Performance of Fama-French Model Inspired Stock Portfolio: An Indonesian Case Study
Abstract
This research implements Fama-French Model (FFM) in constructing the Indonesian stock
portfolio. It aims to assess the performance of FFM inspired Indonesia stock portfolio by
comparing it to the Jakarta Composite Index (JCI). The best combination factor model of FFM
is applied as a constraint in the portfolio construction using normalization method. The result
showed that FFM-inspired portfolio is unable to beat the JCI market in all rebalancing
frequencies. FFM6 was the most favorable in outperforming JCI using rebalancing scenario of
once in every 3 quarters. Nevertheless, FFM3 and FFM5 generate unfavorable result. In
conclusion, FFM-inspired portfolio has the ability to beat the market limited to specific
rebalancing periods.
Keywords: Best combination factor, Fama-French model, Normalization, Portfolio
construction
Introduction
Overtime, methods were developed by researchers to find the optimum way to construct
investment portfolio and gain profits. Several sources claimed JB Williams is the pioneer in
portfolio construction methods, by introducing the Dividend Discount Model (DDM) that
interpret value of investment as expected dividends from present value (Williams, 1939).
Nevertheless, fundamental metrics on value investing as earnings yield, book to price, and
dividend yield were priorly introduced by Graham and Dodd in 1934 (Graham & Dodd, 2009).
In the 1952, inspired by JB William’s “Theory of Investment Value” and the Capital Asset
Pricing Model (CAPM), The mean-variance (MV) model was introduced by Markowitz
(1952;2009). This model significantly impacted the investment portfolio construction world
and now is known as the Modern Portfolio Theory (MPT). The MV model, also known as the
‘Efficient Frontier of Risky Assets’ model suggest alternating diverse investment set of
portfolios in a minimum variance for a targeted return. This model assumes that risk-averse
investors optimize returns based on a specific risk level and provides insight on efficient
diversification to minimize risk for a pre-determined expected return (E. F. Fama & French,
1967). Next, Basu (1977) delineated that low P/E portfolios tend to earn superior returns.
Eugene F. Fama and Kenneth R. French (1992) expanded the value approach by introducing a
model called the Fama-French 3 Factor Model (FFM3) that includes beta (β), firm size (MC),
and book to market ratio. FFM3 is the modified version of CAPM, developed by William
Sharpe (1964), Jack Treynor (1961), John Lintner (1975, 2016), and Mossin (1966) that
introduced β coefficient that explains the use of market sensitivity to estimate stock return.
CAPM is comprehensively used to estimate the relationship between expected return and risk
(Sarva Jayana & Wening Gayatri, 2018). However, it received several criticisms as its inability
to serve the intended original purpose (T. Lai & Stohs, 2021;2015) and useless for what it was
developed to do (Fama & French, 1992).
In 2000, Smart Beta was introduced as a portfolio construction method that combines active
and passive investing (S. Huang, Song, & Xiang, 2020). Also in the same year, Van Der Hart,
Slagter, & Van Dijk (2003) reported that higher book to market and momentum based strategy
are profitable in the emerging market. Supported by Guerard, Xu, & Gultekin (2012) that stated
momentum as one of 3 good strategies in constructing long-run investment portfolio next to
fundamental and expectations. In the same year, the Global Minimum Variance Portfolio
(GMVP) also established as a method in portfolio composition optimization (Engle & Kelly,
2012).
2
Interestingly in 2014, Fama and French introduced the upgraded version of FFM3, namely the
Fama-French 5 Factor Model (FFM5), by adding (1) profitability and (2) investment factors
(Fama & French, 2014). Followed in 2018, Fama and French added momentum factor to FFM5
and this led to the creation of the Fama-French 6 Factor Model (FFM6) (Fama & French, 2018)
which is stated as follows:
𝑅𝑖 − 𝑅𝑓𝑡 = 𝛼𝑖 + 𝛽𝑖 (𝑅𝑚𝑡 − 𝑅𝑓𝑡 ) + 𝑆𝑖 𝑆𝑀𝐵𝑡 + 𝐻𝑖 𝐻𝑀𝐿𝑡
+ 𝑅𝑖 𝑅𝑀𝑊𝑡 + 𝐶𝑖 𝐶𝑀𝐴𝑡 + 𝑈𝑖 𝑈𝑀𝐷𝑡 + 𝑒𝑖𝑡
Where
Ri = Return on investment
Rft = Risk free rate
Rmt = Market portfolio return
SMBt = Firm size factor (Small minus Big)
HMLt = Book to market factor (High minus Low)
RMWt = Profitability factor (Robust minus Weak)
CMAt = Investment factor (Conservative minus Aggressive)
UMDt = Momentum factor (Up minus Down)
Fama-French Model (FFM) is used and able to calculate the targeted return for diversified stock
portfolio in several developed countries as the USA (Panopoulou & Plastira, 2014; Roy &
Shijin, 2018), Germany (Dirkx & Peter, 2020), and Japan (Kubota & Takehara, 2018; Roy,
2021) including developing nations as India (Chaudhary, 2017) and Indonesia (Amanda &
Husodo, 2015; Ekaputra & Sutrisno, 2020; Habib, Shiddiq, Hasnawati, & Huzaimah, 2020).
Several research resulted that FFM3 is the best model used to describe excess portfolio returns
in the emerging Indonesian market compared to CAPM (Sutrisno & Nasri, 2018) and FFM5
(Ekaputra & Sutrisno, 2020; Saleh, 2020). Regarding FFM6, some research tested this method
3
in several countries as the USA (Roy & Shijin, 2018), Germany (Dirkx & Peter, 2020), Japan
(Roy, 2021), and Indonesia (Munawaroh & Sunarsih, 2017).
Fama and French (2006) reported that stocks with a high book equity to market ratio (value
stocks) have higher average returns than the reverse (growth stocks) in the US. Banz (1981),
Fama, and French (2012) stated that stocks with lower market capitalization (small stocks) tend
to have higher average returns. Past year’s winners show positive momentum returns in all size
groups (Fama & French, 2012), supported by the fact by Jegadeesh & Titman (1993) who
revealed that past winner stocks tend to remain future winner compare to past loser stocks.
Fama & French (2005) and Haugen & Baker (1996) says that higher profitability firms have
higher expected return, while firms with higher rates of investment have lower expected returns
(E. F. Fama & French, 2005).
Fama & French's study entitled "A Five-Factor Asset Pricing Model" (2014) stated that FFM5
directed at capturing the size, value, profitability, and investment patterns in average stock
returns performs better than FFM3. Other studies by Erdinç (2018) and Huang (2019) who
compare the models’ performance and specified that the FFM5 performed better than the FFM3
and the CAPM in the Turkish and Chinese stock market respectively, imply that FFM5 model
has proved its superiority compared with the FFM3 and the CAPM in most studies from
developed stock markets.
Furthermore, the study of 18 countries across a broad range of emerging market reported that
the FFM5 outperforms FFM3 in Eastern Europe and Latin America only, while generate
inferior result in Asian sample and doesn’t provide any additional value over the FFM3 (Foye,
2018). Supported by Lin's (2017) finding that investment factor is redundant for emerging
markets in general. One of the main reasons is strong ownership culture in emerging market
4
that use investment to a great degree as a tool to benefit controlling interest and doesn’t provide
meaningful guidance for the future.
