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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">ijbf</journal-id>
      <journal-title-group>
        <journal-title>International Journal of Banking and Finance</journal-title>
        <abbrev-journal-title abbrev-type="publisher">IJBF</abbrev-journal-title>
      </journal-title-group>
      <issn pub-type="ppub">2811-3799</issn>
      <issn pub-type="epub">2590-423X</issn>
      <publisher><publisher-name>UUM PRESS</publisher-name></publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.32890/ijbf2021.16.1.2</article-id>
      <article-id pub-id-type="publisher-id">9099</article-id>
      <article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group></article-categories>
      <title-group>
        <article-title>Selectivity and Market Timing Ability of Mutual Fund Houses in Emerging Countries</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Bani Atta</surname>
            <given-names>Anas Ahmad</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Marzuki</surname>
            <given-names>Ainulashikin</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>shikinmarz@gmail.com</email>
        </contrib>
      </contrib-group>
      <aff id="aff1"><institution>Faculty of Economics and Muamalat Universiti Sains Islam Malaysia</institution>, <country country="MY">Malaysia</country></aff>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2021-01-30">
        <day>30</day><month>01</month><year>2021</year>
      </pub-date>
      <volume>16</volume>
      <issue>1</issue>
      <fpage>21</fpage>
      <lpage>42</lpage>
      <permissions>
        <copyright-statement>Copyright &#169; 2021 UUM PRESS</copyright-statement>
        <copyright-year>2021</copyright-year>
        <license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0">
          <license-p>This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License.</license-p>
        </license>
      </permissions>
      <abstract>
        <p>The paper investigates the selectivity and market timing ability of fund houses in emerging countries. The study uses comprehensive performance models on fund houses from four emerging countries. Data span is from 2007 to 2018. Findings indicate that fund managers benefit from the common facilities provided by the fund houses like market research, diversification and investment opportunity. Fund houses showed good selectivity skills but poor market timing ability. The possible reason is that fund houses manage large and different types of funds. This resulted in more complex management processes and thus reduced the ability to track the fluctuations in the market. The findings are important for investors as they are able to allocate their resources more effectively to funds that are best managed by fund houses while for managers, they are able to position themselves relative to their competing peers.</p>
      </abstract>
      <kwd-group kwd-group-type="author">
        <kwd>Mutual fund, fund house, selectivity ability, market timing ability, emerging countries</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>JEL Classification: G11, G14, G17, G20, G40</title>
    </sec>
    <sec id="sec2">
      <title>INTRODUCTION</title>
      <p>Fund houses act as financial intermediaries offering a variety of mutual funds under their common brand name and via common marketing and distribution channels (Bani Atta &amp; Marzuki, 2019). A fund house is a group of funds that is managed by an asset management company (AMC) (Iqbal, Aleemi, Zeeshan, &amp; Tariq, 2019). The study of mutual fund at the fund house level (instead of at individual fund) is important for several reasons (Nanda, Wang, &amp; Zheng, 2004).</p>
      <p>Firstly, a fund house structure adds economies of scale to the distribution, servicing, and funds promotion. Secondly, a fund house has more flexibility in reallocating its human resources and other capital in response to market opportunities compared with stand- alone funds. Thirdly, the reputation of a fund house will help reassure investors about the investment managers’ selection and monitoring.</p>
      <p>The importance of fund house study is evident with increasing reports that provide classification of fund houses in order to create the most effective investment data and research for investors (examples are Morningstar and Barron’s). According to the reports of Morningstar and Barron, it is possible to use the fund house performance to provide investors a ranking of the fund houses.</p>
      <p>They began reporting on the classification of fund houses using the performance of the fund house (weighted average performance of all funds in the family) to create the most successful investment data and research for investors. The aim of these reports are, firstly, to make it easier for investors to find data about fund houses. Secondly, to remove the information asymmetry and check the statistics provided by the fund houses. Thirdly, provide investors more confidence in the fund house they choose (Laske, 2019).</p>
      <p>Globally, the value of asset under management (AUM) of the mutual fund industry was estimated to be worth approximately USD 79.2 trillion in 2017. The value marked a 12 percent growth from USD 71 trillion in 2016, and it is expected to continue to grow in the future. It is forecasted that the global AUM will triple its value by 2025 (Fages et al., 2018).</p>
      <p>A mutual fund is an investment instrument available in many countries across the world. It is essentially an investment basket that collects funds from investors and allocates them into various securities, typically capital and money market instruments. Mutual funds offer a distinctive advantage over retail investors, as it affords the individual investor the opportunity to invest in a diversified basket of securities without the burden of information collection, administration, and other costs (Bani Atta &amp; Marzuki, 2019). Equity funds make up almost half of these mutual funds. The second and third largest are fixed income and real estate and private equity funds, each constituting respectively 17 and 12 percent of the total.</p>
      <p>The prevalence of fund houses underlies the motivation of this study. Investigating the performance of member funds allows one to identify funds with good performance and then determine amongst them the star fund(s). Because fund houses manage a range of funds, each with their respective strategies, measuring the overall performance of the fund house is altogether a different matter (Gasper &amp; Massa, 2006). Pertinent to the investment decision of the fund are the attributes of the fund house and reputation of the fund house manager. Good reputation emerging from the positive performance of member funds is valuable because it signals the skills of their managers (Adrianto, Chen, &amp; How, 2019). Thus, the paper addresses the issue of whether fund houses can outperform market benchmarks and if they portray market timing abilities.</p>
      <p>This study seeks to contribute in the mutual fund literature by investigating the performance at the fund house level. Most of the previous studies focussed on performance at the individual fund level. It is argued that members of a fund house cannot be treated like standalone funds due to the fact that most of these funds work under the management of the fund house. The performance at the fund house level is important due to most investors using a top-down approach. That means investors firstly choose the fund house and they then choose the funds they will invest in.</p>
    </sec>
    <sec id="sec3">
      <title>LITERATURE REVIEW</title>
      <p>Investment in mutual funds has been rising rapidly in the developed and emerging markets. Fund performance estimation is a mechanical part of investment management and will include investor input for decision-making purposes. The management seeks to exploit potential market inefficiencies with the goal of optimising returns and mitigating risks through various strategies, such as stock-picking (selectivity of securities) and market timing (price anticipation). This active strategy of management seeks to outperform the market, taking competitive positions towards a benchmark. Several studies have been attempted in the past to investigate the fund’s performance, timing ability, and fund selectiveness. In the literature, extensive research has been done on this topic in the general context and in the developed financial markets.</p>
      <p>Every mutual fund is managed by a management company called “fund houses”. A fund house offers different types of funds to cater to specific objectives of every investor, allowing them to diversify their investments within the same fund house. Fund houses may take on different strategies to attract investment. Malhotra and McLeod (1997) concluded that larger houses enjoy economies of scale and, thus, lower the expense ratio and perform better. This is because houses learn from experience and they operate more efficiently over time. Research by Dowen and Mann (2007) concluded with the same results.</p>
      <p>Several studies examined the fund houses’ behaviour and strategies (Khorana &amp; Servaes, 1999; Zhao, 2004; Massa 2003; Guedj &amp; Papastaikoudi, 2004) and several of them analysed the significance of fund house members on the mutual funds (Elton, Gruber, &amp; Green, 2007). Khorana and Servaes (1999) provided evidence that fund houses issue new funds when the possibility to generate more income is substantial. Fund houses attempt to offer more choices to existing investors by launching new funds and promote their visibility by highlighting some of their existing good-performing funds. Elton et al. (2007) investigated the risk effect on mutual fund investors which arises from fund houses’ membership. They studied the impact of risk related to limiting mutual fund investments to one fund house. They used monthly funds returns from 1998 until 2002, and analysed the mutual fund house’s impact on investor risk. The results revealed that funds with the same goal are more correlated within the fund houses than between other fund houses. The increased correlation is due to the tendency of funds within a fund house to hold similar stocks and have similar exposure to total risk factors. Then, they postulated that confining investment to one fund house leads to a greater total portfolio risk than diversifying across different houses.</p>
      <p>Massa (2003), Guedj and Papastaikoudi (2004) and Gasper and Massa (2006) examined how houses shift performance between their funds. They showed that fund houses pass resources between member funds within the fund house to favour those funds that were likely to increase the total fund house values. Massa (2003) examined how fund houses play a role in determining between-fund competition through either category proliferation of fund strategies.</p>
      <p>Fund heterogeneity correlates with between-fund competition between and within houses. After examining more than 18,000 American mutual funds from 1992 to 2000, the author found that the category proliferation strategy positively correlates with fund differentiation. No relationship was found between the proliferation strategy and fund performance, indicating that a fund is independent of its within-fund house peers.</p>
      <p>Fund house performance also affects their constituents. Analysing US funds, Guedj and Papastaikoudi (2004) discovered the persistent performance of member funds within their houses. This persistent excess performance is linked to the number of funds in the fund house, which can be interpreted as a measure of autonomy that the fund house exercises in allocating resources unevenly amongst its members.</p>
      <p>This finding is congruent with the view that houses allocate resources to its members based on their performance, not needs. This result is supported by Gasper and Massa (2006), who investigated whether fund houses strategically transfer performance to members that are more likely to improve the fund houses’ overall return. To do this, they used a sample of USA funds from 1991 to 2001. They discovered that high-value funds, that is, funds with high fees or historically good performers, achieve their superior performance at the expense of low-value funds. These results highlighted how the fund house organisation generates distortions in delegated asset management.</p>
      <p>Clare, O’Sullivan, and Sherman (2014) took a sample of US and European mutual funds from 1999 to 2009 to investigate the competitive and strategic behaviours of fund house funds and to ascertain whether both factors determine risk-taking and performance persistence. They found no evidence to support a superior performance persistence of fund house funds vis-à-vis non-fund house funds. Moreover, based on their historical performance, there is a significant difference between the future performance of fund house and non-fund house funds’ portfolios. There is also compelling evidence that the mid-year ranking of a fund within its own fund house and sector influences its risk-taking for the remainder of the year.</p>
      <p>Fang, Peress, and Zheng (2014) found the strategies carried out by fund houses to coordinate their fund managers by investigating the relationship between managerial placement strategies and market efficiency. As much as 1,869 US mutual funds in the 1991-2010 decade were made as sample. The authors find that fund houses tend to assign highly-skilled managers to less efficient funds, seeing that such managers have the capability to turn the funds around. Fund houses thus intervene in the managers’ duties, and these interventions have the apparent purpose of enhancing the overall value of the fund house instead of maximising investors’ investment value. Cici, Dahm, and Kempf (2018) examined how the efficiency of trading desks operated by mutual fund houses affect portfolio performance and investment behaviour of affiliated funds in the US.</p>
      <p>The results concluded that by operating more efficient trading desks, trading costs can be reduced, and fund houses can then improve the performance of their funds significantly and enable their funds to trade more and hold less liquid portfolios. Aleemi, Tariq, and Zeesha (2019) examined the effects of fund sizes, mainly the induction of new funds and the increase in existing funds, managed by fund houses on their AUM for the mutual fund industry of Pakistan. This was for the period between July 2009 and July 2016. The main findings suggested that both existing and new fund sizes have a positive and significant impact on AUM. Additionally, fund growth is strongly associated with fund house growth.</p>
