The definition of the efficient frontier says that “the efficient frontier represents the set of portfolios that has the maximum rate of return for every given level of risk, or the minimum risk for every level of return.” I plotted standard deviation on x axes and Returns on y axes to interpret efficient frontier. Exhibits also include these and the graphs you asked for as graph2: In our study, we concentrated on the optimal portfolios, the one which has the lowest volatility or risk, for given level of return. The area below the frontier shows the achievable risk-return combinations, there will be at least one portfolio constructible that has the risk and return corresponding to that point. No portfolio on the efficient frontier can dominate any other portfolio on the efficient frontier. All of these portfolios have different return and risk measures, with expected rates of return that increase with higher risk. When we increased the expected return incrementally the weight of BBY and MRK increased until expected return is 2 ,MRK decreasing and BBY increasing afterwards ,whereas weight of WMT, C, IBM and HSY decreased respectively and became 0.Weight of HD is always 0 since it has a very low return/risk ratio compared to others. For the highest return of 2.5 BBY and MRK were optimal combinations since they are highly negatively correlated compared to others. Since BBY is on the efficient frontier, the decision to prefer it or other portfolios to each other depends on risk preference of individuals. The other individual securities are not efficient in these cases since they are on the area below the curve. The portfolios that are closest to the efficient frontier are more diversified since the portfolios on the efficient frontier are the most diversified. As you can see in exhibit 7 the minimum variances that you obtained by making up a portfolio of 7 securities are all below the individual standard deviations for the same level of expected return while they...

...Creating efficientfrontiers using excel.
Suppose we have 3 risky assets whose net return has the mean vector and variancecovariance matrix given below:
Asset Mean VarianceCovariance Matrix
1 2 3 0.06 0.12 0.03 1 0.3 0.3 0.3 1 0.3 0.3 0.3 1
Weights
Ones Mean Portfolio Return
1 1 1 0.176666122
Portfolio Portfolio Portfolio Variance STD Constraint
2.42961 1.558721 1
0.079372 1.603166 -0.68254
To model the portfolio choice problem, I begin by highlighting the mean vector and giving it a name. To do this, left-click on cell c9 and drag down until cell c11 and then release. Then go to the name-box, which is the white box in the upper right just above the "A" column. Click in the name-box, hit backspace, and then type a name for cells c9 - c11. Then hit return. I used the name "mu" for the vector of mean returns as illustrated below:
Then, I follow a similar approach with the variance-covariance matrix by clicking on cell F9 and then dragging across and down to cell H11. After the variance covariance matrix is highlighted, I go to the name box and give the variance covariance matrix the name "vcov" (Note: I don’t use quotes in the names). The efficientfrontier consists of portfolios that only invest in the risky assets. Therefore, I introduce a vector that represents the portfolio weights in each asset. For now, I will
assign the weights arbitrarily. Below, I will use excel to choose the...

...Instructions for Efficient-Frontier Construction
a. Estimation
The goal is to obtain the raw ingredients – expected returns, standard deviations and correlations. Historical data are used for this purpose. As a rule of thumb, five years of daily data are probably right (one year should be the absolute minimum). Keep in mind the following: 1) make sure to use the adjusted close prices to calculate returns (so that you won’t have large, spurious negative returns due to dividend payments or splits), and 2) calculate log returns (so that you can aggregate daily returns to obtain holding period returns, if ever needed).
In Excel, the function for mean and standard deviation are “= average (range)” and “stdev(range).” To calculate the correlation matrix, use “correlation” under “data analysis.”
Please note, in practice, the estimates can be adjusted in view of economic outlooks. This is especially so for expected returns. Sometimes, the realized historical returns are negative or below the risk-free rate. They must be adjusted upward – who would ever buy a stock and expect to receive a return less than the risk-free rate (if the beta is not negative)!?
II. Efficientfrontier construction
Step 1. Variance/covariance matrix, σρσ
The expected return and variance for the portfolio are:
You can think of the variance as the “weighted average” of all the covariances, σiσjρij where the...

...Name: GAO FAN
Student Number: 139030647
Programme Title: Analysis of the Efficient Market Hypothesis
Module Title: FOUNDATIONS OF FINANCIAL ANALYSIS AND INVESTMENT (MN7022)
Assignment Question: Critically review and discuss the concept of market efficiency and empirical approaches to test for it.
Words number: 2994
Analysis of the Efficient Market Hypothesis
INTRODUCTION
The study of “efficient market hypothesis” is originate from Louis Bachelier (1900), he studied the “Brownian motion” and the randomness of the stock price change from the perspective of random process and he found that discounted value reflected in market prices that no matter in the past, present or in the future (Lim & Brooks, 2009). With the use of computer, Kendall (1953) finds that the randomness of stock price changes by the commodity prices and stock prices in Britain and the United States (Lim & Brooks, 2009). Later, Robert (1959) proves that there is no difference between a sequence from the random sequence and the share price of the United States (Lim & Brooks, 2009). In 1964, Osborne puts forward the “random walk theory”, he believes that the change of stock price is similar to the molecular chemistry “Brownian motion” which means that the movement of the particles that suspended in a liquid or gas is continual and chaotic, and that means the change of stock price is unpredictable (Lim & Brooks,...

