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...

...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...

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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...

...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);...

...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...

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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...

...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...

...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...

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