The inclusion of the momentum factor in FFM6 has been proven to have strong explanatory
power in portfolio excess returns, compared to FFM3. Supported by an international study that
states UMD factor possess meaningful improvement in capturing returns when added to the
FFM5 in the North America, Europe, and Asia Pacific regions (Mård, 2020). Other studies in
18 emerging stock markets divided into three emerging regions (Asia, Latin America, and
Eastern Europe) find that strong momentum effect exists for all region but Eastern Europe
(Cakici, Fabozzi, & Tan, 2013).
Both quantitative and qualitatively, several studies proclaimed that the bottom-up method
generate higher information ratio than the top-down method by 40% by average (Lester, 2019)
and able to generate higher excess return over the long run (Bender & Wang, 2016). In using
the top-down method, one needs to build the single-factor portfolios first. Afterwards, the
portfolios are combined into a multifactor portfolio. On the contrary, the bottom-up method
directly integrates all characteristic into a multifactor portfolio (Zurek & Heinrich, 2021).
However, none analyzed the combination factor of FFM as a constraint in portfolio construction
in the Indonesian stock market. This research is highly inspired by FFM theory that introduced
the best combination factor model. Specifically, FFM6 as the most developed version of FFM’s
asset pricing model is used as a constraint in portfolio construction. In addition, the bottom-up
approach is adopted in constructing FFM multifactor stocks portfolio.
To fill this gap, FFM combination was tested in Indonesia because it is one of the emerging
countries with (1) huge market size with one of the fastest-growing middle class in the world,
(2) above-average economic growth, (3) high rate infrastructure development, (4) productive
labor market, (5) geographical location and global connectivity, (6) easiness to import raw
5
materials, (7) rapid adoption and innovation of technology,
(8) ease in doing business,
and (9) government initiatives to make Indonesia investment friendly (Fernandez, Almaazmi,
& Joseph, 2020). Thus, Indonesia is a very captivating market to study especially if one could
find and implement the method that can generate satisfactory return on the stock portfolio
investment.
This research uses quarterly data obtained from all companies listed on universal JCI from 1Q10
to 2Q21. Subsequently, the actual-based transaction costs and rebalancing period were
determined to ascertain whether the actively constructed portfolio generated an optimal return
compared to the Jakarta Composite Index (JCI) performance concerned as a passive investing
proxy.
This research is aimed to test the performance of constructed portfolio based on 60 different
Indonesian stocks quarterly selected using the best combination factor model and comparing to
JCI performance. This is to determine whether FFM inspired portfolio is applicable and can
outperform JCI return. Meanwhile, by comparing these returns, future investors are expected
to consider FFM during the construction process of the Indonesian stock portfolio. As can be
seen later, we found FFM6 can beat the market hence it will be an important result for investor.
In determining 60 stocks for the portfolio, normalization method is used to re-arrange a set of
existing data on a different basis. According to Patro and Sahu (2015), normalization, also
known as scaling or mapping technique is proven constructive in predicting or forecasting
certain tasks. It has been adopted in several financial research such as ‘Technical Analysis on
Financial Forecasting’ carried out by Patro et al. (2015).
This research also incorporates transaction cost in the portfolio construction model. According
to Arnott et al. (1990), and Yoshimoto (1996), ignoring transaction cost tend to lead to an
inefficient portfolio. This finding is supported by Li, Wang, Huang, and Hoi's (2018) research
6
that explains transaction cost led to the creation of a portfolio and improved strategies compared
to zero-cost.
The remaining part of this research is divided as follows, section 2 provides the methodological
framework, which covers data collection, preparation and processing. Section 3 explains the
results and discussion, while section 4 concludes the research.
1. Data and Methodology
All the relevant financial data was retrieved from Bloomberg Terminal, using data for the period
of 1Q10-2Q21. In addition, market capitalization (SMB), book-to-market ratio (HML),
operating profit (RMW), total assets (CMA), and stock prices are used to determine return and
momentum. A total of 46 quarterly observations and all companies listed on the universal JCI
were recorded.
As illustrated in Appendix A, step 1-6 involve data screening and preparation. The missing
quarterly data of the listed companies was rechecked on the published financial statement. The
total available equity is inputted for stocks with missing B/M ratio but have market
capitalization value, assuming it is similar to the book value. The total equity was also divided
by the market capitalization to obtain B/M ratio for the HML factor. Missing data of operating
profitability is obtained from the company’s financial statement using the formula (Revenue –
Cost of Goods Sold – Operating Expenses) for the RMW factor. It also applies for the missing
number of total assets in the CMA factor, by examining the financial statement. The missing
stock prices data was obtained from Yahoo Finance.
Then, in cases involving missing data between quarters, the average values of Q+1 and Q-1
were utilized. For consecutive quarters with missing data, it was ascertained whether the
7
companies had been listed on the JCI or even suspended for a while. In such circumstances, the
missing data remains zero. On the contrary, a year-on-year (y-o-y) growth was adopted for the
missing data on consecutive quarters. The top constituents representing 90% of the total JCI
market capitalization were used as the research sample.
JCI as a modified capitalization-weighted index where its constituents are weighted according
to the total market value of the available outstanding shares. Since this research emphasizes
constructing active mutual funds that maximize investor return, mimicking of managers
avoiding penny stocks which are usually illiquid and inadequately explains the movement of
the market index was adopted (Carpentier & Suret, 2011). Constituent companies representing
top 90% of the total market capitalization serve as a benchmark that helps in sorting. Despite
the fact that the total number listed in JCI keeps increasing from 332 in 1Q10 to 862 firms in
2Q21, the proportion representing 90% of the total JCI market cap is stable approximately 20
to 27%, except from 1Q10 to 2Q10, which was recorded as less than 20% (Appendix B). In this
case, approximately the top one-fifth of the total listed companies with the most significant
market capitalization values represent the entire JCI market.
Step 7 outlines the labelling factor of FFM based on the specified rules, followed by step 9 -10
that assign factor scoring for each factor. All of the factors using 30th and 70th percentiles as
breakpoints, except for SMB factor that use quarterly JCI median market capitalization as a
breakpoint. The CMA factor was obtained using the historical y-o-y growth (total assets in
Q/total assets Q-4)-1). Lastly, the momentum factor, or UMD, was included in quarter Q
(formed at the end of the quarter Q-1), a stock must have a price for the end of Q-4 and a good
return for Q-2. Therefore, stocks that do not have price of Q-4 and have a poor return of Q-2
((price Q-1/price Q-2)-1) were eliminated. Specifically, for UMD factor, the factor scorings are
differed with other factors, which are 1, 0.5, and 0, to eliminate the losers' stock Q-2 during
8
portfolio construction. In this case, the market risk premium factor was not assigned with any
factor scoring value since every quarter stock has a similar value.
Step 11-12 define the factor’s normalization value for each quarterly stock. The long (S-F, HF, R-F, C-F, U-F) and short spread factors (B-F, L-F, W-F, A-F, D-F) were assigned with the
largest number of 1 and the smallest of number of 0, respectively. Normalization facilitates
were interpreted and compared irrespective of different conditions by ensuring equal distances
(Luo, Xiong, Zhan, Wu, & Shi, 2009). The values obtained are shifted and rescaled within 0
and 1. For example, from the quarterly research sample, the firm with the lowest and largest
market cap will have normalization value of 1 and 0 [S (1) B (0)]. The same method is
applicable to other factors [H (1) L (0)], [R (1) W (0)], [C (1) A (0)], and [U (1) D (0)].
