Harry W. Markowitz, the father of “Modern Portfolio theory”, developed the mean-variance analysis, which focuses on creating portfolios of assets that minimizes the variance of returns i.e. risk, given a level of desired return, or maximizes the returns given a level of risk tolerance. This theory aids the process of portfolio construction by providing a quantitative take on it. It integrates the field of quantitative analysis with portfolio management. Mean variance analysis has found wide applications both inside and outside financial economics. However it is based on certain assumptions which do not hold good in practice. Hence there have been certain revisions to it, so as to make it a more useful tool in portfolio management. Mean Variance Analysis

Within the mean variance approach of Markowitz, the basic assumption is that risk is measured by variance, and the investment decision is based on the trade-off between higher mean and lower variance of the returns. The locus of optimal mean-variance combinations is called the efficient frontier, on which all rational investors would desire to be positioned. Asset returns are assumed to be (jointly) normally distributed random variables, and correlations between assets are also assumed to be fixed and constant forever. (Mz)

Other assumptions include: (Mz)

All investors aim to maximize economic utility (in other words, to make as much money as possible, regardless of any other considerations).
All investors are rational and risk averse.
All investors have access to the same information at the same point of time. It assumes efficient market hypothesis holds good and there is no information asymmetry or insider trading.
Investors have an accurate conception of possible returns, i.e., the probability beliefs of investors match the true distribution of returns. Investor’s beliefs are unbiased.
There are no taxes or transaction costs. It assumes perfect markets.
All investors are price takers i.e....

...Analysis of Variance
Lecture 11 April 26th, 2011
A. Introduction
When you have more than two groups, a t-test (or the nonparametric equivalent) is no longer applicable. Instead, we use a technique called analysis of variance. This chapter covers analysis of variance designs with one or more independent variables, as well as more advanced topics such as interpreting significant interactions, and unbalanced designs.
B. One-Way Analysis of Variance
The method used today for comparisons of three or more groups is called analysis of variance (ANOVA). This method has the advantage of testing whether there are any differences between the groups with a single probability associated with the test. The hypothesis tested is that all groups have the same mean. Before we present an example, notice that there are several assumptions that should be met before an analysis of variance is used.
Essentially, we must have independence between groups (unless a repeated measures design is used); the sampling distributions of sample means must be normally distributed; and the groups should come from populations with equal variances (called homogeneity of variance).
Example:
15 Subjects in three treatment groups X,Y and Z.
X Y Z
700...

...INTRODUCTION TO ONE-WAY ANALYSIS OF VARIANCE
Dale Berger, Claremont Graduate University http://wise.cgu.edu
The purpose of this paper is to explain the logic and vocabulary of one-way analysis of variance (ANOVA). The null hypothesis tested by one-way ANOVA is that two or more population means are equal. The question is whether (H0) the population means may equal for all groups and that the observed differences in sample means are due to random sampling variation, or (Ha) the observed differences between sample means are due to actual differences in the population means.
The logic used in ANOVA to compare means of multiple groups is similar to that used with the t-test to compare means of two independent groups. When one-way ANOVA is applied to the special case of two groups, one-way ANOVA gives identical results as the t-test.
Not surprisingly, the assumptions needed for the t-test are also needed for ANOVA. We need to assume:
1) random, independent sampling from the k populations;
2) normal population distributions;
3) equal variances within the k populations.
Assumption 1 is crucial for any inferential statistic. As with the t-test, Assumptions 2 and 3 can be relaxed when large samples are used, and Assumption 3 can be relaxed when the sample sizes are...

... 2/21/2014
274 EXERCISE 36 • Analysis of Variance (ANOVA) I
1. The researchers found a significant difference between the two groups (control and treatment) for change
in mobility of the women with osteoarthritis (OA) over 12 weeks with the results of F(1, 22) 9.619,
p 0.005. Discuss each aspect of these results. F is the statistic for ANOVA. F (1,22) one represents the number of groups in the study and 22 equals the subjects used the error df, and 9.619 is significant as it is P=0.005, it can be said that the intervention group participants face a significant reduction in mobility difficulty.
2. State the null hypothesis for the Baird and Sands (2004) study that focuses on the effect of the GI with
PMR treatment on patients’ mobility level. Should the null hypothesis be rejected for the difference between
the two groups in change in mobility scores over 12 weeks? Provide a rationale for your answer.
Ho 1: Guided imagery (GI) with Progressive Muscle Relaxation reduces pain difficulties of women with OA.
Ho 2: Guided imagery (GI) with Progressive Muscle Relaxation reduces mobility difficulties of women with OA.
The null hypothesis should be accepted study results indicate a significant improvement in mobility and pain difficulties.
3. The researchers stated that the participants in the intervention group reported a reduction in mobility
difficulty at week 12. Was this result statistically significant,...

