The correlation ρ between assets A and B is 0.25, and other data are given in the following table: [Recall the definition ρ = σAB/(σAσB).] Asset ¯r σ A 9.0% 12% B 11.0% 16% (a) Find the proportions α of A and (1 − α) of B that define a portfolio of A and B having minimum standard deviation. (b) What is the value of this minimum standard deviation? (c) What is the expected return of this portfolio?

The correlation ρ between assets A and B is 0.25, and other data are given in the following table: [Recall the definition ρ = σAB/(σAσB).] Asset ¯r σ A 9.0% 12% B 11.0% 16% (a) Find the proportions α of A and (1 − α) of B that define a portfolio of A and B having minimum standard deviation. (b) What is the value of this minimum standard deviation? (c) What is the expected return of this portfolio?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Question

The correlation ρ between assets A and B is 0.25,
and other data are given in the following table: [Recall the definition ρ = σAB/(σAσB).]
Asset ¯r σ
A 9.0% 12%
B 11.0% 16%
(a) Find the proportions α of A and (1 − α) of B that define a portfolio of A and B having minimum standard deviation.
(b) What is the value of this minimum standard deviation?
(c) What is the expected return of this portfolio?

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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