks should outperform, hence the value effect.

These explanations outlined above can be used to understand why value and momentum effects may persist in future. They seek to exploit biases in the reaction of investors. The explanation of quant models can in some cases be made more detail. For example, in some cases it may be possible to identify particular factors that should work in sectors attributable to the sector constituents or structure.

Value tends to work as investors

extrapolate past characteristics too far

into the future, leading to an over-

reaction of valuations in the long run

August 07, 2009


3. Ranking versus exposure in factor selection

When determining whether a factor effectively discriminates between stocks does the position of the stock in the distribution matter or is it the simple ordering that counts? It might seem like throwing away the ’distance information‘ on where a stock is in a given distribution would be a bad idea. After all, extra information is good – right? However, there are in fact several reasons why this might not necessarily the case. First, there is a psychological argument: humans might simply be better at ranking things in order rather than working out how far apart they are. In that case, a simple ranking approach might be best and an exposure approach might just add noise. Second, to apply the distance information when constructing a portfolio requires a functional form to map expected returns (or weights) onto factor exposures. How should we know what function to use? Normally a linear function is used, but that might not be correct. In these cases, exposure stocks could at best be adding noise and at worst add costs by, for example, requiring larger trades in less liquid stocks, but with no added value. There is also a consideration of what to do with outliers. With accounting-based inputs especially, there can be stocks that are genuine outliers from the distribution. In the ranking approach, these would not usually have any special status. If exposures are being used, then the outliers might be excluded, but this could be omitting valuable information, or they can be ’dragged‘ inwards in some way. As an example of the latter, observations over three standard deviations from the mean could have a value set equal to three standard deviations.

Ranking approaches are popular in the process of factor selection as they merely require a monotonic relationship in that the performance of quartile 1≥quantile 2≥ quantile 3, etc. It does not have to assume a given functional form for the cross-section of returns. Note the ≥ sign as there are different ways that the distribution of a factor can relate to forward returns, yet still have a monotonic distribution. A factor could create an even spread of cross-sectional returns or it could be the case that it becomes an important discriminator between stocks only at one extreme, in that case the first three quartiles could have approximately equal returns and the fourth one underperforms strongly.

We show two examples below. Figure1 shows the performance of the P/E factor. The 500 largest stocks globally have been screened on this factor every quarter and formed into quartiles. Stocks with the lowest P/E are in quartile 1 and show consistently the highest return. The factor is ’well behaved‘ in the sense the spread of returns across the market is even and the highest P/E stocks actually yield a negative absolute return. Figure 2, by contrast, shows the return of the Gearing factor. Whether a stock is in quartiles 2 to 4 is irrelevant for its future returns. However, quartile 1 (the highest gearing) underperforms strongly. Note in this case the distribution happens not to be perfectly monotonic as well.

When testing a factor, is the order of

stocks important or where they are in

the distribution?

August 07, 2009


Figure 1: Some factors may generate returns that are evenly distributed across the market – the case of P/E

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Chart shows the annualised return from 1989-2009 of four quartiles formed on 12-month forward P/E and rebalanced quarterly. Quartile 1 has the highest yield/lowest P/E. The universe is the 500 largest stocks in the FTSE World index. Performance is on a total return, local currency basis with stocks equally weighted. Source: Nomura Equity Strategy

Figure 2: Other factors may have an asymmetric payoff where the factor matters only when it reaches an extreme – the case of gearing

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Chart shows the annualised return from 1989-2009 of four quartiles formed on net debt/equity and rebalanced quarterly. Quartile 1 has the highest net debt/equity ratio. The universe is the 500 largest stocks in the FTSE World index. Performance is on a total return, local currency basis with stocks equally weighted. Source: Nomura Equity Strategy

Some factors exhibit a monotonic

distribution...

August 07, 2009


The ranking approach assumes a monotonic relationship. For this it is not generally sufficient to test that the top quantile outperforms or has a higher information ratio than the lowest quantile as there could be middle quantiles with higher or lower returns. A test for monotonicity was developed in a good paper by Patton and Timmermann (20083). They propose a test statistic based on the difference in returns between adjacent quantiles. In the case in which expected returns increase with the factor rank, the test of monotonicity is based on the minimum return of adjacent portfolios. They first define the expected return differential of adjacent quantiles as Δi=μi-μi-1 for i=2...N where μi is the expected return of the ith quantile. We can write this test statistic J as:

iNiTJ Δ== ,...,2min

This is better than a set of pair-wise tests on the difference between the returns of adjacent portfolios as it is hard to summarise all that information into one statistic. The test can easily be applied to the case in which returns decrease with rank and also to two-way sorts.

If quantiles are used, how many ’buckets‘ should be used? The whole objective of allocating stocks to buckets is to get rid of stock-specific effects; to do this effectively, large buckets are better. However, if the buckets are too broad it may be hard to extract information about the cross-sectional distribution of returns. The divisions tend to be quartiles, quintiles or deciles. For our suite of style indices we use quartiles as that can be applied in a consistent way to a large number of regions and countries, and on both a sector-neutral and non-sector-neutral basis without running into problems of too few stocks.

The above discussion is relevant for the process of selecting factors. The process of portfolio construction is beyond the scope of this note, but once factors have been chosen and a portfolio is being constructed, there are a number of options, again ranks can be used or else an exposure-weighted approach. Ranks can be used in two ways, either to form a portfolio of equal-weighted stocks directly or else they can then be used in a regression that could allow for more explicit alpha forecasts. Exposure-weighting can clearly have advantages at this stage in forging an explicit alpha return forecast. A decision has to be made on how stocks are to be weighted. Selected stocks could be equally weighted, cap weighted, exposure weighted and optimisers can also be used.

3 Footnote: Patton, A and Timmermann, A Portfolio Sorts and Tests of Cross-Sectional Patterns in Expected Returns available at http://www.rhsmith.umd.edu/finance/pdfs_docs/SeminarSpring2009/TimmermanAllan.pdf.

...while others have a non-monotonic

cross-section, and in some cases only

discriminate at one end of the

distribution

Test for monotonicity

August 07, 2009


4. Sector-neutral versus non-sector-neutral

There is evidence that systematic rules-driven stock selection approaches are more effective at selecting stocks within sectors than across the whole market. By ”more effective“, we mean they tend to deliver higher return per unit risk. We prefer to leave our sector and style allocation to other models that we run separately.

Figure 3 shows the return-risk trade-off for a selection of strategies applied to Global stocks over the past two decades. On the right are strategies that are based on simply screening across the whole market and forming attractive and unattractive quartile portfolios on the factors shown. The strategies to the left are the result of screenings within each sector on the same factors. It is notable that the move to sector-neutral strategies generally results in the same level of return, but with lower levels of risk. This result is robust across time and therefore has been a feature of our stock-selection models for many years.

