Автор работы: Пользователь скрыл имя, 06 Ноября 2017 в 21:13, реферат
Описание работы
In this report, we discover APT as a model used to provide pricing strategy for stocks in the best possible way by taking into consideration multiple risks that are associated along with the stocks. From the research carried out, it has been found out that there are several macroeconomic and financial factors that influence stock returns. They are: global, political, cyclical, systemic, synergistic and industry factors, and also the investment characteristics of the issuer's position in the region. However, some of these variables can affect the stock return more than others.
Содержание работы
Executive Summary…………………………………………………………………………….…..………p3 Arbitrage Pricing Theory/Introduction…………………………………………………………….p4 Macroeconomic and Financial Factors affecting the stock price……………………………………………………………………………………………………………….p5-6 Constructing the basic regression model and the assessment of its quality……..…………………………………………………………………………………………………..p7-14 Appendix………………………………………………………………………………………………………p15-21 Group Meeting Minutes………………………………………………………………….……………p22-24 References……………………………………………………………………………………………………p25-26
In this report, we discover APT as a model used to provide pricing
strategy for stocks in the best possible way by
taking into consideration multiple risks that are associated along with
the stocks. From the research carried out, it has been found out that
there are several macroeconomic and financial factors that influence
stock returns. They are: global, political, cyclical, systemic,
synergistic and industry factors, and also the investment characteristics
of the issuer's position in the region. However, some of these variables
can affect the stock return more than others.
The APT model is based on the assumption, that the
investor aims to increase profitability of the portfolio without an
increase in risk every time when there is such an opportunity.
APT is an alternative to a CAPM (Capial Asset Pricing
Model) developed by Sharp and based on Markowits's model, APT is based
on a smaller amount of assumptions, thus it is less difficult than CAPM,
despite the fact that it is based on a more complicated mathematical
theory. The CAPM model can be expressed as a simple regression, the
standard calculation of the CAPM model describes the interrelation between
risk and expected return, whereas the APT model is expressed as multiple
linear regression.
Arbitrage Pricing Theory/Introduction
Arbitrage pricing theory or (APT)
is a multifactor mathematical model used to describe the relationship
between the risk and expected return of securities in the financial
markets. APT is grounded on the idea that the return if an asset can
be forecasted using the relationship between the asset in question and
many common risk factors associated with it. Therefore computing the
expected return on a security and its movements in relation to macroeconomic
factors. Accordingly, the results can be used to adjust the price of
the security we will be looking at. (Staff, 2017)
There are three assumptions made
when using this theory:
1. A factor model can be used to
describe the relation between the risk and return of a security
2. Idiosyncratic risk can be diversified
away
3. Efficient markets do not allow
for persisting arbitrage opportunities
The arbitrage pricing theory can
be set up to consider several risk factors, such as the business cycle,
interest rates, inflation rates, and energy prices. These will be discussed
further in this report.
The formula includes a variable for
each factor, and then a factor beta for each factor, representing the
security’s sensitivity to movements. As it includes more variables,
the arbitrage pricing theory can be considered more accurate than the
capital asset pricing model.
Example:
r = E(r) + B1F1 + B2F2 + e
r = return on the security E(r) =
expected return on the security F1 = the first factor B1 = the security’s
sensitivity to movements in the first factor F2 = the second factor
B2 = the security’s sensitivity to movements in the second factor
e = the idiosyncratic component of the security’s return (Wilkinson,
2017)
Macroeconomic and Financial Factors affecting the stock price
The impact of general (fundamental) factors does not depend on the species,
specific characteristics of shares or the issuer status. They fix the
overall macro- and microeconomic environment of the corporate market.
These factors can be global, political, cyclical, systemic, synergistic
and industry factors.
Global factors are caused by changes in the political
and the general economic situation. The greatest impact has a common
state of the global financial market, GDP, inflation processes (Maysami
and Koh 2000), that generate interest and currency risks, gross national
product (GNP) (Al-Qenae, Carmen, and Wearing 2002).
Political factors include the general condition of
society, its stability or susceptibility to crises, government ownership
(Alchain, 1965).
Cyclical factors reflect phases of the stock market
development. The business cycle describes periods of rise and decline
in the economy and has a significant impact on the assessment of the
value of the shares issuers. It is characterized by: trends in consumer
expectations and consumer expenses; actions taken by the Government
to reduce or an increase the money supply; the trajectory of interest
rate (Perotti 1995).
Systemic factors are system characteristics of the
stock market. These factors include the system of regulatory support,
management system and regulation, general economic indicators, which
states use for the purpose of making operational decisions about the
reorientation capital flows from the markets of some countries to the
markets of others.
