Exploiting Predictability in the Returns to Value and Momentum Investment Strategies: A Portfolio Approach

Elton Babameto HSBC

Richard D.F. Harris University of Exeter

Paper Number: 08/09

November 2008

Abstract There is now widespread evidence that investment strategies based on value and momentum have been profitable in the past. Moreover, combining value and momentum into a single investment strategy provides investment performance that is less sensitive to market cyclicality. However, portfolio managers may be reluctant to implement such strategies as they can lead to substantial departures from client-assigned benchmarks. In this paper, we implement a combined value-momentum strategy using the Black-Litterman portfolio optimisation framework, applied to a single global market comprising 177 national industry indices of the US, UK and Japan. We develop forecasting models for zero-investment value and momentum strategies, and incorporate the out-of-sample forecasts from these models into the Black-Litterman approach. The combined value-momentum strategy yields a significant improvement in performance relative to the underlying benchmark. Using the Black-Litterman model, we can effortlessly track the benchmark at the desired tracking error level under full investment, long-only and beta-neutral constraints, while producing an average annual investment outperformance of up to 0.7 percent, even after allowing for substantial transaction costs. Keywords: Portfolio optimisation; Value; Momentum; Black-Litterman; Trading strategies. Address for correspondence: Professor Richard D. F. Harris, Xfi Centre for Finance and Investment, University of Exeter, Exeter EX4 4PU, UK. Tel: +44 (0) 1392 263215, Fax: +44 (0) 1392 263242 Email: R.D.F.Harris@exeter.ac.uk. We are grateful to seminar participants at the 2006 INQUIRE UK conference. The views expressed are those of the authors and do not necessarily reflect the views of HSBC

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1. Introduction

Value and momentum strategies have both been shown to yield excess returns for

investors. Value strategies involve investing in stocks that have low prices relative to

some measure of fundamental value, such as the book value of equity, dividends,

earnings or cash flow. Value strategies are closely linked to the idea that markets

overreact to new information, so that investors benefit from investing in those stocks

that have done badly in the past. A number of studies have shown that value strategies

are able to generate positive excess returns relative to a simple buy-and-hold strategy

(see, for example, Fama and French, 1992; Campbell and Shiller, 1988a; Fama and

French, 1988; Campbell and Shiller, 1988b, 1998; Chan and Hamao and Lakonishok,

1991; Lakonishok, Shleifer and Vishny, 1994). In contrast, momentum strategies

involve investing in those stocks that have done well in the recent past. Like value

strategies, momentum strategies have been shown to provide returns that are superior to

those of a simple buy-and-hold strategy (see, for example, Jegadeesh and Titman, 1993,

2001; Conrad and Kaul, 1998; Richards, 1997; Rouwenhourst, 1998, 1999; Moskowitz

and Grinblatt, 1999; Griffin, Martin and Susan, 2004).

While both value and momentum investment strategies may outperform simple buy-

and-hold strategies, they are far from riskless, and indeed each may underperform

relative to the market index for sustained periods. In particular, returns to momentum

investment strategies tend to be pro-cyclical, while returns to value investment

strategies tend to be counter-cyclical (see Bird and Whitaker, 2004). These contrasting

characteristics of value and momentum investment strategies have prompted some

authors to combine value and momentum into a single trading strategy. For example,

Asness (1997) finds that following a zero-investment strategy that is long in low value-

high momentum stocks and short in low value-low momentum stocks, produces

superior returns. The same is true for a zero-investment strategy that is long in high

value-low momentum stocks and short in low value-low momentum stocks (see also

Bird and Whitaker, 2004). However, a potential problem with value and momentum

investment strategies – and strategies that combine the two – is that they are likely to

lead to substantial departures from client-assigned benchmarks, such as those that are

based on diversified equity indices. As a consequence, investment managers are likely

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to be reluctant to pursue pure value and momentum strategies in spite of the favourable

risk-return trade-off that they ostensibly offer.

In this paper, we address this problem by implementing a combined value and

momentum strategy using the portfolio optimisation model of Black and Litterman

(1990, 1991, 1992). As an illustration, we apply the Black-Litterman approach to a

global investment universe that comprises 177 national industry indices for the US, the

UK and Japan. Our combination of value and momentum investment strategies builds

on previous research in the literature, particularly that of Asness (1997), Asness et al.

(2000) and Bird and Whitaker (2004). First, we extend the findings of Bird and

Whitaker (2004) by using an expanded set of measures to screen for value and

momentum. Second, we use a regression approach to forecast the relative performance

of value and momentum investment strategies, conditioning on the US term spread and

the aggregate book-to-market ratio, respectively. The aim is to form a set of out-of-

sample return forecasts that exploit the cyclical nature of value and momentum

strategies, and which can be incorporated into a broader portfolio formation process.

Our results are promising. Consistent with previous studies, we find that zero-

investment value and momentum strategies outperform the market over the full sample,

although both are highly volatile and each displays prolonged periods of under-

performance. However, the forecasting models for both strategies are able to capture

much of this cyclicality. Incorporating these forecasts into the Black-Litterman model,

we are able to track the market benchmark at any desired tracking error level under full

investment, long-only and beta-neutral constraints, while producing an average

investment outperformance of up to 0.7 percent per annum, even after allowing for

substantial transaction costs. Our results therefore offer investment managers a viable

combined value and momentum investment strategy that is consistent with the need to

follow a specific client-assigned benchmark.

The remainder of this paper is organised as follows. Section 2 describes the data and

methodology used to implement construct the value and momentum portfolios, and to

forecast value and momentum returns. Section 3 reports the performance of the value

and momentum strategies, and the effectiveness of the forecasting models in forecasting

the returns to these strategies. Section 4 incorporates the value and momentum strategy

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return forecasts into the Black-Litterman model. Section 7 concludes and suggests some

potential avenues for future research.

2. Data and Methodology

Our data comprise the Morgan Stanley Capital International (MSCI) indices at the

national industry level. The use of the MSCI indices is appealing for two reasons. First,

MSCI uses identical criteria to construct each index and so the indices represent US

dollar denominated assets that are directly comparable across countries. Second, the

MSCI indices are free from survivorship bias and so returns calculated using these

indices represent investment returns that would have been attainable in practice. We

consider an investment in three countries: the US, the UK and Japan, and use 59

industries from each country. We use the US dollar value of each index and so

effectively assume that the investment is unhedged with respect to exchange rate

fluctuations. We pool the three sets of national MSCI industry indices to create a single

market universe of 177 country-industries.

All data are taken from DataStream and cover the period 31 January 1995 through 30

November 2004. For each MSCI index, in addition to the total return index (TR) and

market capitalisation (MV), we use the following measures of value: dividend yield

(DY), earnings-to-price (EP), book-to-price (BM) and cash-to-price (CP). Throughout

the paper, we work with value-weighted monthly excess returns. From each month-end

total return for each index we subtract the US one-month CD rate. On each date in the

sample, we retain in our dataset only those industries for which we have values for all

the above data types. We also exclude observations for which any of the value

measures is negative. In Section 3, we use overlapping six-month returns, with the

portfolio re-balanced each month. In Section 4, however – with the aim of replicating

real-world conditions – we use only independent returns but rebalance the portfolio

every six months.

Construction of Value and Momentum Portfolios

For the purpose of this study, momentum is defined as the average monthly return over

the previous six months. Since our sample starts in January 1995, the first month in

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which the momentum indicator is defined is June 1995. Value is defined using a

combination of DY, EP, BM and CP ratios. These ratios are calculated on a country-

corrected basis along the lines of Asness, Porter and Stevens (2000). That is, each

month we subtract from each valuation ratio for each country index the value-weighted

ratio for that country for that particular month. This removes any bias that may arise

from systematic differences in valuation ratios across countries. At each month end, we

sort the indices in increasing order according to the momentum indicator and assign the

indices to quintiles where Q1 and Q5 are the low momentum quintile and high

momentum quintile, respectively. Within each of the Q1 and Q5 quintiles, we sort in

increasing order by each value variable (DY, EP, BM and CP). We then compute the

arithmetic average rank across the four value variables for each of the Q1 and Q5

quintiles. We call this the Composite Value Average Rank. We then re-rank the Q1

quintile by the Composite Value Average Rank, assigning each index to one of five

value quintiles, where Q11 is the low momentum-low value portfolio and Q15 is the

low momentum-high value portfolio. The same two-way sort is applied to the Q5

quintile, yielding a high momentum-low value portfolio, Q51, and a high momentum-

high value portfolio, Q55.

We next construct two zero-investment strategies. The first, which represents a pure

momentum strategy, comprises a long position in Q51 and a short position in Q11. The

second, which represents a pure value strategy, comprises a long position in Q15 and a

short position in Q11. Note that both the momentum and value strategies are defined

relative to the Q11 portfolio This portfolio should be unattractive to investors from both

a momentum and a value perspective, and is therefore expected to underperform

relative to all other portfolios under all states of the world. A short position in this

portfolio should therefore enhance both the momentum and value investment strategies.

We first examine the profitability of pure value and momentum investment strategies.