This is not to say that one cannot pick sectors, far from it, but that in sector selection a different approach needs to be used; for example, employing time series valuations.

Figure 3: Sector-neutral versus non sector-neutral strategies (Dec 1989-Jun 2009)

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Sector-Neutral

Figure shows the return and risk trade-off for a selection of sector-neutral and non sector-neutral strategies. All strategies have been based on the 500 largest stocks in the FTSE World index and rebalanced each quarter. Non-sector-neutral strategies refers to screens based on the factors shown across the whole market and taking long and short positions in the extreme quartiles. In this case stocks have been equally weighted. Sector-neutral strategies screen on the factors shown within each sector. In this case stocks have been equally weighted within sectors and sector have been equally weighted. All performance is on a total return, common currency basis. Source: Nomura Equity Strategy

Sector-neutral models for stock selection

tend to have better information ratios

than non-sector-neutral models in the

long run

August 07, 2009


5. Univariate versus multivariate

Another area in which we have a clear preference is in assessing factors in isolation versus a multivariate assessment. The way factors behave in isolation can be very different from how they behave in concert with other factors. Therefore, in constructing a model, it is not sufficient to identify factors that work well by themselves and then put them together. The resulting performance could be lower than the performance of the individual factors suggested. Likewise, it could in fact omit a very effective combination of alternative factors.

An example of this that has featured in our research for many years is the efficacy of earnings momentum. We find that earnings momentum used in isolation as a simple screen across the whole market is not very effective. Adopting a sector-neutral approach improves the performance somewhat, but the factor really comes into its own when used in conjunction with value and on a sector-neutral basis.

In Figure 4, we show the progressive improvement in the return-risk trade-off in moving from market-wide univariate screen on earnings momentum, to a sector-neutral screen and lastly to a sector-neutral value plus momentum screen.

Figure 4: Univariate versus multivariate performance of factors (1989-2008)

Sector Neutral Earnings Momentum

Non Sector Neutral Earnings Momentum

PE (forward) + M EV/SALES + M

EV/EBITDA + MPEG + M

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Sector Neutral Earnings Momentum

Figure shows the return and risk trade-off for a selection of strategies based on Earnings Momentum. All strategies have been based on the 300 largest stocks in the FTSE World Europe index and rebalanced each quarter. Non-sector-neutral earnings momentum is a simple top/bottom quartile screen across the whole market. In this case stocks have been equally weighted. Sector-neutral earnings momentum is a top/bottom quartile screen within each sector. In this case, stocks have been equally weighted within sectors and sector have been equally weighted. The value + momentum screens are based on the intersection of top/bottom half screens on earnings momentum and the value factors shown. On average this results in the same number of stocks for all screens shown. All performance is on a total return, common currency basis. Source: Nomura Equity Strategy

The consequence of this is that a multifactor testing framework has to be adopted when building a model. In our multifactor models, we set up systematic tests of multivariate performance. This avoids some of the problems of simply testing every factor combination, which is (a) downright boring and (b) pure data mining. As an example, suppose we have a model that encompasses factors that could be classified as value, momentum, quality and growth. Our approach would be to run a series of four factor regressions keeping three factors constant and changing one at a time. For example, we would keep the momentum, growth and quality factors constant and rotate through all possible value factors. For a more lengthy discussion of this approach, see our report, Global Multifactor Quantitative Model dated 17 July 2009, section 3.3.

The effectiveness of earnings

momentum improves progressively first

by adding a sector factor and then by

adding a value factor

August 07, 2009


6. Dynamic versus static models

In contrast to the previous two sections, a question for which we do not think there is a clear empirical or theoretical preference either way is on the issue of dynamic versus static models. There are essentially two possible ways of linking future returns to factor exposures. Either one can build a model that tries to latch on to long-term drivers of stock performance (static models) or one can reject the notion of long-term consistent drivers and instead construct a model that adopts different factors over the course of the cycle (dynamic models).

There are pros and cons to each approach. If there are indeed long-term consistent drivers of stock returns, the static model would aim to exploit them and deliver smooth returns over time. It is hard to say whether such factors do exist or not. Regimes do change, which could lead to underperformance of such a model. However, what counts as a temporary change of regime or a rejection of the concept of consistent drivers of return is an open question.

Dynamic models do not need to make any big claims about what factors drive stocks in the long run. They usually work by running regressions over the recent past (eg, 6-12 months) to decide what factors have been working recently. They then postulate that the world will be the same in the next period as it was in the last. Such models can adapt to new regimes that persist for some time but may underperform at sharp turning points when factor leadership changes.

Static models have the merit of being simpler to operate (one just needs to rank on a constant set of factors rather than having to have an updating process for the factors themselves) and more transparent (one can say exactly what factors one will be using n years in the future). We also think that, ceteris paribus, static models will usually have lower turnover. Both models generate turnover as the ranking of stocks in the market changes, however, dynamic models generate extra turnover as the factors themselves change.

There is also a subtle point about what constitutes an acceptable factor exposure in the two approaches. In the dynamic approach one would not normally care what sign a factor coefficient has. After all, the model could legitimately take the view that the world was in a pro-value or anti-value phase and assign a positive sign to a value score or a negative sign accordingly. However, in a static model there is not – or at least we would suggest that there should not be – as much freedom. If the model is trying to latch on to long-term effects that presumably could be explained by some kind of theory, then it would be hard to justify a negative exposure to a value factor or 12-month momentum. Therefore, in constructing static factor models we think that there should be strict limits imposed on the signs for factor coefficients to avoid a charge of data fitting.

Although our Global and European multifactor models (sections 13.1 and 13.2) employ a ’learning’ approach, leading to an evolution of factor coefficients in the history, they are static models because we have chosen to turn off the learning process at least five years before publication date to improve transparency. An example of a dynamic model would be our Style Selector model (section 13.6). Normally dynamic models run a regression of recent returns on a set of factors and choose the set of factors that best fits the recent data.

Static models could outperform if there

are genuinely consistent drivers of stock

returns...

...while dynamic model do not need to

make any big claims about long-run

factor performance

The two approaches (should) have a

different view on what constitutes an

acceptable factor coefficient

August 07, 2009


Our approach is somewhat different, we try to exploit the behavioural biases of under-reaction and over-reaction. To do this, we assume there is short-term persistence of factors as is used in regression-based approaches, but also take account of the valuation of factors to find cases of over-reaction.

Another way of thinking about this is that it uses the persistence of factors that is common in many dynamic weighting approaches but incorporates a view of the valuation of the factor. The rationale for this is that one might become worried by a factor if it performs too well as it could be a sign that there is overconfidence in the factor and that it is overvalued. We can alleviate this problem by monitoring the valuation of a factor defined as the relative multiple of stocks that fall within the top and bottom quartile of the factor.