      <p>On Malaysia, Bani Atta and Marzuki, (2020) investigated the selectivity and timing ability of fund families for the period from 2007 to 2018. They started to compare between Islamic mutual funds</p>
      <p>(IMFs) and conventional mutual funds (CMFs) within the same family, and then examined the performance at the fund family level. The results indicated that the IMFs exhibited some fund selection ability over CMFs. However, both types of funds displayed poor market timing ability. At a fund family level, the results showed the fund families exhibited good fund selection skills but poor market timing ability. The novel result is that the difference in performance between Islamic and conventional funds shrunk compared to the results of previous studies. This was due to the common advantages offered by the families for both types of funds.</p>
      <p>Other studies elaborated the behaviour of individual fund managers within fund houses. Kempf and Ruenzi (2007, 2008) concluded that fund managers contest with other fund managers in the same houses for better ranking. It is more serious in large houses than in the smaller ones. Nevertheless, they find that teams in large houses participated in less rivalry. As a summary, the investors appeared to respond asymmetrically to fund performance. Well-performing funds drew higher capital inflows as opposed to small outflows of capital in poor-performing funds. This convex relationship means that assets under the management of a fund house are supposed to be higher if it produces a one-star fund and some poorly performing funds than if it has a few average performing funds. This influence induces the fund house strategy of star fund generation.</p>
      <p>We conclude that there is a clear gap in the studies of fund performance at the fund house level. Previous studies focused only on the fund level and the characteristics of fund houses, in addition to investigating the impact of these characteristics on fund performance. This study seeks to bridge this gap by providing new evidence about the performance of fund houses, whether related to fund house managers’ skills and ability, and to houses’ attributes specifically in the emerging countries (Saudi Arabia, Malaysia, Indonesia and Pakistan).</p>
      <p>METHODOLOGY Data</p>
      <p>The main source of mutual fund data is collected from Bloomberg. The sample comprises 70 houses. Of this, 25, 20, 14 and 11 fund houses are domiciled in Saudi Arabia, Malaysia, Indonesia, and Pakistan, respectively. The total funds in these 70 houses equal to 503 funds. The performance of the fund house equals the weighted average of the performance of all funds in the fund house. The study period is between January 2007 and December 2018, focusing mainly on monthly returns. Relevant benchmarks were also collected from Bloomberg to compare the performance of the fund house under study. The FTSE Global Islamic Index isof used Determinants Attitudefor global Towards Zakat Islamic benchmark on Employment Income in Nigeria: 29-48 for ofallAttitude Determinants countries andonthe Towards Zakat The International Journal of Banking andrelevant FTSE Employment All-World Income in Nigeria:index Determinants is of Attitude 29-48 the most Towards Zakat on 1 Income Employment Finance, Vol. 13.in Nigeria: 29- Numbe for global funds since it 29-48covers The International market capitalisation Journal of Vol. 13. Number 1, Banking of 2017: and Finance, Vol. 29-48 global equity markets29 (Wilson &amp; Jones, 2002). The risk-free-rate 29-48 29 is the 3-month T-bill rate which is used as a risk-free rate in multiple studies that examine mutual funds’ performance. Monthly returns are Selectivity and Market Timing Selectivity Ability of calculated as follows: Fund Houses in Emerging Countries and Market Timing Ability Mutual Fund Houses in Emerging Countries Fund Houses in Emerging Countries 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 (1) 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡 = Where, 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 is the price of an index in period t, 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1is the price of an index in period t-1.</p>
      <preformat>                                        Selectivity Models
                                                     𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
   inants of Attitude Towards Zakat on Employment Income          𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅29-48
                                                            in Nigeria:            𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                         = ∑𝑛𝑛𝑛𝑛𝑝𝑝𝑝𝑝=1 𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅  1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝
                                                                            𝑛𝑛𝑛𝑛                                                                                                       𝑛𝑛𝑛𝑛
        𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅The                         𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = ∑ models
                                           𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟selectivity             𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                are one                𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅           𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                             𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟                        𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = ∑ used
                                                                                                                                                    𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟commonly                     𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 models
                                                                                                                                                                                                              ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝
                                                                                                                Vol.of13.          the       𝑝𝑝𝑝𝑝 most
 ernational Journal                                         of Banking𝑝𝑝𝑝𝑝=1     and Finance,                                            Number                      1, 2017: 𝑝𝑝𝑝𝑝=1
                                         for evaluating                 29 mutual fund performance. Stock selection models used
                                                                          Determinants      of Attitude        Towards            Zakat        on    Employment               Income  in   Nigeria:          29-48</preformat>
      <p>in this study Theinclude International raw returns Journaland of Banking excess returns as𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 and𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 Finance, well 𝑅𝑅𝑅𝑅Vol. as13. risk 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡Number 1, 2017: 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟 adjusted measures 29-48 which are 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅Sharpe ratio,29Treynor ratio, Jensen alpha, tivity Attitude Towards and ZakatMarket andon Carhart’s Employment Timing 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅Ability Income in Nigeria: four-factor 29-48 of Mutual 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 models. Joo and Park (2011) 1 and Adrianto 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 donalHouses Journal in ofetBanking Emerging al. (2019) Countries calculated and Finance, the Vol.performance 13. Number of 1, 2017:fund houses as the average Selectivity and performance of all funds in the same fund house. In this study, the Market Timing Ability of Mutual fund 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 houseFund 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 performanceHouses in Emerging Countries 𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 will be calculated as the weighted average of 𝑡𝑡𝑡𝑡 = y and 𝑊𝑊𝑊𝑊 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝Market 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝all Timing Ability of𝑊𝑊𝑊𝑊 𝑡𝑡𝑡𝑡−1funds in the fund house using Mutual all measurements. 𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 uses in Emerging Raw Returns Countries 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡 = 𝑡𝑡𝑡𝑡 and Excess 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 Returns 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 𝑡𝑡𝑡𝑡−1</p>
      <p>𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 Raw 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 𝑅𝑅𝑅𝑅 return 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 is = the 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅for return 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 a fund house 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅calculated 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 by = 𝑅𝑅𝑅𝑅the 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡weighted − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝑛𝑛𝑛𝑛 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1 = average 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 ∑𝑝𝑝𝑝𝑝=1 𝑊𝑊𝑊𝑊of ∗raw 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅return 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅of all𝑝𝑝𝑝𝑝 funds in the fund house. 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝</p>
      <preformat>                                                                                       𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                    𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟                     𝑛𝑛𝑛𝑛
                                                                                                𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = ∑𝑝𝑝𝑝𝑝=1 𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝     (2)
               𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                                                                𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                Where, 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 is the raw returns for the fund house,
   𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = ∑𝑛𝑛𝑛𝑛𝑝𝑝𝑝𝑝=1 𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 the   weight
                                         ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅   𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅of      fund
                                                                      𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟         i calculated by the TNA of fund i divided by
                                                                                      𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                              𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 28                                                                              𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                                                         𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                               𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅−𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟            𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 =
                                                                                        𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                                     𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡           𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                                                 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                                  𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                                                𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟
                                                                                                                                                                                     𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
 𝑊𝑊𝑊𝑊                  𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡 − 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1                                                                         𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅       𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                                                      𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
  𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
      𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 =
   𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑡𝑡𝑡𝑡𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝         = 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                        𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑡𝑡−1
                                                             𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                               𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝
                              𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅                      𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                       𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡         =𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟       𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡−=𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                   𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                            𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  the            TNA of fund𝑊𝑊𝑊𝑊house.                𝑊𝑊𝑊𝑊     𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                                         𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝 N is the number of funds in the fund house.