At the end of month t in June 1995, we form the value and momentum zero-investment

portfolios and track their performance from month t through month t+6. Our first

portfolio is formed in June 1995 and we measure portfolio returns over the next six

months from July 1995 to December 1995. We roll this strategy forward each month

until the last portfolio formation period in May 2004, with performance measured from

June 2004 to November 2004. Overall, there are 108 overlapping evaluation periods.

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Although the portfolio return observations are overlapping, all our results are out-of-

sample since we form portfolios in period t employing only information that is

available at time t.

Forecasting Momentum and Value Returns

While the performance of momentum and value strategies is already well-established,

as is their pro-cyclical and counter-cyclical nature, the literature is currently silent on

the issue of forecasting the returns to momentum versus value strategies, and the

variables that would be useful in such an exercise. In our case, the issue is complicated

by the fact that our investment universe is global, and so the choice of conditioning

variables is less obvious. To forecast the returns of the momentum portfolio, Q51-Q11,

we use the US term spread, defined as the difference between the yield on a US 10-year

government bond and the US 3-month Treasury bill rate. The tem structure captures

expected inflation and expected economic growth (see Dalquist and Harvey, 2001. We

would therefore expect the US term structure to be negatively related to momentum

returns. To forecast the returns of the value portfolio, Q15-Q11, we use the book-to-

market ratio of the MSCI global market index. Liu and Zhang (2005) show that the

book-to-market ratio successfully predicts aggregate equity returns. Both the Q15 and

the Q11 portfolios belong to the highest value quintile of the market. The zero-

investment strategy, which is long in Q15 and short in Q11 should be positively related

to the changing book-to-market spread of aggregate market value and growth stocks.

Our forecasting models for the momentum and value portfolios are therefore as follows:

RQ51,t+6 − RQ11,t+6 =α1 + β1TERMt + ε1,t+6 (1)

RQ15,t+6 − RQ11,t+6 =α2 + β2BMt + ε2,t+6 (2)

where RQij,t+6 is the return on quintile Qij between the end of month t and the end of

month t+6, TERMt is the US term spread at the end of month t and BMt is the

aggregate book-to-market ratio at the end of month t. Each regression is estimated by

ordinary least squares using a two-year rolling estimation window to generate out-of-

sample forecasts of momentum and value portfolio returns. In particular, we first

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estimate each regression over the period June 1995 to May 1997, and use this to

forecast portfolio returns over the period June 1997 to November 1997. The regression

is then estimated over the period July 1995 to June 1997 and used to forecast portfolio

returns over the period July 1997 to December 1997, and so on. This yields a total of 84

out-of-sample forecasts of returns for the momentum and value portfolios.

3. The Performance of Value and Momentum Strategies

Table 1 reports the performance of the two zero-investment strategies and the

benchmark market index. Both the value and momentum investment strategies yield

higher average returns than the market index, with the value strategy providing the

highest return. However, the value and momentum strategies are both very volatile, and

consequently perform less well in risk-adjusted terms. Indeed, the Sharpe ratio for both

the value and momentum strategies is significantly lower than that of the market index.

We find, therefore, that consistent with the results of Asness (1997), the zero-

investment momentum and value strategies offer superior performance relative to the

market, but are far from riskless.

[Table 1]

To shed more light on the characteristics of the two zero-investment strategies, Figure 1

shows the performance of the momentum strategy (Panel A) and the value strategy

(Panel B) against the market index. The momentum strategy outperforms the market

particularly when the market return itself is high, for example during the 1995-99

period. In contrast, the value strategy tends to offer superior performance when the

market return is low, for example during the 1999-2000 and 2002-03 periods. These

results are consistent with Bird and Whitaker (2004) who find that the momentum and

value strategies tend to be pro-cyclical and counter-cyclical, respectively.

[Figure 1]

Clearly, to the extent that the returns to momentum and value investment may be

predictable, a strategy that switches between momentum and value would potentially

offer a superior risk-return trade-off. With this in mind, the results of estimating

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regressions (1) and (2) over the full sample are reported in Table 3. The Newey-West

(1987) estimator is used to correct the standard errors of the estimated parameters

allowing for the overlapping dependent variable. The US term spread significantly

predicts variations in the Q51-Q11 portfolio returns with a negative coefficient,

reflecting the fact that this portfolio has a very strong growth component, which will be

more sensitive to changing interest rates. The aggregate book-to-market ratio offers

statistically significant explanatory power for the value strategy returns, with a positive

coefficient consistent with our expectation. However, the overall explanatory power of

the two regressions – as measured by the R-squared coefficient – is relatively modest.

[Table 2]

To further investigate the performance of the two forecasting models, Figure 2 plots

out-of-sample forecast returns for the momentum investment strategy (Panel A) and the

value investment strategy (Panel B), together with realized returns. Clearly, the

forecasting models are not particularly effective at forecasting the short-term

fluctuations in either value or momentum returns, with the exception perhaps of value

strategy returns over the period 2003-04. However, it appears that they are effective at

predicting the longer run changes in value and momentum returns, and thus to some

extent capture the cyclicality that is inherent in value and momentum investment

strategies. In particular, it appears that they correctly forecast the downturn in

momentum returns from 2001 onwards, and the upturn in value strategy returns over

the same period. This suggests that they may be effective tools for discriminating

between the value and momentum strategies.

[Figure 2]

5. Exploiting the Momentum and Value Strategies in a Portfolio Context

In the previous section, we developed forecasting models for the momentum and value

zero-investment strategies. Despite the evident success of these forecasting models, at

least for longer run changes in returns, the portfolios that they suggest would not

typically be considered as viable stand-alone investments since they contain substantial

amounts of idiosyncratic risk. Rather, they would have to be incorporated into a

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diversified, actively managed portfolio that closely followed a specific client-assigned

benchmark (for example, an aggregate market index or a style benchmark portfolio).

While the traditional mean-variance optimisation framework of Markowitz (1952) (and

‘active’ variants of it such as the portfolio optimisation approach of Treynor and Black,

1973) represents a natural starting point for such an exercise, in practice it suffers from

severe limitations. In particular, the portfolios typically produced by mean-variance

optimisation are often unintuitive and concentrated, and are highly input-sensitive

unless many ad hoc constraints are introduced during the optimisation process.

Moreover, it is not possible to incorporate the degree of uncertainty about forecast

returns, and so there is no way to distinguish a firmly-held view about the future

performance of a security from a weakly-held view (Black and Litterman, 1990).

Exploiting the success of momentum and value strategies in a portfolio context, and

incorporating it into a viable investment vehicle that would acceptable to professional

investment managers therefore represents a challenge. We address this issue using the

Bayesian optimisation approach of Black and Litterman (1990, 1991, 1992).1 The

Black-Litterman approach represents a significant departure from the traditional mean-

variance framework of Markowitz (1952). In particular, its starting point is the

observation that there already exists a set of ‘benchmark’ expected returns, namely the

equilibrium expected returns that are consistent with the composition of the market

portfolio. These equilibrium expected returns can be imputed from the market portfolio

weights, the variance-covariance matrix of returns and an assumption about the

market’s coefficient of risk aversion. This immediately removes the need to specify

expected returns for every asset in the investment universe, and in particular for those

about which the investment manager does not hold a view. The equilibrium expected

returns for the universe of assets are combined with forecast expected returns for a

subset of the assets, to yield a set of posterior expected returns and the optimal active

portfolio.

We implement the Black-Litterman model using the 177 country-industry indices. We

form an optimal portfolio every six months from December 2000 to May 2004, with

1 See also He and Litterman (1999), Bevan and Winkelmann (1998), Litterman et al. (2003), Christodoulakis (2002), Lee, 2000; Satchell and Scowcroft, 2000; and Idzorek, 2004.

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views over the momentum and value zero-investment portfolios generated by the

forecasting models (1) and (2). The performance of the Black-Litterman optimal

portfolio is tracked for the six months following its formation, yielding 47 out-of-

sample, non-overlapping monthly portfolio return observations. Table 3 shows the

forecast returns for the Q51-Q11 and Q15-Q11 zero investment portfolios for each of

the eight re-balancing dates. On each re-balancing date, we employ the zero-investment

portfolio (either momentum or value) with the highest forecast return. These forecasts

are combined with estimates of the equilibrium expected returns of the investment

universe available on that date to form the optimal active portfolio. Of course, it is clear

from Table 3 that the forecasting models potentially generate extreme return forecasts.

For example, in December 2002 the Q15 portfolio is forecast to outperform the Q11

portfolio by 177.33%. Using such forecasts in the standard mean-variance optimisation

framework would lead to unreasonable portfolio weights, and almost certainly an

inferior out-of-sample risk-return trade-off. However, in the Black-Litterman model,

these extreme forecasts are tempered according to the degree of confidence that we

attach to them.

[Table 3]

The Black-Litterman approach is implemented as follows. For an investment universe

of N assets, the Nx1 vector of equilibrium expected excess returns is defined as

E[r] = δΣw (3)

where δ = (E[rm ]− rf ) /σm2 is the market risk aversion coefficient, Σ is the NxN

covariance matrix of asset returns, w is the Nx1 vector of market capitalization weights,

][ mrE is the expected return on the market portfolio, fr is the risk free rate and

σm2 = w'Σw is the variance of the market portfolio return.

In the present case, the universe of assets comprises up to 177 global industry indices,

depending on the data items that are available in a particular month. Excess returns are

defined relative to the US ten-year government bond yield obtained from DataStream.