...www.ccsenet.org/ijbm International Journal of Business and Management Vol. 7, No. 10; May 2012
134 ISSN 1833-3850 E-ISSN 1833-8119
Comparative Analysis of Commercial Banks Liquidity Position: The
Case of Tanzania
Xuezhi Qin1 & Dickson Pastory1
1 School of Business Management, Dalian University of Technology, Dalian, China
Correspondence: Dickson Pastory, School of Business Management, Dalian University of Technology, Dalian
116024, China. Tel: 86-188-4268-6991. E-mail: passtory1@yahoo.co.uk
Received: February 11, 2012 Accepted: March 5, 2012 Online Published: May 16, 2012
doi:10.5539/ijbm.v7n10p134 URL: http://dx.doi.org/ijbm.v7n10p134
Abstract
This paper gives an overview picture of commercial banks liquidity position in Tanzania for the period of ten
years (2000 to 2009). The study employed the liquidity measures of commercial banks, and on that basis the
performance in terms of liquidity position was established. The paper used the casual research design as the
methodology of the study since the casual design is best suited to determine cause and effects of the
phenomenon. This paper utilizes secondary data from National Bank of Commerce (NBC), CRDB and National
Microfinance Bank (NMB). The criteria used is total deposit to core funding, liquid asset to demand liabilities
and Gross loans to total deposit Tanzania for the period of ten years, and finally the hypothesis was tested to
know whether there is a significant difference in terms...

...do a varianceanalysis to better understand the plant performance compared to the previous year. The main problem in related to this case is about the falling in revenues, the performance of coal-plant, the price of coal and the quality of coal. All of this problem will be answered in the next sections in the qualitative analysis of Luotang Power.
VARIANCEANALYSIS
QUANTITY VARIANCE
Thevarianceanalysis is defined as the difference between the expected amount and the actual amount of costs or revenues. Varianceanalysis uses this standard or expected amount versus the actual amount to judge performance. The analysis includes an explanation of the difference between actual and expected figures as well as an evaluation as to why the variance may have occurred. The purpose of this detailed information is to assist managers in determining what may have gone right or wrong and to help in future decision-making
Quantity Variance = (Net Generation MWh in Current Year - Net Generation MWh in
Year) x Price per MWh in Prior Year
2011
(3,427,351-3,937,377)x(0.3817)=194,676 MWh (unfavorable)
2010
(3,937,377-3,028,690)x(0.4186)=380,376 MWh (favorable)
Based on analysis of quantity variance, in 2011 showed that unfavorable variance...

...that the sum of error is equal to zero. Thus the error is given by,
Thus we need to minimize the above in such a way that the estimated values minimize the above error variance. Minimizing the above with respect to a and b we get the following two equations to obtain the estimated values of a and b as follows,
and
From the above the estimated b is (to be remembered for your calculation purpose)
And estimated a is (to be remembered)
Apart from calculating in this way there are several computer statistical packages that will give us directly the estimated results once we directly provide the Y input and X input. However there are other parameters the output box provides us.
Test of Significance of b value that implies how significant is the impact of the variation in the explanatory variable on variation caused for dependent variable.
For this we test the null hypothesis b =0. for that we use a test statistic that follows the t- distribution with degrees of freedom n-k, where nis the number of observations and k is the number of parameters estimated In this case n=10 and k=2. therefore d.f=8. the test statistic t is defined as,
as b=0 under null hypothesis and S.E. is the standard error of the estimated b.
The S.E of estimated b is given by
(to be remembered). This means that as standard error of estimated b is high the variation due to unexplained variation is relatively hgher as compared with the variation...

...BUDGET MANAGEMENT ANALYSIS
To have a basis in illustrating the analysis of variance or difference between budgeted and actual figures, the budget of a sampled (unknown) company was utilized (http://www.smallbusinessnotes.com/business-finances/budgeting-systems.html).
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| | | | | |
| | | | | |
|Sample Company | | | | |
|Budget | | | | |
|January 1, xxxx to...

...DESIGN AND ANALYSIS OF EXPERIMENTS
TERM PROJECT PROPOSAL
Subject: Statistical analysis of a sling regarding three factors with three levels.
Aim: Our aim is to statistically analyse the effects of three factors; rubber type, shooting range and tensile distance on the shooting range.
Description: In our project, we will design three slings for three types of rubbers.With these slings, we will try three shooting angles;30, 45, 60 degrees. Also with these factors we will make experiments with three tensile distances, namely the distance that we will pull the rubber; 2, 4 and 6 cm. As response values we will use the range that particular object goes. We will use the same pebble. So there will be no difference in the trials with respect to the used object.
Thus, in the analysis, we will examine the effects of rubber, angle and the distance on the range of the object takes after being released from the sling.
At the end, we will use Design Expert software for ANOVA and interpretations from the related graphs for concluding remarks from the experiment regarding the factors.
[pic]
PROJECT ANALYSIS
As we defined in the outline, we evaluated the effects of three factors such as; rubber type, angle and tensile for the shooting range of a sling. From our experiments we got 81 response values with different levels of the factors.
The structure of the experiment and data can be...