Industry factors include the prospects of the industry,
the degree of industry risk, industry profitability, industrial production
(Zhao 1999).
Special functional factors are the stock returns also associated with the financial
condition of the issuing company (Campbell 2009). A lot of depends on
the individual characteristics of the company, for example their credit
quality and liquidity of shares. Therefore, the correct behavior of
the company with the respect to minority shareholders affects the decrease
in the discount rate and a possible increase in share price.
Special technical factors reflect the specific technical characteristics
of shares and stock market conditions, as well as individual qualitative
and quantitative options. The most important special technical factor
- is the environment of the market.
Quantitative factors include the amount of the issue,
the average price of supply and demand of shares, dividends (Moldovsky
1995, Docking and Koch 2005), and the amount of stock exchange OTC turnover.
Qualitative factors reflect the qualitative parameters
of shares: the dividend increase, the rate of the change of prices and
the volume of transactions.
Constructing the basic regression model and the assessment of its
quality
Descriptive statistics
Descriptive statistics were calculated from our raw
data, rerer to table 1 in appendix.
The descriptive statistics are applied to systematise and describe
the data of observations. The description of data is usually the initial
stage of the analysis of quantitative data and is a frequent first step
to use of the other statistical procedures or tests. (Brooks, 2008)
There statistics do not allow us to make conclusions beyond the data
that has been analysed in our report, consequently conclusions regarding
any hypothesis cannot be drawn. These statistics are simply a way to
showcase our data set.
Examination the model for multicollinearity
Table 2 (in appendix) shows our results for Multicollinearity.
This refers to correlation among the independent variables in a multiple
regression model; it is usually invoked when some correlations are ‘large’,
but an actual magnitude is not well defined. (Wooldridge, 2011)
For detection for multicollinearity of factors, it
is possible to analyse the correlation matrix of these factors. If coefficients
of correlation between some factors are close to 1, it indicates the
close interrelation between them, so the existence of a multicollinearity.
In our sample, it is clearly seen that there is no multicollinearity,
correlations between variables are no more than 0.2. (Statistics Solutions, 2017)
Least Squares Method
The important task in the research of
interrelation of different quantities, is to answer on a question:
how a change of one variable (or several) may influence the value of
another. That is why we used the Least Squares Method.(Miller 2009)
According to the table 3 (in appendix) , we received
the following equation of the constructed model:
According to this test, we can make the following
conclusions:
R- squared
It is also known as the coefficient of determination and is ranged from 0 to 1 (it
is usually interpreted in %, thus 0% -100%). It describes communication
between values of a dependent variable (stock returns) and one or several
independent variables (excess market return, industrial production,
unexpected inflation, money supply, baa aaa spread, treasury bills).
In our case the coefficient of determination is 0.2 (or 20%), which
means that the relation between independent variable and dependent variables
is low.
T value and P value help to understand which variables are the most
significant in our sample, when p value is close to 0, and t value is
high. Thus, the most significant variables in our sample are:
• Excess market return, P value is
0 and t value is 8.3
• Unexpected Inflation, P value is
0.1 and t value is 1.5
• Term structure, P value is 0.1 and
t value is 1.86.
We can also check our results for significance according
to the Stepwise regression. The Stepwise regression is used to determine
which variables are “the most important”. The unexpected inflation,
excess market return and the term structure have been included. So,
we confirm our results due to Least squares, with the help of the t
value and p value. We got the same results, refer to to table 3 in appendix.
The benefits of this Least Squares is the relative
simplicity and universality of computing procedures. However, in an
attempt to describe the studied economic event by means of the mathematical
equation, the forecast will be more accurate for the small period of
time and the equation of regression should be recalculated in process
of receipt of the new information.
Examining the model for the existence
of autocorrelation
The Durbin Watson Test is a measure of autocorrelation (also called
serial correlation) in residuals from regression analysis. Autocorrelation
is the similarity of a time series over successive time intervals. It
can lead to underestimates of the standard error and can cause you
to think predictors are significant when they are not. The Durbin Watson
test looks for a specific type of serial correlation, the autoregressive
process. (Statistics How To, 2017) However, it tests only for the first-order
serial correlation. The test is inconclusive if the computed value lies
between upper limits and lower limits. The test cannot be applied in
models with lagged dependent variables.
DW ratio can be seen in table 3 in
the appendix. DW values lie in an interval from 0 to 4. In case of lack
of autocorrelation of DW it is close to 2. The proximity to 0 tells
about positive autocorrelation, to 4 - about the negative one. In our
sample the DW value is 2,21, it means that there is no autocorrelation.
