Setya Pambudi S3511774 Supervisor: Prof. Dr. R.E. Wessels

(1)

Master Thesis

Empirical Examination of the Profitability of Momentum Investment

Strategies in the United Kingdom Stock Market

University of Groningen

2019

Setya Pambudi S3511774

Supervisor:

Prof. Dr. R.E. Wessels

Abstract

(2)

1 1. Introduction

Many people invest in company stocks with the hope of gaining abnormal returns. However, some

studies show that abnormal returns from the stock market cannot be easily obtained. Fama (1970)

suggests that markets are efficient; in other words, prices will always fully reflect available

information, and it will be impossible to consistently beat the market. Since so many studies have

already shown market efficiency, can any investment strategy be used to obtain abnormal returns

consistently?

Jegadeesh and Titman (1993) show that taking long position on equally weighted, top-performing

decile (winner) portfolios and short position on equally weighted, bottom-performing decile (loser)

portfolios can yield abnormal returns. By utilizing their idea, this paper tests investment strategies

using zero-investment, zero-beta portfolios that are constructed based on the momentum effect.

The portfolios are built from the stocks included in the FTSE 350 Index from 1996 to 2016. This

paper contributes to the financial literature by testing the momentum strategies with the different

methods used by Jegadeesh and Titman (1993), including beta-weighted portfolios and the recent

data available from the United Kingdom stock market. This thesis attempts to answer the question

about the profitability of momentum strategies after controlling for market risks.

To construct zero-investment, zero-beta portfolios, both winner and loser portfolios must be built

beforehand. The winner and the loser portfolios are respectively constructed from the

top-performing and the bottom-top-performing deciles based on a period of historical return. To control

for the risks of the investment portfolios, the winner and the loser portfolios are beta weighted so

that the average beta of both portfolios is 1. The zero-investment, zero-beta portfolios are

constructed by simultaneously taking long position on the winner portfolios and short position on

the loser portfolios.

The rest of this paper continues as follows. Section 2 presents an overview of the literature relevant

to investment strategies and the momentum effect. Sections 3 and 4 describe the methodology and

the data used in this study, respectively. Section 5 reports the main results. Section 6 concludes

this paper.

2. Relevant Literature

(3)

2 selection by using the mean-variance analysis, as well as on Tobin’s (1958) work, where he

presents the separation theorem, a concept that uses lending and borrowing in portfolio formation.

By using the theorem, any investor’s optimal portfolio choice can be constructed by using the

market portfolio and a risk-free instrument, and the portfolio will lie on the capital market line

(CML).

Fama (1965) defines the random walk theory as the condition where the future path of a security’s

price level is no more predictable than the path of a series of cumulated random numbers. To test

the random walk theory, he uses three approaches to determine the dependence of stock price

series—the serial correlation model, the run tests, and Alexander’s filter technique. In his work,

he uses the daily prices for each of the 30 stocks of the Dow Jones Industrial Average from the

end of 1957 to 1962 and concludes that successive price changes are independent.

This finding is continued with his (Fama, 1970) introduction of the efficient market hypothesis

(EMH). The EMH states that a market is efficient when the stock price always reflects all available

information. The idea is that price movements only occur when new, relevant information is

released. As soon as the information is released, the price immediately adjusts to a new

equilibrium. The EMH is divided into three categories, namely weak, semi-strong, and strong

forms of market efficiency. The weak form means that stock prices already reflect all historical

information. The semi-strong form indicates that stock prices already reflect all historical and

publicly available information. The strong form signifies that stock prices already reflect all

historical, publicly available, and private information. Based on the EMH theory, strategies using

technical analysis or the momentum factor must not work since stock prices already reflect all

historical price information, and future stock price movements cannot be predicted by using

historical price information.

(4)

3 Bhandari (1988) discovers that stock returns are positively correlated to the debt-to-equity ratio,

which implies that leverage helps explain the cross-section of expected returns.

Fama and French (1992, 1993, 1996) encapsulate those anomalies in their three-factor model. They

argue that the market beta is insufficient to explain the cross-section of expected returns, so they

add two more factors, namely firm size and book-to-market ratio, to the market factor. Fama and

French (1992) explain that the combination of size and book-to-market equity can absorb the roles

of leverage and earning-to-price ratios. Fama and French (1996) acknowledge that their model

cannot explain the momentum effect identified by Jegadeesh and Titman (1993).

Carhart (1997) employs the CAPM, Fama and French’s (1992) three-factor model, and his own

four-factor model to explain mutual fund performances. He uses the data on 1,892 equity funds

from 1962 to 1993. For the four-factor model, he uses Fama and French’s (1993) three-factor

model and adds the momentum factor to it. In constructing the momentum factor, Carhart (1997)

uses 30

th

- and 70

th

-percentile break points to identify the winner and the loser stocks. He finds that

the four-factor model reduces the average pricing errors of the CAPM and the three-factor model.

He also observes that the returns on buying the previous year’s top-decile mutual funds and selling

the previous year’s bottom-decile mutual funds total approximately 8% per year. Momentum funds

are found to have high expense and turnover ratios, indicating that transaction costs consume the

gains obtained by following the momentum strategy. Lastly, the highly significant momentum

factor in mutual funds is not caused by the funds intentionally following the momentum strategy;

rather, they end up holding the winning stocks from the previous year by chance.

(5)

4 three-factor model or the CAPM in capturing the average returns of the portfolios, depending on

the region.

Jegadeesh and Titman (1993) document the so-called momentum factor. Fundamentally, the

momentum factor refers to the condition where winner stocks (stocks on the decile with the best

performance over the last period) continue to win, and losers stocks (stocks on the decile with the

worst performance over the last period) continue to lose. Jegadeesh and Titman (1993) report that

the investment strategy of buying stocks whose prices have gone up over the past periods and

taking a short position in the stocks with the lowest returns over the same periods can yield

significant, positive abnormal returns.

Jegadeesh and Titman (1993) use the daily returns’ file of stocks listed on the NYSE and the

AMEX from 1965 to 1989 and formulate investment strategies where they base stock selections

on 3-, 6-, 9-, and 12-month historical returns, rank their performance, and form 10 equally

weighted portfolios. The top and the lowest deciles of the ranked stock portfolios are called P10

and P1, respectively. These portfolios are then kept for 3, 6, 9, and 12 months. The study finds that

the zero-investment portfolio J12/K3 (12-month formation period/3-month holding period), which

buys the top decile and sells the lowest decile of the ranked portfolios, yields 1.31% average

monthly returns.

