Performance Evaluation of Pakistan's Mutual Fund through CAPM and Fama French 3-Factor Model

Mutual fund is selection for the common investors for investing in to the capital market. In the research paper Capital Asset Pricing Model (CAPM) and FAMA French 3 factor model applied for the measurement and evaluate the performance of the mutual fund. Daily data of mutual fund which are selected in open ended mutual fund of Pakistan and daily data collected from 2010 to 2016. Then applied these models and Capital Assets Pricing Model showed the significant result and R2 value more co-related with the market returns and premium. FAMA French 3 factor model showed the not good results with the two factors SMB and HML. Time series regression model are applied between two competing models.


INTRODUCTION
With the increase in trend of investment of investors which consider the mutual fund is the key instrument of profitability. Mutual fund is pool saving a number of investors. The underpinning objective of investment in mutual funds is profitability numerous studies documented the same evidence over the period of time. The fund investors have objective for the Common investment by the Asset Management Company (AMC). Mutual fund creates profitability through dividend, capital gain and appreciation of share price. Mutual Fund avail liquidity and portfolio management enterprise, diversification of risk and stability of stock market and mobiles saving which attaching funds from the small investor. Mutual fund categorized in three types: close end mutual fund, open-end mutual fund, and exchange traded fund.
• Open-end mutual fund shares purchase and sale on demand on their net asset value, or NAV, which base on the value of the fund's securities. • Close-end funds are traded between the investors on exchange which have a fixed numbers of shares. Like stock, according to supply and demand their share prices are determined and are traded at discount or premium to their net asset value' • Exchange-traded funds are also traded on their market price value like stock on exchange which are more closely at their net present value than close-end mutual fund and usually stay on the premium and discount within 1% of NAV, with exception of some smaller ETFs that are frequently in trade.
Many tools and measures analyzed the measurement of the performance of the mutual fund. Capital Asset Pricing Model (CAPM) that explain the relationship between expected return of assets and systematic risk, other stocks. Finance for the risky securities of price used by CAPM, explained expected returns for assets given the risk of those assets and calculating cost of capital. Formula for calculating the expected return of an asset its risk is as follows: Ra =Rf + β(Rm -Rf) Rf = risk free rate β = beta of the security Rm = expected market risk In 1990 American economist William p sharp, harry Markowitz and Merton h. miller won the noble prize "for their introducing the new idea and methods in the theory of financial economics". In the 1960's Sharp, taking off from Markowitz's portfolio theory, established the Capital Asset Pricing Model (CAPM) Sharp, 1964. This model is fit in every investor's portfolio on the basis of single mix of risky assets. Investor's wants more return and carry weighted portfolio with the risky asset. Portfolio risk measure cannot be modified without beta. Asset pricing under short sale examined to restrain and analysis about effect of cross sectional idiosyncratic risk Miller, 1977. To forecast the diversified portfolio risk that idiosyncratic risk should be priced when investor hold undiversified and diversified portfolio Merton, 1987. Idiosyncratic risk should be linked with cross section risk. Blume 1970, Friends and Blume 1970 and Black, Jensen and Scholes 1972 examine the portfolios estimated beta instead of individual securities. In portfolio expected return and market betas work combine or same way of CAPM. The critical errors in variables problem are reduced by cross sectional portfolio regression of average return on betas. It reduces statistical power and also reduces the range of betas. To alleviate the problem, researchers classify the securities on beta when float portfolio and 1 st portfolio have lowest beta on the securities, as far as the last portfolios process the highest beta assets. In empirical test is classifying the procedure. Correlation of the residuals in cross section regression is caused on propose a method for addressing for inference the problem.
The time series intercepts monthly slopes and in addition to the standard errors of means. The slopes monthly to monthly variate in regression coefficients and determine the problem actually estimating correlations. The residual correlation effect the regression coefficient. These conversations also become standard in literature. The relationship between market beta and expected return implicit of a time series regression test by Sharp-Lintner in 1968.