August 07, 2009


7. Factor choice

Factor choice is a huge topic. Having decided to adopt a sector-neutral approach (see section 4), the question arises of whether the same factor structure should be imposed across all sectors/regions or whether the factors should be weighted in accordance with their efficacy in sector/regions? Moreover, how should one decide which particular factors to employ from a broad pool of many possible factors?

On the former question, we find that the choice here normally comes down to personal preference and the target investor audience. There is a group of investors who strongly prefer a uniform approach and another who want to let the data decide.

The advantage of choosing different factors for sectors and regions is that the model can respond to any genuine differences between them, for example, in the level of cyclicality, capital structure and so forth. The argument against this would be that a sector-specific approach leaves one open to the charge of data fitting. Imposing a common factor structure may not be the optimal approach, but it is perhaps more transparent and easy to understand.

As it is hard to claim that one approach is definitively better than the other, and the possibility of a ’clientele effect‘ existing anyway we offer both approaches. Our Global and European multifactor models (section 13.1 and 13.2) allow for different factors in each sector whereas our Fundamental Values model (section 13.3) imposes a similar structure for all sectors and regions.

When starting from a large pool of potential factors, how should one work towards a tractable smaller set of final factors? After all, for valuation alone, multiples could be used based on almost any line in the income statement, eg, EV/sales, EV/EBITDA, price/pre-tax profits, P/E pre one-offs, P/E post one-offs with another long list of possible cash flow and balance sheet multiples. Moreover, the whole list could be repeated for reported and expectations data. One route could be to throw all the factors ’into the pot‘, run regressions and see which factors dominate. This might not, however, be desirable as many of these factors could be highly correlated, and it could prove hard to justify the choice of factors resulting from such a data mining approach after the event.

We would generally favour some constraint on the number of factors based on economic rationale, judgment or experience. Our Multifactor models started with a broad, though constrained, list of factors from which we selected short-lists of factors based on how they performed within a multivariate framework.

A key consideration here is the correlation of factors. It is desirable to have model inputs that are relatively uncorrelated. This increases confidence in the likelihood of the model to perform in different environments. Also, in the language of the Grinold (1989) Fundamental Law of active management, the correlation between factors used can determine the number of independent views. The fundamental law tries to assess the value that can be added from a particular active management process. It states that the ex ante information ratio is a function of the information coefficient of the model and the number of independent ’views’.

Should the same factor structure be

imposed across all sectors/regions or

whether the factors should be weighted

in accordance with their efficacy in

sector/regions?

Starting from a pool of potential

factors, how should one work towards

a tractable smaller set of factors?

Factor correlation is key...

August 07, 2009


NICIR .=

Where IC is the information coefficient – in a sense a measure of the quality of the signal – and N is the number of independent ’views‘, or the breath of factors available.

A complication is that factor correlation can change. This can seriously affect the performance of models. As an example, we can consider the case of value and momentum. These are often used as the starting point for quant models. In general, the correlation between them is low, which adds to the appeal of using the two factors together. However, at times their correlation can become large and positive, reducing the number of independent views, or can become large and negative, making it hard to implement the strategy. Over early 2009, the correlation between 12-month price momentum and the price/book factor was -0.95 (Figure 5). In some cases, investors have found it hard to implement a strategy that is true to either

Figure 5: 30-day rolling correlation between value and momentum

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Chart shows the 30 day rolling correlation between value (price/book) and momentum (12m price momentum) Source: Nomura Equity Strategy

...though it can change over time

August 07, 2009


8. Portfolio simulations and regressions

When imposing a common factor structure and a small number of factors (section 7), it is possible to run simulated portfolios and impose weights on the factors from the beginning. Portfolios constructed from such an approach often then assume an equal alpha forecast for each stock and, hence, lead to equal-weighted portfolios. This may also fit well with the overall ethos of the approach in not trying to fit the model too closely to a particular sample of data, but instead to work from some principles.

The case in which many factors are used or if the model is designed explicitly to allow different factor coefficients across sectors, then it is natural to use regressions to assign factor coefficients. Using regressions to assign factor coefficients also has the advantage that at the portfolio construction phase, the model can have an explicit alpha forecast for each stock, which allows for a weighting structure that is not equal and can also be fed into an optimiser if one is being used. But in this case, what regressions exactly should be run?

Probably the simplest regression approach would be to designate an in-sample period, run one large panel regression of forward returns on factor exposures over that time and use that to designate factor coefficients in the out-of-sample period. A problem with this approach is that if only a short data history is available, there may not be enough data to separate a meaningful in- and out-of-sample periods. The performance over the in-sample period in this case would be of limited applicability to the out-of-sample period.

Other approaches include a Fama-Macbeth (1973) cross-sectional approach or panel regressions that can evolve over time. The latter could be rolling window panel regressions in the case of dynamic models of expanding window panels in the case of static models. It is expanding windows that we use in our Global and European multifactor models.

We have assumed that it is easy to identify which regression is the best, but in reality this is not trivial. Presented with regressions from a series of different possible factor combinations, what metric should one use to decide which is best? The natural reaction may be to use the R2 as that will measure the goodness-of-fit of the regression. However, we would argue this is not necessarily the best approach. Ultimately, what we care about is the information ratio (IR) and the smoothness of the IR over time. Moreover, the R2 from a regression of forward returns on a mix of fundamental and technical factors is often is very low.

As a result, in our Global and European multifactor models, our decision of which sets of factors are best is driven by projecting out the coefficients to form portfolios at each point in time and then assessing the IR of the portfolio and how it evolves. Note that the level of the IR alone is not enough. It is important to also assess how consistent it is over time because one would prefer a smooth path to a given IR over a more volatile route.

Choice of regression approaches

How to determine the ‘best’

regression?

August 07, 2009


9. Data

The bedrock of any quant model has to be a good data set. There are many issues that could be mentioned here, and it will depend on the type of model being used, ie, does the model use ’fundamental’ data, technical factors or other sources, eg, expectation data.

When using accounting data, there can be a problem of look-ahead bias. It is important to know when it became publically available back through time, yet this data can be hard to come by for some data sources. As a solution to this, we have tracked in real-time for many years exactly when company accounts became public so that we can use this data when back-testing. Without this kind of data, one has to simply impose a lag after the fiscal year or quarter end before data is allowed to be used.

Another potential source of error is survivorship bias that would exit, for example, if a current set of constituents is used and projected back through time so that ’dead‘ companies are not included in the analysis. This can be countered by using historical constituents as they were at each point in time. Models also have to account for what happens when companies go bankrupt, are delisted or stop trading.

Another aspect is accounting changes. Many (actually from experience we would suggest most) quant analysts find accounting issues painful because they tend not to be schooled in them and the mention of a change in rules or a change in the presentation of accounts quickly leads to a glazed-over expression; however, when data definitions change or when accounting rules change, this can affect quant models. An example of this has been changes in the presentation of IBES data. In 2002, the primary definition of earnings for UK company was switched to a post-goodwill basis causing a large move in the aggregate P/E of the UK market. There was then a subsequent change in 2005 when earnings in IFRS-adopting countries. Users of raw, unadjusted data over this period would have obtained significantly altered results. Over this period, in our database it was necessary to splice series to obtain a consistent approach. Details of changes made to our database at the time are given in IFRS: What Exactly Does an Investor Need to Care About?, dated 6 December 2004.