We use a value of 3.5% for the global market risk premium, which implies a Sharpe

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ratio of about 0.25. The covariance matrix of returns is estimated using a single-factor

model as in Elton et al. (2003). This is necessitated by the large number of assets

relative to the sample available for estimation. On each rebalancing date we use the

previous 60 months of returns to estimate the parameters, iα and iβ of the single factor

model, and an estimate of the residual variance, 2,iεσ , for each industry. The variance of

each industry return is then estimated as 2,

222imii εσσβσ += , and the covariance between

each pair of industries is estimated as 2, mjiji σββσ = , where 2

mσ is the variance of the

market return over the previous 60 months. The covariance matrix is constructed using

annualised values of the individual variances and covariances. As an illustration, Tables

4 and 5 show the capitalisation weights for the 105 global industries that are available

in December 2002, and the equilibrium expected excess returns calculated using (3).

[Tables 4 and 5]

Having defined equilibrium expected returns, the posterior expected return vector,

which combines the equilibrium expected returns given by (3) with our views on a

subset of assets is given by

E[r*] = τΣ( )−1 + P'Ω−1P[ ]−1τΣ( )−1 E[r]+ P'Ω−1Q[ ] (4)

where τ is a scalar, P is a KxN matrix that defines the K assets over which a non-

neutral view is held, Ω is a KxK diagonal matrix that expresses the variance (i.e. the

level of uncertainty) over each view and Q is the Kx1 vector of views in the form of

forecast returns. We define the values of the P matrix as in Idzorek (2004). How much

weight is placed on the vector E[r] (the equilibrium expected returns) and how much is

placed on Q (the forecast expected returns) depends on the values of the scalar τ and

diagonal covariance matrix Ω. In the present case, we incorporate a single set of views,

namely the forecasts for the constituents of either the momentum or the value zero-

investment portfolio, depending on which is forecast to have the highest return.2 For

2 When positive returns are forecast for both the momentum and the value portfolios, both could in principle be incorporated in the Black-Litterman approach. Doing so for

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example, in December 2002, the value strategy Q15-Q11 is forecast to outperform the

momentum strategy, Q15-Q11, and so we incorporate the forecast return for the Q15-

Q11 portfolio. The constituents of the Q15 and Q11 portfolios in December 2002 are

given in Table 6. The equilibrium expected return of the Q15-Q11 portfolio is the

capitalisation weighted average equilibrium expected return of these assets (which can

be deduced from Tables 4 and 5), and is equal to 1.07%. This can be thought of as the

posterior expected return when we attach zero percent confidence to our forecast return

of 177.33%. Conversely, when we attach 100 percent confidence to the forecast return,

our posterior expected return is 177.33%. To incorporate our forecast return for the

Q15-Q11 portfolio, we must therefore specify the confidence with which we hold that

view.

[Table 6]

As in He and Litterman (1999), we calibrate the confidence level on the view expressed

so that the ratio ω i /τ equals the variance of the view, where ω i is the element of the

vector Ω for asset i. The most problematic parameters entering (4) are the scalar τ and

the diagonal covariance matrix of error terms Ω. The off-diagonal elements of Ω are

assumed to be zero because the error terms are residuals, which are assumed to be

independent of one another. The scalar τ determines how close the posterior returns

vector is to the equilibrium returns vector, given the confidence we place on our

forecasts. The more (less) confident we are in our views the larger (smaller) the value

of τ . Since the uncertainty in the mean is much smaller than the uncertainty in the

return itself, τ will be close to zero (see Black and Litterman, 1992). We therefore set

τ to 0.1 and then adjust the confidence level according to our belief about next period’s

performance. Calibrating the confidence level in this remove the need to separately

specify the value of τ since it is only the ratio ω i /τ that enters the Black-Litterman

formula (see He and Litterman, 1999). To adjust the confidence level, we follow Bevan

and Winkelmann (1998) and set ω in such a way that no individual posterior expected

return is more than two standard deviations from its equilibrium value. For the portfolio

formation date December 2002, calibrating the confidence level in this way yields ω =

the first three periods (where both forecast returns are positive for both portfolios) has negligible impact on the overall portfolio performance.

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0.596. Table 7 gives the posterior expected returns for the universe of assets December

2002, including the constituents of the Q15-Q11 portfolio over which we have formed a

view. The posterior expected return of the Q15-Q11 portfolio in December 2000 is

4.15% (compared with the equilibrium expected return of 1.07% and the forecast return

of 177.33%), which implies a confidence level of 1.75%. The weights of the

unconstrained Black-Litterman portfolio are given by

][)( *1 rEwBL−Σ= δ (5)

Table 8 reports the weights of the unconstrained Black-Litterman portfolio in

December 2002.

[Tables 7 and 8]

In practice, of course, investment managers face a variety of constraints (such as the

requirement that only long positions are held, or that the portfolio is beta-neutral with

respect to a particular benchmark). In this paper, we adopt the approach of He and

Litterman (1999) and use the Black-Litterman model to generate posterior expected

returns, and then use the Markowitz model to derive the optimal portfolio subject to a

variety of constraints. Here, we impose the following investment constraints:

• Full investment;

• Portfolio is long-only;

• Benchmark-neutral beta; and

• Tracking error constraint

The long-only constraint applies to those institutional investors that are not allowed

short sell. The benchmark neutrality constraint is based on the assumption that portfolio

managers typically find it very difficult to time the market (see, for example, Grinold

and Kahn, 1999). Finally, we consider three separate tracking error constraints: 300bp,

400bp and 500bp. To impose constraints on the investment portfolio, the posterior

expected returns vector, ][ *rE and the covariance matrix, Σ , are used as inputs to the

standard portfolio optimisation model of Markowitz (1952). Note that the resulting

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constrained portfolio is not optimal, i.e. the excess return per unit of portfolio risk is not

constant across assets. However, the Black-Litterman optimality condition can be

restored by backing out the implied returns from the constrained portfolio using (3),

with the constrained portfolio weights in place of the market portfolio weights. Tables 9

and 10 report the weights, wBL(const ) , and posterior expected returns, E[rconst* ], of the

constrained Black-Litterman portfolio in December 2002 with a tracking error of

300bp.

[Tables 9 and 10]

Before accepting such allocations as final, we analyze the active risk budget. In

particular, we want to ensure that the tracking error of 300bp is made up of risks arising

only from the assets on which we hold a view (for example, in December 2002, from

the five assets in Table 6). In this way, we ensure consistency between our expressed

views and the risks taken by not holding the benchmark portfolio. To measure this, we

employ the marginal risk decomposition method of Litterman (1996), in which the

marginal contribution of asset i is given by

MCi = wBL(const ),i wBL(const )' Σ[ ]wBL(const )

' ΣwBL(const )'[ ]−1/ 2

(6)

Table 11 gives statistics of the constrained Black-Litterman and the benchmark

portfolios in December 2002, assuming a 300bp tracking error. The corresponding

marginal contribution of each of the five assets in Table 6 is given in Table 12. This

shows that the five assets over which we hold views account for over 98% of the

tracking error.

[Tables 11 and 12]

Table 13 reports the annual performance of the constrained Black-Litterman portfolio

from January 2001 through November 2004, for the three levels of tracking error.

Active returns are adjusted for transaction costs, which are very conservatively assumed

to amount to one percent of the transaction value when re-balancing the portfolio. After

allowing for transaction costs, the Black-Litterman portfolio outperforms the

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benchmark on average by 28bp and 68bp for tracking error levels of 400bp and 500bps

respectively. It underperforms the benchmark by 41bp for the tracking error level of

300bp. Although not reported, the Black-Litterman portfolio very significantly

outperforms the benchmark at all three tracking error levels in the absence of

transaction costs. The level of benchmark outperformance therefore increases with

higher active risk levels. Such a conclusion is also confirmed by the ex-post

information ratio. Incorporating the momentum and value zero-investment strategies

into a broader market portfolio therefore avoids large departures from the benchmark

while still producing convincing outperformance, at least at higher tracking error levels,

even in the presence of substantial transaction costs.

[Table 13]

Table 14 reports the annual turnover (as a percentage of portfolio value) arising from

rebalancing the portfolio every six months. We do not report turnover for 2001 since

there is only one rebalancing (in June 2001) and we do not consider the cost of setting

up the portfolio in December 2000. The turnover of the portfolio is relatively modest

given the active returns that it generates, even at the 500bp tracking error level, where

the investment manager has considerable flexibility to alter the portfolio composition.

[Table 14]

Finally, we consider how effective the risk control mechanism is along the lines of

Bevan and Winkelmann (1998). In particular, if our forecasts of risk have been good,

then (roughly) two-thirds of the time, deviations from the benchmark returns should not

exceed the forecast tracking error level.17 The accuracy of our forecasts is directly

related to the confidence level that we have attached to our view assets. We imposed a

two-standard deviation constraint on the Black-Litterman expected returns. To check

how well our confidence level policy has worked, we standardize the monthly active

returns (by dividing actual active returns by the predicted monthly tracking error) for

17 For the annual tracking error of 300bp, the ex ante monthly tracking error is approximately 87bp. This means that the realized monthly return should not deviate from the benchmark return by more than 87bp approximately two-thirds of the time (i.e. for 31 months), under the assumption that returns are normally distributed.