To check whether the returns are due to the systematic risk and the size effect, the CAPM beta and

the average market capitalization are calculated for the portfolios. Jegadeesh and Titman (1993)

find that the beta of P1 is greater than that of P10, and the market capitalization of P10 is larger

than that of P1. These findings suggest that the returns are not due to the systematic risk (since the

loser’s beta is greater than that of the winner) or the size effect (since the winner’s average market

capitalization is larger than that of the loser).

(6)

5 factor has a profound effect on small firms and that a correlation exists between the European and

the US momentum factors, suggesting a common reason driving the abnormal returns. His findings

support those of Jegadeesh and Titman (1993) and confirm the idea that the momentum returns

observed on the United States stock market are not just the results of data snooping.

Conrad and Kaul (1998) implement 120 return-based trading strategies to analyze the cause of

their profits. They investigate all available securities on the NYSE and the AMEX from 1926 to

1989. Their methodology follows those of Lehmann (1990) and Lo and MacKinlay (1990) but

differs from that of Jegadeesh and Titman (1993) by making the security weights proportional to

their past performance. By doing so, they capture the belief that past extreme-price movements are

followed by future extreme-price movements, and the security weights allow them to decompose

the momentum profit. They find that the momentum effect is not only due to the asset price

predictability, but a larger portion of the profit is also due to the cross-sectional dispersion variation

in the mean returns. They conclude that as long as there is dispersion in the mean returns,

momentum profits will be earned. This means that the momentum effect can co-exist with the

random walk hypothesis, which is against the idea of the time-series predictability.

Conrad and Kaul (1998) construct a zero-cost portfolio consisting of a long position on the stocks

that perform above the mean and a short position on the stocks that perform below the mean. They

analyze eight different strategies with equal formation and holding periods ranging between 1

week and 36 months. They investigate several time periods and three equal-sized subperiods. The

36 implemented strategies show an equal amount of positive and negative average returns. Of the

36 strategies, 21 are statistically profitable, and the profitable momentum strategies are from the

3–12-month periods, which are in line with Jegadeesh and Titman’s (1993) results. The best

performing strategies are from the 9-month historical and holding periods with an average monthly

return of 0.71%, followed by the 12-month and the 6-month historical and holding periods with

average monthly returns of 0.7% and 0.36%, respectively. The joint significance test in each time

period shows that the profit of the momentum strategies is statistically significant for the

3–12-month periods for all time periods, except for the 1926–1947 subperiod, when the contrary strategy

is profitable.

(7)

6 methodology used is similar to that of the previous studies, with change in the cutoff to 30% for

the winner and the loser stocks and the exclusion of 5% of the top and the bottom performers to

disregard the extreme performers that can be considered outliers. This study shows that the average

monthly return of the strategy is 0.39%, considerably lower than the result obtained on the

developed market. In contrast to the previous study, the loser portfolios provide positive returns

instead of negative returns.

In their study, which is similar to that of Jegadeesh and Titman (1993), Moskowitz and Grinblatt

(1999) test industries (sectors) instead of individual stocks. They divide the stocks listed on the

NYSE, the AMEX, and the NASDAQ into 20 industries based on their SIC codes and take a long

position on the top three industries (winners) and a short position on the worst three industries.

They reach the same conclusion as that of Jegadeesh and Titman (1993) for the medium term (3–

12-month period) by recording 0.43% monthly profits and show that this strategy is still profitable

after the adjustment of the book-to-market ratio and size. They find that the industry momentum

substantially contributes to the individual stock momentum, capturing the individual stock

momentum profits almost entirely. They argue that in contrast to individual stock momentum

strategies, which seem to be driven mostly by the selling side, industry momentum strategies

generate as much as or more of their profits from their buying side than from their selling side.

However, the momentum effect disappears after the industry effect is taken into account. The

authors conclude that the momentum effect lies within industries, and their strategy has a relatively

low diversification.

(8)

7 Chui, Titman, and Wei (2003) examine the momentum profits in eight Asian markets, namely

Hong Kong, Indonesia, Japan, Korea, Malaysia, Singapore, Taiwan, and Thailand. They examine

the impact of the ownership structure, legal systems, and firm characteristics on the momentum

profits. They construct long-short portfolios based on the past 6-month returns and hold them for

another 6 months. Different from Jegadeesh and Titman’s (1993) method, they use the value

weight instead of the equal weight on the long and the short portfolio construction and use 30% of

the bottom performers for the short portfolios and 30% of the top performers for the long

portfolios. They show that the momentum effect exists in the Asian market. However, compared

with the US and the European markets, the magnitudes of the momentum effect are somewhat

weaker, relatively small and statistically insignificant in Japan and unprofitable in both Korea and

Indonesia. Regarding the ownership and the firm characteristics, they find that foreign investor

ownerships do not impact the momentum effect, and the cross-sectional determinants of the

momentum effects are quite similar in Asia compared with the United States. In particular, small

stocks exhibit more momentum than large stocks, growth stocks exhibit more momentum than

value stocks, and high-turnover stocks exhibit more momentum than low-turnover stocks. The

authors also find that the legal systems affect the momentum effect. The evidence of the

momentum effect can be reliably found in countries with common-law systems, while no evidence

of the momentum effect is observed in countries with civil-law systems.

Griffin, Ji, and Martin (2003) test the momentum strategies in 40 countries to determine whether

the momentum profits can be explained by macroeconomic factors. They use data across

continents with various starting dates, ranging from 1926 to 1990, and December 2000 as the

ending date. Similar to Jegadeesh and Titman’s (1993) methodology, ranking periods from 3 to 12

months and investment periods from 1 to 12 months are used. The portfolios are equally weighted,

with 20% as the cutoff to decide on the winner and the loser stocks. The authors find that the

momentum profits co-move weakly among the 40 countries. The momentum profits also cannot

be explained by macroeconomic factors, such as inflation, term spread, change in industrial

production, GDP growth, industrial production growth, aggregate stock market movements, and

dividend yield. From their paper, it can be concluded that the momentum effect is driven by

country-specific factors that are not known yet.

(9)

8 other countries’ datasets cover approximately 33 years. The authors adopt Jegadeesh and Titman’s

(1993) methodology by using two strategies, namely (1) ranking stocks based on their 12-month

historical performances, skipping 1 month, and holding them for 1 month and (2) ranking stocks

based on their 6-month historical performances, skipping 1 month, and holding them for 6 months.