For details of the Nomura global equity strategy database see Global Multifactor Quantitative Model, dated 17 July 2009 Appendix 1. For details of potential data sources available in Asia and an assessment of their pros and cons, see H. Tamura: Fundamental Data Service for Japanese Companies, dated June 2008 and Earnings Estimate Data in Japan. Also S. Lee Fundamental and forecast data services of Asia Pacific (ex Japan) companies, dated June 2008.

Possible look-ahead bias in data

Accounting changes

August 07, 2009


10. Rebalance frequency

How should a rebalance frequency be decided? When combing factors with very different alpha horizons, what horizon should one take? Certain factors may have very specific horizons over which they are effective and then their discriminatory power decays. In some cases, there will also be a trade-off between an alpha signal of a factor and how it decays with time and a rebalancing cost that will increase with shorter holding periods.

In the tables below, we show an example of the impact of holding period on price/book and price momentum factors. In both cases, we have formed portfolios from December 1989 to the present using holding periods from three months up to 12 months. We find that in this case the value factor is effective for 12 months after the point of portfolio formation. The momentum factor shown here is effective for three months after portfolio formation but actually shows a slight tendency to reversal 12 months forward.

When combining the two factors, the first point to note is that the returns are higher. However, this does decay after three months, implying it is the alpha decay of the shorter factor that is important in this case. This does not provide evidence that this is always the case, but we would suggest this methodology could be applied to a large number of cases. In general, value factors do tend to be effective over a long horizon (eg, 12 months), but momentum factors are effective over shorter horizons.

Figure 6: Effectiveness of price to book over different holding periods Return, % pa Information RatioHolding Period (months) Holding Period (months)

3 6 12 3 6 12

Basic Industry 3.3 5.7 1.8 0.2 0.3 0.1Capital Goods 4.2 6.1 2.3 0.3 0.3 0.1Consumer Staples -1.3 -0.1 0.6 -0.1 0.0 0.0Consumer Cyclicals 3.7 2.8 3.0 0.2 0.2 0.2Energy 6.0 4.1 2.3 0.4 0.3 0.1Financials 6.9 5.4 6.5 0.5 0.4 0.5Healthcare -3.4 -2.6 0.5 -0.2 -0.1 0.0Media 0.0 0.2 -0.9 0.0 0.0 0.0Technology -8.4 -11.6 -9.0 -0.3 -0.4 -0.3Telecom 1.8 1.2 1.1 0.1 0.1 0.1Utilities 5.8 3.9 1.7 0.3 0.2 0.1

Average 2.8 2.5 2.8 0.3 0.3 0.3 Table shows annualised return and information ratio (annualised return/annualised standard deviation) for this factor over the period 1989-2008. Stocks have been sorted into top/bottom quartiles by each factor. Performance is on an equal-weighted, total return, common currency basis. Source: Nomura Equity Strategy

The optimal rebalance frequency is a

function of a number of factors, eg,

alpha decay and rebalancing costs

When using factors that have different

alpha horizons, what is the best

combined rebalance frequency?

August 07, 2009


Figure 7: Effectiveness of 12-month price momentum over different holding periods Return, % pa Information RatioHolding Period (months) Holding Period (months)

3 6 12 3 6 12

Basic Industry -5.0 -7.6 -6.4 -0.2 -0.3 -0.3Consumer Cyclicals -2.2 -2.0 -1.5 -0.1 -0.1 -0.1Capital Goods -0.5 -4.8 -2.5 0.0 -0.3 -0.1Consumer Staples 0.3 0.3 -1.1 0.0 0.0 -0.1Energy -0.3 0.4 -0.8 0.0 0.0 0.0Financials 1.0 -0.4 3.1 0.0 0.0 0.2Healthcare 8.2 5.0 1.9 0.4 0.2 0.1Media -7.6 -9.0 -6.3 -0.4 -0.4 -0.3Technology 6.5 11.4 7.5 0.2 0.4 0.3Telecom 2.5 -1.2 -7.8 0.1 -0.1 -0.4Utilities 2.7 -0.6 -1.3 0.1 0.0 -0.1

Average 1.8 0.5 -0.1 0.1 0.0 0.0 Table shows annualised return and information ratio (annualised return/annualised standard deviation) for this factor over the period 1989-2008. Stocks have been sorted into top/bottom quartiles by each factor. Performance is on an equal-weighted, total return, common currency basis. Source: Nomura Equity Strategy

Figure 8: Effectiveness of price to book and momentum over different holding periods Return, % pa Information RatioHolding Period (months) Holding Period (months)

3 6 12 3 6 12Basic Industry 1.92 -0.58 -0.58 0.09 -0.03 0.05Consumer Cyclicals 4.79 1.75 1.75 0.28 0.10 0.02Capital Goods 2.55 5.45 5.45 0.12 0.26 0.29Consumer Staples 0.50 0.00 0.00 0.04 0.00 -0.01Energy 4.48 4.34 4.34 0.27 0.25 0.09Financials 6.40 4.81 4.81 0.37 0.28 0.56Healthcare -1.31 -4.66 -4.66 -0.07 -0.24 -0.27Media -1.28 -3.73 -3.73 -0.06 -0.17 -0.01Technology 3.61 0.78 0.78 0.14 0.03 -0.05Telecom 3.85 -0.15 -0.15 0.20 -0.01 -0.18Utilities 4.50 4.04 4.04 0.23 0.21 0.11

Average 4.16 2.51 2.33 0.41 0.25 0.25 Table shows annualised return and information ratio (annualised return/annualised standard deviation) for this factor over the period 1989-2008. Stocks have been sorted into top/bottom quartiles by each factor. Performance is on an equal-weighted, total return, common currency basis. Source: Nomura Equity Strategy

August 07, 2009


11. Choice of benchmark

When assessing a quant strategy, it is important to be clear what benchmark it should be assessed against. Likewise, when building a quant strategy a choice has to be made as to the appropriate universe.

The first decision to be made is whether the strategy is long only and therefore needs to be assessed against some measure of the market, or whether it is a long-short market-neutral strategy in which case it could be assessed against cash or possibly a relevant constructed benchmark such as a hedge fund index.

It is also important that the weighting structure of the model is appropriate to the strategy. The weighting of sectors and stocks within sectors should be aligned. It might be appropriate in some cases to construct custom benchmarks. This is not limited to quant strategies, but if a strategy is known to have a value-based approach, say, then it could be convenient to measure the alpha as being relative to a value index and then to regard the value performance as a beta for the strategy.