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the three tracking error levels. If our risk control mechanism is effective, than we would

expect active returns to exceed the one-standard deviation limit no more than

approximately one-third of the time (i.e. 16 out of 47 months). Figures 3 plots the

standardized monthly performances for the three tracking error levels. The number of

months where active returns exceed their respective one standard deviations limits

range from 9 (300 and 400bps tracking error levels) to 12 (500bps tracking error level)

months, all of which are well below the threshold of 16.

[Figure 3]

7. Conclusion

Combined value-momentum strategies have been shown to provide above average

returns while also reducing periods of negative performance. We test the success of

such strategies by forming two zero-investment investment approaches. In our global

investment universe, consistent with the extant literature, such strategies indeed yield

superior returns. However, the large rewards of our zero-investment strategies come at

the expense of very high volatility and substantial idiosyncratic risk. From a practical

perspective, portfolio managers are likely to be reluctant to pursue such investment

strategies owing to the very large tracking errors that they generate relative to typical

client-assigned benchmarks.

We solve this potential problem by incorporating the combined value-momentum

strategies into the Black-Litterman portfolio model. This model makes it possible for us

to deviate from the benchmark only to the extent that we express views on certain

value-momentum assets. We obtain such views by forecasting value and momentum

returns ex ante. These views are combined with the equilibrium expected returns that

are imputed from the capitalisation weights of the market portfolio. We further impose

constraints on short-selling, beta-neutrality with respect to the benchmark portfolio, and

three different tracking error levels. The out-of-sample performance of the constrained

Black-Litterman portfolio is promising. By following a conservative policy with respect

to the confidence level with which the views are held, we are able to outperform the

benchmark on average, even in the presence of substantial transaction costs.

17

REFERENCES

Asness, Cliff, R. Burt Porter and Ross Stevens, 2000, “Predicting Stock Returns Using Industry-relative Firm Characteristics”, On Review with the Journal of Finance. Asness, Clifford S. 1997, The Interaction of Value and Momentum Strategies, Financial Analysts Journal, vol. 53, no. 2, 29-36. Asness, Clifford S., Jacques A. Friedman, Robert J. Krail, and John M. Liew, Spring 2000, “Value Versus Growth,” Journal of Portfolio Management, Vol. 26, Issue 3. Bevan, A., and Winkelmann, K. (1998). “Using the Black-Litterman Global Asset Allocation Model: Three Years of Practical Experience.” Fixed Income Research, Goldman, Sachs and Company. Bird R., Whitaker J. 2004, The performance of value and momentum investment portfolios: Recent experience in the major European markets, Part 2, Journal of Asset Management, vol. 5, no. 3, pp. 157-175(19). Black, Fischer, Universal Hedging: Optimizing Currency Risk and Reward in International Equity Portfolios, Financial Analysts Journal, pages 16-22, July-August 1989. Black, F. and Litterman, R. (1990). “Asset Allocation: Combining Investors Views with Market Equilibrium.” Fixed Income Research, Goldman, Sachs and Company, September. Black, F. and Litterman, R. (1991). “Global Asset Allocation with Equities, Bonds, Currencies.” Fixed Income Research, Goldman, Sachs and Company, October. Black, F. and Litterman, R. (1992). “Global Portfolio Optimization.” Financial Analysts Journal, September/October, 28-43. Campbell, John Y. and Robert J. Shiller, 1988. Stock prices, earnings, and expected dividends. Journal of Finance 43, 661-676. Campbell, John Y. and Robert J. Shiller, 1998. Valuation ratios and the long-run stock market outlook. Journal of Portfolio Management, Winter, 11-26. Chan L.K.C. Hamao Y. and Lakonishok J., 1991, Fundamentals and stock returns in Japan, Journal of Finance 46, 1739-1764. Christodoulakis, G.A. (2002). “Bayesian Optimal Portfolio Selection: the Black-Litterman Approach.” Unpublished paper. November. Available online at http://www.staff.city.ac.uk/~gchrist/Teaching/QAP/optimalportfoliobl.pdf Cochrane J., 2001 Asset Pricing, Princeton University Press, Chapter 20. Conrad, J., and Kaul, G., 1998, “An Anatomy of Trading Strategies,” Review of Financial Studies, 11, 489-519.

18

Dahlquist, Magnus and Campbell R. Harvey, 2001, “Global Tactical Asset Allocation”, Working Paper 57, Duke University. Elton, Edwin J., Gruber, Martin J., Brown, Stephen J., Goetzmann, William N., 2003, Modern Portfolio Theory and Investment Analysis, Sixth Edition, Chapter 7. Fama, E.F. and K.R. French, 1992, The cross-section of expected stock returns, Journal of Finance 47, 427–65. Griffin J.M., Martin J.S., Susan J, 2004, Global momentum strategies: A portfolio perspective, Financial Management Association. Grinold, R.C., and Kahn, R.N. (1999). Active Portfolio Management. 2nd ed. New York: McGraw-Hill. Harvey C., February 24, 2000. Global Tactical Asset Allocation, Fuqua School of Business Duke University. Lecture Series. He, G. and Litterman, R. (1999). “The Intuition Behind Black-Litterman Model”. Goldman Sachs Series. Idzorek T.: Step-by-step guide to the BL-model - Incorporating user-specified confidence levels, July 2004 http://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2005/Idzorek_onBL.pdf Jegadeesh N. and Titman S., 1993 Returns to Buying Winners and Selling Losers: Implications for Market Efficiency," with S. Titman, Journal of Finance 55, 65-91. Jegadeesh, N., and Titman, S., 2001. Profitability of momentum strategies: an evaluation of alternative explanations. Journal of Finance 56, 699-720. Lakonishok, J. Shleifer A. and Vishny R., "Contrarian Investment, Extrapolation and Risk" Journal of Finance, December 1994, pp. 1541-1578. Lee, W. (2000). Advanced Theory and Methodology of Tactical Asset Allocation. New York: John Wiley and Sons. Litterman R. et al. (2003), Modern Investment Management: An Equilibrium Approach, John Wiley and Sons. Litterman R. December 1996, Hot Spots and Hedges, Journal of Portfolio Management, Special Issue: 52–75. Litterman, R. and Winkelmann, K., 1998. “Estimating Covariance Matrices.” Risk Management Series, Goldman Sachs and Company, January. Liu N. and Zhang L., 2005, The value spread as a predictor of returns, NBER Working Paper series, 11326.

19

Moerman G. A. 2004, Diversification in euro area stock markets Country vs Industry. European Central Bank Working Paper series, no. 327. Moskowitz and Grinblatt 1999, "Do Industries Explain Momentum?", Journal of Finance, 54, 1249-1290. Richards, A. J., 1997, “Winner-Loser Reversals in National Stock Market Indices: Can They Be Explained?” Journal of Finance, 52, 2129-2144. Rouwenhorst, K. G., 1998, “International Momentum Strategies,” Journal of Finance, 53, 267-284. Satchell, S. and Scowcroft, A. (2000). “A Demystification of the Black-Litterman Model: Managing Quantitative and Traditional Construction.” Journal of Asset Management, September, 138-150.

20

Figure 1 The Performance of Value and Momentum Strategies Relative to the Market

Panel A Momentum

Panel B Value

Notes: The figure plots the monthly return to the momentum investment strategy (Panel A) and the value investment strategy (Panel B) against the monthly return to an investment in the market portfolio that comprises the 177 global industry indices.

21

Figure 2 Forecast versus Realized Value and Momentum Strategy Returns

Panel A Momentum

Panel B Value

Notes: The figure plots the monthly return to the momentum investment strategy (Panel A) and the value investment strategy (Panel B), against the out-of-sample forecasts from the estimated regression models in Table 2.

22

Figure 3 Standardized Returns of the Constrained Black-Litterman Portfolio

Panel A 300bp Tracking Error

-2

-1

0

1

2

Time

Stan

dard

Dev

iatio

n

Panel B 400bp Tracking Error

-2

-1

0

1

2

Time

Stan

dard

Dev

iatio

n

Panel C 500bp Tracking Error

-2

-1

0

1

2

Time

Stan

dard

Dev

iatio

n

Notes: The figure plots the monthly active return of the constrained Black-Litterman portfolio standardized by the forecast tracking error, at the three tracking error levels.

23

Table 1 The Performance of Value and Momentum Strategies Q51-Q11 Q15-Q11 Market

Mean return 12.06 24.12 8.20 Standard deviation 40.21 83.07 14.10 t-statistic 3.12* 3.01* 6.04** Sharpe ratio 0.30 0.29 0.58 Notes: The table reports the mean return and standard deviation of the momentum investment strategy (Q51-Q11), the value investment strategy (Q15-Q11) and a buy and hold investment in the market portfolio that comprises the 177 global industry indices. The t-statistics test the null hypothesis that the mean return is equal to zero. ‘*’ and ‘**’ indicate significance at the 5% and 1% level, respectively. The table also reports the Sharpe ratio for each of the three investment strategies.

