der the information for assets A, B, and C below: State Boom Average Bust Probability 0.2 0.4 0.4 Return on A Return on B Return on C 0.3 0.2 0.1 0.05 Q.15 0.2 0.1 0.25 0.3 Consider Portfolio (Y) comprising 60% Asset A and 40% Asset C. What is the vari portfolio Y?
der the information for assets A, B, and C below: State Boom Average Bust Probability 0.2 0.4 0.4 Return on A Return on B Return on C 0.3 0.2 0.1 0.05 Q.15 0.2 0.1 0.25 0.3 Consider Portfolio (Y) comprising 60% Asset A and 40% Asset C. What is the vari portfolio Y?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
![**Understanding Asset Performance and Portfolio Variance**
In this section, we will examine the returns on three different assets (A, B, and C) under varying economic conditions, as well as calculate the variance for a specific portfolio composition.
**Asset Information:**
The table provided lists the probability and expected returns for assets A, B, and C under three economic states: Boom, Average, and Bust.
| **State** | **Probability** | **Return on A** | **Return on B** | **Return on C** |
|-----------|------------------|----------------|-----------------|-----------------|
| Boom | 0.2 | 0.3 | 0.05 | 0.1 |
| Average | 0.4 | 0.2 | 0.15 | 0.25 |
| Bust | 0.4 | 0.1 | 0.2 | 0.3 |
**Portfolio Analysis:**
Consider a portfolio \( Y \) consisting of 60% Asset A and 40% Asset C. The task is to calculate the variance of this portfolio \( Y \).
To calculate the variance, apply the following steps:
1. **Compute the Expected Return of Portfolio \( Y \):**
- Expected Return = (Weight of A * Return on A) + (Weight of C * Return on C)
2. **Calculate the Variance:**
- Variance = \( \sum \) [Probability * (Return of \( Y \) in each state - Expected Return of \( Y \))^2]
By solving these calculations, we derive the measure of risk associated with portfolio \( Y \).
This analysis serves to enhance your understanding of portfolio management and risk assessment in various economic conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facc636b4-c810-484a-bf47-001a6f3a3c9e%2Fbef50194-cb40-4619-84cb-459fbe723ee9%2Fwazmy2_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Asset Performance and Portfolio Variance**
In this section, we will examine the returns on three different assets (A, B, and C) under varying economic conditions, as well as calculate the variance for a specific portfolio composition.
**Asset Information:**
The table provided lists the probability and expected returns for assets A, B, and C under three economic states: Boom, Average, and Bust.
| **State** | **Probability** | **Return on A** | **Return on B** | **Return on C** |
|-----------|------------------|----------------|-----------------|-----------------|
| Boom | 0.2 | 0.3 | 0.05 | 0.1 |
| Average | 0.4 | 0.2 | 0.15 | 0.25 |
| Bust | 0.4 | 0.1 | 0.2 | 0.3 |
**Portfolio Analysis:**
Consider a portfolio \( Y \) consisting of 60% Asset A and 40% Asset C. The task is to calculate the variance of this portfolio \( Y \).
To calculate the variance, apply the following steps:
1. **Compute the Expected Return of Portfolio \( Y \):**
- Expected Return = (Weight of A * Return on A) + (Weight of C * Return on C)
2. **Calculate the Variance:**
- Variance = \( \sum \) [Probability * (Return of \( Y \) in each state - Expected Return of \( Y \))^2]
By solving these calculations, we derive the measure of risk associated with portfolio \( Y \).
This analysis serves to enhance your understanding of portfolio management and risk assessment in various economic conditions.
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