Normalization was carried out on stock’s long/ short spread factors to obtain more precise
assessment of each stock’s sequences, complementing the preceding factor scoring method.
The total normalized point from step 13 serves as a constraint in the process of stock selection
for portfolio construction, and thenceforth the sample data of quarterly stocks were selected
(step 14). The equal-weighted method was adopted for the portfolio construction with stocks
with the same weight, the weight for each asset is 1/N, where N refers to the number of the
selected stocks (Karatzas & Kardaras, 2020).
The following step involves rebalancing once every X quarter(s), where X = 1,2,…,8. The aim
is to determine the optimal quarterly period rebalancing. Frequent stock rebalancing leads to
higher transaction costs and lowers net returns. Likewise, infrequent rebalancing generates
suboptimal net return due to incorporating obsolete datasets that tend not to capture the current
market dynamic condition fully. A cut-off was set for a maximum of 8 quarterly periods or the
infrequent rebalancing in this study of every 2-year data period.
9
Step 15 represents the calculation of transaction costs including both buying and selling, which
is assumed to be equivalent to 0.3%. Due to price changes, the fixed-weighting portfolio is
maintained by rebalancing every stock's partial gain or loss with the initial buying and selling
carried out each period. If the stock return is negative, the same amount of loss value is bought
to keep the weight, and vice versa.
The return formula uses price ((Q+1/ Q)-1), instead of ((Q/Q-1)-1) due to the assumption of
forward-looking construction portfolio based on the most recent normalization data, with the
consideration that quarterly financial statements are always published at the end of the period.
For example, the 1Q10 quarterly financial statements can be downloaded on March 31, 2010 at
the earliest, therefore, the portfolio based on the normalization of FFM can only be constructed
on end of Q period at the earliest. Therefore, the quarterly return was assessed using the price
on 2Q10. This indicates the Q data was only used as a sample for portfolio construction in Q+1
period. This means that the stocks were bought at price Q and then sold at Q+1. Assuming the
return of the price ((Q/Q-1)-1) formula was applied, the result shows how FFM was
implemented during the past period and could not represent the real-life portfolio-creating
process.
Optimum rebalancing periods is then determined based on the highest excess return generated
from constructed portfolio to JCI. This research uses FFM6 as a constraint in portfolio
construction. Nevertheless, FFM3 and FFM5 are included in this study as a comparison.
2. Result and Discussion
The results show that FFM-inspired portfolio is unable to beat the JCI market in all rebalancing
frequencies. However, based on the data acquired from 1Q10 to 2Q21, FFM-inspired portfolios,
specifically limited to FFM6 and FFM3, tend to beat the JCI market.
10
FFM6 factors show that only 2 rebalancing scenarios tend to outperform JCI consistently for
11.5 years of the research period. This is followed by FFM3 with only 1 rebalancing scenario.
In contrast, FFM5 factors do not outperform JCI in all rebalancing scenarios. The finding is
consistent with previous research that stated FFM5 does not perform better than FFM3 in the
emerging stock market (Ekaputra & Sutrisno, 2020; Saleh, 2020).
As depicted by the charts in Chart 1, 2, and 3, the highest performance achieved by FFM6
factor, particularly in the rebalancing scenario, is once in every 3 quarters (X=3), which can
outperform JCI with an excess CAGR of 0.8% from 1Q10 to 2Q21. This was followed by the
outperformance of FFM3 and FFM6 factors in the rebalancing scenario that occurred once in
every 3 (X=3), and 4 quarters (X=4) with excess CAGR of 0.6% and 0.3%, respectively.
Chart 1: Net Portfolio Return using FFM6 Factor
Chart 2: Net Portfolio Return using FFM3 Factor
11
Chart 3: Net Portfolio Return using FFM5 Factor
During the research period, historical data realized from 1Q10 to 2Q21 were always used to
start rebalancing. However, the frequency differed towards the end, and this means the
calculated JCI CAGR return was adjusted based on the rebalancing period to ensure that the
constructed portfolio and JCI have a parallel comparison.
Table 1: JCI CAGR Return
JCI
Rebalancing
X
Period
CAGR
Quarter(s)
Return
1
1Q10-2Q21
7.1%
2
1Q10-1Q21
7.2%
3
1Q10-2Q21
7.1%
4
1Q10-1Q21
7.2%
5
1Q10-2Q21
7.1%
6
1Q10-3Q20
5.5%
7
1Q10-3Q20
5.5%
8
1Q10-1Q20
5.0%
In line with the initial premise, transaction costs keep decreasing along with infrequent stock
rebalancing.
12
Table 2: TC among FFM Factors
Rebalancing X Transaction Cost
Quarter(s)
FFM3
FFM5 FFM6
1
1.5%
1.5%
1.5%
2
0.8%
0.8%
0.8%
3
0.5%
0.6%
0.6%
4
0.4%
0.4%
0.5%
5
0.3%
0.3%
0.3%
6
0.3%
0.3%
0.3%
7
0.2%
0.2%
0.3%
8
0.2%
0.2%
0.2%
In accordance with preliminary study, this research reported that FFM3 can capture the excess
returns and even surpass the JCI performance in a specific rebalancing scenario. The
profitability and investment factors in FFM5 do not seem to have additional explanatory power
in portfolio excess returns in the Indonesian market over the FFM3 (Foye, 2018; Lin's, 2017) .
As Fama (1972) stated that portfolio managers’ forecasting skills are subdivided into 2 distinct
components (1) forecasts of price movements of selected individual stocks (security analysis),
and (2) forecasts of price movements of the general or entire stock market (market timing).
Market timing is related to the extent to which investment companies take advantage of time,
namely when to buy and resell securities.
FFM6 factors seem to be competent in capturing both security analysis and market timing. In
the security analysis aspect, FFM6 tends to help users in the stocks’ selection process relating
to the best combination factor model of S-F, H-F, R-F, C-F. In contrast, the momentum factor
of U-F is represented by market timing.
13
From the rebalancing perspective, its occurrence once in every quarter (X=1) is ineffective due
to the high transaction costs of approximately 1.5%, which translates to a consequential
decrease in net return. The subset of the rebalancing frequency, which tends to occur once in
every 2 to 4 quarters (X=2,3,4), generates the most optimal return. It was concluded that the
explanatory power of FFM factors is still valid even in the following 1 year for FFM6 factors.
On the contrary, rebalancing frequency once in every 5 to 8 quarters (X=5,6,7,8) generates a
suboptimal net return, indicating that the explanatory power of FFM factors' normalization is
weak for more than 1-year forward period. This is supported by the fact that rebalancing
frequency once in every 8 quarters (X=8) only generates a modest return of 0.7 to 2.0% for all
FFM variants.