24

Table 2 Forecasting Models for the Value and Momentum Strategies Momentum Value Intercept 0.24

(5.12*) -0.68

(-2.77*)

TERMt -9.08 (-4.70*)

-

BMt - 0.90 (2.99*)

R-Squared 0.113 0.181 Notes: The table reports the results of estimating equations (1) and (2) in the main text. t-statistics are reported in parentheses. ‘*’ and ‘**’ indicate significance at the 5% and 1% level, respectively.

25

Table 3 Forecast Returns for the Value and Momentum Portfolios

Q51-Q11 Q15-Q11

December 2000 46.43% 17.01%

June 2001 32.35% 29.28%

December 2001 8.78% 25.76%

June 2002 -14.43% 14.00%

December 2002 -9.57% 177.33%

June 2003 -8.41% 72.69%

December 2003 -16.64% 28.91%

May 2004 -20.09% 22.96%

Notes: The table reports the forecasts for the momentum zero-investment portfolio (Q51-Q11) and the value zero-investment portfolio (Q15-Q11) on each of the portfolio rebalancing dates.

26

Table 4 Market Capitalization Weights in December 2002 MSCI Industry Weight MSCI Industry Weight

Japan OIL & GAS 0.16 UK HOUSEHOLD PRODUCTS 0.16 Japan CHEMICALS 0.72 UK HEALTH CARE EQUIPMENT & SUPPLIES 0.19 Japan CONTAINERS & PACKAGING 0.03 UK PHARMACEUTICALS 2.66 Japan BUILDING PRODUCTS 0.19 UK DIVERSIFIED FIN. SERVICES 0.27 Japan TRADING COMPANIES & DISTRIBUTORS 0.28 UK REAL ESTATE 0.25 Japan COMMERCIAL SERVICES & SUPPLIES 0.30 UK IT SERVICES 0.03 Japan AIR FREIGHT & LOGISTICS 0.08 UK SOFTWARE 0.06 Japan ROAD & RAIL 0.63 UK ELECTRONIC EQUIPMENT & INSTRUMENTS 0.00 Japan AUTO COMPONENTS 0.32 UK DIVERSIFIED TELECOM. SERVICES 0.43 Japan AUTOMOBILES 1.57 UK WIRELESS TELECOM. SERVICES 1.86 Japan LEISURE EQUIPMENT & PRODUCTS 0.31 UK ELECTRIC UTILITIES 0.30 Japan HOTELS, RESTAURANTS & LEISURE 0.07 UK GAS UTILITIES 0.17 Japan MEDIA 0.05 UK MULTI-UTILITIES & UNREGULATED POWER 0.45 Japan SPECIALTY RETAIL 0.11 US ENERGY EQUIPMENT & SERVICES 1.17 Japan FOOD & STAPLES RETAILING 0.21 US OIL & GAS 5.55 Japan BEVERAGES 0.14 US CHEMICALS 1.68 Japan FOOD PRODUCTS 0.28 US CONSTRUCTION MATERIALS 0.06 Japan TOBACCO 0.07 US CONTAINERS & PACKAGING 0.08 Japan HOUSEHOLD PRODUCTS 0.21 US METALS & MINING 0.55 Japan HEALTH CARE EQUIPMENT & SUPPLIES 0.09 US AEROSPACE & DEFENSE 1.86 Japan HEALTH CARE PROVIDERS & SERVICES 0.01 US BUILDING PRODUCTS 0.14 Japan PHARMACEUTICALS 1.09 US CONSTRUCTION & ENGINEERING 0.03 Japan IT SERVICES 0.13 US ELECTRICAL EQUIPMENT 0.46 Japan SOFTWARE 0.06 US INDUSTRIAL CONGLOMERATES 4.89 Japan OFFICE ELECTRONICS 0.62 US MACHINERY 1.20 Japan ELECTRIC UTILITIES 0.82 US TRADING COMPANIES & DISTRIBUTORS 0.06 Japan GAS UTILITIES 0.19 US COMMERCIAL SERVICES & SUPPLIES 2.25 UK OIL & GAS 3.48 US AIR FREIGHT & LOGISTICS 0.66 UK CHEMICALS 0.17 US AIRLINES 0.04 UK CONSTRUCTION MATERIALS 0.10 US ROAD & RAIL 0.57 UK CONTAINERS & PACKAGING 0.04 US AUTO COMPONENTS 0.22 UK METALS & MINING 0.57 US HOUSEHOLD DURABLES 0.45 UK AEROSPACE & DEFENSE 0.13 US LEISURE EQUIPMENT & PRODUCTS 0.28 UK CONSTRUCTION & ENGINEERING 0.02 US TEXTILES, APPAREL & LUXURY GOODS 0.26 UK ELECTRICAL EQUIPMENT 0.01 US HOTELS, RESTAURANTS & LEISURE 1.08 UK INDUSTRIAL CONGLOMERATES 0.11 US MULTILINE RETAIL 3.29 UK MACHINERY 0.07 US SPECIALTY RETAIL 2.22 UK TRADING COMPANIES & DISTRIBUTORS 0.10 US FOOD & STAPLES RETAILING 1.34 UK COMMERCIAL SERVICES & SUPPLIES 0.31 US BEVERAGES 3.21 UK AIR FREIGHT & LOGISTICS 0.05 US FOOD PRODUCTS 1.20 UK ROAD & RAIL 0.03 US TOBACCO 1.28 UK AUTO COMPONENTS 0.04 US HOUSEHOLD PRODUCTS 2.06 UK HOUSEHOLD DURABLES 0.09 US PERSONAL PRODUCTS 0.62 UK HOTELS, RESTAURANTS & LEISURE 0.49 US HEALTH CARE EQUIPMENT & SUPPLIES 2.05 UK MEDIA 0.84 US HEALTH CARE PROVIDERS & SERVICES 1.99 UK INTERNET & CATALOG RETAIL 0.14 US PHARMACEUTICALS 11.18 UK MULTILINE RETAIL 0.23 US DIVERSIFIED FIN. SERVICES 8.12 UK SPECIALTY RETAIL 0.23 US REAL ESTATE 0.43 UK FOOD & STAPLES RETAILING 0.60 US IT SERVICES 0.36 UK BEVERAGES 0.69 US SOFTWARE 5.11 UK FOOD PRODUCTS 0.62 US COMPUTERS & PERIPHERALS 4.08 UK TOBACCO 0.43 US ELECTRIC UTILITIES 2.50 US GAS UTILITIES 0.27 Notes: The table reports the capitalisation weights of the market portfolio of 177 country-industries for December 2002.

27

Table 5 Equilibrium Expected Returns in December 2002 MSCI Industries Returns MSCI Industries Returns

Japan OIL & GAS 2.69 UK HOUSEHOLD PRODUCTS 0.64 Japan CHEMICALS 3.28 UK HEALTH CARE EQUIPMENT & SUPPLIES 1.60 Japan CONTAINERS & PACKAGING 2.58 UK PHARMACEUTICALS 1.65 Japan BUILDING PRODUCTS 2.79 UK DIVERSIFIED FIN. SERVICES 4.98 Japan TRADING COMPANIES & DISTRIBUTORS 1.76 UK REAL ESTATE 1.93 Japan COMMERCIAL SERVICES & SUPPLIES 2.57 UK IT SERVICES 5.44 Japan AIR FREIGHT & LOGISTICS 3.19 UK SOFTWARE 7.41 Japan ROAD & RAIL 1.01 UK ELECTRONIC EQUIPMENT & INSTRUMENTS 3.44 Japan AUTO COMPONENTS 1.57 UK DIVERSIFIED TELECOM. SERVICES 5.48 Japan AUTOMOBILES 2.66 UK WIRELESS TELECOM. SERVICES 3.71 Japan LEISURE EQUIPMENT & PRODUCTS 1.23 UK ELECTRIC UTILITIES 0.29 Japan HOTELS, RESTAURANTS & LEISURE 0.37 UK GAS UTILITIES 2.09 Japan MEDIA 1.84 UK MULTI-UTILITIES & UNREGULATED POWER 0.53 Japan SPECIALTY RETAIL 1.68 US ENERGY EQUIPMENT & SERVICES 4.99 Japan FOOD & STAPLES RETAILING 0.03 US OIL & GAS 2.41 Japan BEVERAGES 1.51 US CHEMICALS 3.39 Japan FOOD PRODUCTS 1.67 US CONSTRUCTION MATERIALS 2.16 Japan TOBACCO 0.79 US CONTAINERS & PACKAGING 6.13 Japan HOUSEHOLD PRODUCTS 1.06 US METALS & MINING 4.79 Japan HEALTH CARE EQUIPMENT & SUPPLIES 2.09 US AEROSPACE & DEFENSE 3.58 Japan HEALTH CARE PROVIDERS & SERVICES 0.76 US BUILDING PRODUCTS 3.28 Japan PHARMACEUTICALS 1.43 US CONSTRUCTION & ENGINEERING 3.41 Japan IT SERVICES 2.96 US ELECTRICAL EQUIPMENT 4.21 Japan SOFTWARE 3.68 US INDUSTRIAL CONGLOMERATES 4.61 Japan OFFICE ELECTRONICS 2.75 US MACHINERY 3.82 Japan ELECTRIC UTILITIES 1.24 US TRADING COMPANIES & DISTRIBUTORS 2.29 Japan GAS UTILITIES 1.60 US COMMERCIAL SERVICES & SUPPLIES 4.05 UK OIL & GAS 3.22 US AIR FREIGHT & LOGISTICS 2.96 UK CHEMICALS 2.81 US AIRLINES 4.29 UK CONSTRUCTION MATERIALS 3.19 US ROAD & RAIL 1.88 UK CONTAINERS & PACKAGING 2.18 US AUTO COMPONENTS 3.36 UK METALS & MINING 4.88 US HOUSEHOLD DURABLES 4.26 UK AEROSPACE & DEFENSE 3.93 US LEISURE EQUIPMENT & PRODUCTS 2.25 UK CONSTRUCTION & ENGINEERING 2.67 US TEXTILES, APPAREL & LUXURY GOODS 4.03 UK ELECTRICAL EQUIPMENT 3.64 US HOTELS, RESTAURANTS & LEISURE 3.63 UK INDUSTRIAL CONGLOMERATES 2.32 US MULTILINE RETAIL 4.24 UK MACHINERY 5.56 US SPECIALTY RETAIL 5.17 UK TRADING COMPANIES & DISTRIBUTORS 3.53 US FOOD & STAPLES RETAILING 2.20 UK COMMERCIAL SERVICES & SUPPLIES 3.14 US BEVERAGES 2.13 UK AIR FREIGHT & LOGISTICS 3.70 US FOOD PRODUCTS 1.60 UK ROAD & RAIL 2.77 US TOBACCO 1.33 UK AUTO COMPONENTS 2.62 US HOUSEHOLD PRODUCTS 0.99 UK HOUSEHOLD DURABLES 3.34 US PERSONAL PRODUCTS 3.00 UK HOTELS, RESTAURANTS & LEISURE 3.38 US HEALTH CARE EQUIPMENT & SUPPLIES 1.55 UK MEDIA 4.32 US HEALTH CARE PROVIDERS & SERVICES 2.22 UK INTERNET & CATALOG RETAIL 1.13 US PHARMACEUTICALS 2.92 UK MULTILINE RETAIL 1.73 US DIVERSIFIED FIN. SERVICES 5.83 UK SPECIALTY RETAIL 2.50 US REAL ESTATE 0.99 UK FOOD & STAPLES RETAILING 1.14 US IT SERVICES 5.43 UK BEVERAGES 1.06 US SOFTWARE 8.00 UK FOOD PRODUCTS 0.93 US COMPUTERS & PERIPHERALS 6.79 UK TOBACCO 0.44 US ELECTRIC UTILITIES 0.78 US GAS UTILITIES 2.84 Notes: The table reports the equilibrium expected returns for the market portfolio of 177 country-industries imputed using equation (3) in the main text for December 2002.