The break points used to determine the winner and the loser stocks are 20

th

_{and 80}

th

_percentiles,

respectively. The other countries’ datasets extend Griffin, Ji, and Martin’s (2003) study. Dimson,

Marsh, and Staunton (2008) find that the average of the annual momentum return in the United

Kingdom market is 10.26%, and the momentum effect has already existed in that market for over

a century. The momentum strategies are also found to be profitable in the other 17 countries from

2000 to 2008, in line with Griffin, Ji, and Martin’s (2003) findings. Dimson, Marsh, and Staunton

(2008) also find that when adjusted for Fama and French’s (1993) three-factor model, the

momentum effect still generates substantial abnormal returns.

(10)

9 momentum strategy works in the other countries, except China, Japan, Portugal, and Sweden. The

monthly return of the strategy is 0.79% per month if each country is given equal weight.

The empirical studies over the past decades have shown the profitability of the momentum

strategies across stock markets. From those studies, it can also be noted that risk-factor models,

such as the CAPM and Fama and French’s (1993) three-factor model, cannot explain the

momentum returns. Some studies have also tried to incorporate the momentum factor into the

three-factor model to create an asset-pricing model in order to explain stock returns. Concerning

the market-efficient hypothesis proposed by Fama (1970), the momentum return findings

contradict the weak form of market efficiency by showing that historical data can be used to

generate abnormal returns. This present paper contributes to the financial literature by testing the

momentum strategies with different methods from Jegadeesh and Titman (1993), namely using

beta-weighted portfolios and the recent data available from the United Kingdom stock market.

3. Methodology

To test the zero-cost, zero-investment strategies, zero-cost, zero-investment portfolios need to be

constructed. First, each 3-, 6-, 9-, and 12-month historical returns (J3, J6, J9, and J12, respectively)

and 3-, 6-, 9-, and 12-month holding returns (K3, K6, K9, and K12, respectively) are calculated

with the following formula:

(1)

𝑟

_𝑡

= (

𝑝𝑡 + 𝑑

𝑝𝑡−1

) − 1,

where 𝑟

_𝑡

: return at time t

𝑝

_𝑡

: price at time t

𝑝

𝑡−1

: price at time t – 1

𝑑: cash dividend paid from time t – 1 to time t

This thesis does not include stock dividends on the return calculations since the data source does

not provide the data. For the delisted stocks, it is assumed that the delisting process makes the

price of the delisted stocks zero and that investors lose all their investments in the stocks.

To control for risks on the returns of the strategies, historical betas are calculated and will be used

in the portfolio formation.

The betas are calculated with the following formula for each stock:

(2)

𝛽

𝑖

=

𝑐𝑜𝑣(𝑟𝑖,𝑟𝑚)

𝑣𝑎𝑟(𝑟𝑚)

,

(11)

10 𝑐𝑜𝑣(𝑟

𝑖

, 𝑟

𝑚

):

covariance between market return and stock return

𝑣𝑎𝑟(𝑟

𝑚

):

variance of market return

The historical returns used in the beta calculations are 12-month returns. Since not all stocks have

12-month historical returns on the portfolio formation date, stocks are only considered in the

portfolio formation if they have a record of 12-month returns previous to the date of the portfolio

formation.

The historical and the holding returns are calculated for all historical and holding periods on the

last date of each month, as shown in Figure 1, using Equation (1). For each stock, the returns are

calculated for t-13, t-10, t-7, and t-4 to t-1 as the historical returns and t to t+3, t+6, t+9, and t+12

as the holding returns.

The 1-month skip is used to prevent the effects of the bid-ask spread and the price pressure. The

bid-ask spread effect is the measurement error that may occur because the recorded price may

fluctuate between the bidding and the asking price and cause a negative serial correlation. The

price pressure effect is the temporary change in price when large quantities of a security are traded,

thus deviating the price from its efficient level. By adding the 1-month skip, the effect of those

events can be eliminated.

Figure 1.

After the returns are calculated, the returns of each stock from each historical period are then sorted

from the lowest to the largest return, and the holding returns of each stock from each historical

period are discerned. Next, the 1

st

and the 10

th

deciles of the sorted returns are distinguished, and

the weights of each stock are calculated so that all stocks in both portfolios in the 1

st

and the 10

th

deciles have a beta of 1. Taking long and short position on the two portfolios with an average beta

of 1 will simultaneously produce a portfolio that has no systematic risk and requires no investment.

The following formula is used to calculate the weight of each stock to obtain a beta of 1:

(3)

𝑤

𝑖

=

1/𝑛 𝛽𝑖

,

where

𝑤

𝑖

:

weight of a particular stock

(12)

11 The returns of the zero-investment, zero-beta portfolios will be the difference between the return

that is obtained by taking a short position on the 1

st

-decile portfolio of stocks (loser portfolio) and

taking a long position on the 10

th

-decile portfolio of stocks (winner portfolio) for each holding

period (3, 6, 9, and 12 months). The excess weight of the portfolios is invested on a risk-free asset,

while the weight shortage of the portfolios is covered by taking short position in the risk-free asset

(assuming no transaction costs and a zero return of the risk-free asset).

The zero-investment, zero-beta portfolios’ returns for each strategy are then tested for statistical

significance. Since the null hypothesis to be tested is whether the return of the zero-investment,

zero-beta portfolio is greater than zero (whether the strategy is profitable), a one-tailed t-test is

appropriate to assess the significance of the result.

The following formula is used for the t-score calculation:

(4)

𝑡 =

𝑥̅−µ𝑆 √𝑛

,

where

𝑡:

t-value

𝑥̅

:

sample mean

µ

:

population mean

The statistical calculations are performed with the R program and the following hypothesis:

H

0

: µ

j/k

= 0

H

a

: µ

j/k

> 0

The null hypothesis

H

0

: µ

j/k

= 0

states that the return of the zero-investment, zero-beta portfolio with

the J-months/K-months strategy is equal to zero. The alternative hypothesis

H

a

: µ

j/k

> µ

0

states that

the return of the portfolio is significantly larger than zero.

Due to the multiple comparisons of the hypothetical testing, the Bonferroni correction is used to

adjust the significance level (α). For example, with a desired alpha value of 5%, each hypothesis

from four zero-investment, zero-beta strategies is tested at an alpha value of 1.25%.

The Bonferroni correction formula is as follows:

(5)

𝑎𝑑𝑗 𝛼 =

𝛼

𝑛

,

where

𝑎𝑑𝑗 𝛼:

adjusted significance level

𝛼:

significance level

(13)

12 The model for portfolio construction is built using the Visual Basic for Applications (VBA)

programming language. The program scripts can be found in the Appendix section.

