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. Efficient frontier 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 weights are xi and xj. Of course, the variance terms are special cases of the covariances when i=j, and ρij=1. You can calculate the portfolio variance in the spreadsheet in many different ways. The way I do it is to first calculate the variance/covariance matrix, σρσ whose entries are σiσjρij and σi2. To this end, we first construct the standard deviation (std) matrix and the correlation matrix, as shown in the spreadsheet. Then, first multiple the std matrix to the correlation matrix to obtain σρ (multiply the range of b3..g8 to the range of b10..g15). Then, multiple...

...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...

...The definition of the efficientfrontier says that “the efficientfrontier 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 efficientfrontier. 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 efficientfrontier can dominate any other portfolio on the efficientfrontier. 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...

...Construct Development, Scale Creation, and Process Analysis
The purpose of this paper is to find a construct in which I would like to measure. The construct of my choice will be developing a test that measures depression in men and women who have been diagnosed with a terminal illness. An operational definition of depression will be provided using three peer review journal articles as sources and references. In addition to that a method of scaling will be selected to justify my selection. I will then be proposing how I will be norming the instrument.
Depression is a medical illness that causes an individual to a have a persistent feeling of loss of interest and sadness. Depression affects how an individual thinks, feels and behaves, and in addition to that depression causes physical symptoms as well. Depression leads to a variety of physical and emotional problems. An individual may have trouble doing day-to-day activities; it can also make an individual feel, as life is not worth living anymore. Depression is more than just feeling blue, and it is not a weakness, nor can an individual just snap out o it. Depression is considered a chronic illness that will require long-term treatment for some individuals. Most people with depression begin to feel better after psychological counseling, medication, and other forms of treatment. Where are your references??? This is a lot of information without a references…
The...

...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...

...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...

...Summary Paper
Psychology 301 has had much to offer. From theories to self learning to relationships to spirituality all incorporated into one single course. For a summary of the course, the discussion will be that of Erikson, the quest of meaning, the renewal cycle, and the grand adventure. This course helped develop knowledge of what to label experiences as well as categorize different stages of life. Erikson’s stages are still the head of the forefront in personality developmental. The quest of meaning can give an individual purpose beyond what society can. The renewal cycle identifies the stages of life as they pass. The fourth being the grand adventure captivates the age with experience leading to death. Let the discussion begin with that of psychoanalyst, Erik Erikson.
Erikson was born in 1902 in Frankfurt Germany. In 1927 he went to Vienna to teach and that is where he met Anna Freud. It was her that he began his quest in psychoanalysis. Erikson’s theory still remains the most influential in the world of personality development. He developed eight stages each categorized by age and stage. Within each stage a human have the potential to develop different strengths to aid in life. Erikson coined the stages as crisis or dilemmas. He believed that each dilemma in the life stages had to be resolved to live a healthy life. A healthy resolution, according to Erikson, is finding a balance between the two possibilities This is what the...

...US History I Honors
Frontier Thesis
Jan. 14, 2012
Frontier Thesis Analysis
Throughout the early 20th Century, Fredrick Jackson Turner changed many people’s views on evolution by creating his idea of the Frontier Thesis. Throughout his entire thesis he explained that the more west the settlers move, the more distant and individualized they become from their homeland of Europe. After receiving his PhD from Johns Hopkins University and later becoming a professor of history at Wisconsin and Harvard University, he became one of the most intelligent men when it came to history. His encyclopedic knowledge of American history earned him the reputation by 1910 as one of the two or three most influential historians in the country at that time. After completing the US History I class, I can confidently say that I agree with Jackson’s thesis. History has proven that as the years progress so does the evolution of the American people. Not only did people evolve more as they moved west, individuals also established their own religion, government, and education system.
Religion was a topic that was extremely strict in Europe; it was their way or no way. As more immigrants came to America looking for a fresh start, they realized they had more freedom to do as they pleased, for example, the Mormons. The Mormons were not accepted by many, therefore forcing them to move around the country and expand westward into the unknown territory....

...minimum efficient scale (MES)The minimum efficient scale (MES) is the output for a business in the long run where the internal economies of scale have been fully exploited. It corresponds to the lowest point on the long run average total cost curve and is also known as the output of long run productive efficiency. The MES is rarely a single output - more likely it is a range of output levels where average cost is minimized where the firm achieves constant returns to scale. The MES will vary from industry to industry depending on the nature of the cost structure in a particular sector of the economy. When the ratio of fixed to variable costs is very high, there is great potential for reducing the average cost of production.
[pic]
The extent to which economies of scale can be exploited in the long run will vary between different industries. In some the minimum efficient scale is reached at a relatively low level of output. The internal scale economies are limited and there is room for many separate businesses to achieve the MES. With a natural monopoly, the cost structure is different. For example, in industries where massive networks or national distribution channels are required, the overhead costs relative to the running costs are likely to be high. There is also likely to be great potential to exploit technical economies of scale. As a result the MES may be a high proportion of total market demand. There may be room only for...