SUMMATIVE ASSIGNMENT

Project A

Report prepared by:

Abdullah Ali

Z0985564

In this essay, I will discuss the

general approach and how I chooses the model with some findings. Then I will

compare the performance of two fund by going through the factor exposures of

the 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 by

exposure to the market, while beta is the portion of returns that can be

attributed to the market. However, studies have shown that single-factor models

may not adequately explain the relationship between risk and expected return,

and that there are other risk factors at play. For example, under the framework

of Fama and French (1992, 1993) the returns to a portfolio could be better

explained by not only looking at how the overall equity market performed but

also at the performance of size and value factors (i.e., the relative performance between small- and large-cap stocks, and

between cheap and expensive stocks). Adding

these two factors (value and size) to the market created a multi-factor model for asset

pricing. Academics have continued to explore other risk factors, such as

momentum and low-beta or low risk,7 and have shown that these factors have been

effective in explaining long-run average returns. (Ronen, 2005)

I use returns and betas from

regression analysis to decompose portfolio excess return. The first regression

model formed is the CAPM with market factor. Then I added the size factor

followed by adding the value factor. Next, in my final model (which

includes all the factor exposures that the portfolio aims to capture), the

results are consistent with intuition ( attach all regression models at the

end).

Thus, Multiple linear regression

analysis was used to develop a model for predicting Funds’ excessive return

average from Market excess return, value, size and momentum. Basic descriptive statistics and regression

coefficients are shown in Table 1(fund1) and Table 2(fund2).

Mutual fund 1

Table1

starting with the model test, as we can notice that the p-value is 0.000

which is less than 5% confident level so here I can say that the regression

model of mutual fund1 is different from zero and statistically significant at

all 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 model

regression results show that three of the four factors are significantly

different than zero at the 5% level. In other word, they all do have a

significant 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 had

a positive relationship when the market ExrM (risk premium). the market

beta is 3.27 which means that the portfolio has a meaningful exposure to the

market. Also, it is statistically different from zero. Thus, the market factor

is statistically significant and economically meaningful. The second factor SMB, the mimicking return for

size factor, it is observed that it has a positive exposure beta 0.827 which

means the portfolio is predominantly small cap stocks. In that, the portfolio has higher expected returns if small-cap

stocks outperform large-cap stocks. Although this factor is economically

meaningful, it is not statistically significant. The third factor HML, the

mimicking return for book-to-market factor, The result shows that the portfolio

had negative exposure to value (with a beta of -2.50), which means that the

portfolio on average bought growth stocks. In that then the portfolio has

higher expected returns if low book-to-market (growth) stocks outperform high

book-to-market (value) stocks. The value factor is statistically significant

and economically meaningful. Last factor in the portfolio 1 model MoM, we see

that the momentum loading is positive (with a beta of 1.131), which means that

the portfolio on average bought recent winners. well it has economically

meaningful impact on the portfolio as well as is statistically different from

zero.

Mutual fund 2

Table2

from table 2 we notice that the p-value is 0.000 which is less

than 1% confident level so here I can say that the regression model of mutual

fund2 is statistically significant at all level. Moreover, the typical

regression error is 37.718 and it is noticed that 7.56% of the variation in the

excess return in fund2 is explained by the exposure factors.

Moving to individual significance of

each parameters from the p-value, Carhart model regression shows totally

opposite result from the portfolio1 where three of the four factors are not

statistically significant 5% level. In

other word, they all don’t have a significant effect on the excessive return of

the fund2 but only ExrM does. Also, the test shows that the model has no

autocorrelation.

The result of the coefficients show that the portfolio had

a positive relationship when the market ExrM (risk premium). the market

beta is 3.259 which means that the portfolio has a meaningful exposure to the

market. Also, it is statistically different from zero. Thus, the market factor

is statistically significant and economically meaningful. In another word if

the market return increase by 1% the portfolio will increase by 3.259.

The second factor

SMB, the size factor, it is observed that it has a negative exposure

beta (-0.4588) which means the portfolio is predominantly big cap stocks. In that, the portfolio has higher expected returns if big-cap

stocks outperform large-cap stocks. Although this factor is economically

meaningful, it is not statistically significant.

The third factor HML, the

mimicking return for book-to-market factor, The result shows that the portfolio

had negative exposure to value (with a beta of -0.1239), which means that the

portfolio on average bought value stocks. In that then the portfolio has higher

expected returns if low book-to-market (growth) stocks outperform high

book-to-market (value) stocks. The value factor is not statistically

significant and not really economically meaningful. Last factor in the

portfolio 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 momentum

slop is neither economically meaningful nor statistically different from zero.