7. Calculating Returns and Variability. Using the following returns, 01 calculate the average returns, the variances, and the standard deviations for X and Y. Returns Year Y. 16% 36% -17 - 8 13 21 15 -15 24 39 12 3 45
7. Calculating Returns and Variability. Using the following returns, 01 calculate the average returns, the variances, and the standard deviations for X and Y. Returns Year Y. 16% 36% -17 - 8 13 21 15 -15 24 39 12 3 45
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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Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
Question
![**7. Calculating Returns and Variability**
Using the following returns, calculate the average returns, the variances, and the standard deviations for X and Y.
| Year | X | Y |
|------|-----|-----|
| 1 | 16% | 36% |
| 2 | -17%| -8% |
| 3 | 13% | 21% |
| 4 | 15% | -15%|
| 5 | 24% | 39% |
**Instructions:**
To calculate the average returns, sum up all the returns for each variable (X and Y) and then divide by the number of years.
**Average Return Formula:**
\[ \text{Average Return (X or Y)} = \frac{\text{Total Returns}}{\text{Number of Years}} \]
Then, determine the variance for each by calculating the average of the squared differences from the Mean.
**Variance Formula for a Sample:**
\[ \text{Variance} = \frac{\sum (X_i - \bar{X})^2}{n-1} \]
Calculate the standard deviation by taking the square root of the variance.
**Standard Deviation Formula:**
\[ \text{Standard Deviation} = \sqrt{\text{Variance}} \]
This exercise aids in understanding the variability and risk associated with different investment returns.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa848b230-aa9c-442a-931f-b7f827d9b315%2Fe7b2abed-7303-4a8e-a449-86bca1a93dd6%2Fr5iveby_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**7. Calculating Returns and Variability**
Using the following returns, calculate the average returns, the variances, and the standard deviations for X and Y.
| Year | X | Y |
|------|-----|-----|
| 1 | 16% | 36% |
| 2 | -17%| -8% |
| 3 | 13% | 21% |
| 4 | 15% | -15%|
| 5 | 24% | 39% |
**Instructions:**
To calculate the average returns, sum up all the returns for each variable (X and Y) and then divide by the number of years.
**Average Return Formula:**
\[ \text{Average Return (X or Y)} = \frac{\text{Total Returns}}{\text{Number of Years}} \]
Then, determine the variance for each by calculating the average of the squared differences from the Mean.
**Variance Formula for a Sample:**
\[ \text{Variance} = \frac{\sum (X_i - \bar{X})^2}{n-1} \]
Calculate the standard deviation by taking the square root of the variance.
**Standard Deviation Formula:**
\[ \text{Standard Deviation} = \sqrt{\text{Variance}} \]
This exercise aids in understanding the variability and risk associated with different investment returns.
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