  Excess                  returns                    are                measured     𝑛𝑛𝑛𝑛
     𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅   𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                              𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅     𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑅𝑅𝑅𝑅∑𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟
                                                                                     𝑝𝑝𝑝𝑝=1        𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝using
                                                                                              𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡        =∗ 𝑅𝑅𝑅𝑅     𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 the−
                                                                                                                                 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡           following
                                                                                                                                                         𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑝𝑝𝑝𝑝 equation:
                                                                                                                                                 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                       		           𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                     𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                       𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟
                                                                                                            𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡          =
                                                                                                                                            = 𝑅𝑅𝑅𝑅   𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −           − 𝑅𝑅𝑅𝑅   𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                             (3)
        𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                    𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅              𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                           𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                       = 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡           − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  Where, 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 is the raw return                                                                   𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅of𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅    the𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟
                                                                                                                                                       fund         𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡house over the period t,
    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the risk-free𝑅𝑅𝑅𝑅 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡     𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −rate    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 of return over the period t.
    𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅    𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = 𝑅𝑅𝑅𝑅       𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                          𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                              𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                         𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
  Sharpe ratio                    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡(1966)                                𝑅𝑅𝑅𝑅
                                                                     − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                       − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                              𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅
𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                 𝑅𝑅𝑅𝑅
                                         = 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡    𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 =                           𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
      𝑊𝑊𝑊𝑊𝑝𝑝𝑝𝑝
  Sharpe                      introduced                  𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                        𝑅𝑅𝑅𝑅               a ratio to rank                                         𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                                                    mutual fund performance by
                                                         𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                               𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝑅𝑅𝑅𝑅
  deducting                           the          risk-free
                              𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 =                          rate
                                                                                  𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                     𝑅𝑅𝑅𝑅  𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡  −     from
                                                                                                               𝑅𝑅𝑅𝑅 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡        fund               house returns, divided by the
  standard deviation of fund𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                                           house𝜎𝜎𝜎𝜎returns. 𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                 𝑅𝑅𝑅𝑅
                                                                                                                  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡   𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                                    − 𝑅𝑅𝑅𝑅 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
    𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅   𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑟𝑟𝑟𝑟                                                            𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
    𝑅𝑅𝑅𝑅                                                     𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 =𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                    𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅
                                                     𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅               𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                     == − 𝑅𝑅𝑅𝑅                    𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                                       𝑅𝑅𝑅𝑅           − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
         𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                         𝑆𝑆𝑆𝑆ℎ𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑎𝑎𝑎𝑎𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 =𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                     𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                             𝜎𝜎𝜎𝜎
                                                                                                                              𝜎𝜎𝜎𝜎
                                                                                                                                 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                                                                        (4)
                                                                                                                                               𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                               𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
𝑅𝑅𝑅𝑅Where,                    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 is the mean return of the fund house over the period t,
     𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
          𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                     is the          risk-free rate of return over the period t. 𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                                                        𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡   is the standard
                                                                                                                                                                                                             𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  deviation𝑅𝑅𝑅𝑅 of a fund house mean excess return. The Sharpe ratio is
                                   𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
  widely used                 𝑅𝑅𝑅𝑅           as a measure to rank mutual fund performance, especially
𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                      𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  in𝑅𝑅𝑅𝑅recent mutual                               𝑅𝑅𝑅𝑅    fund performance studies.
                                                     𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                          𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝑅𝑅𝑅𝑅
              𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                         2                                                   2𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                     The International JournalThe  International
                                                                                                               of Banking        JournalVol.
                                                                                                                           and Finance, of Banking and Finance,
                                                                                                                                             13. Number 1, 2017: Vol.
                                                                                                                                                                 29-4813. Numb
          𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  Treynor ratio         (1965)                                                                                                    2                                                              The International Journal of Banking and
                                                𝑅𝑅𝑅𝑅            −2𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  Treynor                   ratio
                            𝑓𝑓𝑓𝑓 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡is𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                     similar
                                                     𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡   𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 to
                                                         𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                  the
                                                                         Sharpe ratio, except it uses the beta as
  a measure of systematic risk instead of 𝜎𝜎𝜎𝜎using                                                    𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡standard deviation. The
  Treynor ratio is calculated            𝜎𝜎𝜎𝜎
                                            𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡after subtracting the risk-free rate from the
  fund house return and dividing it 𝜎𝜎𝜎𝜎by                                                    the beta. The beta is considered
                                                                                     𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  the systematic risk between                                   the
                                               𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 fund           house                and
                                                                                                𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −𝑅𝑅𝑅𝑅    𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 the market index. The
  Treynor𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅
                  model is𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡    = 𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅
                                      defined             as
                                                       𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                             𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 =                𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                                                                                         (5)
                                                                                                                                          𝑅𝑅𝑅𝑅        −𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
   𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                                                                 𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                               𝛽𝛽𝛽𝛽
                                                                                         𝑅𝑅𝑅𝑅         −𝑅𝑅𝑅𝑅                                        𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                         𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                               (5)
                                                                                                                                𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
  Where, 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 is the 𝛽𝛽𝛽𝛽
                                  mean      𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                    return of 𝛽𝛽𝛽𝛽
                                    𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                  the          fund house over the period t,
                                                                           𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the risk-free rate of returns over the                          𝑅𝑅𝑅𝑅      period t. 𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the beta
                                                                                       𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
  coefficient for the fund         𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓house,
                                           ℎ,𝑡𝑡𝑡𝑡          estimating
                                                              𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 as follows:
                                                                                                             𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 )
                       𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ =
                                                         𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 )
                                                                             𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ   =                                                                                                                         (6)
                                                                    𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚                              𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚                          𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 )
                                                                                         𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ = 𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
  Beta is a measure of sensitivity                     𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅between
                                                                           𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 )                the market𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚and the fund
                      𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ = 𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
  house. It is calculated by                  dividing 𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚               the covariance between the fund
  house and market return divided by the variance of the market return.