4. Data

The used dataset comprises the end-of-the-month stock prices of all FTSE 350 constituents from

1995 to 2017 that are retrieved from Datastream (Thomson Reuters). However, since a 12-month

period is needed for calculating both historical and holding returns, the portfolio formation dates

are available from January 31, 1996 until December 31, 2016. The dataset comprises 944 stocks

with 109,607 price observations. The quantity of the data in the dataset is lower than in the real

condition since some missing data are unavailable on Datastream. With a complete dataset, there

are supposed to be 151,687 price observations on 944 stocks.

Table 1: Characteristic Distribution of the Data for a 3-Month Historical Period

This table shows the average characteristics of the data for the portfolios formed using a 3-month historical

period. The first, the second, and the third rows respectively indicate the average characteristics of all

eligible stocks, of the stocks included in the 1

st

_{-decile portfolios, and of the stocks included in the 10}

th

_-

decile portfolios during the observation period. The price/equity (P/E) ratio column shows the average of

the price-to-equity ratio on each formation date. The market capitalization column lists the average of the

market capitalization on each formation date. The market/book (M/B) ratio column presents the average of

the market-to-book ratio on each formation date. The standard deviation column shows the average standard

deviation on each formation date based on a 12-month historical price.

P/E Ratio Market

Capitalization (in millions)

M/B Ratio Standard Deviation

All eligible stocks 33.46 3420.86 2.72 79.98

1st_decile _29.46 _2519.15 _1.95 _142.04

10th_decile _33.90 _2488.64 _4.51 _147.62

Table 2: Characteristic Distribution of the Data for a 6-Month Historical Period

This table show the average characteristics of the data for the portfolios formed using a 6-month historical

period. The first, the second, and the third rows respectively comprise the average characteristics of all

eligible stocks, of the stocks included in the 1

st

_{-decile portfolios, and of the stocks included in the 10}

th

-decile portfolios during the observation period. The price/equity (P/E) ratio column shows the average of

the price-to-equity ratio on each formation date. The market capitalization column lists the average of the

market capitalization on each formation date. The market/book (M/B) ratio column indicates the average

of the market-to-book ratio on each formation date. The standard deviation column presents the average

standard deviation on each formation date based on a 12-month historical price.

1st_decile _31.14 _2384.58 _1.07 _159.23

(14)

13 Table 3: Characteristic Distribution of the Data for a 9-Month Historical Period

This table shows the average characteristics of the data for the portfolios formed using a 9-month historical

period. The first, the second, and the third rows comprise the average characteristics of all eligible stocks,

of the stocks included in the 1

st

_{-decile portfolios, and of the stocks included in the 10}

th

_{-decile portfolios}

during the observation period. The price/equity (P/E) ratio column shows the average of the price-to-equity

ratio on each formation date. The market capitalization column presents the average of the market

capitalization on each formation date. The market/book (M/B) ratio column indicates the average of the

market-to-book ratio on each formation date. The standard deviation column lists the average standard

deviation on each formation date based on a 12-month historical price.

1st_decile _31.39 _2201.86 _0.43 _124.76

10th_decile _43.18 _2466.92 _5.86 _203.73

Table 4: Characteristic Distribution of the Data for a 12-Month Historical Period

This table shows the average characteristics of the data for the portfolios formed using a 12-month historical

period. The first, the second, and the third rows comprise the average characteristics of all eligible stocks,

of the stocks included in the 1

st

_{-decile portfolios, and of the stocks included in the 10}

th

_{-decile portfolios}

during the observation period. The price/equity (P/E) ratio column shows the average of the price-to-equity

ratio on each formation date. The market capitalization column lists the average of the market capitalization

on each formation date. The market/book (M/B) ratio column indicates the average of the market-to-book

ratio on each formation date. The standard deviation column presents the average standard deviation on

each formation date based on a 12-month historical price.

1st_decile _32.91 _2152.29 _0.80 _94.45

10th_decile _43.20 _2299.14 _6.15 _239.04

Table 5: Industry Distribution of the Stocks

This table shows the total number of stocks per industry during the observation period. Each percentage

shows the number of stocks per industry relative to the total number of stocks.

Industry No.

Finance 264 27.97%

Consumer services 182 19.28%

Industrials 173 18.33%

Oil and gas 41 4.34%

(15)

14 Table 6: Industry Distribution of the Stocks for a 3-Month Historical Return Period

This table shows the total number of stocks per industry for all portfolio formation periods. The all eligible

stocks column comprises all eligible stocks during the formation period. The 1

st

_{-decile column lists all}

stocks included in the 1

st

_{-decile portfolios during the formation period. The 10}

th

_{-decile column presents all}

stocks included in the 10

th

_{-decile portfolios during the formation period. Each percentage shows the number}

of stocks per industry relative to the total number of stocks.

Industry All Eligible Stocks 1st_Decile ₁₀th_Decile

Finance 29,815 27.88% 1,562 14.60% 1,577 14.74%

Consumer services 20,753 19.41% 2,570 24.03% 2,381 22.25%

Industrials 25,040 23.41% 2,632 24.61% 2,549 23.82%

Oil and gas 3,475 3.25% 482 4.51% 580 5.42%

Basic materials 4,889 4.57% 716 6.69% 639 5.97% Healthcare 2,738 2.56% 294 2.75% 348 3.25% Technology 5,787 5.41% 1,023 9.56% 1,144 10.69% Consumer goods 10,364 9.69% 1,047 9.79% 1,116 10.43% Telecommunications 1,185 1.11% 141 1.32% 145 1.35% Utilities 2,895 2.71% 230 2.15% 223 2.08% Total 106,941 100% 10,697 100% 10,702 100%

Table 7: Industry Distribution of the Stocks for a 6-Month Historical Return Period

This table shows the total number of stocks per industry for all portfolio formation periods. The all eligible

stocks column comprises all eligible stocks during the formation period. The 1

st

_{-decile column presents all}

stocks included in the 1

st

_{-decile portfolios during the formation period. The 10}

th

_{-decile column consists of}

all stocks included in the 10

th

_{-decile portfolios during the formation period. Each percentage shows the}

number of stocks per industry relative to the total number of stocks.