When choosing an investible universe, it could be desirable to take the concept of factor richness into account. This is a measure of the number of possible factors that could explain risk and return within a universe. This could be done by taking a series of factors and seeing how many of them are needed to explain the variance in the cross-section of returns. The potential problem with this approach is that it may simply miss some factors. Thus, a more generalised way of measuring this is to run a principal component analysis on the benchmark and determine the number of factors that are required to explain a given proportion of the cross-section of returns, say, 90%; this way, potential benchmarks can be compared. Our hypothesis would be benchmarks that require more factors to explain the variance of returns offer a more fruitful ground for the construction of quant models as there are more potential factors for investors to use. As an aside, we would also point out that the same technique can be used in a time-series sense to assess the richness of a factor set at each point in time for a given benchmark.

August 07, 2009


12. Recent developments: Has back-testing gone out of fashion? How to avoid overcrowding

Between 6 and 9 August 2007, the Hedge Fund Research Equity Market Neutral Index that contains many quant hedge funds fell 6.3%. A large fall in the context of the volatility of the series up to that point (Figure 9). The fall in some individual funds was considerably higher. The episode was referred to by some as ’quantmare‘. With hindsight, it appears to have resulted from a rapid deleveraging of a quant fund or funds. It transpired that many quant funds had similar exposures, the sharp underperformance thus led many other funds to de-lever. The episode was studied in detail by Khandani and Lo (2007) and Fabozzi et al (2008)4.

Figure 9: Equity market neutral hedge fund returns

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115

Jan-05 Jul-05 Jan-06 Jul-06 Jan-07 Jul-07 Jan-08 Jul-08 Jan-09 Jul-09

1st Jan 2005 = 100August 2007

Chart shows the performance the Hedge Fund Research equity market neutral hedge fund index and the Nomura Global Multifactor Model. Returns are on a long-short total return, common currency basis. Portfolios are rebalanced quarterly. We use the equity market neutral category of hedge funds to give the closest approximation to “fundamental”-based quant models. Note however that this hedge fund category can include both non quant approaches and also statistical arbitrage funds. Source: Hedge Fund Research, Bloomberg, Nomura Equity Strategy

Non-quant investors could be forgiven for wondering what all the fuss was about. The performance of the market over those days was not out of the ordinary (the FTSE World Index rose by 0.6%). Also, many strategies recovered strongly over the subsequent two weeks. For investors who could stay invested in strategies through that period, returns could potentially be made back up. However, as an event, it shook up the world of quant investing by showing there was a high correlation between many strategies as a result of similar exposures. It also led to outflows from some funds over subsequent months that in some cases led to a further bout of underperformance in the closing months of 2007 and the beginning of 2008.

One consequence of this was that some investors felt their models were no longer appropriate and effectively turned them off. It could be said that back-testing went out of fashion. In a sense, this was nothing more than a response to a perceived large regime change. If models were not suited to the new regime, then some investors would have come

4 Khandani, A and Lo, A: What Happened to the Quants in August 2007? September 2007 available at http://web.mit.edu/alo/www/Papers/august07.pdf and Fabozzi, F, Focardi, S and Jonas, C: Challenges in Quantitative Equity Management, CFA Institue Research Foundation

August 2007 saw a sharp fall in many

quant strategies caused by de-

leveraging of similar exposures across

different funds

Back-testing went out of fashion

August 07, 2009


to the conclusion that more judgment had to be used or different model adopted. However, it also shook the confidence of some investors in quant strategies. Back-testing will remain an important part of assessing quant models. We think that in future, back-tested results will draw great scrutiny and, in particular, it is important for quant strategies to show they are not correlated with the market or other strategies.

A second consequence was that since August 2007, there has been a concerted effort to avoid overcrowding in quant strategies. Until August, we were never asked in meetings with clients about crowding in certain strategies. With the benefit of hindsight, this seems remarkable. Since then, it has been a frequent topic of discussion. Crowding in strategies is hard to measure because it cannot be observed directly. One way of inferring that we have used it for some time is by running regressions of the performance of fund categories on factor returns.

As an example, in Figure 10 we show the coefficient on the price/book factor resulting from a regression of returns to the Hedge Fund Research Equity Market Neutral Index on a set of our factor indices over 60-day rolling periods. The chart can be interpreted as showing the return from the index at any point that would result from a unit move in the price/book factor with other factors remaining constant. A large positive coefficient implies a large positive loading on that factor and could be a warning of possible overcrowding. The hedge funds in this sample have tended to be long this value factor. Early 2009 was unusual in that there was actually a negative exposure to value as they turned more defensive. That negative exposure has been removed in just the last two months.

Figure 10: Coefficient on price/book factor

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Aug-08

Ratio

Figure shows the evolution of the regression coefficient on the price/book factor from overlapping period 60-day multifactor regressions of the Hedge Fund Research Equity Market Neutral Index and Nomura style indices. Data is for a global universe. A positive coefficient indicates quant funds are overweight risky stocks. The Nomura risk style is based on a screening on 12-month return volatility, 12-month volatility in earnings forecasts changes and 12-month beta. Source: Hedge Fund Research, Nomura research

August 07, 2009


13. Nomura quantitative models

In this final section of the report, we illustrate many of the issues that we have discussed above with the models that we run. These show examples of models for stock selection and also more ’macro‘ models for region, country or style selection.

Where we have strong views that a model ought to be constructed in a certain way, then the models will follow that (eg, sector neutrality). However, if we believe there is a genuine choice, then we can offer alternative models in some cases.

This section lists only models run by the London quant strategy team. For details of the global models published by the New York team please see US Quant Monthly: June 2009 Failure of the multi-factor gambit, dated 10 June 2009. For a survey of the 17 quant models run by our Tokyo team, please see Nomura Japanese quants model performance review 2009 Q1, dated 20 April 2009. For details of the models run by our Hong Kong team please see Nomura Equity Quant models: Asia Quantitative Strategies June 2009.

August 07, 2009


13.1 Global multifactor model

This model selects stocks from the 500 largest stocks globally. The distinguishing feature is that it employs a non-linear term to measure the level of agreement between the value and momentum terms. This is in addition to the ’normal’ multivariate terms such as value, growth, quality and momentum.

Coefficients are assigned to factors through a regression process. We use expanding window panel regressions so that the model ’learns’ over time. The learning process stops in 2003, allowing an out-of-sample period. We allow a very different factor exposure in each sector so that the model can weight factors that are most effective.

For full details of this model, please see Global Multifactor Model July 17 2009.