Conclusion
Using factor scoring and normalization method as well as including transaction costs as an
actual-based parameter, this research implies that FFM-inspired portfolio consistently
outperformed JCI realized return during the 1Q10 to 2Q21 period using FFM6 and FFM3
factors based on the CAGR return. The explanatory power of FFM6 factors is still valid until
1-year forward, indicating that the net return CAGR of rebalancing frequency X=3,4 surpasses
JCI performance. The highest net return was obtained from the rebalancing frequency X=3
using FFM6 factors. FFM3 outperforms JCI using the rebalancing frequency of X=3. Thus,
investors could consider this FFM method to construct Indonesian stock portfolio. However,
documented empirical evidence in this article indicate that implementation models still can be
enhanced.
Further research can conduct similar research in other stock markets with alike characteristics
of Indonesian market, especially in the scope of emerging markets, in order to cover the
14
knowledge gap, which is indicated by the existence of dissimilarity results between FFM variant
factors in different markets. Furthermore, researchers may consider broadening the
investigation period and choosing another methodology in using FFM factors as a constraint in
constructing the stock portfolio.
Reference
Amanda, C., & Husodo, Z. A. (2015). Empirical test of Fama French three factor model and
illiquidity premium in Indonesia. Corporate Ownership and Control, 12(2Continued1),
369–380. Retrieved from https://doi.org/10.22495/cocv12i2c3p2
Arnott, R. D., & Wagner, W. H. (1990). The Measurement and Control of Trading Costs.
Financial
Analysts
Journal,
46(6),
73–80.
Retrieved
from
https://doi.org/10.2469/faj.v46.n6.73
Banz, R. W. (1981). The Relationship Between Return and Market Value of Common Stocks,
9.
Basu, S. (1977). Investment Performance of Common Stocks in Relation to Their PriceEarnings Ratois: A Test of The Efficient Market Hypothesis, 32(3), 663–682.
Bender, J., & Wang, T. (2016). Can the whole be more than the sum of the parts? Bottom-up
versus top-down multifactor portfolio construction. Journal of Portfolio Management,
42(5), 39–50. Retrieved from https://doi.org/10.3905/jpm.2016.42.5.039
Cakici, N., Fabozzi, F. J., & Tan, S. (2013). Size, value, and momentum in emerging market
stock
returns.
Emerging
Markets
Review,
16,
46–65.
Retrieved
from
https://doi.org/10.1016/j.ememar.2013.03.001
Carpentier, C., & Suret, J. M. (2011). The survival and success of Canadian penny stock IPOs.
15
Small
Business
Economics,
36(1),
101–121.
Retrieved
from
https://doi.org/10.1007/s11187-009-9190-x
Chaudhary, P. (2017). Fama-French Model for Indian and Us Stock Market. Journal of
Commerce & Accounting Research, 6(2), 1.
Dirkx, P., & Peter, F. J. (2020). The Fama-French Five-Factor Model Plus Momentum:
Evidence for the German Market. Schmalenbach Business Review, 72(4), 661–684.
Retrieved from https://doi.org/10.1007/s41464-020-00105-y
Ekaputra, I. A., & Sutrisno, B. (2020). Empirical tests of the Fama-French five-factor model in
Indonesia and Singapore. Afro-Asian Journal of Finance and Accounting, 10(1), 85–111.
Retrieved from https://doi.org/10.1504/AAJFA.2020.104408
Engle, R., & Kelly, B. (2012). Dynamic equicorrelation. Journal of Business and Economic
Statistics, 30(2), 212–228. Retrieved from https://doi.org/10.1080/07350015.2011.652048
Erdinç, Y. (2018). Comparison of CAPM, Three-Factor Fama-French Model and Five-Factor
Fama-French Model for the Turkish Stock Market. Financial Management from an
Emerging Market Perspective. Retrieved from https://doi.org/10.5772/intechopen.70867
Fairfield, P. M., Whisenant, J. S., & Yohn, T. L. (2003). Accrued earnings and growth:
Implications for future profitability and market mispricing. Accounting Review, 78(1),
353–371. Retrieved from https://doi.org/10.2308/accr.2003.78.1.353
Fama, E. F. (1972). Components of Investment Performance. The Journal of Finance, 73(6),
3025–3025. Retrieved from https://doi.org/10.1111/jofi.12742
Fama, E. F., & French, K. R. (1967). The Capital Asset Pricing Model: Theory and Evidence.
Angewandte Chemie International Edition, 6(11), 951–952., 13(April), 15–38.
Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns.
16
Fama, E. F., & French, K. R. (2005). Profitability, Investment, and Average Returns, 12 Suppl
1(9),
1–29.
Retrieved
from
http://www.ncbi.nlm.nih.gov/pubmed/810049%0Ahttp://doi.wiley.com/10.1002/anie.197
505391%0Ahttp://www.sciencedirect.com/science/article/pii/B9780857090409500205%
0Ahttp://www.ncbi.nlm.nih.gov/pubmed/21918515%0Ahttp://www.cabi.org/cabebooks/
ebook/20083217094
Fama, E. F., & French, K. R. (2012). Size, Value, and Momentum in Internation Stock Returns.
Journal of Financial Economics, 105(3), 457–472.
Fama, E. F., & French, K. R. (2014). A Five-Factor Asset Pricing Model. SSRN Electronic
Journal, (September), 52.
Fama, E. F., & French, K. R. (2018). Choosing factors. Journal of Financial Economics, 128(2),
234–252. Retrieved from https://doi.org/10.1016/j.jfineco.2018.02.012
Fama, E., & French, K. (2006). The Value Premium and the CAPM. CFA Digest, 37(2), 67–
68.
Fernandez, M., Almaazmi, M. M., & Joseph, R. (2020). Foreign Direct Investment in Indonesia:
an Analysis From Investors Perspective. International Journal of Economics and
Financial Issues, 10(5), 102–112. Retrieved from https://doi.org/10.32479/ijefi.10330
Foye, J. (2018). A comprehensive test of the Fama-French five-factor model in emerging
markets.
Emerging
Markets
Review,
37,
199–222.
Retrieved
from
https://doi.org/10.1016/j.ememar.2018.09.002
Graham, B., & Dodd, D. L. (2009). Security Analysis (6th ed.). New York: McGraw-Hill.
Retrieved from https://doi.org/10.1036/0071592539
Guerard, J. B., Xu, G., & Gultekin, M. (2012). Investing with Momentum: The Past, Present,
17
and Future, 68–80.
Habib, M., Shiddiq, N., Hasnawati, S., & Huzaimah, R. A. F. (2020). Fama-French Three Factor
Model: A Study on LQ 45 Companies In Indonesia Stock Exchange. IOSR Journal of
Economics and Finance, 11(3), 25–30. Retrieved from https://doi.org/10.9790/59331103062530
Haugen, R. A., & Baker, N. L. (1996). Commonality in the determinants of Expected Stock
Returns.
Huang, S., Song, Y., & Xiang, H. (2020). The Smart Beta Mirage. SSRN Electronic Journal.
Retrieved from https://doi.org/10.2139/ssrn.3622753
Huang, T. L. (2019). Is the Fama and French five-factor model robust in the Chinese stock
market? Asia Pacific Management Review, 24(3), 278–289. Retrieved from
https://doi.org/10.1016/j.apmrv.2018.10.002
Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers:
Implications for Stock Market Efficiency. The Journal of Finance, 48(1), 65–91. Retrieved
from https://doi.org/10.1111/j.1540-6261.1993.tb04702.x
Karatzas, I., & Kardaras, C. (2020). Portfolio Theory and Arbitrage: A Course in Mathematical
Finance.
