Use the following data to answer the question regarding the performance of Guardian Stock Fund and the market portfolio. The risk- free return during the sample period was 5%. Average return. Standard deviation of returns Beta Residual standard deviation Guardian 14% 26% 1.2 (0.80) X 4% Calculate the information ratio measure of performance for Guardian Stock Fund. (Round your answer to 2 decimal places. Do not round intermediate calculations.) > Answer is complete but not entirely correct. Information ratio Market Portfolio 10% 21% 1 0%
Use the following data to answer the question regarding the performance of Guardian Stock Fund and the market portfolio. The risk- free return during the sample period was 5%. Average return. Standard deviation of returns Beta Residual standard deviation Guardian 14% 26% 1.2 (0.80) X 4% Calculate the information ratio measure of performance for Guardian Stock Fund. (Round your answer to 2 decimal places. Do not round intermediate calculations.) > Answer is complete but not entirely correct. Information ratio Market Portfolio 10% 21% 1 0%
Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 6P
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Transcribed Image Text:Use the following data to answer the question regarding the performance of Guardian Stock Fund and the market portfolio. The risk-
free return during the sample period was 5%.
Average return
Standard deviation of returns
Beta
Residual standard deviation
Guardian
14%
26%
1.2
(0.80)
4%
X Answer is complete but not entirely correct.
Information
ratio
Market Portfolio
Calculate the information ratio measure of performance for Guardian Stock Fund. (Round your answer to 2 decimal places. Do not
round intermediate calculations.)
10%
21%
1
0%
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![### Performance Evaluation of Guardian Stock Fund and Market Portfolio
In this example, we aim to calculate the information ratio measure of performance for the Guardian Stock Fund using the provided data. The risk-free return during the sample period was 5%.
#### Provided Data:
| | Guardian | Market Portfolio |
|-------------------|----------|------------------|
| **Average return** | 14% | 10% |
| **Standard deviation of returns** | 26% | 21% |
| **Beta** | 1.2 | 1 |
| **Residual standard deviation** | 4% | 0% |
#### Question:
Calculate the information ratio measure of performance for the Guardian Stock Fund. **Ensure your answer is rounded to two decimal places without rounding intermediate calculations.**
### Solution:
#### Calculating the Information Ratio:
The information ratio is calculated as:
\[ \text{Information Ratio} = \frac{\alpha_p}{\sigma_e} \]
Where:
- \( \alpha_p \) is the fund's alpha
- \( \sigma_e \) is the residual standard deviation
#### Step-by-Step Calculation:
1. **Alpha (\( \alpha_p \)) Calculation:**
\[ \alpha_p = ( R_p - R_f ) - \beta_p \times (R_m - R_f) \]
Where:
- \( R_p \) = Return of the portfolio (Guardian) = 14%
- \( R_f \) = Risk-free rate = 5%
- \( R_m \) = Return of the market portfolio = 10%
- \( \beta_p \) = Beta of the portfolio = 1.2
Plug in the values:
\[ \alpha_p = (14\% - 5\%) - 1.2 \times (10\% - 5\%) \]
\[ \alpha_p = 9\% - 1.2 \times 5\% \]
\[ \alpha_p = 9\% - 6\% \]
\[ \alpha_p = 3\% \]
2. **Residual Standard Deviation (\( \sigma_e \)):**
\[ \sigma_e = 4\% \] (given)
3. **Calculate the Information Ratio:**
\[ \text{Information Ratio} = \frac{3\%}{4\%} \]
\[ \text{Information Ratio}](https://content.bartleby.com/qna-images/question/f1fd60a6-e122-44a6-b63f-53f11d7f8fb8/86fac086-070a-49b4-b81e-5c1c7ca49298/t69vwyr_processed.png)
Transcribed Image Text:### Performance Evaluation of Guardian Stock Fund and Market Portfolio
In this example, we aim to calculate the information ratio measure of performance for the Guardian Stock Fund using the provided data. The risk-free return during the sample period was 5%.
#### Provided Data:
| | Guardian | Market Portfolio |
|-------------------|----------|------------------|
| **Average return** | 14% | 10% |
| **Standard deviation of returns** | 26% | 21% |
| **Beta** | 1.2 | 1 |
| **Residual standard deviation** | 4% | 0% |
#### Question:
Calculate the information ratio measure of performance for the Guardian Stock Fund. **Ensure your answer is rounded to two decimal places without rounding intermediate calculations.**
### Solution:
#### Calculating the Information Ratio:
The information ratio is calculated as:
\[ \text{Information Ratio} = \frac{\alpha_p}{\sigma_e} \]
Where:
- \( \alpha_p \) is the fund's alpha
- \( \sigma_e \) is the residual standard deviation
#### Step-by-Step Calculation:
1. **Alpha (\( \alpha_p \)) Calculation:**
\[ \alpha_p = ( R_p - R_f ) - \beta_p \times (R_m - R_f) \]
Where:
- \( R_p \) = Return of the portfolio (Guardian) = 14%
- \( R_f \) = Risk-free rate = 5%
- \( R_m \) = Return of the market portfolio = 10%
- \( \beta_p \) = Beta of the portfolio = 1.2
Plug in the values:
\[ \alpha_p = (14\% - 5\%) - 1.2 \times (10\% - 5\%) \]
\[ \alpha_p = 9\% - 1.2 \times 5\% \]
\[ \alpha_p = 9\% - 6\% \]
\[ \alpha_p = 3\% \]
2. **Residual Standard Deviation (\( \sigma_e \)):**
\[ \sigma_e = 4\% \] (given)
3. **Calculate the Information Ratio:**
\[ \text{Information Ratio} = \frac{3\%}{4\%} \]
\[ \text{Information Ratio}
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