Figure 11: Performance statistics

Return, % paAnnualised

monthly volatilityAnnualised monthly IR

Whole Period 10.35 7.37 1.40Jun 04 - Jul 09 4.12 3.90 1.06Dec 92 - Jun 04 12.99 8.28 1.57

Figure shows the performance of our stock selection model on a long-short basis over the periods shown. The portfolio has been rebalanced each quarter. Stocks have been equally weighted within sectors and sectors equally weighted. Source: Nomura Equity Strategy

Figure 12: Performance of model (long - short)

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Dec-91 Dec-93 Dec-95 Dec-97 Dec-99 Dec-01 Dec-03 Dec-05 Dec-07

Dec 91 = 100Out of sample

Figure shows the performance of our stock selection model on a long-short basis. The portfolio has been rebalanced each quarter. Stocks have been equally weighted within sectors and sectors equally weighted. Source: Nomura Equity Strategy

August 07, 2009


13.2 European multifactor model

This model selects stocks from the 300 largest stocks in Europe. The distinguishing feature is that is employs a non-linear term to measure the level of agreement between the value and momentum terms. This is in addition to the ’normal‘ multivariate terms such as value, growth, quality and momentum.

Coefficients are assigned to factors through a regression process. We use expanding window panel regressions so that the model ’learns‘ over time. The learning process stops in 2002, allowing an out-of-sample period. We allow a very different factor exposure in each sector so that the model can weight factors which are most effective.

For full details of this model, please see European Multifactor Model November 3 2008.


Return, % pa

Annualised monthly volatility

Annualised monthly IR

Dec 91 - Jun 03 11.8 6.9 1.7Jun 03 - Jul 09 4.3 5.4 0.8whole period 9.1 6.5 1.4



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Dec-91 Dec-93 Dec-95 Dec-97 Dec-99 Dec-01 Dec-03 Dec-05 Dec-07

Dec 91 = 100Out of sample

Figure shows the performance of our stock selection model on a long-short basis. The portfolio has been rebalanced each quarter. Stocks have been equally weighted within sectors and sectors equally weighted.. Source: Nomura Equity Strategy

August 07, 2009


13.3 Fundamental values

Fundamental Values is a suite of stock selection models for the global stock market and also for individual regions. It uses a value and momentum approach within a sector-neutral framework.

The model imposes a top-down view on the stock selection process so that a similar approach is used for all sectors and regions. Rather than simply equal-weighting the input factors, we use an intersection approach so that stocks are selected as attractive or unattractive if the two inputs are in agreement.

It is available in both a regional form, where stocks are selected relative to their regional sector, or in a global form with no regional constraint. We show the performance of both versions below. The Global Fundamental Values approach was first published in December 1999.

Returns for the individual regional components are available upon request.


Return, % pa

Standard Deviation (annualised)

Return/standard deviation

Global Large Cap Fundamental Values 5.7 7.1 0.8

Global Region-Neutral Fundamental Values 7.1 4.3 1.7



1 0 0

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9 1 9 3 9 5 9 7 9 9 0 1 0 3 0 5 0 7

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Region-Neutral Fundamental Values

Global Large Cap Fundamental Values

Figure shows the performance of our stock selection model on a long-short basis. The portfolio has been rebalanced each quarter. Stocks have been equally weighted within sectors and sectors equally weighted. Source: Nomura Equity Strategy

August 07, 2009


13.4 Emerging market country selector

Our emerging market country selection model uses a combination of valuation, sentiment and technical indicators to select between 19 emerging market countries each month. The factors are relatively uncorrelated and contribute to the performance at different stages in the cycle. The sentiment measure uses fund flows as a contrarian indicator over overconfidence. The technical factor is price acceleration, ie, the change in price momentum. For valuation we use a blend of P/E and EV/EBITDA.

This is an example of a model where the weighting is based on rankings rather than exposures. A linear combination of the rankings on the input factors is used to decide the over/underweight position in each country based on its benchmark weight.

Figure 17: Table of factors with effectiveness Factors/ Combination Excess Return Vol Info Ratio % of instances

outperformedPE 1.5% 2.0% 0.77 55%EVEBITDA 1.1% 1.8% 0.61 60%Fund Flows 1.9% 1.6% 1.16 64%Price mom, 3mo change, 2nd der 0.6% 1.7% 0.33 53%

Combined, PE+EVEBITDA+FF+Price mom 4.3% 3.7% 1.14 64% Source: Nomura Equity Strategy

Figure 18: Performance of model relative to benchmark

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July 2000=100

Source: Nomura Equity Strategy

August 07, 2009


13.5 Regional selector

Our regional selector model selects from the six major work regions including emerging markets each month. The inputs are valuation in the form of the equity risk premium, change in earnings revisions and price acceleration.

The ordering of regions is based on the average rank across the three input factors.

For full details of this model, please see ‘Regional Equity Selector’, 12 June 2009

Figure 19: Benchmark relative performance over rolling periods 1-year 3-year

No. of periods 161 137

Proportion of periodsoutperformed 80% 98%

Average annualised benchmark 0.8% 0.8%relative return Source: Nomura Equity Strategy

Figure 20: Performance of model: Benchmark relative performance using combined valuation, earnings revisions and momentum signals

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Annualised return 1% pa, IR 0.8 (with 10% max deviation from benchmark)

Index

Figure shows the cumulative benchmark relative return of the regional model assuming a maximum deviation constraint of 10% from the benchmark weight, with monthly rebalancing. The performance is based on the developed regions until June 2000 and includes Emerging Markets from July 2000. Returns are based on the FTSE AW series of indices from when they are available and on the FTSE W series prior to that. All returns in total returns, $ terms and prior to transactions costs. Source: Nomura Equity Strategy

August 07, 2009


13.6 Style selector

Our style selection model relies on over- and under-reaction at the style level. We assume there is short-term persistence in style performance, which we can capture through momentum; however, we suggest investors can become over confident in styles, which leads to overvaluation in the long run and then subsequent underperformance. We can measure the valuation of the styles by their P/E and price/book valuation relative to history. Figure 21 shows the performance of alternative style-switching approach with our favoured one being value and momentum. Figure 22 shows our favoured approach alone. For full details of this model, please see ‘European Style Selector’, 5 June 2009.

Figure 21: Performance of alternative style selection models

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Value + Momentum

Momentumonly

May 91=100

Value only

Figure shows the relative performance of attractive and unattractive styles according to a range of switching models on a long-short basis. Portfolio holdings have been rebalanced each month. Stocks have been equally weighted within the style portfolio at the beginning of each holding period and styles are equally weighted. Style performance is on a total return, common currency basis. From 2000 a five-day implementation lag is introduced as each rebalancing point to allow for a conservative trading horizon. The investable universe is the 300 largest companies in the FTSE World Europe index. Source: Nomura, WorldScope, FTSE, Exshare

Figure 22: Performance of preferred model (long - short)

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May-91 May-93 May-95 May-97 May-99 May-01 May-03 May-05 May-07 May-09

May 91 = 100

Return, % paAnnualised

monthly volatilityAnnualised monthly IR

5.02 7.03 0.71

Figure shows the cumulative relative return of attractive and unattractive styles according to our Style Selector methodology on a long-short basis. Portfolio holdings have been rebalanced each month. Stocks have been equally weighted within the style portfolio at the beginning of each holding period and styles are equally weighted. Style performance is on a total return, common currency basis. From 2000 a three-day implementation lag is introduced as each rebalancing point to allow for a conservative trading horizon. The investable universe is the 300 largest companies in the FTSE World Europe index. Source: Nomura Equity Strategy

August 07, 2009


13.7 Islamic-compliant quantitative strategies

For investors who use an Islamic-compliant benchmark, this model selects attractive stocks each quarter from among the 500 largest stocks in the DJ Islamic Market Index. The model has been developed specifically for this Islamic-compliant universe rather than being adapted from another approach.