Finance 29,815 27.88% 1,473 13.77% 1,551 14.49%

Industrials 25,040 23.41% 2,564 23.97% 2,480 23.17%

Oil and gas 3,475 3.25% 504 4.71% 634 5.92%

Basic materials 4,889 4.57% 732 6.84% 676 6.32% Healthcare 2,738 2.56% 276 2.58% 392 3.66% Technology 5,787 5.41% 1,030 9.63% 1,215 11.35% Consumer goods 10,364 9.69% 997 9.32% 1,024 9.57% Telecommunications 1,185 1.11% 139 1.30% 147 1.37% Utilities 2,895 2.71% 266 2.49% 203 1.90% Total 106,941 100% 10,698 100% 10,704 100%

Table 8: Industry Distribution of the Stocks for a 9-Month Historical Return Period

This table shows the total number of stocks per industry for all portfolio formation periods. The all eligible

stocks column comprises all eligible stocks during the observation period. The 1

st

_{-decile column lists all}

stocks included in the 1

st

_{-decile portfolios during the observation period. The 10}

th

_{-decile column consists}

of all stocks included in the 10

th

_{-decile portfolios during the observation period. Each percentage shows the}

number of stocks per industry relative to the total number of stocks.

Finance 29,815 27.88% 1,465 13.70% 1,572 14.69%

Industrials 25,040 23.41% 2,530 23.66% 2,403 22.45%

(16)

15

Basic materials 4,889 4.57% 751 7.02% 655 6.12% Healthcare 2,738 2.56% 252 2.36% 408 3.81% Technology 5,787 5.41% 1,050 9.82% 1,262 11.79% Consumer goods 10,364 9.69% 974 9.11% 1,023 9.56% Telecommunications 1,185 1.11% 134 1.25% 132 1.23% Utilities 2,895 2.71% 261 2.44% 177 1.65% Total 106,941 100.00% 10,695 100.00% 10,704 100.00%

Table 9: Industry Distribution of the Stocks for a 12-Month Historical Return Period

This table shows the total number of stocks per industry for all portfolio formation periods. The all eligible

stocks column comprises all eligible stocks during the observation period. The 1

st

_{-decile column consists}

of all stocks included in the 1

st

_{-decile portfolios during the observation period. The 10}

th

_{-decile column lists}

all stocks included in the 10

th

_{-decile portfolios during the observation period. Each percentage shows the}

number of stocks per industry relative to the total number of stocks.

Finance 29,815 27.88% 1,346 12.59% 1,642 15.34%

Industrials 25,040 23.41% 2,626 24.55% 2,286 21.36%

Oil and gas 3,475 3.25% 515 4.82% 668 6.24%

Basic materials 4,889 4.57% 754 7.05% 654 6.11% Healthcare 2,738 2.56% 218 2.04% 403 3.76% Technology 5,787 5.41% 1,044 9.76% 1,344 12.56% Consumer goods 10,364 9.69% 986 9.22% 975 9.11% Telecommunications 1,185 1.11% 134 1.25% 144 1.35% Utilities 2,895 2.71% 220 2.06% 143 1.34% Total 106,941 100.00% 10,695 100.00% 10,704 100.00%

Tables 1 to 4 show the distributions of the characteristics across the data, while Tables 5 to 9 list

the distributions of the industries across the data. Based on Tables 1 to 4, the average

price-to-equity (P/E) ratio for all eligible stocks is 33.46, the average market capitalization for all eligible

stocks is £3420.86 million, the average market-to-book (M/B) ratio for all eligible stocks is 2.72,

and the average standard deviation for all eligible stocks is £79.98.

The average P/E ratio for the 10

th

-decile stocks is higher than that for the 1

st

-decile stocks. The

average P/E ratio for the 10

th

-decile stocks is approximately 40 for the portfolios formed using

6-, 9-6-, and 12-month historical return periods6-, while for the portfolios formed using the 3-month

historical return period, the average P/E ratio is 33. The average P/E ratio for the 1

st

-decile stocks

is approximately 29 to 33 for the portfolios formed using 3-, 6-, 9-, and 12-month historical

periods. It can be concluded that stocks categorized as winners are those with high P/E ratios

(relative to all eligible stocks and loser stocks).

(17)

16 £2,400 million for the portfolios formed using 3-, 6-, 9-, and 12-month historical return periods.

The average market capitalization for the 1

st

-decile stocks is approximately from £2,100 to £2,500

for the portfolios formed using 3-, 6-, 9-, and 12-month historical return periods. Among the

portfolios formed using , 6-, 9-, and 12-month historical periods, only those formed using the

3-month historical returns have 1

st

_{-decile higher average market capitalization than their 10}

th

_-decile

counterparts. It can be concluded that the stocks categorized as winners are those with high market

capitalization (relative to all eligible stocks and loser stocks).

The average M/B ratio for the 10

th

_{-decile stocks is higher than that for the 1}

st

_{-decile stocks. The}

average M/B ratio for the 10

th

-decile portfolios is approximately 4.5 to 6 for the portfolios formed

using 3-, 6-, 9-, and 12-month historical return periods. The average M/B ratio for the 1

st

-decile

portfolios is approximately 0.5 to 2 for the portfolios formed using 3-, 6-, 9-, and 12-month

historical return periods. It can be concluded that the stocks categorized as winners are those with

a high M/B ratio (relative to all eligible stocks and loser stocks).

The average standard deviation for the 10

th

-decile stocks is higher than that for the 1

st

-decile stocks.

The average standard deviation for the 10

th

-decile portfolios is approximately £148 to £240 for the

portfolios formed using 3-, 6-, 9-, and 12-month historical return periods. The average standard

deviation for the 1

st

-decile portfolios is approximately £95 to £160. It can be concluded that the

stocks categorized as winners are those with a high standard deviation (relative to all eligible stocks

and loser stocks).

Table 5 shows the distribution of stocks per industry. The data are divided into 10 sectors, namely

finance, consumer services, industrials, oil and gas, basic materials, healthcare, technology,

consumer goods, telecommunication, and utilities. Notably, the data are dominated by the

financial-sector stocks (almost 30% of the total stocks), followed by consumer services and

industrials (approximately 20% of the total stocks).

Tables 6, 7, 8, and 9 show the industry distribution of the stocks based on the portfolio formation

data for 3-, 6-, 9-, and 12-month historical returns, respectively. The percentage patterns of all

eligible stocks for all historical returns are similar to the pattern shown on Table 5. However, under

all 1

st

_{-decile and 10}

th

_{-decile columns, the financial stocks’ percentages decrease in both 1}

st

_-decile

(18)

17 the winner and the loser portfolios comprise more consumer service and technology stocks than

all eligible stocks for each formation date and less financial stocks than all eligible stocks for each

formation date.