                      𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅     𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                           𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −=
                                                                                                        𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡         𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                     𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅        𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅              = 𝛼𝛼𝛼𝛼−𝑝𝑝𝑝𝑝 +
                                                                                                                                              𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                           𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 +
                                                                                                                                  𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅                 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                                                                        29𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅              − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                     𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 − 𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅     𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅                 +−
                                                                                                                                                 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                �𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡         𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                                                           𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                    𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ
                                                                                                                                                                                                    𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                  𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                             = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡− 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅       𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 +
                                                                                                                                                                                  𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅
                                                                                                                   𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                 𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚
                                                                                                                                                                                                              𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 )
   𝜎𝜎𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                                                                                                                       𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ =
                                  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                    𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                 𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅            = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡  − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼 +            𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚
                                                                                                        𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                           𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝑝𝑝𝑝𝑝
            The International Journal of Banking
                                         𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −𝑅𝑅𝑅𝑅and
                                                             𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 Finance, Vol. 16, Number 1 (January) 2021, pp: 21–42
                              𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 =                                                       𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 (5)
                                                                                  𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                 𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 +
          A higher           𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅beta
                                                              𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 )
                                                         indicates
                                         𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ 𝑅𝑅𝑅𝑅=𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡             that a fund house is highly                associated
                                                                                                                            𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − with                   𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝐽𝐽𝐽𝐽𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                                                                            𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅the         𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                                                                                                  � + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                                                                             𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                                                                                       = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
   𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅
          market𝑅𝑅𝑅𝑅and                    =                             𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚                                                  𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 ) (5)
                                   𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 is playing                                   a dominant role either       with
                              𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                    𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                   𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ positive
                                                                                                                                         = 𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓or negative                                                                       𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅
                                                                                                                                                                   𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚
         returns. Moreover,    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 the higher the Treynor ratio, the better the ranking
         and fund house performance; it also may indicate that such a fund
    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓house
             ℎ,𝑡𝑡𝑡𝑡 is well-diversified.
                        𝛽𝛽𝛽𝛽𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                               𝑅𝑅𝑅𝑅 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                               = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 +
                                                                                     𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                        𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅𝑚𝑚𝑚𝑚 )                                                                                              𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝜀𝜀𝜀𝜀𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                            𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � +                             = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                           𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ =                                                                                                                                                     𝑅𝑅𝑅𝑅 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                                                       𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                                                                                                 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
            Single Factor                               CAPM
                                                          𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚Model                  (Jensen, 1968).                                                                                        𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅
                                           𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
            Jensen𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶
                        Alpha    (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ ,𝑅𝑅𝑅𝑅is 𝑚𝑚𝑚𝑚 )
                                                            the first risk-adjusted return measure used in this
𝐵𝐵𝐵𝐵𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅section.
            𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ = Jensen                             explains
                           𝑅𝑅𝑅𝑅𝑉𝑉𝑉𝑉𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
                                          𝑟𝑟𝑟𝑟𝑚𝑚𝑚𝑚                           𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 how to measure risk-adjusted abnormal
            performance           𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                           𝑅𝑅𝑅𝑅in𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡the       market          𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡by  = capturing
                                                                                                           𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡the
                                                                                                                                               − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                                  abnormal   𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 =
                                                                                                                                                                                   excess𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + returns
                                                                                                                                                                                           𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
            of a fund house using Jensen’s alpha.                                                          𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 −𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
                                                                                                                                                        𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                             𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                             𝐽𝐽𝐽𝐽𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅             𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 +
                           𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡𝛽𝛽𝛽𝛽                                                                                                                                               𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 (7)
                                                                                  𝛽𝛽𝛽𝛽�𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
          Where, 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 is the return                    𝛽𝛽𝛽𝛽 on the fund house, 𝑅𝑅𝑅𝑅 is the risk-free rate
                                                                                                                                    𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
          of return,𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡𝛼𝛼𝛼𝛼is𝑝𝑝𝑝𝑝 the return on the relative market benchmark, 𝛽𝛽𝛽𝛽 measures                                                                             Determinants of Attitude Towards Zakat on
          the sensitivity between the excess return of the market benchmark 𝑅𝑅𝑅𝑅 − 𝑅𝑅𝑅𝑅 = 𝛼𝛼𝛼𝛼
                                                                                                                                                                                                             𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡      𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
         𝑅𝑅𝑅𝑅with
              𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡    the fund house, 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 captures
                       Determinants of Attitude Towards Zakat
                                                                                                   any excess𝑅𝑅𝑅𝑅returns
                                                                              on Employment Income in Nigeria:                       29-48
                                                                                                                                                             above market3
                                                                                                                                     𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                                                         + 𝛽𝛽𝛽𝛽
          benchmark,           𝛽𝛽𝛽𝛽 𝜀𝜀𝜀𝜀𝑝𝑝𝑝𝑝,𝑡𝑡𝑡𝑡 while is the term error. The Jensen alpha measures                                                                    𝛼𝛼𝛼𝛼Zakat              the
                                            𝑅𝑅𝑅𝑅          − 𝑅𝑅𝑅𝑅           =  𝛼𝛼𝛼𝛼     +  𝛽𝛽𝛽𝛽  �𝑅𝑅𝑅𝑅
                              𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 over or underperformance; if positive and significant,
                                               𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡      𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡          𝑝𝑝𝑝𝑝       1                  −   𝑅𝑅𝑅𝑅
                                                                                                            Determinants
                                                                                                      𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡         𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � of+       𝛽𝛽𝛽𝛽
                                                                                                                                         Attitude  2 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵
                                                                                                                                                         Towards 𝑡𝑡𝑡𝑡
                                                                                                                                                                               𝑝𝑝𝑝𝑝 on Employment Income in Nigeria: 29-4
          fund house’s
          then the fund house is𝜀𝜀𝜀𝜀over-performing                         + 𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻𝑡𝑡𝑡𝑡 + 𝛽𝛽𝛽𝛽4and
                                                                    𝑝𝑝𝑝𝑝,𝑡𝑡𝑡𝑡
                                                                                                                𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆        +𝑅𝑅𝑅𝑅𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                         it 𝑡𝑡𝑡𝑡indicates