Stocks are selected using a combination of value and momentum factors, as described in Figure 23. An intersection approach is used, so stocks are selected as attractive if they rate as attractive on both the measures independently. Stocks are selected relative to their sector peers and the portfolio is rebalanced each quarter. The strategy is long only.

Figure 23: Preferred screens by sector

Sector Screen

Basic Industries EV/EBITDA+momentumCapital Goods FCF yld+momentumConsumer Cyclicals PE fwd+momentumConsumer Staples EV/EBITDA+momentumEnergy div yld+momentumHealthcare FCF yld+momentumMedia PE fwd+momentum

TechnologyPE/growth+ normalised price momentum

Telecoms EV/FCF+momentumUtilities EV/EBITDA+momentum

Source: Nomura Equity Strategy

Figure 24: Performance of model relative to DJ World Islamic Index

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Since December 1991 Return, % paStandard Deviation

(annualised)Return/Standard

Deviation

Islamic-Compliant Strategy 19.0 16.5 1.1

DJ World Islamic 6.8 17.5 0.4

Sector-Neutral Islamic benchmark 12.6 14.1 0.9

Figure shows the performance of our stock selection model relative to the market. The portfolio has been rebalanced each quarter. Stocks have been equally weighted within sectors and sectors weighted in line with their benchmark weight. Note that the model returns are available from 1991, though the DJ World Islamic benchmark starts in 1996. Source: Nomura Equity Strategy

August 07, 2009


Bibliography

Barberis, Schleifer and Vishny (1998), Model of Investor Sentiment, Journal of Financial Economics vol 49, pp307-43

Fama, E and Macbeth, J (1973) Risk, Return and Equilibrium: Empirical Tests, The Journal of Plitical Economy vol 81 No 3 May-June 1973

Grinold, R (1989) The Fundamental Law of Active Management, Journal of Portfolio Management vol 15, no 3

Jegadeesh and Titman (2005) Momentum in Advances in Behavioral Finance Volume II edited by R. Thaler, Russell Sage Foundation 2005

Lakonishok, Schleifer and Vishny (1994): Contrarian Investment, Extrapolation and Risk, Journal of Finance 49(5) December 1994 pp 1541-78

Patton, J and Timmermann, A (2008) Portfolio Sorts and Tests of Cross-Sectional Patterns in Expected Returns. Available at http://www.rhsmith.umd.edu/finance/pdfs_docs/SeminarSpring2009/TimmermanAllan.pdf

Khandhani, A and Lo, A (2007) What Happened to the Quants in August 2007? Available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1015987&rec=1&srcabs=8156

Fabozzi, F Focardi, S and Jonas, C, Challenges in Quantitative Equity Management, CFA Institute Research Foundation

Rouwenhorst, K International Momentum Strategies Journal of Finance Vol 53 No 1 February 1998

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Analyst Certification: I, Inigo Fraser-Jenkins, hereby certify (1) that the views expressed in this Industry Report accurately reflect my personal views about any or all of the subject securities or issuers referred to in this Industry Report and (2) no part of my compensation was, is or will be directly or indirectly related to the specific recommendations or views expressed in this Industry Report. Important Disclosures:

All share prices mentioned are closing prices unless otherwise stated.

ISSUER SPECIFIC REGULATORY DISCLOSURES

Online availability of research and additional conflict-of-interest disclosures:

Nomura Japanese Equity Research is available electronically for clients in the US on NOMURA.COM, REUTERS, BLOOMBERG and THOMSON ONE ANALYTICS. For clients in Europe, Japan and elsewhere in Asia it is available on NOMURA.COM, REUTERS and BLOOMBERG.

Important disclosures may be accessed through the left hand side of the Nomura Disclosure web page http://www.nomura.com/research or requested from Nomura Securities International, Inc., on 1-877-865-5752. If you have any difficulties with the website, please email [email protected] for technical assistance.

The analysts responsible for preparing this report have received compensation based upon various factors including the firm's total revenues, a portion of which is generated by Investment Banking activities.

Distribution of Ratings:

Nomura Global Equity Research has 1613 companies under coverage. 36% have been assigned a Buy or Buy rating which, for purposes of mandatory disclosures, are classified as a Buy rating; 33% of companies with this rating are investment banking clients of the Nomura Group*. 41% have been assigned a Neutral rating which, for purposes of mandatory disclosures, is classified as a Hold rating; 61% of companies with this rating are investment banking clients of the Nomura Group*. 21% have been assigned a Reduce or Sell rating which, for purposes of mandatory disclosures, are classified as a Sell ratings; 6% of companies with this rating are investment banking clients of the Nomura Group*. As at 30 September 2008. *The Nomura Group as defined in the Disclaimer on the back page of this report. Explanation of Nomura's equity research rating system in Europe, Middle East and Africa, US and Latin America for ratings published after 27 October 2008:

The rating system is a relative system indicating expected performance against a specific benchmark identified for each individual stock. Analysts may also indicate absolute upside to price target defined as (fair value - current price)/current price, subject to limited management discretion. In most cases, the fair value will equal the analyst's assessment of the current intrinsic fair value of the stock using an appropriate valuation methodology such as discounted cash flow or multiple analysis, etc.

Stocks:

• A rating of "1", or “Buy”, indicates that the analyst expects the stock to outperform the Benchmark over the next 12 months. • A rating of "2", or “Neutral”, indicates that the analyst expects the stock to perform in line with the Benchmark over the next 12 months. • A rating of "3", or “Reduce”, indicates that the analyst expects the stock to underperform the Benchmark over the next 12 months. • A rating of “RS-Rating Suspended” indicates that the rating and target price have been suspended temporarily to comply with applicable regulations and/or firm policies in certain circumstances including when Nomura is acting in an advisory capacity in a merger or strategic transaction involving the company. Benchmarks are as follows: United States: S&P 500, MSCI World Technology Hardware & Equipment; Europe: Please see valuation methodologies for explanations of relevant benchmarks for stocks (accessible through the left hand side of the Nomura Disclosure web page: http://www.nomura.com/research); Global Emerging Markets (ex-Asia): MSCI Emerging Markets ex-Asia.

