# SUMMATIVE the performance of size and value factors

SUMMATIVE ASSIGNMENT

Project A

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Report prepared by:

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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.  