                                                                                                                                                         − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽1 �𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝛽𝛽𝛽𝛽
                                                                                                                                               𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 that                 managers
                                 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 returns on the fund house due to stock selection                                   𝛽𝛽𝛽𝛽                              Determinants of Attitude Towards Zakat on Employ
          earned extra                                                                                                                                                𝜀𝜀𝜀𝜀𝑝𝑝𝑝𝑝,𝑡𝑡𝑡𝑡+ability.
                                                                                                                                                                        𝑅𝑅𝑅𝑅          𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻𝑡𝑡𝑡𝑡 + 𝛽𝛽𝛽𝛽4 𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡 + 𝜀𝜀𝜀𝜀
                                                                                                                                                                              𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
         𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡        𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                                                                                                                  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽
          Carhart
              𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 Four-Factor Model (1997)
                               𝜀𝜀𝜀𝜀                                                                                             𝛼𝛼𝛼𝛼
                                                                                                                                                                                                                            + 𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆
                           Determinants                                                             𝑝𝑝𝑝𝑝 29-48
                                  𝑝𝑝𝑝𝑝,𝑡𝑡𝑡𝑡 of Attitude Towards Zakat on Employment Income in Nigeria:                                                                                                                         3
                                                                                                                                 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                            𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
         𝑅𝑅𝑅𝑅Carhart
              𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡     𝛽𝛽𝛽𝛽expanded
                                     𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 the     Fama
                                                    − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝French
                                                                               + 𝛽𝛽𝛽𝛽1 �𝑅𝑅𝑅𝑅three-factor
                                                                                                    𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � +model, 𝛽𝛽𝛽𝛽2 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡taking into
          consideration           Determinants of Attitude Towards Zakat on Employment Income in Nigeria: 29-48
                                      momentum +factor                                 in addition                to size                 and value factors.                                                                                                 3
              𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                           𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻         + 𝛽𝛽𝛽𝛽 𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆        𝑡𝑡𝑡𝑡 + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                                                     𝜀𝜀𝜀𝜀𝑝𝑝𝑝𝑝,𝑡𝑡𝑡𝑡             𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
          The Carhart model is 𝑅𝑅𝑅𝑅defined                 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅               =𝑡𝑡𝑡𝑡 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 +4 𝛽𝛽𝛽𝛽1 �𝑅𝑅𝑅𝑅
                                                                              as𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡follows:                             𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝛽𝛽𝛽𝛽2 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡
                                                                     𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 in Nigeria: 29-48
              Determinants of Attitude Towards Zakat on Employment Income                                                                                                                𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                        3
       𝛽𝛽𝛽𝛽                        𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅                                              + 𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻          ++𝛽𝛽𝛽𝛽4𝛽𝛽𝛽𝛽𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆            + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                               𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽1 �𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                                                      𝑡𝑡𝑡𝑡 �            2 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡
            𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                                                                                                     𝑅𝑅𝑅𝑅                          (8)
                                                                 + 𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻𝑡𝑡𝑡𝑡 + 𝛽𝛽𝛽𝛽4 𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡 + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                                                                           𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                        𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡
         𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝                        𝜀𝜀𝜀𝜀 ,𝑡𝑡𝑡𝑡 is the mean return of the fund house over the period
          Where, 𝑝𝑝𝑝𝑝𝑅𝑅𝑅𝑅                         𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
          t,𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵
                     𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡is
                                  𝑡𝑡𝑡𝑡 the risk-free rate of return over the period t, 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the return
      𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
          on the relative market benchmark. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡 is the difference                                                                𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻
                                                                                                                                                      in 𝑡𝑡𝑡𝑡return
       𝜀𝜀𝜀𝜀𝑝𝑝𝑝𝑝,𝑡𝑡𝑡𝑡
          between 𝑅𝑅𝑅𝑅a small-cap portfolio and a large-cap portfolio at time t,
             𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻                          𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡while is the difference in return between a portfolio                                                  of 𝑡𝑡𝑡𝑡high-book-
                                                                                                                                   𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵
      𝑅𝑅𝑅𝑅to-market
           𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                               stock and a low-book-to market          𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻𝑡𝑡𝑡𝑡 stock at time t. 𝛽𝛽𝛽𝛽1 measures
          the sensitivity between the market and the fund house. If it is positive
          and               significant,
             𝛽𝛽𝛽𝛽1𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵              𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 then the fund house is highly associated                              𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻with          market
                                      𝑡𝑡𝑡𝑡                                                                                                     𝑡𝑡𝑡𝑡
    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                                          𝛽𝛽𝛽𝛽
                                                                                                                                                           𝛽𝛽𝛽𝛽2</preformat>
      <preformat>               𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻𝛽𝛽𝛽𝛽𝑡𝑡𝑡𝑡2 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡                                                                                                                       𝛽𝛽𝛽𝛽1
                                                                                                                                              𝛽𝛽𝛽𝛽2                                       𝛽𝛽𝛽𝛽3
                                                                                                                         𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                     𝛽𝛽𝛽𝛽1
                   𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
                                     𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡                          𝛽𝛽𝛽𝛽1
The𝑅𝑅𝑅𝑅International                      𝛽𝛽𝛽𝛽1
             𝛽𝛽𝛽𝛽1 Journal of Banking and Finance, Vol. 16, Number 1 (January) 2021, pp: 21–42
          𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                                                                  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                    𝛽𝛽𝛽𝛽2
               𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                               𝛽𝛽𝛽𝛽2
                                          𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡
movements,                            𝛽𝛽𝛽𝛽2 is a coefficient that measures                            𝛽𝛽𝛽𝛽2                          the fund house exposure,
  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡                                                                                                        𝛽𝛽𝛽𝛽 house is associated                                 𝛽𝛽𝛽𝛽3 with
if seen positive and significant then the fund
              𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵
small-capitalisation                    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 stocks. 3 a coefficient that measures the fund
                               𝑡𝑡𝑡𝑡                                            𝛽𝛽𝛽𝛽
house exposure          𝛽𝛽𝛽𝛽                        and       if      positive        𝛽𝛽𝛽𝛽3and significant, then the fund house
    𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡 3                                                                                                                                                         𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡
is exposed                        to high-book-to-market stocks,𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 measures the selectivity
ability𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻   where  𝑡𝑡𝑡𝑡             if positive and                          significant,
                                                                              𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡                                 then                the    fund               house              has
                                          𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡
superior𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆       stock selection ability,                                  𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆        𝑡𝑡𝑡𝑡 is the different in return between
  𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻                           𝑡𝑡𝑡𝑡
high       minus 𝑡𝑡𝑡𝑡                low momentum (prior one year                                                      𝜀𝜀𝜀𝜀𝑝𝑝𝑝𝑝,𝑡𝑡𝑡𝑡return) at time t. 𝛽𝛽𝛽𝛽4 is the
coefficient𝛽𝛽𝛽𝛽1                    that measures the𝛽𝛽𝛽𝛽4fund house’s exposure and if positive
and significant,                        𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻
                                                  then  𝑡𝑡𝑡𝑡 the fund house
                        𝛽𝛽𝛽𝛽4                                                         𝛽𝛽𝛽𝛽4 is exposed to high momentum.
  𝛽𝛽𝛽𝛽1</preformat>
      <sec id="sec3-1">
        <label>3.3</label>
        <title>Market Timing Mod</title>
        <p>Market Timing 𝛽𝛽𝛽𝛽 𝛽𝛽𝛽𝛽1 Models 3.3 Market Timing Models</p>
        <preformat>                     3.3                                                             3.3 Market Timing Models
Market𝛽𝛽𝛽𝛽timing       2 Market                          Timing Models
                                              is measured using the Treynor and Mazuy (TM) (1966)
and Henriksson𝛽𝛽𝛽𝛽3                                    and Merton (HM) (1981) approaches. The
                                                        𝛽𝛽𝛽𝛽2                                                                                                                 𝑇𝑇𝑇𝑇𝑆𝑆𝑆𝑆aim   = 𝑅𝑅𝑅𝑅is  𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝
to investigate whether                                                 fund house managers exhibit market timing
    𝛽𝛽𝛽𝛽3 Market timing models                                               𝑇𝑇𝑇𝑇𝑆𝑆𝑆𝑆 = 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 + 𝛾𝛾𝛾𝛾𝑝𝑝𝑝𝑝 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 )2 +
ability.                                                                               identify fund house managers’ ability
                                                                                                                                                                           2 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 + 𝛾𝛾𝛾𝛾𝑝𝑝𝑝𝑝 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 )2
to develop           𝑇𝑇𝑇𝑇𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡=
              𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆          timing  𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 −strategies             +𝑇𝑇𝑇𝑇𝑆𝑆𝑆𝑆
                                                               𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 to    𝛽𝛽𝛽𝛽shift  = 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
                                                                                              𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 −    𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓−+𝑅𝑅𝑅𝑅𝛾𝛾𝛾𝛾between
                                                                                                               capital
                                                                                                                                               = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝−+𝑅𝑅𝑅𝑅𝛽𝛽𝛽𝛽𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅
                                                                                                                                      𝑓𝑓𝑓𝑓𝑝𝑝𝑝𝑝 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓     safe𝑓𝑓𝑓𝑓 ) 𝑓𝑓𝑓𝑓+ and  𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎrisky
                                          𝛽𝛽𝛽𝛽
securities based on whether the market is expected toDeterminants
                                              3                                                                                                                             do well                 or
                                                                                                                                                                                            of Attitude Towards Zakat on Em
   𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆
bad.       Over-performing
                      𝑡𝑡𝑡𝑡                                        fund houses are able to forecast entry and exit
                                                                                                                                                                                              𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝
strategies    𝛽𝛽𝛽𝛽4 in the market for their funds.