Sectors:

A "Bullish" stance, indicates that the analyst expects the sector to outperform the Benchmark during the next 12 months. A "Neutral" stance, indicates that the analyst expects the sector to perform in line with the Benchmark during the next 12 months. A "Bearish" stance, indicates that the analyst expects the sector to underperform the Benchmark during the next 12 months. Benchmarks are as follows: United States: S&P 500; Europe: Dow Jones STOXX® 600; Global Emerging Markets (ex-Asia): MSCI Emerging Markets ex-Asia.

August 07, 2009


Explanation of Nomura's equity research rating system in Japan (and ratings in Europe, Middle East and Africa, US and Latin America published prior to 27 October 2008):

Stocks:

• A rating of "1", or "Strong buy", indicates that the analyst expects the stock to outperform the Benchmark by 15% or more over the next six months. • A rating of "2", or "Buy", indicates that the analyst expects the stock to outperform the Benchmark by 5% or more but less than 15% over the next six months. • A rating of "3", or "Neutral", indicates that the analyst expects the stock to either outperform or underperform the Benchmark by less than 5% over the next six months. • A rating of "4", or "Reduce", indicates that the analyst expects the stock to underperform the Benchmark by 5% or more but less than 15% over the next six months. • A rating of "5", or "Sell", indicates that the analyst expects the stock to underperform the Benchmark by 15% or more over the next six months. • Stocks labelled "Not rated" or shown as "No rating" are not in Nomura's regular research coverage. Nomura might not publish additional research reports concerning this company, and it undertakes no obligation to update the analysis, estimates, projections, conclusions or other information contained herein.

Sectors:

A "Bullish" stance, indicates that the analyst expects the sector to outperform the Benchmark during the next six months. A "Neutral" stance, indicates that the analyst expects the sector to perform in line with the Benchmark during the next six months. A "Bearish" stance, indicates that the analyst expects the sector to underperform the Benchmark during the next six months.

Benchmarks are as follows: Japan: TOPIX; United States: S&P 500, MSCI World Technology Hardware & Equipment; Europe, by sector — Hardware/Semiconductors: FTSE W Europe IT Hardware; Telecoms: FTSE W Europe Business Services; Business Services: FTSE W Europe; Auto & Components: FTSE W Europe Auto & Parts; Communications equipment: FTSE W Europe IT Hardware; Ecology Focus: Bloomberg World Energy Alternate Sources; Global Emerging Markets: MSCI Emerging Markets ex-Asia.

Explanation of Nomura rating system for Asian companies under coverage ex Japan:

Stocks:

Stock recommendations are based on absolute valuation upside (downside), which is defined as (Fair Value - Current Price)/Current Price, subject to limited management discretion. In most cases, the Fair Value will equal the analyst's assessment of the current intrinsic fair value of the stock using an appropriate valuation methodology such as Discounted Cash Flow or Multiple analysis etc. However, if the analyst doesn't think the market will revalue the stock over the specified time horizon due to a lack of events or catalysts, then the fair value may differ from the intrinsic fair value. In most cases, therefore, our recommendation is an assessment of the difference between current market price and our estimate of current intrinsic fair value. Recommendations are set with a 6-12 month horizon unless specified otherwise. Accordingly, within this horizon, price volatility may cause the actual upside or downside based on the prevailing market price to differ from the upside or downside implied by the recommendation. • A "Strong buy" recommendation indicates that upside is more than 20%. • A "Buy" recommendation indicates that upside is between 10% and 20%. • A "Neutral" recommendation indicates that upside or downside is less than 10%. • A "Reduce" recommendation indicates that downside is between 10% and 20%. • A "Sell" recommendation indicates that downside is more than 20%.

Sectors:

A "Bullish" rating means most stocks in the sector have (or the weighted average recommendation of the stocks under coverage is) a positive absolute recommendation. A "Neutral" rating means most stocks in the sector have (or the weighted average recommendation of the stocks under coverage is) a neutral absolute recommendation. A "Bearish" rating means most stocks in the sector have (or the weighted average recommendation of the stocks under coverage is) a negative absolute recommendation.

Price targets

Price targets, if discussed, reflect in part the analyst's estimates for the company's earnings. The achievement of any price target may be impeded by general market and macroeconomic trends, and by other risks related to the company or the market, and may not occur if the company's earnings fall short of estimate.

DISCLAIMERS

This publication contains material that has been prepared by the Nomura entity identified on the banner at the bottom of page 1 herein and, if applicable, with the contributions of one or more Nomura entities whose employees and their respective affiliations are specified on page 1 herein or elsewhere identified in the publication. Affiliates and subsidiaries of Nomura Holdings, Inc. (collectively, the "Nomura Group"), include: Nomura Securities Co., Ltd. ("NSC") Tokyo, Japan; Nomura International plc, United Kingdom; Nomura Securities International, Inc. ("NSI"), New York, NY; Nomura International (Hong Kong) Ltd., Hong Kong; Nomura Singapore Ltd., Singapore; Nomura Australia Ltd., Australia; P.T. Nomura Indonesia, Indonesia; Nomura Malaysia Sdn. Bhd., Malaysia; Nomura International (Hong Kong) Ltd., Taipei Branch, Taiwan; Nomura International (Hong Kong) Ltd., Seoul Branch, Korea

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Opinions expressed are current opinions as of the original publication date appearing on this material only and the information, including the opinions contained herein, are subject to change without notice. If and as applicable, NSI's investment banking relationships, investment banking and non-investment banking compensation and securities ownership (identified in this report as "Disclosures Required in the United States"), if any, are specified in disclaimers and related disclosures in this report. In addition, other members of the Nomura Group may from time to time perform investment banking or other services (including acting as advisor, manager or lender) for, or solicit investment banking or other business from, companies mentioned herein. Further, the Nomura Group, and/or its officers, directors and employees, including persons, without limitation, involved in the preparation or issuance of this material may, to the extent permitted by applicable law and/or regulation, have long or short positions in, and buy or sell, the securities (including ownership by NSI, referenced above), or derivatives (including options) thereof, of companies mentioned herein, or related securities or derivatives. In addition, the Nomura Group, excluding NSI, may act as a market maker and principal, willing to buy and sell certain of the securities of companies mentioned herein. Further, the Nomura Group may buy and sell certain of the securities of companies mentioned herein, as agent for its clients.

Investors should consider this report as only a single factor in making their investment decision and, as such, the report should not be viewed as identifying or suggesting all risks, direct or indirect, that may be associated with any investment decision.

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The securities described herein may not have been registered under the U.S. Securities Act of 1933, and, in such case, may not be offered or sold in the United States or to U.S. persons unless they have been registered under such Act, or except in compliance with an exemption from the registration requirements of such Act. Unless governing law permits otherwise, you must contact a Nomura entity in your home jurisdiction if you want to use our services in effecting a transaction in the securities mentioned in this material.

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