5. The Returns of Momentum Investment Strategies

Tables 10, 11, 12, and 13 report the mean returns of 3-, 6-, 9-, and 12-month holding periods of

the winner and the loser portfolios, as well as the zero-investment, zero-beta portfolios,

respectively. The tables show varying results and no relationship between the historical and the

holding periods and the returns. Moreover, only the J9/K12 (9-month historical/12-month holding

periods) strategy obtains a statistically significant result. However, similar to the other strategies,

the return is not economically significant (merely 0.18% per month).

Both 3- and 6-month holding period strategies show a similar pattern, that is, negative returns on

the strategies based on 3- and 6-month historical returns and positive returns on the strategies based

on 9- and 12-month historical returns. For the 3-month holding period strategies, those formed

using 3- and 6-month historical return periods result in -1.3% and -1.2% returns, respectively. The

strategies formed using 9- and 12-month historical return periods result in 0.16% and 0.37%

returns, respectively. For the month holding period strategies, those formed using 3- and

6-month historical return periods result in -0.18% and -0.14% returns, respectively. The strategies

formed using 9- and 12-month historical return periods result in 0.11% and 0.16% returns,

respectively.

Both 9- and 12-month holding period strategies yield positive returns for all historical return

periods. For the 9-month holding period strategies, those formed using 3-, 6-, 9-, and 12-month

historical return periods result in 0.28%, 0.24%, 0.18%, and 0.15% monthly returns, respectively.

For the 12-month holding period strategies, those formed using 3-, 6-, 9-, and 12-month historical

return periods result in 0.38%, 0.62%, 0.18%, and 0.23% monthly returns, respectively.

(19)

18 Table 10: Returns of 3-Month Holding Period Strategies

This table shows the monthly returns and the t-statistics for 3-month holding periods for different historical

return periods. The returns are shown in decimal numbers, and statistical significance is indicated with

asterisks (e.g., *** means that the result is significant at the 1% significance level).

Historical Return Period Used As

Portfolio Formation Base

Long Portfolios’

Returns Short Portfolios’ Returns

Long-Short Portfolios’ Returns 3 0.001308 0.014513 -0.01321 (-0.84) 6 -0.00015 0.012275 -0.01241 (-0.78) 9 -0.00016 -0.00175 0.001601 (0.78) 12 0.00004 -0.00363 0.003668 (1.03)

Table 11: Returns of 6-Month Holding Period Strategies

This table shows the monthly returns and the t-statistics for 6-month holding periods for different historical

return periods. The returns are shown in decimal numbers, and statistical significance is indicated with

asterisks (e.g., *** means that the result is significant at the 1% significance level).

(20)

19 Table 12: Returns of 9-Month Holding Period Strategies

This table shows the monthly returns and the t-statistics for 9-month holding periods for different historical

return periods. The returns are shown in decimal numbers, and statistical significance is indicated with

asterisks (e.g., *** means that the result is significant at the 1% significance level).

Long-Short Portfolios’ Returns 3 0.00192 -0.00087 0.002783 (1.71) 6 0.000614 -0.00175 0.00237 (1.86) 9 0.000645 -0.00111 0.001764 (1.92) 12 0.000478 -0.00099 0.001465 (1.22)

Table 13: Returns of 12-Month Holding Period Strategies

This table shows the monthly returns and the t-statistics for 12-month holding periods for different historical

return periods. The returns are shown in decimal numbers, and statistical significance is indicated with

asterisks (e.g., *** means that the result is significant at the 1% significance level).

(21)

20 6. Conclusion

Jegadeesh and Titman (1993) introduce the momentum factor, which means that by taking a long

position on winners and taking a short position on losers on equally weighted portfolios, substantial

returns can be attained. This thesis has attempted to answer the question about the profitability of

momentum strategies after controlling for market risks. This thesis applies the idea on the United

Kingdom stock market by creating zero-investment, zero-beta portfolios using the data on the

end-of-the-month stock prices of the FTSE 350 constituents from 1995 to 2017, with the same number

of historical and holding periods as that employed by Jegadeesh and Titman (1993).

The dataset shows that the winner portfolios consist of stocks with high P/E ratios, high market

capitalization, high M/B ratios, and high standard deviations relative to the stocks on the loser

portfolios. However, compared with all eligible stocks on the formation dates, the stocks on the

winner portfolios have high P/E ratios, low market capitalization, high M/B ratios, and high

standard deviations. In contrast, the loser portfolios comprise stocks with low P/E ratios, low

market capitalization, low M/B ratios, and low standard deviations relative to the winner

portfolios. However, compared with all eligible stocks on the formation dates, the stocks in the

loser portfolios have low P/E ratios, low market capitalization, and low M/B ratios but high

standard deviations.

The reported results show that after controlling for risks, the strategies based on the momentum

effect cannot obtain abnormal returns. The results are quite remarkable since they differ from those

reported in previous papers. The different results are caused by the different methodology used in

the other studies. This study uses zero-beta portfolios (lacking market exposure), while the

previous studies mostly use equally weighted portfolios. In line with capital asset pricing model

(CAPM) theory, zero-beta portfolios yield zero returns. However, results similar to those of

previous studies are obtained if equally weighted portfolios are used instead of zero-beta portfolios

(the results are not reported here). In conclusion, market exposure is needed to make momentum

strategies perform as expected.

(22)

21 Bibliography

Banz, R. W. 1981. The Relationship Between Return and Market Value of Common Stocks.

Journal of Financial Economics, Vol 9 No 1.

Basu, S. 1977. Investment Performance of Common Stocks in Relation to Their Price-Earnings

Ratio: A Test of the Efficient Market Hypothesis. The Journal of Finance, Vol 32 No 3.

Basu, S. 1983. The Relationship Between Earnings` Yield, Market Value, and Return for NYSe

Common Stocks: Further Evidence. Journal of Financial Economics, Vol 12 No 1.

Bhandari, L. C. 1988. Debt/Equity Ratio and Expected Common Stock Returns: Empirical

Evidence. The Journal of Finance, Vol 43 No 2.

Carhart, M. M. 1997. On Persistence in Mutual Fund Performance. The Journal of Finance, Vol

52 No 1.

Chui, A., Titman, S., and Wei, J. 2003. Momentum, Legal Systems and Ownership Structure: An

Analysis of Asian Stock Market. Working Paper, University of Texas Austin. 2003.

Chui, A., Titman, S., and Wei, J. 2011. Individualism and Momentum Around the World. The

Journal of Finance. Vol 65 No 1.

Conrad, J., and Kaul, G. 1998. An Anatomy of Trading Strategies. Review of Financial Studies.

Vol 11 No 3.