                                         𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡                                                                                                                                                                    + 𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻
         Determinants of Attitude Towards Zakat on Employment Income in Nigeria: 29-48                                                                                                                      3
    𝛽𝛽𝛽𝛽
Treynor 4                  &amp; Mazuy (TM) Model (1966)
                                           𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽1 �𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 � + 𝛽𝛽𝛽𝛽2 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡</preformat>
      </sec>
      <sec id="sec3-2">
        <label>3.3</label>
        <title>Market Timing Models</title>
        <preformat>Treynor   and Mazuy
              𝛽𝛽𝛽𝛽4  (1966)
                          + built       a model
                            𝛽𝛽𝛽𝛽3 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻              that recognises good market
                                               𝑡𝑡𝑡𝑡 + 𝛽𝛽𝛽𝛽4 𝑆𝑆𝑆𝑆𝑀𝑀𝑀𝑀𝑆𝑆𝑆𝑆𝑡𝑡𝑡𝑡 + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡
timing of fund houses. The market timing is cached by the square of</preformat>
      </sec>
      <sec id="sec3-3">
        <label>3.3</label>
        <title>Market Timing Models</title>
        <p>market returns. The model is as follows: 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡2 𝑇𝑇𝑇𝑇𝑆𝑆𝑆𝑆 = 𝑅𝑅𝑅𝑅3.3 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 Market Timing Models 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 + 𝛾𝛾𝛾𝛾𝑝𝑝𝑝𝑝 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 ) + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ (9)</p>
        <p>Where, is 𝑅𝑅𝑅𝑅the 𝑇𝑇𝑇𝑇𝑆𝑆𝑆𝑆 = 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑓𝑓𝑓𝑓 =mean 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽return 𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 − of 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 the + 𝛾𝛾𝛾𝛾𝑝𝑝𝑝𝑝fund (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 −house 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 )2 over + 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎthe period t, 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the risk-free rate of returns over the period t,𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the return on the relative𝑇𝑇𝑇𝑇𝑆𝑆𝑆𝑆 market = 𝑅𝑅𝑅𝑅benchmark, 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + measures 𝛽𝛽𝛽𝛽𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 −selectivity 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 + 𝛾𝛾𝛾𝛾𝑝𝑝𝑝𝑝 (𝑅𝑅𝑅𝑅ability, +2 𝜀𝜀𝜀𝜀is𝑓𝑓𝑓𝑓ℎ 𝑓𝑓𝑓𝑓 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓𝑅𝑅𝑅𝑅)𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 the squared market return, and 𝛾𝛾𝛾𝛾𝑝𝑝𝑝𝑝,t indicates market timing where if𝑅𝑅𝑅𝑅positive 𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 and significant, then the fund houses are𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵 successful 𝑡𝑡𝑡𝑡 and exposure to the market is increased when markets are doing well.</p>
        <p>Henriksson 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝐵𝐵𝑡𝑡𝑡𝑡 &amp; Merton (HM) Model (1981) 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆𝐻𝐻𝐻𝐻𝑡𝑡𝑡𝑡 𝛾𝛾𝛾𝛾𝑝𝑝𝑝𝑝,t</p>
        <p>𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 31 𝛽𝛽𝛽𝛽1 𝛽𝛽𝛽𝛽2 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅 𝐻𝐻𝐻𝐻𝑆𝑆𝑆𝑆 = 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 = 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 + 𝛽𝛽𝛽𝛽𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 + 𝛿𝛿𝛿𝛿𝑝𝑝𝑝𝑝 (𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 − 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓 )𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 + 𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓ℎ 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 𝛿𝛿𝛿𝛿𝑝𝑝𝑝𝑝 𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 Where 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓ℎ,𝑡𝑡𝑡𝑡is the mean return of the fund house over the period t, 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the risk-free rate of return over the period t, 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡is the return on the relative market benchmark, 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 measures selectivity ability, 𝛿𝛿𝛿𝛿𝑝𝑝𝑝𝑝 is the market timing coefficient, 𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 is a dummy variable that takes a value the market return is positive and zero otherwise, and 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 of one if𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 is the error term. 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 𝛿𝛿𝛿𝛿𝑝𝑝𝑝𝑝 𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 ANALYSIS OF RESULTS 𝑅𝑅𝑅𝑅𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 𝛿𝛿𝛿𝛿𝑝𝑝𝑝𝑝 This section provides the results 𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 for the analysis of fund houses’ 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 performance which include fund house managers’ selectivity and timing ability performance. 𝛼𝛼𝛼𝛼𝑝𝑝𝑝𝑝 𝛿𝛿𝛿𝛿𝑝𝑝𝑝𝑝 Descriptive Statistics 𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 Table 1 presents the descriptive statistics of monthly returns of the fund house, 𝛿𝛿𝛿𝛿𝑝𝑝𝑝𝑝 market benchmarks, and other risk factors from 2007 𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 to 2018. As shown in Table 1, the empirical characteristics 𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 of negative skewness, excess kurtosis, and non-normality in most portfolio returns are the dominant features of the data. The mean of fund houses’ returns is positive 𝐷𝐷𝐷𝐷𝑡𝑡𝑡𝑡 and equal 0.0920. While the mean returns for Islamic𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓and 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡 conventional benchmarks are negative and equal -0.0615 and -0.0061, respectively.</p>
        <table-wrap id="tbl1">
          <label>Table 1</label>
          <caption><title>𝜀𝜀𝜀𝜀𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑡𝑡𝑡𝑡</title></caption>
          <table>
            <thead>
              <tr>
                <th colspan="2">Descriptive Statistics</th>
                <th colspan="6"></th>
              </tr>
              <tr>
                <th colspan="3"></th>
                <th>FTSE</th>
                <th colspan="4"></th>
              </tr>
              <tr>
                <th></th>
                <th>Fund</th>
                <th>FTSE</th>
                <th colspan="5"></th>
              </tr>
              <tr>
                <th colspan="3"></th>
                <th>all</th>
                <th>SMB</th>
                <th>HML</th>
                <th>MOM</th>
                <th>TB</th>
              </tr>
              <tr>
                <th></th>
                <th>house</th>
                <th>Islamic</th>
                <th colspan="5"></th>
              </tr>
              <tr>
                <th colspan="3"></th>
                <th>world</th>
                <th colspan="4"></th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td>Mean</td>
                <td>0.092</td>
                <td>-0.062</td>
                <td>-0.006</td>
                <td>-0.080</td>
                <td>0.046</td>
                <td>-0.019</td>
                <td>0.065</td>
              </tr>
              <tr>
                <td>Med.</td>
                <td>0.132</td>
                <td>-0.063</td>
                <td>-0.003</td>
                <td>0.132</td>
                <td>-0.156</td>
                <td>0.209</td>
                <td>0.063</td>
              </tr>
              <tr>
                <td>Max.</td>
                <td>0.693</td>
                <td>0.458</td>
                <td>0.117</td>
                <td>0.184</td>
                <td>0.429</td>
                <td>0.209</td>
                <td>0.139</td>
              </tr>
              <tr>
                <td>Min.</td>
                <td>-0.583</td>
                <td>-0.454</td>
                <td>-0.235</td>
                <td>-0.406</td>
                <td>-0.156</td>
                <td>-0.925</td>
                <td>0.018</td>
              </tr>
              <tr>
                <td>SD.</td>
                <td>0.037</td>
                <td>0.057</td>
                <td>0.047</td>
                <td>0.281</td>
                <td>0.267</td>
                <td>0.519</td>
                <td>0.030</td>
              </tr>
              <tr>
                <td>Skew</td>
                <td>-1.158</td>
                <td>-1.982</td>
                <td>-0.657</td>
                <td>-0.219</td>
                <td>0.669</td>
                <td>-0.645</td>
                <td>0.521</td>
              </tr>
              <tr>
                <td>Kurt.</td>
                <td>25.763</td>
                <td>24.796</td>
                <td>1.863</td>
                <td>-1.881</td>
                <td>-1.483</td>
                <td>-1.520</td>
                <td>1.489</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p>Table 2 displays the Pearson correlation coefficients of the fund house, and the risk factors, and also below the correlation coefficients are p-value for tests of significance of coefficients. This is to check if the problem of multicollinearity exists. Fund house returns indicate a low correlation with returns of both markets’ benchmarks of FTSE Global Islamic and FTSE All-World. Similarly, the market indices show low correlation with each other, with significantly positive correlation coefficients. None of the variables or independent variables are highly correlated. The highest reported figure is 30.46 percent, the correlation between FTSE Islamic returns and Treasury bill rate. Hence, the estimation is less likely to suffer the multicollinearity problem.</p>
        <table-wrap id="tbl2">
          <label>Table 2</label>
          <caption><title>Correlation Matrix</title></caption>
          <table>
            <thead>
              <tr>
                <th>Fund</th>
                <th></th>
                <th>FTSE</th>
                <th colspan="3"></th>
              </tr>
              <tr>
                <th></th>
                <th>FTSE (I)</th>
                <th></th>
                <th>SMB</th>
                <th>HML</th>
                <th>MOM</th>
                <th>TB</th>
              </tr>
              <tr>
                <th>house</th>
                <th></th>
                <th>(AW)</th>
                <th colspan="3"></th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td>Fund house 1.000</td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>-.</td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>FTSE (I)</td>
