# Risk Assessment using Scatter Diagrams & Regression Analysis

2. You are given the following set of data:

Historical Rates of Return

Year NYSE Stock Y

1 4.0% 3.0%

2 14.3 18.2

3 19.0 9.1

4 (14.7) (6.0)

5 (26.5) (15.3)

6 37.2 33.1

7 23.8 6.1

8 (7.2) 3.2

9 6.6 14.8

10 20.5 24.1

11 30.6 18.0

Mean = 9.8% 9.8%

σ = 19.6% 13.8%

a. Construct a scatter diagram showing the relationship between returns on

Stock Y and the market, and then draw a freehand approximation of the

regression line. What is the approximate value of the beta coefficient? If you

have a calculator with a linear regression function or a spreadsheet, check

the approximate value of beta obtained from the graph.

b. Give a verbal interpretation of what the regression line and the beta

coefficient show about Stock Y's volatility and relative riskiness as compared

with those of other stocks.

c. Suppose the scatter of points had been more spread out, but the regression

line was exactly where your present graph shows it. How would this effect

(1) the firm's risk if the stock is held in a one-asset portfolio and (2) the actual

risk premium on the stock if the CAPM holds exactly?

d. Suppose the regression line had been downward sloping and the beta

coefficient had been negative. What would this imply about (1) Stock Y's

relative riskiness, (2) its correlation with the market, and (3) its probable risk

premium?

e. Construct an illustrative probability distribution graph of returns on

portfolios consisting of (1) only Stock Y, (2) 1% each of 100 stocks with beta

coefficients similar to that of Stock Y, and (3) all stocks (i.e. the distribution

of returns on the market). Use as the expected rate of return the arithmetic

mean as given previously for both Stock Y and the market and assume that

the distributions are normal. Are the expected returns "reasonable"; that is,

is it reasonable that % 8 . 9 ? ? = = M Y k k ?

https://brainmass.com/statistics/regression-analysis/132160

#### Solution Preview

Hello

a. Construct a scatter diagram showing the relationship between returns on

Stock Y and the market, and then draw a freehand approximation of the

regression line. What is the approximate value of the beta coefficient? If you

have a calculator with a linear regression function or a spreadsheet, check

the approximate value of beta obtained from the graph.

Approximate Value of Beta is 0.6 - please see the attached excel sheets for calculations and scatter diagram

b. Give a verbal interpretation of what the regression line and the beta

coefficient show about Stock Y's volatility and relative riskiness as compared

with those of other stocks.

The Beta Coefficient is a measure of risk, it shows how volatile stock Y is with respect to the NYSE index. A Beta Value of 0.6 means ...

#### Solution Summary

The solution contains a word document and an excel file that answer the questions posted. Questions are about drawing a scatter diagram, assessing the risk of a stock when held alone and within a portfolio.