Dimson, E., Marsh, P., and Staunton, M. 2008. Momentum in the Stock Market. Global Investment

Returns Yearbook 2008. London: ABN-AMRO, 2008.

Dimson, E., Marsh, P., and Staunton, M. 2017. Factor Based Investing: The Long-Term Evidence.

Journal of Portfolio Management. Vol 43 No 5.

Fama, E. F. 1965. The Behavior of Stock Market Prices. The Journal of Business. Vol 38 No 1.

Fama, E. F. 1970. Efficient Capital Markets: A Review of Theory and Empirical Work. The

Journal of Finance, Vol 25 No 2.

Fama, E. F., and French, K. R. 1992. The Cross-Section of Expected Stock Returns. The Journal

of Finance, Vol 47 No 2.

Fama, E. F., and French, K. R. 1993. Common Risk Factors in the Returns on Stocks and Bonds.

The Journal of Financial Economics, Vol 33 No 1.

(23)

22 Fama, E. F., and French, K. R. 2012. Size, Value, and Momentum in International Stock Returns.

Journal of Financial Economics, Vol 105 No 3.

Griffin, J. M., Ji, X., and Martin, J. S. 2003. Momentum Investing and Business Cycle Risk:

Evidence from Pole to Pole. The Journal of Finance. Vol 58 No 6.

Jegadeesh, N., and Titman, S. 1993. Returns to Buying Winners and Selling Losers: Implications

for Stock Market Efficiency. The Journal of Finance, Vol 48 No 1.

Jegadeesh, N., and Titman, S. 2001. Profitability of Momentum Strategies: An Evaluation of

Alternative Explanations. The Journal of Finance, Vol 56 No 2.

Lehmann, B. N. 1990. Fads, Martingales, and Market Efficiency. The Quarterly Journal of

Economics, Vol 105 No 1.

Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock

portfolios and capital budgets. The Review of Economics and Statistics, Vol. 47, No. 1.

Lo, A. W., and MacKinlay, A. C. 1990. When Are Contrarian Profits Due to Stock Market

Overeaction? The Review of Financial Studies. Vol 3 No 2.

Markowitz, H., 1952. Portfolio selection. The Journal of Finance, Vol. 7, No. 1

Moskowitz, T. J., & Grinblat, M. 1999. Do Industries Explain Momentum? The Journal of

Finance, Vol 54 No 4.

Rosenberg, B., Reid, K., and Lanstein, R. 1985. Persuasive Evidence of Market Inefficiency.

Journal of Portfolio Management, Vol. 11, No. 3.

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

Rouwenhorst, K. 1999. Local Return Factors and Turnover in Emerging Stock Markets. The

Journal of Finance, Vol 54 No 4.

Sharpe, W. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk.

The Journal of Finance, Vol 19 No 3.

Stattman, D. 1980. Book Values and Stock Returns. The Chicago MBA: A Journal of Selected

Papers, Vol 4.

(24)

23 Appendix

This appendix shows the scripts for portfolio formation process and statistical testing. The

portfolio formation model is created using Visual Basic Application (VBA) programming

language and the statistical testing is created using R programming language.

Sub copyPriceAndDividend()

ChDir "D:\A_Groningen\T_Thesis MSc Finance\Data\data_momentum" Workbooks.Open fileName:= _ "D:\A_Groningen\T_Thesis MSc Finance\Data\data_momentum\data_priceCleaned.xlsx" Sheets("priceCleaned").Select Cells(1, 1).Select Range(Selection, Selection.End(xlDown)).Select Range(Selection, Selection.End(xlToRight)).Select Selection.Copy Workbooks("A_returnAndBetaCalculation").Activate Sheets("returnCalculation").Select Cells(1, 1).Select ActiveSheet.Paste

(25)

24

Sub pricePlusDividendCalculation()

Dim nTotal As Integer Dim tTotal As Integer

Cells(1, 1).Select

nTotal = Range(ActiveCell, ActiveCell.End(xlToRight)).Columns.Count - 1 'count the number of stocks tTotal = Range(ActiveCell, ActiveCell.End(xlDown)).Rows.Count - 2 'count the number of months

Cells(1, 1).Select Range(Selection, Selection.End(xlDown)).Select Selection.Copy Cells(1, 1894).Select ActiveSheet.Paste Cells(1, 1).Select ActiveCell.Offset(0, 1).Select

ActiveCell.Resize(2, nTotal - 1).Select Selection.Copy Cells(1, 1894).Select ActiveCell.Offset(0, 1).Select ActiveSheet.Paste Cells(1, 1894).Select ActiveCell.Offset(2, 1).Select ActiveCell.FormulaR1C1 = "=(R[]C[-1893]+R[]C[-946])" ActiveCell.Copy

ActiveCell.Resize(tTotal, nTotal - 1).Select ActiveSheet.Paste

'Selection.SpecialCells(xlCellTypeFormulas, 16).Select ' Selection.ClearContents

End Sub

(26)

25

Sub returnCalculation()

Dim nTotal As Integer Dim tTotal As Integer

Cells(1, 1).Select

nTotal = Range(ActiveCell, ActiveCell.End(xlToRight)).Columns.Count - 2 'counts the number of stocks tTotal = Range(ActiveCell, ActiveCell.End(xlDown)).Rows.Count - 2 'counts the number of months

'--- calculate historical return 3 month

Cells(1, 2841).Select 'write and copy stock names ActiveCell.FormulaR1C1 = "Name"

ActiveCell.Offset(1, 0).FormulaR1C1 = "Code" Cells(1, 1).Select ActiveCell.Offset(0, 1).Select ActiveCell.Resize(2, nTotal).Select Selection.Copy Cells(1, 2841).Select ActiveCell.Offset(0, 1).Select ActiveSheet.Paste

Cells(1, 1).Select 'copy the date from Jan 1996 - Dec 2016 ActiveCell.Offset(15).Select ActiveCell.Resize(252).Select Selection.Copy Cells(1, 2841).Select ActiveCell.Offset(2, -1).Select ActiveSheet.Paste

ActiveCell.Offset(0, 1).Select 'write historical return 3 month ActiveCell.FormulaR1C1 = "historicalReturn3Month"

ActiveCell.Copy

ActiveCell.Resize(252).Select ActiveSheet.Paste

(27)

26

ActiveCell.FormulaR1C1 = "=R[12]C[-947]/R[9]C[-2840]-1" 'calculate 3 month historical return ActiveCell.Copy

