Momentum Paper - Ver 1

8/2/2019 Momentum Paper - Ver 1

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Capturing Alpha using Momentum Strategies in Sector Funds

Abstract

Momentum is a widely researched topic in academia and has been shown to be persistent throughout time

and across various asset classes. In this paper, we use industry focused mutual funds and indexes to study

momentum. We found a consistent and statistically significant alpha generation in momentum-based

portfolio using industry-focused mutual funds. To separate the performance attributed to momentum

phenomenon from managerial skills, we also study momentum-based portfolio performance using passive

indexes, based on industrial classification. We report annualized excess returns of 3.29% for industry

focused mutual funds and 3.91% for industry-based passive indexes, over S&P 500 Index.


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Capturing Alpha using Momentum Strategies in Sector Funds

Investment using momentum strategies require that investors invest in securities or portfolios that

have outperformed the rest of the stock universe based on short-term historical performance. In a way, it

is contrarian view to the famous investment philosophy Buy Low Sell high because momentum says

Buy High Sell higher. The expectations of the investor are that the investments superior prior

performance will continue into the future causing the investment to earn an abnormally high risk-adjusted

return.

There has been extensive research on individual stocks momentum and their ability to generate

abnormal stock returns. In simple terms, momentum strategy comprises of buying past winners and

selling past losers. Jegadeesh and Titman (1993) studied intermediate term correlation in the 1965-89

periods and uncovered a momentum effect for 3 to12-month holding periods. They found that stock

selections based on 6-month stock performance and holding the portfolio for the following 6 months

realized annualized abnormal returns of about 12%. In 1999, Chan, Jegadeesh and Lakonishok (1996)

discovered a similar price momentum in the 1973-93 and 1994-98 (out-of-sample) periods. During the

same period, Schierek, De Bondt and Weber (1999) found that stocks on the Frankfurt Stock Exchange

also exhibit intermediate-term momentum.

There has been various studies performed on other asset classes and various global capital

markets. Rouwenhorst(1998) showed the presence of momentum returns in International equity markets

using data from 1980-1995. Asness, Liew and Stevens (1997) studied the influence of Momentum along

with Book-to-Market ratio, market equity on cross-section of expected individual stocks returns within

US and other countries. Okunev and White(2003) examined momentum trading strategies in foreign

exchange markets throughout 1980s and 1990s. Finally, a comprehensive study by Asness, Moskowitz

and Pedersen(2008) supported the presence of momentum-based excess returns in global equity and

fixed-income markets, currencies and commodities. Various explanations and hypothesis have been


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proposed to explain the presence of abnormal returns by momentum strategies. Daniel, Hirshleifer and

Subramanyam(1998, 2001) proposed that investor overconfidence and biased self-attribution are two

major reasons for Market Under- and Overreactions, especially self-attribution causes positive short-lag

autocorrelation which is momentum phenomenon. Similarly, Barberis, Shleifer and Vishny(1998)

provided a parsimonious model of investment sentiment causing underreaction and overreaction in stock

prices. Moskowitz and Grinblatt (1999) made two major classifications of theories to explain momentum

behavioral and rational. Their studies showed that individual stock momentum is substantially

explained by industry momentum. Grinblatt and Han(2005) proposed prospect theory and mental

accounting responsible for momentum phenomenon. The study also showed that past returns have no

predictability for the cross-section of returns once a variable proxying for aggregate unrealized capital

gains is controlled (mental accounting theory).

ONeal(2000) shows that the strategy of buying previous intermediate-term top-performing sector

funds outperformed S&P500 Index over the 10-year period from May 1989 through April 1999 on a total-

return basis. This paper explores the persistence of momentum phenomenon and the presence of superior

risk-adjusted return of momentum-based portfolios. This paper offers out-of-sample testing of the

hypothesis testing, that buying winner and selling losers offer abnormal returns in a consistent manner.

Eakins and Stansell (2004) reports that momentum strategies outperformed benchmarks according to the

Sharpe Ratio. They also reported that a short look-back, a time-period used for performance ranking,

period provided a better risk profile. They also noted that by dropping an Internet sector out of studies

most combinations of look-back and holding period of momentum strategies underperformed.

Moskowitz and Grinblatt used the CRSP data base to for industry based market-value portfolios.

They showed that individual stock momentum strategies generate large returns because of the profitability

of industry momentum strategies. They also showed that industry momentum is present after controlling

for size (measured by market capitalization) and Book Equity/Market Equity (book-to-price ratio) factors.