Rhode
Island.
Retrieved
from
https://books.google.co.id/books?hl=en&lr=&id=eSREEAAAQBAJ&oi=fnd&pg=PR9&
dq=Portfolio+Theory+and+Arbitrage:+A+Course+in+Mathematical+Finance+&ots=_SP
aU89i1Q&sig=kTrejWIy7EQ2UeOC17NZV1zk4s&redir_esc=y#v=onepage&q=Portfolio Theory and Arbitrage%3A A Course
Kubota, K., & Takehara, H. (2018). Does the Fama and French Five-Factor Model Work Well
in Japan? International Review of Finance, 18(1), 137–146. Retrieved from
18
https://doi.org/10.1111/irfi.12126
Lai, T., & Stohs, M. H. (2021). CAPM and Asset Pricing, (November).
Lai, T. Y., & Stohs, M. H. (2015). Yes, CAPM is dead. International Journal of Business,
20(2), 144–158.
Lester, A. (2019). On the theory and practice of multifactor portfolios. Journal of Portfolio
Management, 45(3), 87–100. Retrieved from https://doi.org/10.3905/jpm.2019.45.3.087
Li, B., Wang, J., Huang, D., & Hoi, S. C. H. (2018). Transaction cost optimization for online
portfolio selection.
Quantitative Finance, 18(8), 1411–1424. Retrieved from
https://doi.org/10.1080/14697688.2017.1357831
Lin, Q. (2017). Noisy prices and the Fama–French five-factor asset pricing model in China.
Emerging
Markets
Review,
31(2016),
141–163.
Retrieved
from
https://doi.org/10.1016/j.ememar.2017.04.002
Lintner, J. (1975). The Valuation of Risk Assets and The Selection of Risky Investments in Stock
Portfolios and Capital Budgets. Stochastic Optimization Models in Finance (Vol. 37).
ACADEMIC PRESS, INC. Retrieved from https://doi.org/10.1016/b978-0-12-7808505.50018-6
Lintner, J. (2016). Securitu Prices, Risk, and Maximal Gains from Diversification, 20(4), 587–
615.
Luo, P., Xiong, H., Zhan, G., Wu, J., & Shi, Z. (2009). Information-theoretic distance measures
for clustering validation: Generalization and normalization. IEEE Transactions on
Knowledge
and
Data
Engineering,
21(9),
1249–1262.
Retrieved
from
https://doi.org/10.1109/TKDE.2008.200
Mård, R. (2020). Momentum and the Fama-French Five-Factor Model: International Evidence.
19
Markowitz, H. (1952). Portfolio Selection Harry Markowitz. The Journal of Finance, 7(1), 77–
91.
Markowitz, H. M. (2009). The early history of portfolio theory: 1600-1960. Harry Markowitz:
Selected Works, (2), 31–42. Retrieved from https://doi.org/10.2469/faj.v55.n4.2281
Mossin, J. (1966). Equilibrium in a Capital Asset Market. Econometrica, 34(4), 768–783.
Munawaroh, U., & Sunarsih. (2017). Fama-French Six Factor: Evidence from Indonesia Sharia
Stock Index. Вестник Росздравнадзора, 6, 5–9.
Panopoulou, E., & Plastira, S. (2014). Fama French factors and US stock return predictability.
Journal
of
Asset
Management,
15(2),
110–128.
Retrieved
from
https://doi.org/10.1057/jam.2014.15
Patro, S. G. K., Sahoo, P. P., Panda, I., & Sahu, K. K. (2015). Technical Analysis on Financial
Forecasting. Retrieved from http://arxiv.org/abs/1503.03011
Patro, S. G. K., & sahu, K. K. (2015). Normalization: A Preprocessing Stage. Iarjset, 2(3), 20–
22. Retrieved from https://doi.org/10.17148/iarjset.2015.2305
Roy, R. (2021). A six‐factor asset pricing model: The Japanese evidence. Financial Planning
Review, 4(1), 1–18. Retrieved from https://doi.org/10.1002/cfp2.1109
Roy, R., & Shijin, S. (2018). A six-factor asset pricing model. Borsa Istanbul Review, 18(3),
205–217. Retrieved from https://doi.org/10.1016/j.bir.2018.02.001
Saleh, M. (2020). Empirical Testing of the Five-Factor Model of Fama and French in Indonesia
as an Emerging Capital Market. Journal of Economics and Business, 3(1). Retrieved from
https://doi.org/10.31014/aior.1992.03.01.175
Sarva Jayana, N., & Wening Gayatri, H. (2018). Selection of Leading Sectors Share Portfolio
20
using Capital Asset Pricing Model (Capm) in Indonesia Stock Exchange (IDX) Period.
International Journal of Innovative Science and Research Technology, 3(6). Retrieved
from www.finance.yahoo.com.
Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions
of Risk. The Journal of Finance.
Sutrisno, B., & Nasri, R. (2018). Is More Always Better? An Empirical Investigation of the
CAPM and the Fama-French Three-factor Model in Indonesia. KnE Social Sciences,
3(10), 454. Retrieved from https://doi.org/10.18502/kss.v3i10.3148
Treynor, J. L. (1961). Market Value, Time, and Risk. Records Management Journal, 1(2), 1–
15.
Retrieved
from
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5042&rep=rep1&type=pdf
%0Ahttps://www.ideals.illinois.edu/handle/2142/73673%0Ahttp://www.scopus.com/inw
ard/record.url?eid=2-s2.033646678859&partnerID=40&md5=3ee39b50a5df02627b70c1bdac4a60ba%0Ahtt
van der Hart, J., Slagter, E., & van Dijk, D. (2003). Stock selection strategies in emerging
markets.
Journal
of
Empirical
Finance, 10(1–2), 105–132. Retrieved from
https://doi.org/10.1016/S0927-5398(02)00022-1
Williams, J. B. (1939). The Theory of Investment Value. The Economic Journal, 49(193), 121.
Retrieved from https://doi.org/10.2307/2225202
Yoshimoto, A. (1996). The mean-variance approach to portfolio optimization subject to
transaction costs. Journal of the Operations Research Society of Japan, 39(1), 99–117.
