Investors in mutual funds keep a sharp eye on the total return on their money. T
ID: 3195876 • Letter: I
Question
Investors in mutual funds keep a sharp eye on the total return on their money. They also are
aware of the risk involved in their investment, commonly measured by a fund’s volatility (the
greater the volatility, the higher the risk). Below is a list of 30 mutual funds randomly selected in
1998 from Fortune’s list of stock and bond funds, together with their 5-year total return (%) and
risk assessment:
Fund Name Total Return Risk
MFS Emerging Growth 21.5 20.6
Kaufmann 19.7 18.4
AIM Constellation A 17.6 18.4
Weitz Hickory 29.9 19.7
Oak Value 25.6 13.0
Gabelli Westwood Equity 23.0 12.3
Nationwide 24.3 12.0
Fidelity Growth/Income 22.6 13.0
Stratton Growth 21.3 11.8
GAM International A 22.6 19.9
Scudder International 14.3 13.7 .
Janus Worldwide 23.6 13.7
Oppenheimer Global A 19.0 14.4
New Perspective 18.8 12.1
Putnam Europe Growth A 22.7 14.6
AIM Balanced A 1 5.9 10.8
Delaware A 13.6 8.6
Greenspring 14.0 7.2
Calamos Convertible A 14.3 9.9
Managers Bond 10.3 5.4
Harbor Bond 7.3 4.4
Northeast Investors 3.6 5.5
Strong Gov’t. Securities 7.0 4.4
Lexington GNMA Income 6.9 3.5
Marshall Gov’t. Income 5.8 3.7
Wright U.S. Treasury 6.3 7.5
Excelsior Tax-Exempt 7.6 6.7
Vanguard Municipal 6.5 5.5
Goldman Sachs Global 7.2 4.1
Capital World Bond 5.9 4.9
Suppose that the question you wish to address using this data is whether the total return on the investment is affected by the risk of the investment. You also want to know if you can predict the total return based on the risk. You will attempt a Linear Regression Analysis Using Microsoft Excel 2010 to help you answer these questions.
QUESTION 1
Which variable in this problem would be considered the independent variable?
Company
Total Revenue
Risk
Time
QUESTION 2
Which variable in this problem would be considered the dependent variable?
Company
Total Revenue
Risk
Time
QUESTION 3
Sketch a scatter plot (scatter diagram) of the data above. The graph indicates that the relationship between Total Return and Risk is
positive-as risk increases, total return increases.
negative- as risk increases, total return decreases.
zero- as risk increases, total return remains relatively constant.
does not exist—total risk remains relatively constant.
QUESTION 4
Use Micrsoft Excel 2010 to run a linear regression analysis. What is the value of R2 (R-squared)?
QUESTION 5
What does this value for R2 (R-squared) suggest about the linear equation that Excel determines as the line of best fit?
This equation will be a very good predictor of related data values.
This equation will be an acceptable predictor of related data values.
This equation will be a poor predictor of related data values.
Inconclusive value
QUESTION 6
Identify the coefficients from the Excel Output summary that are used to write the line of best fit for this data. If the equation was written as
y = b1x + b0,
where y if the total return value and x is the risk, what is the value of b0?
QUESTION 7
Identify the coefficients from the Excel Output summary that are used to write the line of best fit for this data. If the equation was written as
y = b1x + b0,
where y if the total return value and x is the risk, what is the value of b1?
QUESTION 8
What does the value of b0 represent?
the amount total revenue will change when the risk is increased by 1
the value of the total revenue if the risk was 0
the value of the risk if the total revenue was 0
the amount that risk will increase if total revenue increases by 1
QUESTION 9
What does the value of b1 represent?
the amount total revenue will change when the risk is increased by 1
the value of the total revenue if the risk was 0
the value of the risk if the total revenue was 0
the amount that risk will increase if total revenue increases by 1
QUESTION 10
Use the line of best fit to predict the total return (y-value) for a risk of x = 11?
Total Return = _________ ?
Investors in mutual funds keep a sharp eye on the total return on their money. They also are
aware of the risk involved in their investment, commonly measured by a fund’s volatility (the
greater the volatility, the higher the risk). Below is a list of 30 mutual funds randomly selected in
1998 from Fortune’s list of stock and bond funds, together with their 5-year total return (%) and
risk assessment:
Fund Name Total Return Risk
MFS Emerging Growth 21.5 20.6
Kaufmann 19.7 18.4
AIM Constellation A 17.6 18.4
Weitz Hickory 29.9 19.7
Oak Value 25.6 13.0
Gabelli Westwood Equity 23.0 12.3
Nationwide 24.3 12.0
Fidelity Growth/Income 22.6 13.0
Stratton Growth 21.3 11.8
GAM International A 22.6 19.9
Scudder International 14.3 13.7 .
Janus Worldwide 23.6 13.7
Oppenheimer Global A 19.0 14.4
New Perspective 18.8 12.1
Putnam Europe Growth A 22.7 14.6
AIM Balanced A 1 5.9 10.8
Delaware A 13.6 8.6
Greenspring 14.0 7.2
Calamos Convertible A 14.3 9.9
Managers Bond 10.3 5.4
Harbor Bond 7.3 4.4
Northeast Investors 3.6 5.5
Strong Gov’t. Securities 7.0 4.4
Lexington GNMA Income 6.9 3.5
Marshall Gov’t. Income 5.8 3.7
Wright U.S. Treasury 6.3 7.5
Excelsior Tax-Exempt 7.6 6.7
Vanguard Municipal 6.5 5.5
Goldman Sachs Global 7.2 4.1
Capital World Bond 5.9 4.9
Suppose that the question you wish to address using this data is whether the total return on the investment is affected by the risk of the investment. You also want to know if you can predict the total return based on the risk. You will attempt a Linear Regression Analysis Using Microsoft Excel 2010 to help you answer these questions.
Explanation / Answer
1) independent variable
is Risk
2) dependent variable is
total revenue
3)
positive-as risk increases, total return increases.
8)
the value of the total revenue if the risk was 0
9)
the amount total revenue will change when the risk is increased by 1
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