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The current paper uses Fidelity Select Mutual Funds to verify if momentum strategies and its

abnormal profits were the result of data-mining or a temporary market phenomenon or a persistent market

anomaly which could be exploited for abnormal profits. We carry out our analysis using investable

vehicle, mutual funds, using time-period of 1995-2010, which involved different equity regimes, i.e. 3-

bull (1996-1999, 2002-2006, 2009-2010) and 2-bear (2000-2001, 2008-2009) cycle as well as time period

with high-volatility and low-volatility markets, to provide robust results of our strategy performance.

This paper is organized as follows. Section I discusses the data and methodology, along with

characteristics of the mutual funds and indexes used in this study. Section II explores the presence of the

momentum phenomenon in the Fidelity Select Mutual Funds series, and motivates the further study of

exploring industries momentum phenomenon using passive indexes. Section III analyzes interplay of

momentum phenomenon and active management, including analysis of passively managed industry

indexes from the Dow Jones, during the same time period. Section IV examines the effect of economic

cycles on momentum and Section V examines duration of the momentum and value effect. Section VI

summarizes the conclusion.

I.

Data and Methodology

a. Sector Mutual FundsWe used 33 mutual funds of Fidelity Select series, including money-market funds, to explore any

momentum phenomenon present in mutual funds focusing on specific sectors1. Fidelity Sector mutual

funds are widely used in investment management industry, and they offer a wide variety of sector mutual

funds. As mentioned in Neal(2000), there are two advantages of using Sector mutual funds as opposed to

using individual stocks that fall under a specific official classification sector. First, transaction costs for

mutual funds are precisely known2. Second sector mutual funds allow the investors to adopt manageable

investment vehicles. It is more difficult for investors to obtain a large number of equity stocks within a

particular industry/sector. Due to these reasons, the results of this study have direct implications and


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d. MethodologyPortfolio ConstructionThe momentum phenomenon is examined by using 11 months to rank the funds and a one month

holding period. Following is the detailed procedure used to explore the momentum phenomenon:

Monthly returns for each individual sector fund are calculated December 31, 1994 to November30, 1995.

The total returns for each of the 33 sector mutual funds are sorted in descending order. The top 11mutual funds were used to create a Winner portfolio, consist of equal-weighted Winner sector

mutual funds. The last 11 funds in descending order were used to create a Loser portfolio, again

with equal-weighted Loser sector mutual funds. The remaining 11 funds that fall in between

Winner and Loser ranking, are used to create an equal-weighted Middle portfolio. A zero cost,

self-financing portfolio with zero risk consisting of Winners minus Losers (WML) is also created.

Total returns for the momentum-based portfolios are calculated by compounding monthly returns,to account for the variability in returns, whereas total returns for benchmarks are holding period

returns. The reason behind the difference of treatment is to compare portfolio results versus

benchmark buy-and-hold strategy.

All the portfolios are held for one month and then ranked and rebalanced again, based on theirprevious 11 months performance. For example, on January 1, 1996, funds are ranked based upon

their performance during February 1995December 1995. Notice, that 10 months considered

for ranking are same as used earlier. In other words, overlapping returns are used for ranking

purpose, with only one month added for the first time.

In addition to Winner and Loser portfolios, the ranking position of each fund is noted.

II. Momentum and Active Industry Mutual Funds


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First, the total holding period return is examined. Table 1 indicates the dollar value if $100 was

invested in each of the four portfolios on December 1, 1995and the portfolio strategy followed until

December 31, 2010. The WML Portfolio with a return of $300.25 clearly outperforms of the other

portfolios followed by the Winner Portfolio with $259.19, the SP1500 with $221.71., the SP500 with

$207.75, the Middle Portfolio with $102.03 and lastly the Loser Portfolio with $58.90.

Table.I Descriptive Statistics of Momentum-based portfolios and Benchmark Indexes

AverageMonthlyReturn

MonthlyStandardDeviation

SharpeRatio

MaximumDrawdown

BestMonth

WorstMonth

MADPositiveMonths

NegativeMonths

%Pos %Neg

S&P500 0.394% 4.790% 0.0265 56.87% 9.2% -18.6% 3.64% 110 60 64.7% 35.3%

S&P1500 0.431% 4.810% 0.0339 54.72% 9.6% -19.2% 3.67% 109 71 60.6% 39.4%

Winner 0.758% 5.730% 0.0756 59.33% 16.4% -22.0% 4.43% 107 73 59.4% 40.6%

Middle 0.228% 5.290% -0.0127 61.54% 15.5% -24.0% 3.98% 100 80 55.6% 44.4%

Loser -0.017% 6.590% -0.0476 78.47% 17.2% -22.1% 5.00% 96 84 53.3% 46.7%

WML 0.776% 5.730% 0.0821 43.44% 23.8% -15.1% 4.11% 106 74 58.9% 41.1%

From the results above, it is clear that Winner and WML portfolio has better risk-return characteristics,

while their Sharpe ratio is compared against their benchmarks, nonetheless both Winner and WML

portfolio exhibit higher volatility of returns then their benchmarks. Interestingly, Loser Portfolio has even