...Pathfinder, Hawkeye, and Natty Bumppo are just some of the names associated with James Fenimore Cooper’s heroic main character in stories such as The Deerslayer, and The Last of the Mohicans. Cooper introduces the American public to his character who embodies everything they strived to be in their new surroundings and in their ever-changing culture. Bumppo has many admirable morals compared to the men of his time, is unafraid of the many precarious situations he is thrown into, and prevails against any foe he shall face due to the superior set of skills that he has acquired. James Fenimore Cooper’s text of “A Rescue” from The Deerslayer and The Last of the Mohicans, both the text and film versions, show all the characteristics of the American frontier hero in order to highlight what is, and was viewed as heroic in the United States.
Stereotypically every hero has a certain ability that sets them apart from the rest of the community. Natty Bumppo is a phenomenal shooter, and an example of this is in “A Rescue” from The Deerslayer and The Last of the Mohicans (film version). In this scene from The Deerslayer, Bumppo watches two enemy Indians from the view of a hill above, “Deerslayer watched his opportunity, and finding two of his recent tormentors in a range, his rifle first broke the silence of the terrific scene. The bullet brought down both at one discharge” (Cooper 125). To kill one man in a single shot must require good aim, however, to bring down...

...Discuss:
“The concept of efficient diversification implies that for an investor wishing to efficiently assume risk in their portfolio; the risky part of the portfolio should consist of weighted proportions of all possible risky assets.”
Abstract: Minimizing investor’s portfolio risk was a dominant goal influencing decision making of investment. The effective method of reducing risks was to efficient diversifying the portfolio. The author’s purpose in this article was to share thoughts and concerns about the statement and analyze whether investors actually followed the concept of efficient diversification in their investment.
Efficient diversification was a term familiar with most investors. The concept of the term suggested that putting all of your eggs in one basket was a risky decision. (Bodie, Kane and Marcus, 2009) Efficient diversification was an organizing principle of modern portfolio theory, which largely defined by the work of Harry Markowitz (1991), maintaining that any risk-averse investors would pursue after the highest expected returns for any particular level of portfolio risks. Essential efficient diversification meant that for an investor who wanted to take risks in their portfolio, then he should select a proportion of all possible assets that existed in the world.
The objective of efficient diversification was to minimize the portfolio risk with...

...Case on Mean-Variance Frontiers
1. Ignoring the risk-free asset, draw the frontier in mean-std space.
We solve the problem by Matlab:
clear; clc;
% input data
temp = xlsread('30_Industry_Portfolios');
ret = temp(:,2:end)/100; （this step is to get all the returns from the file）
rf = 0.01/100; (The risk free rate is rf =0.01%= 0.0001 per month.)
% compute moments
er = (mean(ret))'; (the (30.1)vector of returns on the 30 industries)
V = cov(ret); (the covariance matrix of the returns)
% draw the frontier
reqrets = 0.00:0.001:0.02;
for i = 1:length(reqrets)
[trash, rfront(i), varfront(i)] = frontierp(reqrets(i),V,er);
end
figure (1);
plot (varfront.^.5,rfront);
title ('Mean-Std Frontier');
ylabel('E[ret]'); xlabel('\sigma(ret)');
2. Now also consider the risk-free rate. Draw the eﬃcientfrontier (do it on the same ﬁgure as 1).
% now add frontier with rf
for i = 1:length(reqrets)
[trash, rfront(i), varfront(i)] = rffrontierp(reqrets(i),V,er,+rf);
end
hold on;
plot(varfront.^.5,rfront);
hold off
3. Compute the tangency portfolio and plot it in the ﬁgure. Write the expected return and standard deviation of the portfolio.
clear;
% input data
temp = xlsread('30_Industry_Portfolios');
ret = temp(:,2:end)/100;
rf = 0.01/100;
% compute moments
er = (mean(ret))';
V = cov(ret);
>> one = ones(T,1); % unit vector
>> T = length(er)
T =
30...

...business a picture of what the outcome could be both positive and negative outcomes.
3. Describe in at least two paragraphs the quantitative analysis approach, to include a high level overview of the importance of identifying the problem, developing a model, acquiring input data, developing a solution, testing the solution, analyzing results, and implementation.
4. Respond to at least two other posts to receive full credit.
Assignment Week 2
Answer the following questions in 1 to 2 pages:
1. What benefit does a variable provide when developing and examining models?
2. Explain the purpose of simple linear regression and scatter diagrams. Please provide a simple linear regression model and define each variable used.
3. Describe multiple regression analysis and discuss potential uses for this model
4. Discuss the different types of forecasts to include time-series, causal, and qualitative models. When might a researcher or project manager utilize exponential smoothing? What benefit does a Delphi technique provide when working with qualitative-based decision making?
Respond to at least two other posts to receive full credit.
Assignment Week 3
Answer the following questions:
1. Discuss the importance of inventory control with respect to supply and demand.
2. What benefit can tools such as ABC analysis and just-in-time controls provide for an organization?
3. How can an enterprise...

...Cost Eﬃcient Gait Analysis Using Lasers
Isac Zia isac.zia@hotmail.com
under the direction of Prof. Hamed Hamid Muhammed School of Technology and Health KTH
Research Academy for Young Scientists July 11, 2012
Abstract Gait analysis is the methodic measurement, description and evaluation of factors that aﬀect human locomotion. It can be used for rehabilitation purposes, for optimizing sport results and lower risks of injury and as a diagnostic tool for neurological diseases, example given Parkinson. Hitherto, there are many precise methods of doing gait analysis. However, expensive equipment is often required, otherwise the only option is visual analysis, which is less reliable. This study will construct an inexpensive method to analyze gait, that is both reliable and portable. One laser was attached to each shoulder and two on a helmet put on the subjects’ heads. The lasers formed a formation of laser dots on the ceiling. The test subjects walked on a treadmill, which caused the laser dots to move. These were recorded with a camera. The video sequences were then analyzed with a program written in Matlab. The results showed the laser movement, as intended. By analysing the laser movement in diﬀerent walking conditions, for example with diﬀerent shoes, it was shown in this study that they diﬀered and the method could be useful to compare gait. However, further research needs to be undertaken in...