28

Table 6 Composition of the Q15 and Q11 Portfolios in December 2002 Q15 – Expected Outperforming Assets Q11 – Expected Underperforming Assets

UK AEROSPACE & DEFENSE UK AUTO COMPONENTS

UK INDUSTRIAL CONGLOMERATES US CONSTRUCTION & ENGINEERING

UK MEDIA

Notes: The table reports the country-industries in the Q15 portfolio (which is expected to outperform and the Q11 portfolio (which is expected to underperform) in December 2002.

29

Table 7 Posterior Expected Returns for the Market Portfolio in December 2002 MSCI Industries Returns MSCI Industries Returns

Japan OIL and GAS 2.85 UK HOUSEHOLD PRODUCTS 0.67 Japan CHEMICALS 3.47 UK HEALTH CARE EQUIPMENT and SUPPLIES 1.69 Japan CONTAINERS and PACKAGING 2.73 UK PHARMACEUTICALS 1.73 Japan BUILDING PRODUCTS 2.95 UK DIVERSIFIED FIN. SERVICES 5.26 Japan TRADING COMPANIES and DISTRIBUTORS 1.86 UK REAL ESTATE 2.04 Japan COMMERCIAL SERVICES and SUPPLIES 2.72 UK IT SERVICES 5.76 Japan AIR FREIGHT and LOGISTICS 3.38 UK SOFTWARE 7.84 Japan ROAD and RAIL

1.07 UK ELECTRONIC EQUIPMENT and INSTRUMENTS 3.64

Japan AUTO COMPONENTS 1.66 UK DIVERSIFIED TELECOM. SERVICES 5.79 Japan AUTOMOBILES 2.81 UK WIRELESS TELECOM. SERVICES 3.91 Japan LEISURE EQUIPMENT and PRODUCTS 1.30 UK ELECTRIC UTILITIES 0.30 Japan HOTELS, RESTAURANTS and LEISURE 0.39 UK GAS UTILITIES 2.20 Japan MEDIA

1.95 UK MULTI-UTILITIES and UNREGULATED POWER 0.56

Japan SPECIALTY RETAIL 1.78 US ENERGY EQUIPMENT and SERVICES 5.26 Japan FOOD and STAPLES RETAILING 0.03 US OIL and GAS 2.53 Japan BEVERAGES 1.59 US CHEMICALS 3.58 Japan FOOD PRODUCTS 1.77 US CONSTRUCTION MATERIALS 2.28 Japan TOBACCO 0.83 US CONTAINERS and PACKAGING 6.48 Japan HOUSEHOLD PRODUCTS 1.12 US METALS and MINING 5.06 Japan HEALTH CARE EQUIPMENT and SUPPLIES 2.21 US AEROSPACE and DEFENSE 3.78 Japan HEALTH CARE PROVIDERS and SERVICES 0.81 US BUILDING PRODUCTS 3.47 Japan PHARMACEUTICALS 1.50 US CONSTRUCTION and ENGINEERING 1.62 Japan IT SERVICES 3.12 US ELECTRICAL EQUIPMENT 4.46 Japan SOFTWARE 3.89 US INDUSTRIAL CONGLOMERATES 4.86 Japan OFFICE ELECTRONICS 2.91 US MACHINERY 4.03 Japan ELECTRIC UTILITIES 1.31 US TRADING COMPANIES and DISTRIBUTORS 2.42 Japan GAS UTILITIES 1.70 US COMMERCIAL SERVICES and SUPPLIES 4.28 UK OIL and GAS 3.39 US AIR FREIGHT and LOGISTICS 3.13 UK CHEMICALS 2.97 US AIRLINES 4.54 UK CONSTRUCTION MATERIALS 3.38 US ROAD and RAIL 1.98 UK CONTAINERS and PACKAGING 2.31 US AUTO COMPONENTS 3.56 UK METALS and MINING 5.16 US HOUSEHOLD DURABLES 4.51 UK AEROSPACE and DEFENSE 4.47 US LEISURE EQUIPMENT and PRODUCTS 2.38 UK CONSTRUCTION and ENGINEERING 2.82 US TEXTILES, APPAREL and LUXURY GOODS 4.26 UK ELECTRICAL EQUIPMENT 3.85 US HOTELS, RESTAURANTS and LEISURE 3.83 UK INDUSTRIAL CONGLOMERATES 2.69 US MULTILINE RETAIL 4.47 UK MACHINERY 5.88 US SPECIALTY RETAIL 5.46 UK TRADING COMPANIES and DISTRIBUTORS 3.73 US FOOD and STAPLES RETAILING 2.32 UK COMMERCIAL SERVICES and SUPPLIES 3.32 US BEVERAGES 2.24 UK AIR FREIGHT and LOGISTICS 3.91 US FOOD PRODUCTS 1.68 UK ROAD and RAIL 2.93 US TOBACCO 1.39 UK AUTO COMPONENTS 1.58 US HOUSEHOLD PRODUCTS 1.04 UK HOUSEHOLD DURABLES 3.53 US PERSONAL PRODUCTS 3.17 UK HOTELS, RESTAURANTS and LEISURE 3.58 US HEALTH CARE EQUIPMENT and SUPPLIES 1.63 UK MEDIA 6.33 US HEALTH CARE PROVIDERS and SERVICES 2.34 UK INTERNET and CATALOG RETAIL 1.20 US PHARMACEUTICALS 3.05 UK MULTILINE RETAIL 1.83 US DIVERSIFIED FIN. SERVICES 6.14 UK SPECIALTY RETAIL 2.65 US REAL ESTATE 1.04 UK FOOD and STAPLES RETAILING 1.21 US IT SERVICES 5.74 UK BEVERAGES 1.12 US SOFTWARE 8.42 UK FOOD PRODUCTS 0.98 US COMPUTERS and PERIPHERALS 7.15 UK TOBACCO 0.47 US ELECTRIC UTILITIES 0.81 US GAS UTILITIES 3.00

Notes: The table reports the posterior expected returns for the market portfolio of 177 country-industries in December 2002, computed using equation (4) in the main text, incorporating the views on the assets in the Q15 and Q11 portfolios.