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higher volatility of returns on a monthly basis. The results show that volatility of all four momentum-

based portfolios are higher than benchmarks. The WML had the highest Shape ratio of 0.0821 followed

by the Winner portfolio with a ratio of 0.0756. Both these portfolios have better risk-return characteristics

than the S&P500 (Sharpe ratio = 0.0265) and S&P1500 (Sharpe ratio = 0.0339). The maximum

drawdown explains the downside that a portfolio has experienced from its peak. It is clear that from

1995-2010, performance drawdown would be present during 2007-2009 economic turmoil for this

research. The Winner, Middle and Loser portfolios all had higher drawdown compared to the

benchmarks, but the WML portfolio had the smallest drawdown of only 43.44%, and it is attributed to the

short positions in the WML portfolio acting as a hedge during downturn of 2007-2009. Higher % of

months with Positive returns of SP500 and SP1500 is consistent with higher volatility exhibited by

Momentum portfolios.

Figure 2 represent the dollar returns that an investor would have realized if a portfolio consisted of

corresponding ranked fund for every $ 100 invested on December 1, 1995. For example, if an investor

had invested 100% of her funds into the second ranked fund, with a monthly rebalancing, the investor

would have accrued $292.25 on December 31, 2010. Please note that fourth ranked fund seemed to be an

outlier. Our detailed analysis of Winner funds on rank 4 revealed that this extra-ordinary performance of

rank 4 is clearly by chance, i.e. it is not driven by any particular fund during any time period. Obviously,

there is no theoretical rationale backing the superior performance of any particular ranked fund.


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Regression Results of Momentum-based portfolio

The one-factor model is used to explore the alpha of momentum investing. Regression analysis

with the momentum-based portfolio excess returns as the independent variable and the benchmark returns

as the independent variable are estimated. Specifically,

where, represents, monthly time series momentum-based portfolio returns excess the risk-free

rate, represents monthly time-series of index returns, is risk-free 3 month treasury bill yield, is

standard error of regression.

Table. II Regression results of Momentum-based Portfolios (CAPM Model)


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SP500 Index as benchmark

Portfolio Alpha Beta R2 p-value Std. Error IR

Winner0.590%

2.13(0.035)

0.929416.13

(0.000)0.592 0.0000 0.0014 0.0833

Middle 0.070%-0.75(0.450)

1.003621.51(0.000)

0.820 0.0000 0.0005 -0.0851

Loser-0.200%

0.43(0.667)

1.170828.60

(0.000)0.721 0.0000 0.0012 -0.1218

WML0.780%

1.86(0.065)

-0.2414-2.74

(0.000)0.040 0.0067 0.0032 0.0421

SP1500 Index as benchmark

Portfolio Alpha Beta R2 p-value Std. Error IR

Winner0.550%

2.08

(0.040)

0.949117.24

(0.000)

0.624 0.0000 0.0013 0.0945

Middle0.030%

-0.94

(0.351)

1.011822.06

(0.000)

0.842 0.0000 0.0004 -0.0963

Loser-0.240%

0.22

(0.825)

1.172930.93

(0.000)

0.731 0.000 0.0012 -0.1270

WML0.780%

1.87

(0.063)

-0.2238-2.55

(0.0117)

0.035 0.0114 0.0032 0.0424

The results in Table 2 indicate that the WML portfolio successfully captured 0.78% alpha per month, and

the Winner portfolio captured 0.59% alpha per month. Alpha generated by WML and Winner portfolios

are statistically significant 10% and 5% level, respectively. Interestingly, they exhibit better risk-return

profile and higher alpha with lower beta (negative beta in case of WML) compared to other momentum-

based portfolios. Information ratio is a measure of risk-adjusted return and is calculated by expected

active return divided by tracking error and is used to measure the skills of managers. Both, Winner and

WML portfolios have high positive information ratio indicating their superior risk-adjusted performance.

Similar results are obtained using the SP1500 index as benchmark.


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III: Momentum or Active Managerial Skills

One counter-argument that could be made against the results above which imply the presence of positive

alpha in momentum-based portfolios is that these alphas could be a result of managerial skills (i.e. stock

picking skills of mutual fund manager).

We take three different approaches to test the hypothesis that these alphas are substantially, if not

completely attributed to momentum: (A) distribution analysis, (B) regression analysis, and (C) passive-

managed index based momentum portfolios.