                <td>1.000</td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>.002</td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>FTSE -.083</td>
                <td>.085</td>
                <td>1.000</td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>(AW) .000</td>
                <td>.000</td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>.002</td>
                <td>.001</td>
                <td>.149</td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>SMB</td>
                <td></td>
                <td></td>
                <td>1.000</td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>.041</td>
                <td>.055</td>
                <td>.000</td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>.007</td>
                <td>.051</td>
                <td>.128</td>
                <td>.064</td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>HML</td>
                <td></td>
                <td></td>
                <td></td>
                <td>1.000</td>
                <td></td>
              </tr>
              <tr>
                <td>.047</td>
                <td>.000</td>
                <td>.000</td>
                <td>.000</td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>-.010</td>
                <td>-.068</td>
                <td>-.161</td>
                <td>-.055</td>
                <td>-.418</td>
                <td></td>
              </tr>
              <tr>
                <td>MOM</td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
                <td>1.000</td>
              </tr>
              <tr>
                <td>.029</td>
                <td>.000</td>
                <td>.000</td>
                <td>.000</td>
                <td>.000</td>
                <td></td>
              </tr>
              <tr>
                <td>.044</td>
                <td>-.305</td>
                <td>-.109</td>
                <td>-.007</td>
                <td>-.025</td>
                <td>.015 1.000</td>
              </tr>
              <tr>
                <td>TB</td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
                <td></td>
              </tr>
              <tr>
                <td>.000</td>
                <td>.000</td>
                <td>.000</td>
                <td>.439</td>
                <td>.011</td>
                <td>.138</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <sec id="sec3-3-1">
          <title>Selectivity Skills Models</title>
          <p>This section reports the finding of the empirical analysis of six performance measures to gauge the performance of the fund house comparative to benchmarks. The performance measures used are: raw returns, excess returns, the Sharpe ratio, the Treynor ratio, the one factor model (Jensen’s alpha), and the Carhart’s four-factor model.</p>
          <p>Raw Return, Excess Return, the Sharpe Ratio, and the Treynor Ratio</p>
          <p>Table 3 presents monthly means for raw returns and excess returns, the Sharpe ratio and Treynor ratio for the fund house. The fund houses’ performance are compared using two market indices. The mean raw returns for fund houses are 0.07 percent per month, and for Islamic and conventional benchmarks are 0.003 and 0.002 percent per month, respectively. However, after taking into account the risk-free rate, the mean excess returns of fund houses remain positive at 0.009 percent per month, but the mean excess returns for both market benchmarks which are Islamic and conventional are negative at -0.061 and -0.082, respectively. Both the mean returns and mean excess returns for fund houses are higher than both the market benchmarks. Although the fund houses’ returns exceed the returns of the market benchmarks, the returns are less volatile. In addition, the beta of fund houses is lower than that of market beta (1.000). This gives an initial indicator of the attractiveness of fund houses that yield higher returns but lower risks, both total and systematic. This could be due to the diversification which are provided by the houses.</p>
          <p>The Sharpe ratio represents the calculation of mean excess returns relative to the total risk indicated by the standard deviation. This measure gives the unit of return earned while taking an additional unit of total risk. The results indicate that investment in fund houses earn a Sharpe ratio of 0.39 percent per month, but the Sharpe ratio for both market benchmarks is negative -1.08 and -1.34, respectively. That means the investment in fund houses is better than investment in both market benchmarks Islamic and conventional. The Treynor ratio refers to the calculation of mean excess returns relative to the systemic risk posed by beta. The Treynor ratio shows positive results using both market benchmarks. That means the fund houses show better performance and are well diversified.</p>
          <p>The findings of these essential performance models are used to conclude that the fund house outperforms both the market benchmarks when relative performance measures are used. This is justified by the increased diversification provided by houses which in turn offers advantages of improving the overall performance of fund houses. This corresponds to the modern portfolio theory (MPT) which suggests that the risk-reduction advantages associated with maintaining a diversified portfolio of assets are that it maximises the anticipated return based on a given degree of market risk. Although the relative performance measures are commonly used in practice, these measures can only be used in ranking funds in relation to their peers in that they provide no fundamental statistical or economic meaning. Therefore, the next sections provide the results of the single and multi-factor models. These performance models, based on the CAPM, give an estimate of the intercept (alpha), which refers to fund performance in relation to the benchmark return.</p>
          <p>One Factor Model (Jensen, 1968)</p>
          <p>Table 4 provides the results for the analysis of performance employing the one-factor model (Jensen, 1968) using both market benchmarks, FTSE Global Islamic and FTSE All-World. Alpha indicates the monthly abnormal returns of the fund houses. As shown, the alpha estimate for fund houses is positive and equals 0.19 percent per month for FTSE Global Islamic and 0.20 percent per month for FTSE All- World. That indicates that the fund houses outperformed both market benchmarks. This result is also in line with the results of the traditional measures in the previous section.</p>
          <table-wrap id="tbl3">
            <label>Table 3</label>
            <caption><title>Mean Raw Returns, Mean Excess Returns, Sharpe Ratio, and Treynor</title></caption>
            <table>
              <thead>
                <tr>
                  <th>Ratios</th>
                  <th colspan="3"></th>
                </tr>
                <tr>
                  <th></th>
                  <th>Fund House</th>
                  <th>FTSE Islamic</th>
                  <th>FTSE All World</th>
                </tr>
                <tr>
                  <th colspan="3">Panel A: Mean raw, mean excess return, and Sharpe ratio</th>
                  <th></th>
                </tr>
              </thead>
              <tbody>
                <tr>
                  <td>Mean raw returns</td>
                  <td>0.0740</td>
                  <td>0.0032</td>
                  <td>0.0023</td>
                </tr>
                <tr>
                  <td>Mean excess return</td>
                  <td>0.0093</td>
                  <td>-0.0615</td>
                  <td>-0.0824</td>
                </tr>
                <tr>
                  <td>Std. Dev</td>
                  <td>0.0317</td>
                  <td>0.0569</td>
                  <td>0.0465</td>
                </tr>
                <tr>
                  <td>Sharpe ratio</td>
                  <td>0.3936 Panel B: Beta and Treynor ratio using FTSE Islamic as benchmark</td>
                  <td>-1.0812</td>
                  <td>-1.3424</td>
                </tr>
                <tr>
                  <td>Beta</td>
                  <td>0.1307</td>
                  <td>1.0000</td>
                  <td>------</td>
                </tr>
                <tr>
                  <td>Treynor</td>
                  <td>0.0711 Panel C: Beta and Treynor ratio using FTSE All world as benchmark</td>
                  <td>------</td>
                  <td>------</td>
                </tr>
                <tr>
                  <td>Beta</td>
                  <td>0.1166</td>
                  <td>------</td>
                  <td>1.0000</td>
                </tr>
                <tr>
                  <td>Treynor</td>
                  <td>0.0797</td>
                  <td>------</td>
                  <td>------</td>
                </tr>
              </tbody>
            </table>
          </table-wrap>
          <p>The adjusted R2 for fund houses are 81 percent and 85 percent for FTSE Global Islamic and FTSE All-World, respectively. The high adjusted R2 also indicates that the fund managers pursue a passive approach by watching the market closely, but are unable to perform well. The results also show the alpha using a conventional benchmark is better than the alpha using the Islamic benchmark, that due to some restrictions are placed on Islamic investments that may limit performance.</p>
          <table-wrap id="tbl4">
            <label>Table 4</label>
            <caption><title>One Factor Model (Jensen, 1968)</title></caption>
            <table>
              <thead>
                <tr>
                  <th></th>
                  <th colspan="2">FTSE Global Islamic</th>
                  <th></th>
                  <th colspan="2">FTSE All World</th>
                  <th></th>
                </tr>
              </thead>
              <tbody>
                <tr>
                  <td></td>
                  <td>Alpha</td>
                  <td>Beta</td>
                  <td>Adj. R</td>
                  <td>2 Alpha</td>
                  <td>Beta</td>
                  <td>Adj. R2</td>
                </tr>
                <tr>
                  <td>Coeff</td>
                  <td>0.1942</td>
                  <td>-0.2435</td>
                  <td>0.81</td>
                  <td>0.2025</td>
                  <td>-0.1067</td>
                  <td>0.85</td>
                </tr>
                <tr>
                  <td>Std.err</td>
                  <td>0.0072</td>
                  <td>0.0801</td>
                  <td>-----</td>
                  <td>0.0077</td>
                  <td>0.0916</td>
                  <td>-----</td>
                </tr>
                <tr>
                  <td>p-value</td>
                  <td>0.0002</td>
                  <td>0.0023</td>
                  <td>-----</td>
                  <td>0.0001</td>
                  <td>0.2441</td>
                  <td>-----</td>
                </tr>
                <tr>
                  <td>Source: Jensen (1968).</td>