30

Table 8 Weights of the Unconstrained Black-Litterman Portfolio in December 2002

MSCI Industries Weights MSCI Industries Weights

Japan OIL and GAS 0.16 UK HOUSEHOLD PRODUCTS 0.16 Japan CHEMICALS 0.72 UK HEALTH CARE EQUIPMENT and SUPPLIES 0.19 Japan CONTAINERS and PACKAGING 0.03 UK PHARMACEUTICALS 2.66 Japan BUILDING PRODUCTS 0.19 UK DIVERSIFIED FIN. SERVICES 0.27 Japan TRADING COMPANIES and DISTRIBUTORS 0.28 UK REAL ESTATE 0.25 Japan COMMERCIAL SERVICES and SUPPLIES 0.30 UK IT SERVICES 0.03 Japan AIR FREIGHT and LOGISTICS 0.08 UK SOFTWARE 0.06 Japan ROAD and RAIL

0.63 UK ELECTRONIC EQUIPMENT and INSTRUMENTS 0.00

Japan AUTO COMPONENTS 0.32 UK DIVERSIFIED TELECOM. SERVICES 0.43 Japan AUTOMOBILES 1.57 UK WIRELESS TELECOM. SERVICES 1.86 Japan LEISURE EQUIPMENT and PRODUCTS 0.31 UK ELECTRIC UTILITIES 0.30 Japan HOTELS, RESTAURANTS and LEISURE 0.07 UK GAS UTILITIES 0.17 Japan MEDIA

0.05 UK MULTI-UTILITIES and UNREGULATED POWER 0.45

Japan SPECIALTY RETAIL 0.11 US ENERGY EQUIPMENT and SERVICES 1.17 Japan FOOD and STAPLES RETAILING 0.21 US OIL and GAS 5.55 Japan BEVERAGES 0.14 US CHEMICALS 1.68 Japan FOOD PRODUCTS 0.28 US CONSTRUCTION MATERIALS 0.06 Japan TOBACCO 0.07 US CONTAINERS and PACKAGING 0.08 Japan HOUSEHOLD PRODUCTS 0.21 US METALS and MINING 0.55 Japan HEALTH CARE EQUIPMENT and SUPPLIES 0.09 US AEROSPACE and DEFENSE 1.86 Japan HEALTH CARE PROVIDERS and SERVICES 0.01 US BUILDING PRODUCTS 0.14 Japan PHARMACEUTICALS 1.09 US CONSTRUCTION and ENGINEERING -9.71 Japan IT SERVICES 0.13 US ELECTRICAL EQUIPMENT 0.46 Japan SOFTWARE 0.06 US INDUSTRIAL CONGLOMERATES 4.89 Japan OFFICE ELECTRONICS 0.62 US MACHINERY 1.20 Japan ELECTRIC UTILITIES 0.82 US TRADING COMPANIES and DISTRIBUTORS 0.06 Japan GAS UTILITIES 0.19 US COMMERCIAL SERVICES and SUPPLIES 2.25 UK OIL and GAS 3.48 US AIR FREIGHT and LOGISTICS 0.66 UK CHEMICALS 0.17 US AIRLINES 0.04 UK CONSTRUCTION MATERIALS 0.10 US ROAD and RAIL 0.57 UK CONTAINERS and PACKAGING 0.04 US AUTO COMPONENTS 0.22 UK METALS and MINING 0.57 US HOUSEHOLD DURABLES 0.45 UK AEROSPACE and DEFENSE 2.41 US LEISURE EQUIPMENT and PRODUCTS 0.28 UK CONSTRUCTION and ENGINEERING 0.02 US TEXTILES, APPAREL and LUXURY GOODS 0.26 UK ELECTRICAL EQUIPMENT 0.01 US HOTELS, RESTAURANTS and LEISURE 1.08 UK INDUSTRIAL CONGLOMERATES 1.98 US MULTILINE RETAIL 3.29 UK MACHINERY 0.07 US SPECIALTY RETAIL 2.22 UK TRADING COMPANIES and DISTRIBUTORS 0.10 US FOOD and STAPLES RETAILING 1.34 UK COMMERCIAL SERVICES and SUPPLIES 0.31 US BEVERAGES 3.21 UK AIR FREIGHT and LOGISTICS 0.05 US FOOD PRODUCTS 1.20 UK ROAD and RAIL 0.03 US TOBACCO 1.28 UK AUTO COMPONENTS -9.30 US HOUSEHOLD PRODUCTS 2.06 UK HOUSEHOLD DURABLES 0.09 US PERSONAL PRODUCTS 0.62 UK HOTELS, RESTAURANTS and LEISURE 0.49 US HEALTH CARE EQUIPMENT and SUPPLIES 2.05 UK MEDIA 15.77 US HEALTH CARE PROVIDERS and SERVICES 1.99 UK INTERNET and CATALOG RETAIL 0.14 US PHARMACEUTICALS 11.18 UK MULTILINE RETAIL 0.23 US DIVERSIFIED FIN. SERVICES 8.12 UK SPECIALTY RETAIL 0.23 US REAL ESTATE 0.43 UK FOOD and STAPLES RETAILING 0.60 US IT SERVICES 0.36 UK BEVERAGES 0.69 US SOFTWARE 5.11 UK FOOD PRODUCTS 0.62 US COMPUTERS and PERIPHERALS 4.08 UK TOBACCO 0.43 US ELECTRIC UTILITIES 2.50 US GAS UTILITIES 0.27

Notes: The table reports the weights of the unconstrained portfolio in December 2002, computed using equation (5) in the main text.

31

Table 9 Weights of the Constrained Black-Litterman Portfolio in December 2002 MSCI Industries Weights MSCI Industries Weights

Japan OIL & GAS 0.13 UK HOUSEHOLD PRODUCTS 0.18 Japan CHEMICALS 0.62 UK HEALTH CARE EQUIPMENT & SUPPLIES 0.16 Japan CONTAINERS & PACKAGING 0.00 UK PHARMACEUTICALS 2.41 Japan BUILDING PRODUCTS 0.15 UK DIVERSIFIED FIN. SERVICES 0.19 Japan TRADING COMPANIES & DISTRIBUTORS 0.25 UK REAL ESTATE 0.21 Japan COMMERCIAL SERVICES & SUPPLIES 0.25 UK IT SERVICES 0.01 Japan AIR FREIGHT & LOGISTICS 0.05 UK SOFTWARE 0.01 Japan ROAD & RAIL 0.57 UK ELECTRONIC EQUIPMENT & INSTRUMENTS 0.00 Japan AUTO COMPONENTS 0.28 UK DIVERSIFIED TELECOM. SERVICES 0.35 Japan AUTOMOBILES 1.40 UK WIRELESS TELECOM. SERVICES 1.67 Japan LEISURE EQUIPMENT & PRODUCTS 0.28 UK ELECTRIC UTILITIES 0.30 Japan HOTELS, RESTAURANTS & LEISURE 0.08 UK GAS UTILITIES 0.13 Japan MEDIA 0.03 UK MULTI-UTILITIES & UNREGULATED POWER 0.42 Japan SPECIALTY RETAIL 0.09 US ENERGY EQUIPMENT & SERVICES 1.03 Japan FOOD & STAPLES RETAILING 0.22 US OIL & GAS 5.00 Japan BEVERAGES 0.12 US CHEMICALS 1.47 Japan FOOD PRODUCTS 0.24 US CONSTRUCTION MATERIALS 0.03 Japan TOBACCO 0.07 US CONTAINERS & PACKAGING 0.04 Japan HOUSEHOLD PRODUCTS 0.19 US METALS & MINING 0.45 Japan HEALTH CARE EQUIPMENT & SUPPLIES 0.07 US AEROSPACE & DEFENSE 1.64 Japan HEALTH CARE PROVIDERS & SERVICES 0.03 US BUILDING PRODUCTS 0.11 Japan PHARMACEUTICALS 0.99 US CONSTRUCTION & ENGINEERING 0.00 Japan IT SERVICES 0.10 US ELECTRICAL EQUIPMENT 0.32 Japan SOFTWARE 0.05 US INDUSTRIAL CONGLOMERATES 4.34 Japan OFFICE ELECTRONICS 0.54 US MACHINERY 1.03 Japan ELECTRIC UTILITIES 0.74 US TRADING COMPANIES & DISTRIBUTORS 0.03 Japan GAS UTILITIES 0.17 US COMMERCIAL SERVICES & SUPPLIES 1.91 UK OIL & GAS 3.12 US AIR FREIGHT & LOGISTICS 0.58 UK CHEMICALS 0.13 US AIRLINES 0.00 UK CONSTRUCTION MATERIALS 0.06 US ROAD & RAIL 0.50 UK CONTAINERS & PACKAGING 0.03 US AUTO COMPONENTS 0.17 UK METALS & MINING 0.46 US HOUSEHOLD DURABLES 0.34 UK AEROSPACE & DEFENSE 3.92 US LEISURE EQUIPMENT & PRODUCTS 0.23 UK CONSTRUCTION & ENGINEERING 0.01 US TEXTILES, APPAREL & LUXURY GOODS 0.19 UK ELECTRICAL EQUIPMENT 0.00 US HOTELS, RESTAURANTS & LEISURE 0.91 UK INDUSTRIAL CONGLOMERATES 3.23 US MULTILINE RETAIL 2.92 UK MACHINERY 0.04 US SPECIALTY RETAIL 1.93 UK TRADING COMPANIES & DISTRIBUTORS 0.07 US FOOD & STAPLES RETAILING 1.19 UK COMMERCIAL SERVICES & SUPPLIES 0.25 US BEVERAGES 2.90 UK AIR FREIGHT & LOGISTICS 0.02 US FOOD PRODUCTS 1.08 UK ROAD & RAIL 0.02 US TOBACCO 1.16 UK AUTO COMPONENTS 0.00 US HOUSEHOLD PRODUCTS 1.87 UK HOUSEHOLD DURABLES 0.06 US PERSONAL PRODUCTS 0.54 UK HOTELS, RESTAURANTS & LEISURE 0.40 US HEALTH CARE EQUIPMENT & SUPPLIES 1.85 UK MEDIA 5.50 US HEALTH CARE PROVIDERS & SERVICES 1.79 UK INTERNET & CATALOG RETAIL 0.13 US PHARMACEUTICALS 10.12 UK MULTILINE RETAIL 0.20 US DIVERSIFIED FIN. SERVICES 7.23 UK SPECIALTY RETAIL 0.19 US REAL ESTATE 0.39 UK FOOD & STAPLES RETAILING 0.54 US IT SERVICES 0.29 UK BEVERAGES 0.63 US SOFTWARE 4.58 UK FOOD PRODUCTS 0.56 US COMPUTERS & PERIPHERALS 3.65 UK TOBACCO 0.40 US ELECTRIC UTILITIES 2.28 US GAS UTILITIES 0.22

Notes: The table reports the weights of the constrained portfolio in December 2002, computed using standard mean-variance optimisation with the posterior expected returns from Table 7 and the estimated variance-covariance matrix of returns as inputs.