III.A: Distribution AnalysisFirst, consider the frequency distribution of individual funds among all portfolios. That is observing how

many of times a particular fund was allocated to the Winner, Middle and Loser portfolios. If the results

of momentum-based portfolios are driven by managerial skills, then the frequency distribution in the

Winner portfolio would be skewed towards those funds with skilled managers. Figure 3 shows the

frequency distribution of each fund in the Winner, Middle and Loser portfolios. Visual inspection reveals

that the distributions are fairly uniform among all 33 mutual funds. This result rejects the idea that only a

few funds ran by skilled managers are generating the alphas in the momentum-based portfolios in this

study.


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III.B: One-Factor CAPM and Two-Factor Momentum based RegressionRegression analysis is used to further explore the relationship between managerial skills and momentum-

based portfolio alpha. This time the dependent variable is monthly time-series returns for all 33 mutual

funds and the independent variable is the monthly returns on the S&P500 or S&P1500. Average alpha of

33 mutual funds, is 0.153% per month against SP500 and 0.114% per month against SP1500 as

benchmark with 10% significance level. By comparing this 0.153% alpha per month with 0.590% alpha

per month of Winner portfolio, it is clear that momentum-based portfolio generated alpha is not

attributed (at least not completely), to mutual fund manager skills. The complete results of individual

mutual fund regressions are presented in appendix.

Table. III One-Factor CAPM Regression results of Individual Mutual Funds (CAPM Model)

Benchmark Alpha Beta R

2

p-value Std. Error

SP500 0.153%0.41

(0.551)

1.03513.70

(0.000)0.474 0.0000 0.003

SP1500 0.114%0.31

(0.568)

1.04514.09

(0.000)0.486 0.000 0.003


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To further examine the source of alpha, the moving average return for the past 11-months is included as a

second independent variable in the regression model. The results found the alpha of 0.023%, and

coefficient for risk premium is 0.99 with coefficient for momentum factor is 0.437 against benchmark

SP500 Index. This alpha is significant at 10% significance level whereas coefficient for momentum is

significant at 5% level. Similar results are obtained by using SP1500 index as benchmark. These factor

models show that most of the alpha generated by mutual funds underthe one-Factor model is attributed

to Momentum. It is still clear that the earlier results (presented in Table II.) of alpha from Momentum-

based portfolios are not because of active managerial skills.

Table. IV Two-Factor Regression results of Individual Mutual Funds

Benchmark Alpha Beta Momentum R2 p-value Std. Error

SP500 0.023%0.09

(0.741)

0.98912.84

(0.000)

0.4372.58

(0.050)0.512 0.0000 0.003

SP1500 0.000%-0.00

(0.739)

1.00013.21

(0.000)

0.4262.55

(0.053)0.524 0.0000 0.003

III. C. Momentum and Passively managed IndexesIn this section, we try to compare the results of momentum-based portfolio and its alpha, this time using

passively managed indexes. As mentioned in Data and Methodology, we use 37 Dow Jones Global

Indexes series as sector indexes. The same portfolio construction and ranking methodology developed

previously were used. Figure 4 provides the NPV results of depositing $100 on December 1, 1995. Once

again, the WML Portfolio outperforms its peer, by returning $319.76 for every $100 invested, followed

by the Winner Portfolio which returned$307.65, SP 1500 returning $221.71, and the SP 500 returning

$207.75. In agreement with the mutual fund portfolio results, the Middle Portfolio and Loser portfolio

underperformed their benchmarks with returning $119.37 and $87.89 only. Interestingly, momentum-

based portfolio using passively managed indexes outperforms momentum-based portfolios using actively


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managed mutual funds Winner Portfolio using passive indexes returns $307.65 compared to Winner

Portfolio using Active mutual funds which returns$259.19.

The individual rank-based portfolio performance was studied, and results are shows in Figure 5. It is

evident that higher ranked portfolios (1-11) tend to outperform lower-ranked (12-33) portfolios. It is

shown that $100 invested in, only 3rd ranked fund, with monthly rebalancing, would have returned

$344.44 on 31st Dec, 2010. Once again we see a portfolio made using Rank 7 is an outlier (same as Rank

4 in case of Active mutual fund).


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IV.Following Momentum (and Value)The results in this paper have shown a significant momentum effect present in sector mutual funds and

passive sector indices. We now explore how long the momentum effects last, in other words, how long

does Winner stays winner and how long does Loser take to become winner . Figure 6 shows the

relationship between the average realized monthly returns and number of months following the ranking

period for all three portfolios, namely Winning, Middle and Loser portfolio. The results indicate a

sharply decreasing pattern of average monthly returns as the follow-up period increases. It suggests that

the, momentum effect fades away very quickly. This justifies a short holding period of momentum-based

portfolio after ranking.


