Chapter 11, Problem 35QAP

a.

Summary Introduction

Adequate information:

State	Probability of Outcome	Return on Security 1	Return on Security 2	Return on Security 3
1	0.15	0.20	0.20	0.05
2	0.35	0.15	0.10	0.10
3	0.35	0.10	0.15	0.15
4	0.15	0.05	0.05	0.20

To compute: The expected return and standard deviation of Security 1, Security 2, and Security 3.

Introduction: Expected return simply refers to the return that is anticipated on the investment.

b.

Summary Introduction

Adequate information:

State	Probability of Outcome	Return on Security 1	Return on Security 2	Return on Security 3
1	0.15	0.20	0.20	0.05
2	0.35	0.15	0.10	0.10
3	0.35	0.10	0.15	0.15
4	0.15	0.05	0.05	0.20

To compute: The covariance and correlations between the securities.

Introduction: The relationship between two securities is referred to as covariance.

c.

Summary Introduction

Adequate information:

State	Probability of Outcome	Return on Security 1	Return on Security 2	Return on Security 3
1	0.15	0.20	0.20	0.05
2	0.35	0.15	0.10	0.10
3	0.35	0.10	0.15	0.15
4	0.15	0.05	0.05	0.20

Weight of security 1 (W₁) = 50% or 0.50

Weight of security 2 (W₂) = 50% or 0.50

Expected return of Security 1 [E(R₁)] = 0.1250 or 12.50%

Expected return of Security 2 [E(R₂)] = 0.1250 or 12.50%

Standard deviation of Security 1 (σ₁) = 0.0461 or 4.61%

Standard deviation of Security 2 (σ₂) = 0.0461 or 4.61%

Correlation between Security 1 and Security 2 (?_1,2) = 0.59

To compute: The expected return and standard deviation of a portfolio if half of the funds are invested in Security 1 and a half in Security 2.

Introduction: Expected return on the portfolio refers to the return that is anticipated on the portfolio as a whole.

d.

Summary Introduction

Adequate information:

State	Probability of Outcome	Return on Security 1	Return on Security 2	Return on Security 3
1	0.15	0.20	0.20	0.05
2	0.35	0.15	0.10	0.10
3	0.35	0.10	0.15	0.15
4	0.15	0.05	0.05	0.20

Weight of security 1 (W₁) = 50% or 0.50

Weight of security 3 (W₃) = 50% or 0.50

Expected return of Security 1 [E(R₁)] = 0.1250 or 12.50%

Expected return of Security 2 [E(R₃)] = 0.1250 or 12.50%

Standard deviation of Security 1 (σ₁) = 0.0461 or 4.61%

Standard deviation of Security 2 (σ₃) = 0.0461 or 4.61%

Correlation between Security 1 and Security 3 (?_1,3) = -1

To compute: The expected return and standard deviation of a portfolio if half of the funds are invested in Security 1 and half in Security 3.

Introduction: Expected return on the portfolio refers to the return that is anticipated on the portfolio as a whole.

e.

Summary Introduction

Adequate information:

State	Probability of Outcome	Return on Security 1	Return on Security 2	Return on Security 3
1	0.15	0.20	0.20	0.05
2	0.35	0.15	0.10	0.10
3	0.35	0.10	0.15	0.15
4	0.15	0.05	0.05	0.20

Weight of security 2 (W₂) = 50% or 0.50

Weight of security 3 (W₃) = 50% or 0.50

Expected return of Security 2 [E(R₂)] = 0.1250 or 12.50%

Expected return of Security 3 [E(R₃)] = 0.1250 or 12.50%

Standard deviation of Security 2 (σ₂) = 0.0461 or 4.61%

Standard deviation of Security 3 (σ₃) = 0.0461 or 4.61%

Correlation between Security 2 and Security 3 (?_2,3) = -0.59

To compute: The expected return and standard deviation of a portfolio if half of the funds are invested in Security 2 and a half in Security 3.

Introduction: Expected return on the portfolio refers to the return that is anticipated on the portfolio as a whole.

f.

Summary Introduction

Adequate information:

State	Probability of Outcome	Return on Security 1	Return on Security 2	Return on Security 3
1	0.15	0.20	0.20	0.05
2	0.35	0.15	0.10	0.10
3	0.35	0.10	0.15	0.15
4	0.15	0.05	0.05	0.20

To compute: About diversification by considering Parts (a), (c), (d), (e).

Introduction: Correlation defines how two or more securities in the portfolio are related to each other.