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Table 10 Expected Returns of the Constrained Black-Litterman Portfolio in December 2002

MSCI Industries Returns MSCI Industries Returns

Japan OIL & GAS 2.71 UK HOUSEHOLD PRODUCTS 0.64 Japan CHEMICALS 3.29 UK HEALTH CARE EQUIPMENT & SUPPLIES 1.60 Japan CONTAINERS & PACKAGING 2.60 UK PHARMACEUTICALS 1.64 Japan BUILDING PRODUCTS 2.80 UK DIVERSIFIED FIN. SERVICES 5.00 Japan TRADING COMPANIES & DISTRIBUTORS 1.76 UK REAL ESTATE 1.94 Japan COMMERCIAL SERVICES & SUPPLIES 2.58 UK IT SERVICES 5.47 Japan AIR FREIGHT & LOGISTICS 3.21 UK SOFTWARE 7.45 Japan ROAD & RAIL 1.01 UK ELECTRONIC EQUIPMENT & INSTRUMENTS 3.46 Japan AUTO COMPONENTS 1.58 UK DIVERSIFIED TELECOM. SERVICES 5.50 Japan AUTOMOBILES 2.67 UK WIRELESS TELECOM. SERVICES 3.70 Japan LEISURE EQUIPMENT & PRODUCTS 1.24 UK ELECTRIC UTILITIES 0.29 Japan HOTELS, RESTAURANTS & LEISURE 0.37 UK GAS UTILITIES 2.10 Japan MEDIA 1.85 UK MULTI-UTILITIES & UNREGULATED POWER 0.53 Japan SPECIALTY RETAIL 1.69 US ENERGY EQUIPMENT & SERVICES 5.00 Japan FOOD & STAPLES RETAILING 0.03 US OIL & GAS 2.40 Japan BEVERAGES 1.51 US CHEMICALS 3.40 Japan FOOD PRODUCTS 1.68 US CONSTRUCTION MATERIALS 2.17 Japan TOBACCO 0.79 US CONTAINERS & PACKAGING 6.16 Japan HOUSEHOLD PRODUCTS 1.07 US METALS & MINING 4.81 Japan HEALTH CARE EQUIPMENT & SUPPLIES 2.10 US AEROSPACE & DEFENSE 3.58 Japan HEALTH CARE PROVIDERS & SERVICES 0.77 US BUILDING PRODUCTS 3.30 Japan PHARMACEUTICALS 1.43 US CONSTRUCTION & ENGINEERING 3.42 Japan IT SERVICES 2.97 US ELECTRICAL EQUIPMENT 4.23 Japan SOFTWARE 3.70 US INDUSTRIAL CONGLOMERATES 4.61 Japan OFFICE ELECTRONICS 2.76 US MACHINERY 3.83 Japan ELECTRIC UTILITIES 1.25 US TRADING COMPANIES & DISTRIBUTORS 2.30 Japan GAS UTILITIES 1.61 US COMMERCIAL SERVICES & SUPPLIES 4.07 UK OIL & GAS 3.22 US AIR FREIGHT & LOGISTICS 2.97 UK CHEMICALS 2.82 US AIRLINES 4.32 UK CONSTRUCTION MATERIALS 3.21 US ROAD & RAIL 1.88 UK CONTAINERS & PACKAGING 2.19 US AUTO COMPONENTS 3.38 UK METALS & MINING 4.90 US HOUSEHOLD DURABLES 4.28 UK AEROSPACE & DEFENSE 4.48 US LEISURE EQUIPMENT & PRODUCTS 2.26 UK CONSTRUCTION & ENGINEERING 2.68 US TEXTILES, APPAREL & LUXURY GOODS 4.04 UK ELECTRICAL EQUIPMENT 3.66 US HOTELS, RESTAURANTS & LEISURE 3.64 UK INDUSTRIAL CONGLOMERATES 2.73 US MULTILINE RETAIL 4.24 UK MACHINERY 5.58 US SPECIALTY RETAIL 5.18 UK TRADING COMPANIES & DISTRIBUTORS 3.55 US FOOD & STAPLES RETAILING 2.20 UK COMMERCIAL SERVICES & SUPPLIES 3.16 US BEVERAGES 2.12 UK AIR FREIGHT & LOGISTICS 3.72 US FOOD PRODUCTS 1.60 UK ROAD & RAIL 2.79 US TOBACCO 1.31 UK AUTO COMPONENTS 2.63 US HOUSEHOLD PRODUCTS 0.98 UK HOUSEHOLD DURABLES 3.36 US PERSONAL PRODUCTS 3.01 UK HOTELS, RESTAURANTS & LEISURE 3.40 US HEALTH CARE EQUIPMENT & SUPPLIES 1.55 UK MEDIA 4.90 US HEALTH CARE PROVIDERS & SERVICES 2.22 UK INTERNET & CATALOG RETAIL 1.14 US PHARMACEUTICALS 2.88 UK MULTILINE RETAIL 1.74 US DIVERSIFIED FIN. SERVICES 5.82 UK SPECIALTY RETAIL 2.52 US REAL ESTATE 0.99 UK FOOD & STAPLES RETAILING 1.15 US IT SERVICES 5.45 UK BEVERAGES 1.06 US SOFTWARE 7.97 UK FOOD PRODUCTS 0.93 US COMPUTERS & PERIPHERALS 6.77 UK TOBACCO 0.44 US ELECTRIC UTILITIES 0.77 US GAS UTILITIES 2.85

Notes: The table reports the expected returns of the constrained portfolio in December 2002, imputed from Equation (3) in the main text, using the constrained weights from Table (9) in place of the market portfolio weights.

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Table 11 Characteristics of the Benchmark Portfolio and the Constrained Black-Litterman Portfolio in December 2002

Benchmark

Portfolio

Black-Litterman

Portfolio

Return 3.500% 3.637%

Standard Deviation 15.16% 15.45%

Beta 1.00 1.00

Active Return - 0.137%

Active Risk - 3.00%

Sharpe ratio 0.2308 0.2354

Information Ratio - 0.0457 Notes: The table reports the return, standard deviation, beta and Sharpe ratio of the benchmark portfolio and the constrained Black-Litterman Portfolio, and the active risk, active return and information ratio of the Black-Litterman portfolio in December 2002.

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Table 12 Contribution of Active Risk of the View Assets at 300bp Tracking Error in December 2002

Q15 – Expected Outperforming Assets Percent Contribution

UK AEROSPACE & DEFENSE 35.00

UK INDUSTRIAL CONGLOMERATES 35.40

UK MEDIA 28.52

Q11 – Expected Underperforming Assets

UK AUTO COMPONENTS 0.00

US CONSTRUCTION & ENGINEERING 0.00

Total Share of the Tracking Error 98.92

Notes: The table reports the marginal contribution of each of the view assets to the active risk of the constrained Black-Litterman portfolio using the decomposition given by Equation (6) in the main text.

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Table 13 Performance of the Constrained Black-Litterman Portfolio 300 bps 400 bps 500 bps 2001 -0.64 -0.70 -0.17 2002 0.63 1.19 0.10 2003 -0.65 -1.21 -3.35 2004 -0.99 1.88 6.16 Average -0.41 0.28 0.68 Ex-Post Information Ratio -0.14 0.07 0.14 Notes: The table reports the transaction cost adjusted performance of the constrained Black-Litterman portfolio at tracking error levels of 300bp, 400bp and 500bp. The table reports the excess return (in percent) over the market portfolio in each of the four evaluation years and the average across the four years. It also reports the ex post information ratio.

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Table 14 Turnover of the Black-Litterman Portfolio

Notes: The table reports the turnover (as a percentage of portfolio value) of the constrained Black-Litterman Portfolio in each of the four years of the evaluation period and the average across all four years..

300bp 400bp 500bp

2001 - - - 2002 35.91 53.72 58.45 2003 39.34 51.44 63.26 2004 37.56 49.30 60.91 Average 37.60 51.49 60.87