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Over the three years following the ranking, the Winner portfolio has almost 0% per month average

returns. A similar pattern for Winner portfolio is observed using Dow Jones indexes as demonstrated in

Figure 7. Interestingly, it also shows that after a holding period of 3 years, the Winners, Middle and

Loser portfolios return similar returns of about 0.15% average monthly.


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These results support the hypothesis that value stocks tend to outperform growth in long-term.

Empirically researchers have shown that value stocks have outperformed the equity market in general,

(Fama and French (1998) and Lakonishok, Shleifer and Vishny (1994)). Asness (1997) has done an

exceptional job in explaining the interaction between value and momentum. Our results support the

negative correlations among value and momentum stocks as well as ability to delivery excess returns by

both value and momentum stocks, although over the different time horizon.

V. Economic Rationale, Proposed Theories & Practical ApplicationVarious theories have been proposed by other researchers, to explain the persistence of momentum in

various asset classes as well as in global financial market. The results indicate, that alpha is

significantly explained by momentum-factor, not by individual stock selections.


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interesting results. A further research avenue is to find the optimal number of funds to include in a

momentum portfolio, to reduce turnover and transaction costs. We focused our studies on direct

investment vehicles, compared to large number of individual securities. The results of this study have

direct application in practitioners world. One sentence explanation is needed

Notes

1, Please note in this paper, Sector refers to the classification used by Mutual fund manager, that is Fidelity and

has no relation with any other official classification system. Also, in this paper Sector and Industry are used

interchangeably.

2, We do not use transaction costs or mutual fund managers fees (i.e. Expense ratio) in our analysis. Since

transaction costs and management expenses vary according to investors preferences and holding period; we focus

our studies on gross results.

3, Using price history of ETFs that track industry-focused indexes would be a better approach, but due to lack ofenough history of ETFs, we used passive indexes. We believe due to low-tracking error between ETFs and passive

indexes, our results remain applicable to ETFs to replicate the strategy without any significant loss of performance.

Perhaps, the result of this study will motivate ETFs sponsors to design more passive products based on sector

indexes and momentum-based indexes (One example of Momentum-based index is AQR Momentum Index).

4, Our focus on this paper is to study the results of momentum phenomenon with practical implications. Thus,

instead of using CRSP Value-Weighted portfolio as benchmark, we chose to use SP500 and SP1500, which are

widely used proxy market index.

5, Of course, it assumes the availability of investable products like ETFs on those passively managed indexes.

References:

Asness, C., Liew, J., Stevens, R., Parallels Between the Cross-sectional Predictability of Stock andCountry Returns, The Journal of Portfolio Management, vol. 23, no. 3, 79-97, Spring 1997.

Asness, C.S., Moskowitz, T.J., Pedersen, L.H., Value and Momentum Everywhere,AFA 2010 Atlanta

Meetings Paper

Working Paper Series, Available at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1363476

Asness, C.S., The Interaction of Value and Momentum Strategies, Financial Analysts Journal, vol. 53,

no.2, March/April 1997.

Barberis, N., Shleifer, A., Vishny, R., A Model of Investor Sentiment, Journal of Financial Economics,

vol. 49, no.3, Sept. 1998.

Chan, K.C., Jegadessh, N., Lakonishok, J. Momentum Strategies The Journal of Finance, vol.51, no.5,

Dec 1996

Daniel, K. D., D. Hirshleifer, and A. Subrahmanyam, Investor psychology and security market under- and

over-reactions, The Journal of Finance, vol. 53, no. 6, Dec. 1998.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1363476http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1363476


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Eakins, S.G., Stansell, S.R. Do Momentum Strategies Work? The Journal of Investing, vol.13, no. 3,

Fall 2004

Fama, E.F., French, K.R., Value versus Growth: The International Evidence, The Journal of Finance,

vol 53, no. 6, Dec. 1998.

Grinblatt, M., Han. B.. Prospect Theory, Mental Accounting, and Momentum. Journal of Financial

Economics, vol. 78, no.2, Nov. 2005.

Jegadeesh, N., and Titman, S., 1993, "Returns to buying winners and selling losers: Implications for stock

market efficiency", Journal of Finance, vol. 48, no.2, 65-91

Lakonishok, J., Shleifer, A., Vishny, R., Contrarian investment, extrapolation, and risk, Journal of

Finance, vol. 49, no. 5, 1994.

Moskowitz, T.J., Grinblatt, M., Do Industries Explain Momentum? The Journal of Finance, vol. 54, no.