Retrieved from https://doi.org/10.15807/jorsj.39.99
Zurek, M., & Heinrich, L. (2021). Bottom-up versus top-down factor investing: an alpha
21
forecasting perspective. Journal of Asset Management, 22(1), 11–29. Retrieved from
https://doi.org/10.1057/s41260-020-00188-9
22
Appendicies
Appendix A: End-to-end process from data collection until the result flowchart
23
24
Appendix B: Recapitulation of total companies in data sampling
Date
28/03/2010
28/06/2010
28/09/2010
28/12/2010
28/03/2011
28/06/2011
28/09/2011
28/12/2011
28/03/2012
28/06/2012
28/09/2012
28/12/2012
28/03/2013
28/06/2013
28/09/2013
28/12/2013
28/03/2014
28/06/2014
28/09/2014
28/12/2014
28/03/2015
28/06/2015
28/09/2015
28/12/2015
28/03/2016
28/06/2016
28/09/2016
28/12/2016
28/03/2017
28/06/2017
28/09/2017
28/12/2017
28/03/2018
28/06/2018
28/09/2018
28/12/2018
28/03/2019
28/06/2019
28/09/2019
28/12/2019
28/03/2020
28/06/2020
28/09/2020
28/12/2020
28/03/2021
28/06/2021
Total Companies in
JCI Market (A)
332
339
347
355
359
372
378
387
391
395
405
414
421
428
438
445
449
454
457
462
470
478
481
485
487
490
499
504
506
521
524
538
542
561
578
597
603
611
631
643
661
661
675
671
677
682
Total Companies Represent
Top 90% JCI MC (B)
64
64
70
77
77
83
85
89
92
93
96
101
106
116
120
122
122
123
125
120
115
129
123
119
118
119
119
128
131
130
130
129
138
151
148
148
149
150
156
145
144
141
154
144
179
177
Ratio (B/A)
19.3%
18.9%
20.2%
21.7%
21.4%
22.3%
22.5%
23.0%
23.5%
23.5%
23.7%
24.4%
25.2%
27.1%
27.4%
27.4%
27.2%
27.1%
27.4%
26.0%
24.5%
27.0%
25.6%
24.5%
24.2%
24.3%
23.8%
25.4%
25.9%
25.0%
24.8%
24.0%
25.5%
26.9%
25.6%
24.8%
24.7%
24.5%
24.7%
22.6%
21.8%
21.3%
22.8%
21.5%
26.4%
26.0%
Net data
sampling
61
64
69
70
70
81
84
86
89
93
94
98
105
115
116
118
120
120
122
119
113
126
121
119
117
118
117
127
131
129
127
126
136
147
141
141
121
124
125
111
114
104
108
91
112
109
25
Appendix C: Top 60 Stocks Based on Total Normalized Point Quarterly
No
Attribute
1 BNBR IJ Equity
2 BMTR IJ Equity
3 MEDC IJ Equity
4 IMAS IJ Equity
5 SCMA IJ Equity
6 INKP IJ Equity
7 TLKM IJ Equity
8 MNCN IJ Equity
9 ELTY IJ Equity
10 NISP IJ Equity
11 MPPA IJ Equity
12 JPFA IJ Equity
13 GJTL IJ Equity
14 BTEL IJ Equity
15 EMTK IJ Equity
16 TSPC IJ Equity
17 TINS IJ Equity
18 BBTN IJ Equity
19 INCO IJ Equity
20 AUTO IJ Equity
21 BRPT IJ Equity
22 LPKR IJ Equity
23 SMAR IJ Equity
24 BBRI IJ Equity
25 DOID IJ Equity
26 MEGA IJ Equity
27 DSSA IJ Equity
28 BMRI IJ Equity
29 SMMA IJ Equity
30 BBNI IJ Equity
31 AKRA IJ Equity
32 FASW IJ Equity
33 ADRO IJ Equity
34 INDF IJ Equity
35 MYOR IJ Equity
36 SMRA IJ Equity
37 BTPN IJ Equity
38 TOWR IJ Equity
39 GGRM IJ Equity
40 AMRT IJ Equity
41 PWON IJ Equity
42 PLIN IJ Equity
43 ADMF IJ Equity
44 JSMR IJ Equity
45 BDMN IJ Equity
46 PGAS IJ Equity
47 HMSP IJ Equity
48 LSIP IJ Equity
49 INTP IJ Equity
50 SMGR IJ Equity
51 AALI IJ Equity
52 BBCA IJ Equity
53 KLBF IJ Equity
54 ASII IJ Equity
55 PTBA IJ Equity
56 ANTM IJ Equity
57 UNTR IJ Equity
58 BYAN IJ Equity
59 ISAT IJ Equity
60 CPIN IJ Equity
61 BSDE IJ Equity
62 SMCB IJ Equity
63 UNVR IJ Equity
64 BNGA IJ Equity
65 PNBN IJ Equity
66 EXCL IJ Equity
67 BNII IJ Equity
68 INDY IJ Equity
69 BUMI IJ Equity
70 ITMG IJ Equity
A
Market Normalized
Cap
MC
6.09E+12
1.00E+00
8.95E+12
9.87E-01
1.12E+13
9.76E-01
7.57E+12
9.93E-01
6.82E+12
9.97E-01
8.97E+12
9.87E-01
1.60E+14
2.82E-01
1.29E+13
9.68E-01
6.27E+12
9.99E-01
9.88E+12
9.82E-01
8.31E+12
9.90E-01
6.53E+12
9.98E-01
8.02E+12
9.91E-01
6.69E+12
9.97E-01
6.26E+12
9.99E-01
7.70E+12
9.93E-01
1.38E+13
9.64E-01
1.43E+13
9.62E-01
4.84E+13
8.03E-01
1.08E+13
9.78E-01
8.17E+12
9.90E-01
1.47E+13
9.60E-01
1.44E+13
9.61E-01
1.30E+14
4.25E-01
1.09E+13
9.77E-01
1.01E+13
9.81E-01
1.39E+13
9.64E-01
1.36E+14
3.93E-01
1.12E+13
9.76E-01
7.23E+13
6.92E-01
6.56E+12
9.98E-01
7.12E+12
9.95E-01
8.16E+13
6.49E-01
4.28E+13
8.29E-01
8.24E+12
9.90E-01
7.49E+12
9.93E-01
1.50E+13
9.59E-01
1.32E+13
9.67E-01
7.70E+13
6.70E-01
9.95E+12
9.82E-01
9.03E+12
9.86E-01
7.06E+12
9.95E-01
1.20E+13
9.72E-01
2.33E+13
9.20E-01
4.80E+13
8.05E-01
1.07E+14
5.29E-01
1.23E+14
4.54E-01
1.75E+13
9.47E-01
5.87E+13
7.55E-01
5.61E+13
7.67E-01
4.13E+13
8.36E-01
1.58E+14
2.94E-01
3.30E+13
8.75E-01
2.21E+14
0.00E+00
5.29E+13
7.82E-01
2.34E+13
9.20E-01
7.92E+13
6.60E-01
6.00E+13
7.49E-01
2.93E+13
8.92E-01
3.02E+13
8.88E-01
1.57E+13
