You currently own a portfolio of eight stocks. Using the Markowitz model,you computed the optimal mean/variance portfolio. Theweights of these two portfolios are shown in the following table:StockAв сBD EFG HYour Portfolio 0.12 0.15 0.13 0.10 0.20 0.100.12 0.08M/V Portfolio 0.02 0.05 0.25 0.06 0.18 0.100.22 0.12You would like to rebalance your portfolio in order to be closer to the M/Vportfolio. To avoid excessively high transaction costs, you decide to rebalanceonly three stocks from your portfolio. Let xi denote the weight of stock i inyour rebalanced portfolio. The objective is to minimize the quantity|x1-0.02|+|x2-0.05|+|x3-0.25|+.+|x8-0.12||which measures how closely the rebalanced portfolio matches the M/Vportfolio. Formulate this problem as a mixed integer linear program.

In this scenario, you have an existing portfolio of eight stocks and an optimal mean/variance (M/V)…

Answered: You would like to rebalance your…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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You currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. Theweights of these two portfolios are shown in the following table: Stock A B C D E F G HYour Portfolio 0.12 0.15 0.13 0.10 0.20 0.10 0.12 0.08M/V Portfolio 0.02 0.05 0.25 0.06 0.18 0.10 0.22 0.12 You would like to rebalance your portfolio in order to be closer to the M/V portfolio. To avoid excessively high transaction costs, you decide to rebalance only three stocks from your portfolio. Let xi denote the weight of stock i in your rebalanced portfolio. The objective is to minimize the quantity |x1-0.02|+|x2-0.05|+|x3-0.25|+...+|x8-0.12| which measures how closely the rebalanced portfolio matches the M/V portfolio. Formulate this problem as a mixed integer linear program.
Here are returns for two Shares, calculate the covariance (please remember excel is not acceptable to submit). Share Share ABC XYZ 2019 14.29% 5.00% 2020 -37.50% 61.90% 2021 50.00% -25.93% 13.66% Average 8.93%
The dummy variables in a model of human capital can be used to: Select one: a. None of these b. Identify an existing gender wage gap c. All of these d. Study the behavior of the stochastic error term e. Determine that there is gender discrimination
Clearly describe the advantages of portfolio diversification. Suppose, the rates of return on two stocks X and Y are normally distributed as x = N (10%, 9%) and y = N (10%, 16%). Assuming that the variance of the diversified portfolio (that has both stocks X and Y) is V = 6.26 + 6c where c is the correlation between x and y, calculate the maximum value of c beyond which portfolio diversification is not helpful.
a.State the predictors available in this model.
Consider the following data: Stock M N Average return 26% 16% Risk (Std. Dev.) 20% 10% If the return on stocks M and N are perfectly negatively correlated, what is the range of risk (std dev) associated with all possible portfolio combinations? A. Range of the risk: between 0= risk s10 % OB. Range of the risk: between 0 < risk 10% OC. Range of the risk: between 5% and 10%. OD. Range of the risk (std. dev): between 15% to 20% OE. None of the above
Two investments, X and Y, have the characteristics shown below. E(X) = $60, E(Y) = $90, o = 10,000, o? = 17,000 and axy = 6,500 If the weight of portfolio assets assigned to investment X is 0.8, calculate the a. portfolio expected return and b. portfolio risk. a. If the weight of portfolio assets assigned to investment X is 0.8, the portfolio expected return is $ (Type an integer or a decimal.) b. If the weight of portfolio assets assigned to investment X is 0.8, the portfolio risk is approximately $. (Round to two decimal places as needed.)
Caterpillar, Inc., manufactures and sells heavy construction equipment worldwide. The performance of Caterpillar’s stock is likely to be strongly influenced by the economy. For example, during the Great Recession, the value of Caterpillar’s stock plunged dramatically. Monthly data for Caterpillar’s risk-adjusted return (R − Rf) and the risk-adjusted market return (RM − Rf) are collected for a five-year period (n = 60). A portion of the data is shown in the accompanying table. (You may find it useful to reference the t table.) Month Year R_Rf RM_Rf Jan 2012 0.0510 0.0403 Feb 2012 -0.0682 0.0304 Mar 2012 -0.0360 -0.0083 Apr 2012 -0.1446 -0.0635 May 2012 -0.0318 0.0387 Jun 2012 -0.0091 0.0117 Jul 2012 0.0188 0.0188 Aug 2012 0.0073 0.0232 Sept 2012 -0.0154 -0.0209 Oct 2012 0.0101 0.0018 Nov 2012 0.0504 0.0062 Dec 2012 0.1036 0.0497 Jan 2013 -0.0619 0.0104 Feb 2013 -0.0595 0.0350 Mar 2013 -0.0273 0.0172 Apr 2013 0.0193 0.0202 May 2013 -0.0390 -0.0154…
Consider an AR(2) model: STEPS; -Write the equation of the AR(2) model- Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.- Assume that there is an initial value of the returns, denoted by $r_0$, and we have the AR(2) model at time rt, convert the AR(2) model into its equivalent MA(t)
When wildebeest are more abundant, they graze the grass more heavily, so there are fewer fires and moretrees grow. Lions feed more successfully when there are more trees, so the lion population increases. Thedata on one part of this cycle, wildebeest abundance (in thousands of animals) and the percent of the grassarea that burned in the same year are on the spreadsheet. To what extent do these data support the claim that more wildebeest reduce the percent of grasslands that burn? How rapidly does burned area decrease as the number of wildebeest increases? To answer these questions, create a scatterplot and add the regression line. Describe the scatterplot. Interpret the slope and intercept in context of the problem. Does the intercept explanation make sense in the real world? Find the correlation coefficient and coefficient of determination. What do they tell us about the relationship between number of wildebeest and percent of grassland burned? Beest (in 1000s) Percent Burned…
State University has increased its tuition for in-state and out-of-state students in each of the past 5 years to offset cuts in its budget allocation from the state legislature. The university administration always thought that the number of applications received was independent of tuition; however, drops in applications and enrollments the past 2 years have proved this theory to be wrong. University admissions officials have developed the following relationships between the number of applicants who accept admission and enter State and the cost of tuition per semester (in-state) (out-of-state) The university would like to develop a planning model that will indicate the in-state and out-of-state tuitions, as well as the number of students that could be expected to enroll in the freshman class. The university doesn’t have enough classroom space for more than 1,400 freshmen, and it needs at least 700 freshmen to meet all its class-size x2 = 35,000 - 6t2 x1 = 21,000 - 12t1 (xi) (ti):…
Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications. He produces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlation coefficient of 0.454012. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1503.578103 Sx = 107.836402 y freshman year GPA y = 3.299812 Sy = 0.517403 r = 0.454012 Determine the slope, b, of the least squares regression line for this data. Give your answer precise to four decimal places. Avoid rounding until the last step. b %D

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