4, August 1999

ONeal, E.S. Industry Momentum and Sector Mutual Funds. Financial Analysts Journal, vol. 56, no. 4,

July/August 2000.

Okunev, J., and D. White, Do momentum-based strategies still work in foreign currency markets? Journal

of Financial and Quantitative Analysis, vol. 38, no.2, 2003.

Rouwenhorst, K., International Momentum Strategies, Journal of Finance, vol. 53, no.1, 267-284, 1998.

Schiereck, D., De Bondt, W., Weber, M., Contrarian and Momentum Strategies in Germany, Financial

Analysts Journal, vol. 55, no. 6, Nov./Dec. 1999.

Appendix

Appendix I. Fidelity Select Mutual Funds

All the following funds do not have Entry or Exit Load. Maximum redemption Fee & Early Withdrawalpenalty is 0.75%.

No. Name %Expense Ratio %Turnover MeanMonthlyReturn

StdDeviation

1 Select Air Transportation Portfolio (FSAIX) 0.91 161 0.65% 7.15%

2 Select Automotive Portfolio (FSAVX) 0.91 91 0.76% 8.39%


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3 Select Banking Portfolio (FSRBX) 0.88 73 0.10% 6.80%

4 Select Biotechnology Portfolio (FBIOX) 0.86 119 0.78% 8.23%

5 Select Brokerage and Investment Mgt Portfolio (FSLBX) 0.86 153 0.85% 7.39%

6 Select Chemicals Portfolio (FSCHX) 0.89 108 0.69% 6.04%

7 Select Communications Equipment Portfolio (FSDCX) 0.9 85 0.60% 10.07%

8 Select Computers Portfolio (FDCPX) 0.88 141 0.63% 10.11%

9 Select Construction and Housing Portfolio (FSHOX) 0.98 101 0.52% 6.52%

10 Select Consumer Discretionary Portfolio (FSCPX) 0.95 196 0.30% 5.10%

11 Select Consumer Finance Portfolio (FSVLX) 0.98 161 -0.36% 6.41%

12 Select Consumer Staples Portfolio (FDFAX) 0.86 57 0.37% 3.94%

13 Select Defense and Aerospace Portfolio (FSDAX) 0.88 43 0.72% 5.64%

14 Select Electronics Portfolio (FSELX) 0.86 101 0.82% 10.97%

15 Select Energy Portfolio (FSENX) 0.85 107 0.86% 7.19%

16 Select Energy Service Portfolio (FSESX) 0.85 85 1.49% 10.49%

17 Select Environment and Alternative Energy Portfolio (FSLEX) 1.07 190 0.35% 5.65%

18 Select Financial Services Portfolio (FIDSX) 0.88 242 0.18% 6.29%

19 Select Gold Portfolio (FSAGX) 0.89 35 1.06% 10.79%

20 Select Health Care Portfolio (FSPHX) 0.82 99 0.24% 4.69%21 Select Industrial Equipment Portfolio (FSCGX) 0.88 82 0.38% 6.53%

22 Select Insurance Portfolio (FSPCX) 0.91 193 0.50% 5.90%

23 Select Leisure Portfolio (FDLSX) 0.89 112 0.52% 5.80%

24 Select Materials Portfolio (FSDPX) 2.1 87 0.74% 6.54%

25 Select Medical Delivery Portfolio (FSHCX) 0.88 55 0.52% 6.28%

26 Select Multimedia Portfolio (FBMPX) 0.94 76 0.42% 6.33%

27 Select Natural Gas Portfolio (FSNGX) 0.88 167 0.93% 7.79%

28 Select Retailing Portfolio (FSRPX) 0.93 191 0.57% 6.19%

29 Select Software and Computer Services Portfolio (FSCSX) 0.83 189 0.85% 9.21%

30 Select Technology Portfolio (FSPTX) 0.83 136 0.76% 10.07%

31 Select Telecommunications Portfolio (FSTCX) 0.91 72 0.29% 7.52%

32 Select Transportation Portfolio (FSRFX) 0.9 114 0.69% 6.00%

33 Select Utilities Portfolio (FSUTX) 0.87 238 0.20% 4.97%

Appendix II. Individual Mutual Fund regression resultsOne-Factor CAPM

II. A. One-Factor CAPM Regression results against SP500 Index

No. Alpha Beta R2 F-Stats p-value Error

1 0.242% 1.035 0.433 145.78 0.000 0.003

2 0.229% 1.322 0.571 254.06 0.000 0.003

3 -0.270% 0.965 0.415 135.77 0.000 0.003

4 0.342% 0.781 0.206 49.64 0.000 0.005

5 0.382% 1.373 0.748 568.09 0.000 0.001


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6 0.381% 0.893 0.490 183.22 0.000 0.002