9.55E-01
1.72E+13
9.48E-01
1.26E+14
4.42E-01
4.80E+13
8.05E-01
2.75E+13
9.00E-01
4.51E+13
8.18E-01
4.39E+13
8.24E-01
2.46E+13
9.14E-01
6.28E+13
7.36E-01
5.73E+13
7.61E-01
B
Normalized
BV/MC
1.7825
0.9605
0.6373
0.3373
0.7210
0.3829
0.1408
0.0672
0.2010
0.0999
1.8552
1.0000
0.2998
0.1537
0.3762
0.1953
1.4668
0.7887
0.6133
0.3243
0.7360
0.3910
0.4270
0.2229
0.4707
0.2467
0.5527
0.2913
0.4407
0.2304
0.3307
0.1705
0.3009
0.1543
0.4358
0.2277
0.2949
0.1510
0.3881
0.2017
0.8477
0.4518
0.6482
0.3432
0.3866
0.2009
0.2585
0.1312
0.0173
0.0000
0.4575
0.2395
0.1149
0.0531
0.2618
0.1330
0.4443
0.2323
0.4833
0.2535
0.4280
0.2235
0.2376
0.1199
0.2455
0.1242
0.3861
0.2006
0.2289
0.1151
0.2684
0.1366
0.3155
0.1622
0.1092
0.0500
0.2632
0.1338
0.1090
0.0499
0.2137
0.1069
0.2819
0.1440
0.3162
0.1626
0.3323
0.1714
0.3296
0.1699
0.1422
0.0680
0.0918
0.0405
0.3178
0.1635
0.2484
0.1257
0.2340
0.1179
0.2110
0.1054
0.2020
0.1005
0.1667
0.0813
0.2370
0.1195
0.1345
0.0637
0.4416
0.2309
0.2118
0.1058
0.0492
0.0173
0.6570
0.3481
0.1341
0.0635
0.4172
0.2176
0.4474
0.2340
0.0347
0.0094
0.2898
0.1483
0.4380
0.2289
0.2623
0.1333
0.1760
0.0863
0.2457
0.1243
0.1300
0.0613
0.1227
0.0573
BV/ MC
C
Profit and Normalized
Loss
PNL
3.18E+11
0.0686
3.83E+11
0.0795
-2.15E+10
0.0116
1.69E+11
0.0436
2.62E+11
0.0592
2.19E+11
0.0519
5.30E+12
0.9051
2.82E+11
0.0626
1.12E+11
0.0340
2.66E+11
0.0598
1.39E+10
0.0175
5.79E+11
0.1125
3.06E+11
0.0666
8.76E+07
0.0152
2.13E+11
0.0509
1.03E+11
0.0324
6.87E+11
0.1307
4.15E+11
0.0849
1.38E+12
0.2468
1.69E+11
0.0435
2.93E+11
0.0643
2.68E+11
0.0601
7.34E+11
0.1385
5.86E+12
1.0000
2.81E+11
0.0623
3.94E+11
0.0813
1.10E+11
0.0336
4.06E+12
0.6965
5.97E+11
0.1154
1.27E+12
0.2281
-4.06E+10
0.0084
1.02E+11
0.0323
5.43E+12
0.9275
1.87E+12
0.3292
2.36E+11
0.0548
1.24E+11
0.0360
3.48E+11
0.0737
1.86E+11
0.0465
1.61E+12
0.2860
1.36E+11
0.0380
2.02E+11
0.0491
3.29E+10
0.0207
5.12E+11
0.1012
4.17E+11
0.0852
1.13E+12
0.2045
2.04E+12
0.3578
2.42E+12
0.4213
5.19E+11
0.1024
1.09E+12
0.1978
1.28E+12
0.2306
1.21E+12
0.2177
2.76E+12
0.4790
5.03E+11
0.0997
4.30E+12
0.7368
6.71E+11
0.1279
7.00E+11
0.1328
1.24E+12
0.2228
4.44E+11
0.0898
9.12E+11
0.1684
7.04E+11
0.1335
5.54E+11
0.1083
3.67E+11
0.0768
1.14E+12
0.2059
1.01E+12
0.1851
2.21E+11
0.0523
1.33E+12
0.2379
9.28E+10
0.0308
-9.03E+10
0.0000
8.09E+11
0.1511
5.77E+11
0.1121
D
Total Normalized
Asset
Assets
3.18E+13
0.6126
1.44E+13
0.7671
2.04E+13
0.7834
7.99E+12
0.2083
2.52E+12
0.7658
5.30E+13
0.0000
9.98E+13
0.8171
8.20E+12
0.7584
1.71E+13
0.3148
5.01E+13
0.6053
1.14E+13
0.7486
6.98E+12
0.6724
1.04E+13
0.6521
1.24E+13
0.7490
4.31E+12
0.7378
3.59E+12
0.7280
5.88E+12
0.6045
6.84E+13
0.6518
1.96E+13
0.8212
5.59E+12
0.6141
1.59E+13
0.0000
1.62E+13
0.4702
1.25E+13
0.5927
4.04E+14
0.5330
7.60E+12
0.6676
5.16E+13
0.5056
5.95E+12
0.6907
4.50E+14
0.6838
2.78E+13
0.3798
2.49E+14
0.7362
7.67E+12
0.5446
4.50E+12
0.5898
4.00E+13
0.0000
4.74E+13
0.6467
4.40E+12
0.4447
6.14E+12
0.4208
3.45E+13
0.2281
7.41E+12
0.0000
3.07E+13
0.6959
4.26E+12
0.2944
4.93E+12
0.3753
4.43E+12
0.0000
7.60E+12
0.0000
1.90E+13
0.6483
1.18E+14
0.6182
3.19E+13
0.7153
2.05E+13
0.6630
5.56E+12
0.6768
1.53E+13
0.6659
1.56E+13
0.6151
8.79E+12
0.6601
3.24E+14
0.6738
7.03E+12
0.7449
1.13E+14
0.5403
8.72E+12
0.7506
1.22E+13
0.5844
2.97E+13
0.5980
8.33E+12
0.6554
5.28E+13
0.0000
6.52E+12
0.5964
1.17E+13
0.5583
1.04E+13
0.3541
8.70E+12
0.6586
1.44E+14
0.4600
1.09E+14
0.3955
2.73E+13
0.0000
7.51E+13
0.5810
1.14E+13
0.0000
6.30E+13
0.0000
9.74E+12
0.0000
E
F
G
H
I
J
AxF + BxG
Price Normalized
+ CxH +
SMB HML RMW CMA UMD
Growth
UMD
DxI + ExJ
-0.0526
0.0000 1.000 0.999 0.666 0.666 0.000
2.4132
0.1667
0.0259 1.000 0.999 0.666 0.999 0.500
2.1559
0.1271
0.0213 1.000 0.999 0.333 0.999 0.500
2.1556
8.4000
1.0000 1.000 0.333 0.333 0.333 1.000
2.0994
2.1696
0.2629 1.000 0.333 0.666 0.999 1.000
2.0973
0.2568
0.0366 1.000 0.999 0.333 0.999 0.500
2.0212
0.1948
0.0293 0.500 0.666 0.999 0.999 0.500
1.9784
0.1667
0.0259 1.000 0.666 0.666 0.999 0.500
1.9105
0.0694
0.0144 1.000 0.999 0.333 0.333 0.000
1.9032
1.2283
0.1515 1.000 0.999 0.666 0.666 1.000
1.9008
0.0215
0.0088 1.000 0.999 0.333 0.666 0.000
1.8847
1.6821
0.2052 1.000 0.666 0.666 0.666 1.000
1.8744
1.0412
0.1294 1.000 0.999 0.666 0.666 1.000
1.8456
0.3824
0.0515 1.000 0.999 0.333 0.666 0.500
1.8178
0.6167
