Question

Chapter 06: Assignment - An Introduction to Portfolio Management

Given:
E(R 1) = 0.13
E(R2) = 0.17
E(o 1) = 0.04
E(02) 0.05
Calculate the expected returns and expected standard deviations of a two-stock portfolio having a correlation coefficient of 0.75 under the conditions given
below. Do not round intermediate calculations. Round your answers to four decimal places.
a. w11.00
Expected return of a two-stock portfolio:
A.
Expected standard deviation of a two-stock portfolio:
b. w 1 0.70
Expected return of a two-stock portfolio:
Expected standard deviation of a two-stock portfolio:
C. W 10.60
Expected return of a two-stock portfolio:
Expected standard deviation of a two-stock portfolio:
d. w1 0.20
Expected return of a two-stock portfolio:
Expected standard deviation of a two-stock portfolio:
e. w₁ 0.05
Expected return of a two-stock portfolio:
Expected standard deviation of a two-stock portfolio:
Choose the correct risk-return graph for weights from parts (a) through (e) when r -0.75; 0.00; 0.75.

Answer 1

Two-stock portfolio analysis:

• Calculated expected returns and standard deviations for various weightings.
• Provided information for risk-return graph with different correlations (negative, no, positive).

Portfolio Expected Return and Standard Deviation

Given:

• E(R₁) = 0.13
• E(R₂) = 0.17
• σ₁ = 0.04
• σ₂ = 0.05
• ρ = 0.75
• a) w₁ = 1.00:

Expected return:

E(R_p) = w₁ * E(R₁) + w₂ * E(R₂)

E(R_p) = 1.00 * 0.13 + 0.00 * 0.17

E(R_p) = 0.13

Expected standard deviation:

σ_p = sqrt(w₁² * σ₁² + w₂² * σ₂² + 2 * w₁ * w₂ * ρ * σ₁ * σ₂)

σ_p = sqrt(1.00² * 0.04² + 0.00² * 0.05² + 2 * 1.00 * 0.00 * 0.75 * 0.04 * 0.05)

σ_p = 0.04

b) w₁ = 0.70:

Expected return:

E(R_p) = 0.70 * 0.13 + 0.30 * 0.17

E(R_p) = 0.15

Expected standard deviation:

σ_p = sqrt(0.70² * 0.04² + 0.30² * 0.05² + 2 * 0.70 * 0.30 * 0.75 * 0.04 * 0.05)

σ_p = 0.038

c) w₁ = 0.60:

Expected return:

E(R_p) = 0.60 * 0.13 + 0.40 * 0.17

E(R_p) = 0.148

Expected standard deviation:

σ_p = sqrt(0.60² * 0.04² + 0.40² * 0.05² + 2 * 0.60 * 0.40 * 0.75 * 0.04 * 0.05)

σ_p = 0.036

d) w₁ = 0.20:

Expected return:

E(R_p) = 0.20 * 0.13 + 0.80 * 0.17

E(R_p) = 0.158

Expected standard deviation:

σ_p = sqrt(0.20² * 0.04² + 0.80² * 0.05² + 2 * 0.20 * 0.80 * 0.75 * 0.04 * 0.05)

σ_p = 0.042

e) w₁ = 0.05:

Expected return:

E(R_p) = 0.05 * 0.13 + 0.95 * 0.17

E(R_p) = 0.167

Expected standard deviation:

σ_p = sqrt(0.05² * 0.04² + 0.95² * 0.05² + 2 * 0.05 * 0.95 * 0.75 * 0.04 * 0.05)

σ_p = 0.046

Risk-Return Graph

The risk-return graph will show the expected return (E(R_p)) on the y-axis and the expected standard deviation (σ_p) on the x-axis.

The graph will have five points, each corresponding to one of the weights (w₁) calculated above.

For different values of the correlation coefficient (ρ):

• ρ = -0.75: The points will form a concave curve towards the origin, indicating a negative correlation between the two assets.
• ρ = 0.00: The points will be collinear, indicating no correlation between the two assets.
• ρ = 0.75: The points will form a convex curve away from the origin, indicating a positive correlation between the two