7 -0.136% 1.550 0.503 193.57 0.000 0.005

8 -0.107% 1.528 0.471 170.21 0.000 0.006

9 0.175% 0.979 0.500 190.85 0.000 0.002

10 0.051% 0.882 0.649 353.92 0.000 0.001

11 -0.692% 0.862 0.363 108.71 0.000 0.003

12 0.224% 0.497 0.341 98.69 0.000 0.001

13 0.432% 0.903 0.540 223.96 0.000 0.001

14 -0.031% 1.712 0.512 200.32 0.000 0.006

15 0.467% 0.903 0.345 100.43 0.000 0.003

16 0.745% 1.254 0.307 84.79 0.000 0.008

17 0.063% 0.875 0.510 198.99 0.000 0.002

18 -0.164% 1.088 0.638 337.05 0.000 0.001

19 0.415% 0.565 0.063 12.81 0.000 0.010

20 0.045% 0.621 0.372 113.07 0.000 0.001

21 -0.002% 1.177 0.692 429.48 0.000 0.001

22 0.198% 0.903 0.514 202.02 0.000 0.002

23 0.213% 1.007 0.657 366.20 0.000 0.001

24 0.378% 1.009 0.507 196.39 0.000 0.002

25 0.226% 0.635 0.215 52.21 0.000 0.003

26 0.067% 1.110 0.679 404.38 0.000 0.001

27 0.502% 0.859 0.264 68.62 0.000 0.004

28 0.244% 0.935 0.505 194.70 0.000 0.002

29 0.230% 1.370 0.485 179.96 0.000 0.004

30 0.023% 1.611 0.557 240.33 0.000 0.00431 -0.176% 1.262 0.604 291.54 0.000 0.002

32 0.375% 0.926 0.521 207.41 0.000 0.002

33 -0.028% 0.752 0.495 187.11 0.000 0.001

Mean 0.153% 1.035 0.475 204.37 0.000 0.003

II. B. One-Factor CAPM Regression results against SP1500 Index

No. Alpha Beta R2 F-Stats P-Value Error

1 0.203% 1.044 0.445 153.31 0.000 0.003

2 0.178% 1.340 0.592 277.55 0.000 0.003

3 -0.303% 0.959 0.414 135.13 0.000 0.003

4 0.311% 0.799 0.218 53.37 0.000 0.005

5 0.334% 1.370 0.753 581.93 0.000 0.001

6 0.348% 0.902 0.505 194.48 0.000 0.002

7 -0.193% 1.557 0.513 201.02 0.000 0.005


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8 -0.162% 1.531 0.478 174.66 0.000 0.006

9 0.136% 0.999 0.526 211.56 0.000 0.002

10 0.019% 0.886 0.663 375.15 0.000 0.001

11 -0.724% 0.866 0.369 111.86 0.000 0.003

12 0.207% 0.493 0.339 97.78 0.000 0.001

13 0.398% 0.916 0.561 243.70 0.000 0.001

14 -0.094% 1.725 0.525 211.26 0.000 0.006

15 0.431% 0.923 0.364 109.20 0.000 0.003

16 0.693% 1.297 0.333 95.19 0.000 0.007

17 0.028% 0.896 0.541 225.26 0.000 0.001

18 -0.202% 1.081 0.637 334.99 0.000 0.001

19 0.388% 0.608 0.074 15.16 0.000 0.010

20 0.024% 0.614 0.367 110.73 0.000 0.001

21 -0.046% 1.189 0.713 475.62 0.000 0.001

22 0.166% 0.900 0.515 202.75 0.000 0.002

23 0.176% 1.014 0.673 393.20 0.000 0.001

24 0.339% 1.024 0.528 213.63 0.000 0.002

25 0.199% 0.662 0.236 58.99 0.000 0.003

26 0.026% 1.118 0.695 435.98 0.000 0.001

27 0.466% 0.891 0.287 76.87 0.000 0.004

28 0.209% 0.945 0.520 206.93 0.000 0.002

29 0.180% 1.372 0.491 184.59 0.000 0.004

30 -0.036% 1.620 0.570 252.73 0.000 0.004

31 -0.220% 1.256 0.605 292.23 0.000 0.002

32 0.341% 0.933 0.533 218.35 0.000 0.00233 -0.053% 0.740 0.483 178.30 0.000 0.001

