Stocks The table presents the 2016 percentage change in the stock price for six well-known companies. (Data from: finance.yahoo.com .) Company Percentage Change American Express +10.6% Coca-Cola − 1.0 % ExxonMobil +14.9% Hewlett Packard +63.1% Ford − 5.7 % Red Robin Gourmet Burgers − 8.0 % Suppose that we wish to determine the difference in percentage change between two of the companies in the table, and suppose that we are interested only in the magnitude, or absolute value, of this difference. Then we subtract the two entries and find the absolute value. For example, the difference in percentage change of stock price for American Express and Ford is | 10.6 % − ( − 5.7 % ) | = 16.3 % Find the absolute value of the difference between the two indicated changes in stock price. American Express and ExxonMobil
Stocks The table presents the 2016 percentage change in the stock price for six well-known companies. (Data from: finance.yahoo.com .) Company Percentage Change American Express +10.6% Coca-Cola − 1.0 % ExxonMobil +14.9% Hewlett Packard +63.1% Ford − 5.7 % Red Robin Gourmet Burgers − 8.0 % Suppose that we wish to determine the difference in percentage change between two of the companies in the table, and suppose that we are interested only in the magnitude, or absolute value, of this difference. Then we subtract the two entries and find the absolute value. For example, the difference in percentage change of stock price for American Express and Ford is | 10.6 % − ( − 5.7 % ) | = 16.3 % Find the absolute value of the difference between the two indicated changes in stock price. American Express and ExxonMobil
Solution Summary: The author calculates the absolute value of the difference between the stock price of American Express and ExxonMobil.
Stocks The table presents the 2016 percentage change in the stock price for six well-knowncompanies. (Data from:finance.yahoo.com.)
Company
Percentage Change
American Express
+10.6%
Coca-Cola
−
1.0
%
ExxonMobil
+14.9%
Hewlett Packard
+63.1%
Ford
−
5.7
%
Red Robin Gourmet Burgers
−
8.0
%
Suppose that we wish to determine the difference in percentage change between two of the companies in the table, and suppose that we are interested only in the magnitude, or absolute value, of this difference. Then we subtract the two entries and find the absolute value. For example, the difference in percentage change of stock price for American Express and Ford is
|
10.6
%
−
(
−
5.7
%
)
|
=
16.3
%
Findthe absolute value of the difference between the two indicated changes in stock price.
9 (Portfolio allocation)
Suppose R₁ and R2 are returns of 2 assets and with expected return and
variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find
−∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest
risk.
7 (Multivariate random variable)
Suppose X, €1, €2, €3 are IID N(0, 1) and
Y2
Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3.
=
(In models like this, X is called the common factors of Y₁, Y₂, Y3.)
Y = (Y1, Y2, Y3).
(a) Find E(Y) and cov(Y).
(b) What can you observe from cov(Y).
Write
1 (VaR and ES) Suppose X ~ f(x) with
1+x, if 0> x > −1
f(x) =
1−x
if 1 x > 0
Find VaRo.05 (X) and ES0.05 (X).
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