EXPECTED VALUE OF AN ASSET'S EXCESS RETURN= Rᵢᵗ -Rᶠ
Rᵢᵗ = asset's return Rᶠ = risk free interest rate It determine expected risk premium of CAPM which its beta time of expected value.
Risk premium = Rᵐ -Rᶠ Rᵐ = Market risk Rᶠ = Risk free interest rate Jenson Alpha suggested intercept term in the time-series regression.
(Time series regression) "ᵢt-Rf=αᵢ+βᵢm*(Rmt-Rft)+ɛᵢt In Sharp-Lintner version of CAPM, have positive relation between beta and average return. In this model cross section model intercept the risk free rate and coefficient of beta is expected market return more than risk free rate. Fama and Macbeth(1973) introduced further explain about cross section regression test, like Fama and French(1992).It confirmed in time series tests due to relationship between beta and average return. Fama French 2-factor and Fama French 3-factor expanded after Fama French single model of (Fama, 1993). Charhart extended to these factors with the help of CAPM and introduced Fama French 4-factor model in (1997). Beta, Size factor and value factor covered in the 3-factor model. Fama French 4-factor model used to measure mutual fund performance in Developed Countries.it is also known as MOM factor (monthly momentum). An active management and mutual fund evaluation model worked as a 4-factor model. Monthly momentum explained about the stock price tendency which continuously up and down.
In different financial market has been determined mutual funds by extensive research and in Pakistan limited work on mutual fund. The purpose of this study is to point out the significant variables influencing the fund performance provide the manager of open ended and close ended Pakistan's mutual funds and benefit for small investor (Rauf, 2009).
All used traditional methods to determine the performance of the mutual fund of Pakistan and also arise question about the credibility of modern methods of Mutual Fund performance in Pakistan. To evaluate, measure and test mutual fund performance are organized for filling the gap of this study through competing the models i.e. CAPM and Fama French 3-factor models to forecast and evaluate the performance of mutual fund and explain that which one is better performed for portfolio return. Research focused to achieve following objectives: • To evaluate and measure the performance of the mutual fund through competing models like CAPM model and Fama French 3-factor model. • To investigate and test viable of these models and explain which one model is better perform in mutual fund of Pakistan.
LITERATURE REVIEW Efficient Market portfolio, investors fascinated and discussed about the portfolio minimize the risk and maximize the assets return. Most of the mutual fund employees earn on the basis of Modern Portfolio Theory managed the funds and also specified of efficient portfolio frontier (Makowitz, 1952).In 1960 sharp and Lintner 1965 modified the capital asset pricing model. Investors have desired to carry more return and weighted portfolio with risky asset. Portfolio risk measured and modified without beta and introduced the risk free asset in the Model (Sharp, 1964). In 1973 Fama and Macbeth explained the cross section of regression test model. In 1977 Miller examined the assets pricing model under the short sale restrain and analysis about effect of cross sectional idiosyncratic risk. (Stephen F. Witt, 1979) In 1987 Merton forecast the diversified portfolio risk that idiosyncratic risk priced when investor hold diversified portfolio and create positive relationship between cross section return and risk. Idiosyncratic risk linked with cross section risk. (French, Common Risk Factors in the Returns on Stock and bond, 1993) Fama French further explained to the factors which effected on risk beta and return. Fama French 2 factors and 3 factors evaluate the performance of mutual fund and took the results of value, size and market factors. 4 factors model established for evaluate the performance of stock and fund. Researcher used momentum which calculated weighted average of the low performance the firm from the equal performance high weighted average of firm (Carhart, 1997). In describe towards a strategic theory of risk premium moving beyond CAPM .In Pakistan used the old methods for evaluation of the mutual fund performance (S, 1990). In 2003 Eugene F. Fama and Kenneth R.French introduced the CAPM theory and evidence and create relationship between risk and expected returns. In The CAPM theory evaluated the risk and market return and its evidence (French, 2004). The performance evaluate of mutual fund of Pakistan. In this study calculate the sharp ratio analysis for measuring the risk and return. 26 close end mutual fund has been selected some are private and some are public sector. The open end Mutual funds and close end mutual funds total net assets value merge and then graphically show the model. 14 funds out of 33 funds reset and operationally used for research purpose (Hijazi, 2005). Sharp ratio, Treynor model, Jensen differential measure is used in this research. Capital Asset Pricing Model is also used in that study (Rauf, 2009). The performance analyzed the mutual fund. Its provide the open ended Pakistan's mutual fund and benefits to the small investor and sharp ratio measure the performance of the mutual fund with the help of time series and cross sectional data and focus on fund size expenses, age etc (Nawaz, 2010). In this research create the size and value of market return and also calculated the stock returns and check the momentum in risk and returns. The Capital Asset Pricing Model (CAPM) explained with drawdown measure the active portfolio management (French, Siza, Value, and Momentum in International Stock Returns, 2010), (Michael Zabarankin, 2014), (Marios, 2014) Analyze of mutual fund performance using multiple measure for calculating the causality and normality in the data. Implement on the Fama French Factor Model for calculating the risk which correlated between market risks premiums (Asim Shah, 2014) (Babar Rafi, 2014). Fama French model used to check the momentum variation. Studied about applicability of Fama French, Three-Factor Model on the bases of KSE 100 index and explained cross-sectional return on equity market of Pakistan (Nahzat Abbas, 2015). In this research daily data collected of KSE100 index and merge and calculate returns then checked daily fluctuation in the market. SMB and HML calculate for Fama French 3 factor model and applied time series regression model for checking relationship between dependent and independent variable (Andleeb, 2014). Fama French and Capital Asset Pricing Models implement in stock market of Saudi Arabia through compared the real rate with the returns using CAPM and FF.Fama French 3factor investigated the size, book-to-market and market return to Saudi Arabia which approach use for measuring the dependent and independent variables and effects on risk factors affected on the return (Abdulaziz Aldaarmi, 2015).