Mean 0.114% 1.045 0.487 215.26 0.000 0.003

Appendix III. Individual Mutual Fund regression resultsTwo-Factor Regression

III. A. Two-Factor Regression results against SP500 Index

No. Alpha Beta Mom R2 F-Stats P-Value Error

1 0.064% 0.982 0.406 0.478 82.01 0.000 0.003

2 0.160% 1.288 0.239 0.583 125.30 0.000 0.003

3 -0.208% 0.908 0.572 0.463 77.09 0.000 0.003

4 -0.061% 0.696 0.859 0.266 32.47 0.000 0.005

5 0.310% 1.352 0.132 0.764 290.08 0.000 0.001

6 0.207% 0.871 0.403 0.515 94.90 0.000 0.002

7 -0.131% 1.447 0.407 0.537 103.61 0.000 0.005

8 -0.136% 1.446 0.347 0.500 89.44 0.000 0.006


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9 0.015% 0.937 0.543 0.534 102.40 0.000 0.002

10 0.017% 0.858 0.192 0.673 184.59 0.000 0.001

11 -0.356% 0.794 0.673 0.470 79.37 0.000 0.002

12 0.042% 0.477 0.572 0.392 57.75 0.000 0.001

13 0.179% 0.865 0.436 0.583 125.31 0.000 0.001

14 -0.084% 1.646 0.276 0.541 105.52 0.000 0.006

15 0.182% 0.861 0.568 0.383 55.51 0.000 0.003

16 0.217% 1.200 0.651 0.353 48.92 0.000 0.007

17 -0.021% 0.847 0.516 0.552 110.20 0.000 0.001

18 -0.170% 1.057 0.251 0.670 181.76 0.000 0.001

19 -0.133% 0.502 1.192 0.139 14.51 0.000 0.010

20 -0.008% 0.585 0.381 0.402 60.20 0.000 0.001

21 -0.028% 1.149 0.249 0.722 232.06 0.000 0.001

22 0.073% 0.863 0.375 0.544 106.71 0.000 0.002

23 0.157% 0.983 0.180 0.677 187.39 0.000 0.001

24 0.224% 0.985 0.335 0.537 103.81 0.000 0.002

25 -0.049% 0.616 0.861 0.319 41.88 0.000 0.003

26 0.031% 1.082 0.178 0.701 209.39 0.000 0.001

27 0.150% 0.819 0.588 0.305 39.21 0.000 0.004

28 0.153% 0.896 0.276 0.524 98.53 0.000 0.002

29 0.074% 1.302 0.367 0.506 91.50 0.000 0.004

30 -0.042% 1.539 0.300 0.580 123.37 0.000 0.004

31 -0.167% 1.213 0.223 0.619 145.69 0.000 0.002

32 0.187% 0.896 0.407 0.550 109.36 0.000 0.002

33 -0.071% 0.690 0.480 0.542 106.03 0.000 0.001Mean 0.023% 0.989 0.437 0.513 109.57 0.000 0.003

III. B. Two-Factor Regression results against SP1500 Index

No. Alpha Beta Mom R2 F-Stats P-Value Error

1 0.033% 0.993 0.392 0.490 86.15 0.000 0.003

2 0.117% 1.309 0.216 0.604 136.54 0.000 0.003

3 -0.239% 0.903 0.578 0.463 77.03 0.000 0.003

4 -0.079% 0.714 0.838 0.276 34.07 0.000 0.005

5 0.262% 1.349 0.131 0.769 297.90 0.000 0.001

6 0.186% 0.880 0.376 0.528 100.10 0.000 0.002

7 -0.184% 1.455 0.400 0.545 107.41 0.000 0.005

8 -0.188% 1.451 0.341 0.506 91.78 0.000 0.005

9 -0.015% 0.958 0.520 0.558 112.96 0.000 0.002

10 -0.014% 0.863 0.193 0.687 196.76 0.000 0.001


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Software andComputerServicesPortfolio

TelecomPortfolio

UtilitiesPortfolio

Software andComputerServicesPortfolio

TechnologyPortfolio

Loser

Comm.Equip.Portfolio

GoldPortfolio

MaterialsPortfolio

MedicalDeliveryPortfolio

TelecomPortfolio

Biotech. Portfolio Comm. Equip.

Portfolio

ComputersPortfolio

ElectronicsPortfolio

Environment andAlternativeEnergy Portfolio

MultimediaPortfolio

Natural GasPortfolio

Software andComputerServices Portfolio

TechnologyPortfolio

Telecom Portfolio Utilities Portfolio

BankingPortfolio

Cons. Discre.Portfolio

ConsumerFinance Portfolio

FinancialServicesPortfolio

MultimediaPortfolio

ConsumerFinance Portfolio

Energy ServicePortfolio

FinancialServicesPortfolio


UtilitiesPortfolio

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RetailingPortfolio

TelecomPortfolio

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Momentum Paper - Ver 1

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