                  <td>Four-Factor Model (Carhart, 1997)</td>
                  <td></td>
                  <td></td>
                  <td></td>
                  <td></td>
                  <td></td>
                </tr>
              </tbody>
            </table>
          </table-wrap>
          <p>For the four-factor model, the factor returns for the four-factor models are not easily available, hence the researcher used the data made available at the Fama and French websites, which in turn employs the FTSE All-World database to construct monthly for the four-factor model. Table V provides the results of the four-factor model for fund houses using FTSE All-World as a market benchmark. As shown in</p>
          <table-wrap id="tbl5">
            <label>Table 5</label>
            <caption><title>, the four-factor alpha for fund houses was 0.20 percent and</title></caption>
          </table-wrap>
          <p>significant, which indicates that on average, the fund houses are able to outperform the four-factor benchmarks. In addition, the results indicate that the fund houses exhibit lower risks with beta of -0.14. This result is similar to the results using the one-factor model.</p>
          <p>In terms of size preference, fund houses prefer small stocks than big stocks, given the SMB factor loading is -0.03 and statistically significant. The HML factor for fund houses is -0.05 and statistically significant, suggesting a preference for growth-to-value stock. The</p>
          <p>MOM factor for fund houses is not significant. The fund houses display a relative preference for small-cap and growth-oriented stock. In conclusion, the preference of fund houses for smaller cap and lower beta results in the significant out-performance of fund houses over the four-factor benchmarks. Fund houses also display a preference for the growth-to-value stock. Finally, the MOM factor for fund houses is not significant.</p>
          <p>Fund houses’ superior performance can be attributed to that the fund houses remove unsystematic risks by diversification, which means the houses make funds work within these houses comprising only market risks (systematic risks). This should make for a stronger relationship, if there is one, in any subsequent time-series regression, especially if there is time-series autocorrelation. The constant or error term in the subsequent regression helps to remove any remaining unsystematic risk.</p>
          <table-wrap id="tbl5">
            <label>Table 5</label>
            <caption><title>Carhart’s Four Factor Model</title></caption>
            <table>
              <thead>
                <tr>
                  <th></th>
                  <th>Coef</th>
                  <th>Std.err</th>
                  <th>p-value</th>
                </tr>
              </thead>
              <tbody>
                <tr>
                  <td>Alpha</td>
                  <td>0.2011</td>
                  <td>-0.0079</td>
                  <td>0.0001</td>
                </tr>
                <tr>
                  <td>Market</td>
                  <td>-0.1400</td>
                  <td>0.0974</td>
                  <td>0.0505</td>
                </tr>
                <tr>
                  <td>SMB</td>
                  <td>-0.0336</td>
                  <td>0.0023</td>
                  <td>0.0488</td>
                </tr>
                <tr>
                  <td>HML</td>
                  <td>-0.0538</td>
                  <td>0.0022</td>
                  <td>0.0015</td>
                </tr>
                <tr>
                  <td>MOM</td>
                  <td>-0.0022</td>
                  <td>0.0017</td>
                  <td>0.2042</td>
                </tr>
                <tr>
                  <td>Adj. R 2</td>
                  <td>-----</td>
                  <td>0.88</td>
                  <td>-----</td>
                </tr>
              </tbody>
            </table>
          </table-wrap>
        </sec>
        <sec id="sec3-3-2">
          <title>Market Timing Models</title>
          <p>Table 6 presents the results for the analysis of security selection and market timing ability using the Treynor-Mazuy model (TM) and Hendrickson-Merton model (HM) using ordinary least square (OLS), for fund houses. In the panel “A”, according to the Treynor-Mazuy model (TM), fund houses have good selectivity skills but appear to have poor market timing ability irrespective of the benchmarks using both market benchmarks “FTSE Global Islamic and FTSE All-World”. Alpha is positive and equals to 0.195 and 0.193, respectively, and Gamma is negative and equals to -0.12 and -0.34, respectively. In the panel “B”, according to the Hendrickson-Merton model (HM), fund houses have good selectivity skills but appear poor in market timing ability irrespective of the benchmarks using both market benchmarks “FTSE Global Islamic and FTSE All-World”. Alpha is positive and equals to 0.19 and 0.20, respectively, and Gamma is negative and equals to -0.08 and -0.30, respectively.</p>
          <table-wrap id="tbl6">
            <label>Table 6</label>
            <caption><title>Market Timing Models: Treynor-Mazuy Model and Hendrickson-</title></caption>
            <table>
              <thead>
                <tr>
                  <th colspan="2">Merton Model</th>
                  <th colspan="5"></th>
                </tr>
                <tr>
                  <th></th>
                  <th colspan="3">FTSE Global Islamic</th>
                  <th></th>
                  <th>FTSE AllWorld</th>
                  <th></th>
                </tr>
                <tr>
                  <th></th>
                  <th>Alpha</th>
                  <th>Gamma\</th>
                  <th>Adj.</th>
                  <th></th>
                  <th>Alpha</th>
                  <th>Gamma\</th>
                  <th>Adj.</th>
                </tr>
                <tr>
                  <th colspan="2"></th>
                  <th>Delta</th>
                  <th>R2</th>
                  <th></th>
                  <th>Delta</th>
                  <th>R2</th>
                </tr>
                <tr>
                  <th colspan="6">Panel A: Market timing measure; Treynor-Mazuy model</th>
                  <th></th>
                </tr>
              </thead>
              <tbody>
                <tr>
                  <td>Coeff</td>
                  <td>0.1953</td>
                  <td>-0.1292</td>
                  <td>0.74</td>
                  <td>0.1933</td>
                  <td>-0.3466</td>
                  <td>0.92</td>
                </tr>
                <tr>
                  <td>Std.err</td>
                  <td>0.0075</td>
                  <td>0.2547</td>
                  <td>-----</td>
                  <td>0.0082</td>
                  <td>0.0870</td>
                  <td>-----</td>
                </tr>
                <tr>
                  <td>p-value</td>
                  <td>0.1914</td>
                  <td>0.6118 Panel B: Market timing measure; Hendrickson-Merton model</td>
                  <td>-----</td>
                  <td>0.5611</td>
                  <td>0.0006</td>
                  <td>-----</td>
                </tr>
                <tr>
                  <td>Coeff</td>
                  <td>0.1935</td>
                  <td>-0.0807</td>
                  <td>0.76</td>
                  <td>0.1986</td>
                  <td>-0.3068</td>
                  <td>0.79</td>
                </tr>
                <tr>
                  <td>Std.err</td>
                  <td>0.0072</td>
                  <td>0.1190</td>
                  <td>-----</td>
                  <td>0.0079</td>
                  <td>0.1609</td>
                  <td>-----</td>
                </tr>
                <tr>
                  <td>p-value</td>
                  <td>0.0002</td>
                  <td>0.4980</td>
                  <td>-----</td>
                  <td>0.0001</td>
                  <td>0.0311</td>
                  <td>-----</td>
                </tr>
              </tbody>
            </table>
          </table-wrap>
          <p>Overall, both market timing ability measures (Treynor-Mazuy model (TM) and Hendrickson-Merton model (HM)) provide similar results, where there is strong evidence that fund house managers have good selectivity skills and this results in supporting results of the one-factor and four-factor models. This is due to the benefits provided by the advantages of fund houses like diversification and more investment opportunities. However, fund houses have weak market timing ability. The possible reason is that the fund houses contain large and different types of funds, and thus the management process becomes more difficult. This may reduce the ability and efficiency of managers.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec4">
      <title>CONCLUSION</title>
      <p>This study seeks to contribute by providing new evidence about the mutual fund performance at the fund house level. Firstly, the study concluded that managers benefit from the advantages provided by the fund house like diversification and more investment opportunity. So, fund house managers show good selectivity skills. At the same time, fund house managers show poor market timing ability. The possible reason is that the fund houses contain large and different types of funds, and thus the management process becomes more difficult. This may reduce the ability and efficiency of managers to track the fluctuations and constant movements in the market.</p>
      <p>The results are useful for both investors and managers. Managers should take the requisite decision or changes to make themselves more efficient in comparison with their competing colleagues. The investors can more effectively allocate their money to better controlled funds. In addition, the results help investors make the correct investment decision, since most of the investors use the top-down approach. The results are also important to academics and regulators because they provide an overview of the mutual fund industry generally, and fund houses specifically.</p>
      <p>From the results of this study, there are two recommendations that must be considered. Firstly, due to limited evidence about performance at the fund house level, it is important to increase the focus upon the fund house level because the advantages of fund houses may lead to improved performance as the results showed.</p>
      <p>It is then highly recommended to extend the focus to characteristics of these houses and their effects on houses and funds’ performance. Secondly, since most of the previous studies focussed on developed countries like the USA and UK, then it is highly recommended to academics and researchers to extend such studies to other emerging countries like the Middle-East and South-Asia countries.</p>
    </sec>
  </body>
  <back>
    <ack>
      <title>ACKNOWLEDGMENT</title>
      <p>This research received no specific grant from any funding agency.</p>
    </ack>
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