Mutual Fund evaluated performance and validated the CAPM and Fama French 3 model. One
hundred open ended Pakistan mutual funds collected month wise data from 2009 to 2015 by both models . Capital Asset Pricing Model showed significant and checked the relationship between 2 variables. SMB and HML evaluated the performance of actual risk premium with the help of size of market capitalization and market to book value size and arrange the portfolio returns (Bhatti, 2015). The Capital Asset Pricing Mode evaluated risk then calculated the Alfa with help of CAPM. This research focus on the returns through CAPM model compare with high and low returns after the comparison high returns does not show the variation in the market and need to other methods for calculating the and measures the variations in to the market. This research needs to best measurement tools for evaluation of Mutual Funds.

RESEARCH MODEL Capital Asset Pricing Model (CAPM) and Fama French-3 factor model explained bellow:
• Capital Asset Pricing Model (CAPM): CAPM model is used for evaluating the mutual fund performance of Pakistan .

FAMA FRENCH-3 MODEL:
In the studies tested for the Mutual Fund performance evaluation by .
(Ri -Rf) represents stock risk premium. β(Rm -Rf) represent the expected risk premium SMB denotes the daily premium of the factor size of the returns of the portfolio that contain small caps funds and HML denotes the daily market factors and contains large caps. SML and HML calculated for returns portfolio of market and stock and then intercepts with Alfa #. SMB and HML calculated for FAMA French-3 factor Model, Rm and Rf is also used for Capital Asset Pricing Model (CAPM).

DATA ANALYSIS
Capital Assets Pricing Model (CAPM) and Fama French model measures the mutual fund performance. In this table the results are showing the CAPM. These results show that due to market factor significantly related with all portfolio returns. All portfolios of returns P1 to P24 have significant coefficient. The portfolio of higher return do not properly explain and predict bigger in values compare with the lower perform portfolios. The portfolios with the high return have significant intercept but compared with the high and low portfolios of return. The results show that CAPM perform poorly in explaining with the high and low returns. Fund with higher and lower returns are not predicted good by CAPM which mean that fund manager do not cope well capture the market variation.   In table 3, selected the 24 funds of companies in which mean value is much closer to the zero. Beta shows that measurement of risk but some companies have negative beta but they have positive coefficient relationship between market return and companies return. CAPM perform well as compared to the Fama French model.

FINDINGS AND CONCLUSIONS
Mutual fund plays important role for common investors in the world, mutual fund gives the more opportunities and benefits for the capital investment through skillful and professional management. In this research apply suitable models for measuring the performance of mutual