# SUMMATIVE the performance of size and value factors

SUMMATIVE ASSIGNMENTProject A         Report prepared by: Abdullah AliZ0985564  In this essay, I will discuss thegeneral approach and how I chooses the model with some findings.

Then I willcompare the performance of two fund by going through the factor exposures ofthe portfolios. the CAPM single-factor world,we can use linear regression analysis to decompose returns into two components:alpha and beta. Alpha is the portion of returns that cannot be explained byexposure to the market, while beta is the portion of returns that can beattributed to the market. However, studies have shown that single-factor modelsmay not adequately explain the relationship between risk and expected return,and that there are other risk factors at play. For example, under the frameworkof Fama and French (1992, 1993) the returns to a portfolio could be betterexplained by not only looking at how the overall equity market performed butalso at the performance of size and value factors (i.

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e., the relative performance between small- and large-cap stocks, andbetween cheap and expensive stocks). Addingthese two factors (value and size) to the market created a multi-factor model for assetpricing. Academics have continued to explore other risk factors, such asmomentum and low-beta or low risk,7 and have shown that these factors have beeneffective in explaining long-run average returns. (Ronen, 2005) I use returns and betas fromregression analysis to decompose portfolio excess return. The first regressionmodel formed is the CAPM with market factor. Then I added the size factorfollowed by adding the value factor.

Next, in my final model (whichincludes all the factor exposures that the portfolio aims to capture), theresults are consistent with intuition ( attach all regression models at theend).  Thus, Multiple linear regressionanalysis was used to develop a model for predicting Funds’ excessive returnaverage from Market excess return, value, size and momentum.  Basic descriptive statistics and regressioncoefficients are shown in Table 1(fund1) and Table 2(fund2).          Mutual fund 1 Table1starting with the model test, as we can notice that the p-value is 0.000which is less than 5% confident level so here I can say that the regressionmodel of mutual fund1 is different from zero and statistically significant atall level.

Moreover, the typical regression error is 96 and it is noticed that 9.76%of the variation in the excess return in fund1 is explained by the independent variables(exposure factors)moving to individual significance of each parameters from the p-value, Carhart modelregression results show that three of the four factors are significantlydifferent than zero at the 5% level. In other word, they all do have asignificant effect on the excessive return of the fund but SMB not. Also, the model has no autocorrelation as it was proved statistically.The result of the coefficients show that the portfolio hada positive relationship when the market ExrM (risk premium). the marketbeta is 3.27 which means that the portfolio has a meaningful exposure to themarket.

Also, it is statistically different from zero. Thus, the market factoris statistically significant and economically meaningful. The second factor SMB, the mimicking return forsize factor, it is observed that it has a positive exposure beta 0.827 whichmeans the portfolio is predominantly small cap stocks. In that, the portfolio has higher expected returns if small-capstocks outperform large-cap stocks. Although this factor is economicallymeaningful, it is not statistically significant. The third factor HML, themimicking return for book-to-market factor, The result shows that the portfoliohad negative exposure to value (with a beta of -2.50), which means that theportfolio on average bought growth stocks.

In that then the portfolio hashigher expected returns if low book-to-market (growth) stocks outperform highbook-to-market (value) stocks. The value factor is statistically significantand economically meaningful. Last factor in the portfolio 1 model MoM, we seethat the momentum loading is positive (with a beta of 1.131), which means thatthe portfolio on average bought recent winners. well it has economicallymeaningful impact on the portfolio as well as is statistically different fromzero.  Mutual fund 2 Table2  from table 2 we notice that the p-value is 0.000 which is lessthan 1% confident level so here I can say that the regression model of mutualfund2 is statistically significant at all level.

Moreover, the typicalregression error is 37.718 and it is noticed that 7.56% of the variation in theexcess return in fund2 is explained by the exposure factors.Moving to individual significance ofeach parameters from the p-value, Carhart model regression shows totallyopposite result from the portfolio1 where three of the four factors are notstatistically significant  5% level. Inother word, they all don’t have a significant effect on the excessive return ofthe fund2 but only ExrM does.

Also, the test shows that the model has noautocorrelation. The result of the coefficients show that the portfolio hada positive relationship when the market ExrM (risk premium). the marketbeta is 3.259 which means that the portfolio has a meaningful exposure to themarket. Also, it is statistically different from zero. Thus, the market factoris statistically significant and economically meaningful.

In another word ifthe market return increase by 1% the portfolio will increase by 3.259.The second factorSMB, the size factor, it is observed that it has a negative exposurebeta (-0.4588) which means the portfolio is predominantly big cap stocks.

In that, the portfolio has higher expected returns if big-capstocks outperform large-cap stocks. Although this factor is economicallymeaningful, it is not statistically significant.  The third factor HML, themimicking return for book-to-market factor, The result shows that the portfoliohad negative exposure to value (with a beta of -0.1239), which means that theportfolio on average bought value stocks.

In that then the portfolio has higherexpected returns if low book-to-market (growth) stocks outperform highbook-to-market (value) stocks. The value factor is not statisticallysignificant and not really economically meaningful. Last factor in theportfolio 2 MoM, we see that the momentum factor is negative (with a beta of -0.14484),which means that the portfolio on average bought recent losers.

The momentumslop is neither economically meaningful nor statistically different from zero. ## Author: Lucia Hansen

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