ActiveCell.Resize(252, nTotal).Select ActiveSheet.Paste

'Selection.SpecialCells(xlCellTypeFormulas, 16).Select 'delete errors 'Selection.ClearContents

ActiveCell.Copy

ActiveCell.Offset(0, 1).Select

(28)

27

ActiveCell.Copy

' Selection.SpecialCells(xlCellTypeFormulas, 16).Select 'delete errors ' Selection.ClearContents

ActiveCell.Copy

(29)

28

ActiveCell.Copy

ActiveCell.FormulaR1C1 = "=R[12]C[-3788]/RC[-5681]-1" 'calculate 12 month historical return ActiveCell.Copy

(30)

29

ActiveSheet.Paste

'--- calculate realized return 3 month

ActiveCell.Offset(0, 1).Select 'write realized return 3 month ActiveCell.FormulaR1C1 = "realizedReturn3Month"

ActiveCell.Copy

ActiveCell.FormulaR1C1 = "=R[16]C[-4735]/R[13]C[-6628]-1" 'calculate 3 month realized return ActiveCell.Copy

(31)

30

ActiveCell.Copy

(32)

31

ActiveCell.Copy

(33)

32

' Selection.ClearContents

ActiveCell.Offset(1, 0).FormulaR1C1 = "Code" Cells(1, 1).Select ActiveCell.Offset(0, 1).Select ActiveCell.Resize(2, 944).Select Selection.Copy Cells(1, 9470).Select ActiveCell.Offset(0, 1).Select ActiveSheet.Paste

ActiveCell.Copy

ActiveCell.FormulaR1C1 = "=R[25]C[-7576]/R[13]C[-9469]" 'calculate 12 month realized return ActiveCell.Copy

(34)

33

'--- calculate return per month for beta calculation

Cells(1, 10418).Select 'write and copy stock names for return per month calculations ActiveCell.FormulaR1C1 = "Name"

ActiveCell.Offset(1, 0).FormulaR1C1 = "Code" Cells(1, 1).Select

ActiveCell.Resize(2, nTotal + 1).Select Selection.Copy

Cells(1, 10418).Select ActiveCell.Offset(0, 1).Select ActiveSheet.Paste

Cells(1, 1).Select 'copy the date from Feb 1995- Dec 2016 ActiveCell.Offset(4, 0).Select ActiveCell.Resize(263).Select ActiveCell.Resize(263).Select Selection.Copy Cells(1, 10418).Select ActiveCell.Offset(4, -1).Select ActiveSheet.Paste

ActiveCell.Offset(0, 1).Select 'write return per month ActiveCell.FormulaR1C1 = "returnPerMonth"

ActiveCell.Copy

ActiveCell.Offset(0, 1).Select 'calculate return per month ActiveCell.FormulaR1C1 = "=R[]C[-10417]/R[-1]C[-10417]-1"

ActiveCell.Copy

ActiveCell.Resize(263, nTotal + 1).Select ActiveSheet.Paste

(35)

34

Cells(1, 11366).Select 'write and copy stock names for beta calculations ActiveCell.FormulaR1C1 = "Name"

ActiveCell.Offset(1, 0).FormulaR1C1 = "Code" Cells(1, 1).Select ActiveCell.Offset(0, 1).Select ActiveCell.Resize(2, 944).Select Selection.Copy Cells(1, 11366).Select ActiveCell.Offset(0, 1).Select ActiveSheet.Paste

Cells(1, 1).Select 'copy the date from Jan 1996 - Dec 2016 ActiveCell.Offset(15).Select ActiveCell.Resize(252).Select ActiveCell.Resize(252).Select Selection.Copy Cells(1, 11366).Select ActiveCell.Offset(2, -1).Select ActiveSheet.Paste

ActiveCell.Offset(0, 1).Select 'Beta ActiveCell.FormulaR1C1 = "Beta" ActiveCell.Copy ActiveCell.Resize(252).Select ActiveSheet.Paste ActiveCell.Offset(0, 1).Select ActiveCell.FormulaR1C1 = _ "=SLOPE(R[2]C[-948]:R[13]C[-948],R[2]C11363:R[13]C11363)" ActiveCell.Copy ActiveCell.Resize(252, nTotal).Select ActiveSheet.Paste End Sub ‘’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ Sub J3K3()

(36)

35

'Application.Calculation = xlCalculationManual 'to make the xl calculation to manual 'Application.ScreenUpdating = False 'to make the screen updating off

Dim i As Integer 'number of iteration

Dim rw As Integer 'number of row used on each f ormation Dim nTotal As Integer 'number of total stocks

Dim tFormation As Integer 'number of portfolio formation (monthly, from Jan 1996 to Dec 2016)

Dim nFormation As Integer 'number of available stocks on formation date Dim nPerDecile As Integer 'number of stocks on each dec ile

Dim j As Integer 'number of historical months Dim k As Integer 'number of realized months Dim rng As Range 'range for the error finding

j = 3 'set number of historical mon ths k = 3 'set number of realized months

ThisWorkbook.Activate 'choose and rename active she et ActiveSheet.Name = "J" & j & "K" & k & ""

Workbooks("returnAndBetaCalculation").Activate 'choose returnAndBetaCalculation Workbook

Cells(1, 2841).Select 'copy historical return j month ActiveCell.Offset(0, -1).Select

ActiveCell.Resize(254, 946).Select Selection.Copy

ThisWorkbook.Activate 'paste historical return j mo nth Cells(1, 2).Select

ActiveCell.Offset(0, -1).Select ActiveSheet.Paste

(37)

36

Workbooks("returnAndBetaCalculation").Activate 'choose returnAndBetaCalculation Workbook

Cells(1, 6629).Select 'copy realized return k month ActiveCell.Offset(0, -1).Select

ThisWorkbook.Activate 'paste realized return k mont h Cells(1, 949).Select ActiveCell.Offset(0, -1).Select ActiveSheet.Paste Selection.PasteSpecial Paste:=xlPasteValues Selection.Interior.Pattern = xlNone

Workbooks("returnAndBetaCalculation").Activate 'open returnAndBetaCalculatio n Workbook

Cells(1, 11366).Select 'copy beta ActiveCell.Offset(0, -1).Select

ThisWorkbook.Activate 'paste beta Cells(1, 1896).Select ActiveCell.Offset(0, -1).Select ActiveSheet.Paste Selection.PasteSpecial Paste:=xlPasteValues Selection.Interior.Pattern = xlNone Cells(1, 2).Select

nTotal = Range(ActiveCell, ActiveCell.End(xlToRight)).Columns.Count - 1 'counts the number of total stocks