Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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**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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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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