0.0792 1.000 0.999 0.333 0.666 1.000
1.8169
0.6000
0.0772 1.000 0.666 0.333 0.666 1.000
1.6789
0.4651
0.0613 1.000 0.666 0.666 0.666 1.000
1.6176
0.0706
0.0146 1.000 0.666 0.666 0.666 0.000
1.6041
0.3000
0.0417 0.500 0.666 0.999 0.999 0.500
1.5898
0.3716
0.0502 1.000 0.666 0.333 0.666 0.500
1.5612
0.2233
0.0326 1.000 0.999 0.666 0.999 0.500
1.5009
0.1200
0.0204 1.000 0.999 0.666 0.333 0.000
1.4994
0.5143
0.0671 1.000 0.666 0.999 0.333 1.000
1.4982
0.0753
0.0151 0.500 0.666 0.999 0.333 0.000
1.4764
0.0404
0.0110 1.000 0.333 0.666 0.666 0.000
1.4636
0.1321
0.0219 1.000 0.999 0.666 0.333 0.500
1.4541
0.0704
0.0146 1.000 0.333 0.333 0.666 0.000
1.4525
0.2000
0.0299 0.500 0.666 0.999 0.666 0.500
1.4513
0.0000
0.0062 1.000 0.999 0.666 0.333 0.000
1.4118
0.5638
0.0729 0.500 0.999 0.999 0.666 1.000
1.3903
0.4245
0.0565 1.000 0.666 0.333 0.333 1.000
1.3872
0.6711
0.0856 1.000 0.666 0.333 0.333 1.000
1.3678
0.0176
0.0083 0.500 0.666 0.999 0.999 0.000
1.3335
0.3133
0.0433 0.500 0.666 0.999 0.666 0.500
1.3293
0.4748
0.0624 1.000 0.333 0.666 0.333 1.000
1.2753
0.2941
0.0410 1.000 0.666 0.333 0.333 0.500
1.2571
0.4788
0.0629 1.000 0.666 0.666 0.333 1.000
1.2547
2.0833
0.2527 1.000 0.333 0.333 0.999 1.000
1.2516
0.5088
0.0664 0.500 0.666 0.999 0.666 1.000
1.2397
0.6190
0.0795 1.000 0.333 0.333 0.333 1.000
1.1888
0.2500
0.0358 1.000 0.333 0.333 0.333 0.500
1.1811
0.5217
0.0680 1.000 0.666 0.333 0.999 1.000
1.1662
0.0802
0.0157 1.000 0.666 0.666 0.333 0.000
1.1482
0.5802
0.0749 0.500 0.666 0.666 0.666 1.000
1.1375
0.0741
0.0150 0.500 0.666 0.999 0.666 0.000
1.1316
-0.0065
0.0055 0.500 0.333 0.999 0.666 0.000
1.1209
0.1796
0.0275 0.500 0.333 0.999 0.666 0.500
1.1166
0.1867
0.0283 0.500 0.666 0.666 0.666 0.500
1.1153
0.1646
0.0257 0.500 0.666 0.999 0.666 0.500
1.1152
0.1314
0.0218 0.500 0.666 0.999 0.666 0.500
1.1131
0.0698
0.0145 0.500 0.333 0.999 0.666 0.000
1.1103
0.1261
0.0211 0.500 0.333 0.999 0.666 0.000
1.1075
0.2143
0.0316 0.500 0.333 0.666 0.666 0.500
1.0426
0.1739
0.0268 0.500 0.666 0.999 0.333 0.500
1.0089
0.1275
0.0213 0.500 0.333 0.666 0.666 0.500
1.0080
0.2242
0.0328 0.500 0.999 0.666 0.333 0.500
0.9899
0.0907
0.0170 0.500 0.333 0.999 0.666 0.000
0.9859
0.7578
0.0959 0.500 0.333 0.666 0.666 1.000
0.9724
0.1111
0.0194 0.500 0.999 0.999 0.999 0.000
0.9618
1.4507
0.1779 0.500 0.333 0.666 0.333 1.000
0.9303
0.3333
0.0457 0.500 0.666 0.666 0.333 0.500
0.9033
0.1149
0.0198 0.500 0.999 0.666 0.333 0.000
0.8769
-0.0088
0.0052 0.500 0.333 0.999 0.666 0.000
0.8686
0.2150
0.0317 0.500 0.666 0.999 0.333 0.500
0.8551
0.1176
0.0201 0.500 0.999 0.666 0.333 0.000
0.8455
0.3252
0.0447 0.500 0.666 0.999 0.999 0.500
0.7580
0.1404
0.0228 0.500 0.333 0.333 0.333 0.500
0.6558
0.1667
0.0259 0.500 0.666 0.333 0.999 0.500
0.5526
0.1303
0.0216 0.500 0.333 0.999 0.999 0.500
0.5500
0.1198
0.0204 0.500 0.333 0.666 0.999 0.000
0.4744
26
Appendix D: Formulas
No
Item
1
Min-Max
Normalization
Formula
Description
𝐵 − 𝑚𝑖𝑛 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴
𝑋=(
) ∗ (𝐷 − 𝐶)
𝑚𝑎𝑥 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴 − 𝑚𝑖𝑛 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴
+𝐶
A = The set of quarterly
data
B = The current position
C & D = is the new
predefined lower and
upper
boundaries,
respectively
2
Net Return of
𝑁𝑅𝑊 =
‘Whole’
𝑃𝑠𝑁(𝑄+𝑋) − 𝑇𝐶 𝑠𝑒𝑙𝑙 𝑥 𝑃𝑠𝑁(𝑄+𝑋)
−1
𝑃𝑠𝑁(𝑄) + 𝑇𝐶 𝑏𝑢𝑦 𝑥 𝑃𝑠𝑁(𝑄)
Transaction
NRW = Net Return of
Stocks
in
Whole
Scenario
TC = Transaction Cost
P 𝑆𝑁(𝑄) = Price of stock
N in Q period
P 𝑆𝑁(𝑄+𝑋) = Price of
stock N in Q+X period
X
=
Rebalancing
frequency (once in
every X quarter(s))
3
Net Return of
‘Partial Buy/
𝑃𝑠𝑁(𝑄+𝑋)
|)
𝑃𝑠𝑁(𝑄)
𝑃𝑠𝑁(𝑄) 𝑥 (1 + 𝑇𝐶)
𝑃𝑠𝑁(𝑄+𝑋) (1 − 𝑇𝐶 𝑥 |
𝑁𝑅𝑃 =
Sell’
NRP = Net Return of
Stocks
in
Partial
Scenario
Transaction
4
The EqualWeighted
𝑅𝑝𝑄 =
𝑅𝑝𝑄 = Portfolio return in
Q period
∑𝑁=60
𝑅𝑠𝑁𝑄
1
𝑁
𝑅𝑠𝑁𝑄 = Return of stock N
in Q period
Portfolio
Returns
5
6
Portfolio
Quarter-onQuarter Return
Portfolio
Return in
CAGR
𝑅𝑝 𝑄 − 𝑜 − 𝑄 = (
1
𝐸𝑛𝑑𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑅𝑝𝑄𝑍
)(𝑍−𝐴)
𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑅𝑝𝑄𝐴
4
Rp CAGR = [(1 + Rp Q − o − Q )𝑋 ] − 1
Rp Q-o-Q = Portfolio
Return Q-o-Q growth
𝑄𝑍
=
Ending
rebalancing period
Q
𝑄𝐴 = Beginning
rebalancing period
Q
Rp CAGR = Portfolio
Return in CAGR
X
=
Rebalancing
frequency (once in
every X quarter(s))
27