Autocorrelation is a characteristic of data in which the correlation
between the values of the same variables is based on related objects.
(Statistics Solutions, 2017). The autocorrelation ( Box and Jenkins,1976)
function can be used for the following two purposes: To detect non-randomness
in data and identify an appropriate time series model if the data are
not random.
Normality test
Figure 1 Normality test
Figure 1 illustrates a non-normal distribution.
Our skewness is negative (-2,7), it means that we have the right asymmetry.
The largest part of the figure is on the top right, which shows a histogram
of a number of columns. As we can see, the tallest columns (which has
results of 0 and 2,5) on the right side of our histogram, and the smallest
with results of -50 and -65 on the left side. The standard deviation
measures how concentrated the data are around the mean; in our sample
the standard deviation = 12, 46, it means that the values in the data
set are farther away from the mean, on average. Kurtosis is an indicator
reflecting the sharpness of the peak, in our case it is positive (14.03),
which means it has a sharp peak. The P-value is 0, thus, the null hypothesis
is rejected.
Examination for heteroscedasticity
using the White test
Please refer to table 4 in appendix.
Heteroscedasticity – The variance of the error term, given the explanatory
variables, is not constant.
White Test
The advantage of this test is, unlike the others, it does not rely
on the normality assumption. It is therefore easy to implement. White
(1980) proposed this test for heteroscedasticity that adds the squares
and cross products of all the independent variables. It intends to test
for forms of heteroscedasticity that invalidate the usual OLS standard
errors and test statistics. (Wooldridge, 2011)
Test statistics information to us,
we need to determine the homogeneity of variance assumption is valid.
The Chi-square test is usually consists of a square error sum, or through
the sample variance. Using chi-square test statistics, from an assumption
of independent normal distribution of data, it is effective in many
cases because of the central limit theorem. Chi-square test data can
be used to try to refuse to null hypothesis is independent.
Our Chi-Square is more than 0.05 (it is >0.09), so we do not reject
the null hypothesis and it means that there is no heteroscedasticity.
Regression model for the period
before crisis (2003-2006) and after 2009-2012
Please refer to table 6 and 7 in the appendix.
The "t'' statistic is computed by dividing the estimated value
of the parameter by its standard error. The t Statistic of SRSANDP is 6.97. So
we can get the conclusion that the actual value of the parameter could
be zero.
In statistics, the T-statistic is a ratio to estimate
the deviation of the parameters and its nominal value with standard
error. The T-Statistic and Standard Error relationship is T-Statistic=Average/Standard
Error. Their relationship is an inverse relation. The T -
statistic is used to test if there is a significant difference. According
the result of two tables. The Std. Error of DSPREAD is more than 40.51
in 2003-2006 and 6.36 in the 2009-2012. So we get the conclusion that
is significant.
The "Prob (t)'' value is the probability of
obtaining the estimated value of the parameter if the actual parameter
value is zero. There are more significant the parameter when the smaller
the value of Prob (t) is zero. In 2009-2012, the Prob (t) Wiof ERSANDP
is zero that mean this parameter is very important.
With regards to R-squared, in our findings the coefficient
of determination is 0.14 in 2003-2006, this means that the relation
between the independent variable and dependent variables is low. Thus
showing that the model explains little if not no variability of the
response data around its mean. However, it is 0.58 in 2009-2012 which
indicates that the relationship between independent variable and dependent
variables is above the average.
The parameter of Adjusted R-squared is 0.51 in 2009-2012.
It means that, 51% of a variation of a dependent variable is explained
by a variety of independent variables. However, the number is 0 in 2003-2006,
while means no variation in the equation and the number
of data observations. Although R-squared provides an estimate
of how strong the relationship between the model and the response variable,
it does not provide a formal hypothesis test for this relationship.
The F-test of overall significance determines whether this relationship is statistically significant. The Prob (F) statistics test the overall significance
of the regression model. Specifically, it tests the null hypothesis
that all of the regression coefficients are equal to zero. The result
of table in 2009-2012 is 0, that is meant the regression does have some
validity in fitting the data. However, the number is 0.47 in 2003-2006,
that mean the independent variables are purely random with respect to
the dependent variable.
The "Durbin-Watson test for autocorrelation'' is a statistic
that indicates the likelihood that the deviation (error) values for
the regression have a first-order auto regression component. The regression
models assume that the error deviations are uncorrelated. Usually the
values of the Durbin-Watson statistic less than 0.8 indicate the presence
of autocorrelation. These two result table is more than 0.8 that are
2.16 and 1.99 in 2003-2006 and 2009-2012. The conclusion is that there
are not manifest autocorrelation. (Hilmer and Hilmer)