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# Variance portfolio; proportions of stock; price of the stock

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Problem 1
Given:
E(RÌ?A) = 10% Ï?2A = 0.25
E(RÌ?B) = 12% Ï?2B = 0.35
PAB = 0.56 Target Return = 11.5%

Minimize: X2A(0.25) + X2B(0.35) + 2XAXB(0.56)(0.25)0.5(0.35)0.5

Subject to:
1 XA(10%) + XB(12%) = 11.5% E(RÌ?P) = 11.5%
2 XA + XB = 1.0 Investments total 100%
3 XA>0, XB>0 Proportions are positive

Solution:
XA = 25%, XB = 75%

Suppose there is a third security ©, with these characteristics: E(Rc) = 10%; Ï?2=0.20; Pac=0.78; and Pbc = 0.56. Construct the quadratic program that would minimize the risk of a three-security portfolio consisting of A, B, and C.

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Problem 2

A B C D E
98' 0.200 0.300 0.100 0.000 -0.100
99' -0.100 0.000 0.000 0.100 0.200
00' 0.400 0.500 0.100 0.400 0.300
01' 0.100 0.200 0.300 -0.100 0.000
02' 2.000 0.300 0.300 -0.200 0.200
03' -0.200 -0.200 -0.100 0.100 0.400
04' 0.500 0.500 0.000 0.300 0.300
05' -0.100 0.100 0.200 0.300 -0.100
06' 0.000 -0.100 0.200 0.100 -0.200
07' 0.300 0.400 0.300 0.100 0.000
E(RÌ?) 0.130 0.200 0.140 0.110 0.100
Ï? 0.219 0.232 0.136 0.176 0.195

A two-security portfolio contains Stocks B and C from above table. Using a spreadsheet package, do the following:
a. Prepare a plot showing the portfolio variance for various combinations of Stocks B and C.
b. Find the minimum variance portfolio.
c. Find the proportions of Stocks B and C that constitute a portfolio with the same risk as Stock C alone.

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Problem 3
"Consider the following information:
Stock price = \$46.69
Current dividend = 1.98
Future dividend growth rate = 5.5%
Beta = 1.10
30-day T-bill rate = 2.55%

For this stock you want to set a buy limit at 90% of the intrinsic value of the stock as determined using the dividend discount model. What should that price be?"

https://brainmass.com/statistics/variance/variance-portfolio-proportions-of-stock-price-of-the-stock-341016

#### Solution Preview

See the attached file.

Problem 1
Given: E(R&#771;A) = 10% &#963;2A = 0.25
E(R&#771;B) = 12% &#963;2B = 0.35
PAB = 0.56 Target Return = 11.5%
Minimize: X2A(0.25) + X2B(0.35) + 2XAXB(0.56)(0.25)0.5(0.35)0.5
Subject to:
1 XA(10%) + XB(12%) = 11.5% E(R&#771;P) = 11.5%
2 XA + XB = 1.0 Investments total 100%
3 XA>0, XB>0 Proportions are positive
Solution:
XA = 25%, XB = 75%
Suppose there is a third security ©, with these characteristics: E(Rc) = 10%; &#963;2=0.20; Pac=0.78; and Pbc = 0.56. Construct the quadratic program that would minimize the risk of a three-security portfolio consisting of A, B, and C.

E(R&#771;A) 10% &#963;2A 0.25
E(R&#771;B) 12% &#963;2B 0.35
E(R&#771;C) 10% &#963;2C ...

#### Solution Summary

This post shows how to calculate the minimum variance portfolio, proportions of stocks and the price of stock. It shows how to prepare a plot showing the portfolio variance for various combinations of stock

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