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Regression Equation and Statistical Analysis of Stock Return

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The returns from an electronic firm's stock and the corresponding returns for the market portfolio for the past 15 years are given below. (See attached file for better table representation)

Market Return (%) Stock's Return (%)
16.02 21.05
12.17 17.25
11.48 13.1
17.62 18.23
20.01 21.52
14 13.26
13.22 15.84
17.79 22.18
15.46 16.26
8.09 5.64
11 10.55
18.52 17.86
14.05 12.75
8.79 9.13
11.6 13.87

1. Carry out the regression and find the B for the stock. What is the regression equation.
2. Does the value of the slope indicate that the stock is above-average risks?
3. Give a 95% confidence interval for this B. Can we say the risk is above the average 95% confidence?
4. If the market portfolio return for the current year is 10%, what is the stock's return predicted by the regression equation? Give a 95% confidence interval for this prediction.
5. Construct a residual plot. Do the residuals appear random?
6. Construct a normal probability plot. Do the residuals appear to be normally distributed?

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Solution Summary

This in-depth solution calculates the beta of the stock to find the regression equation, determines the risk at 95% confidence level, predicts the stock return, and constructs a residual and normal probability plot. Explanations are provided at each step.

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5. A product manager at Proctor & Gamble seeks to determine whether her company should market a new brand of toothpaste, called Tim's of Massachusetts. If the new brand succeeds, then P&G estimates that it would earn $2,000,000 in NPV. If Tim's fails, then the company expects to lose approximately $800,000 in NPV. If P&G decides not to market this new brand, the product manager believe there would be little, if any, impact on the profits earned through sales of P&G's other products. The manager has estimated that the new brand has a 40% chance of succeeding. Before making her decision, the manager can decide to spend $75,000 on a market research study. Such a study of consumer of consumer preferences will yield either a positive recommendation with probability 0.50 or a negative recommendation with probability 0.50. A positive recommendation by the market research study will indicate that the probability of success for Tim's is 70%; whereas a negative recommendation will indicate that the probability of success for Tim's is 20%.
a) Construct a decision tree of the product manager's decision.
b) Calculate the EMV of the two alternatives and identify the course of action that maximizes EMV.
c) The product manager though it prudent to run a sensitivity analysis on 5 variables:
 The probability of success
 Success Profit
 Failure Profit
 Prob of success if market research indicates launch, and
 Prob of success if market research indicates not to launch.
The following shows the tornado diagram and two of the five sensitivity graphs. What conclusions can you draw from each of these graphs? State a sentence or two for each graph below.

6. Nicklaus Electronics manufactures electronic components used in the computer and space industries. The following analysis is based on the annual rate of return on the market portfolio and the annual rate of return on Nicklaus Electronics stock for the last 36 months. The company wants to calculate the "systematic risk" of its common stock. (It is systematic in the sense that it represents the part of the risk that Nicklaus shares with the market as a whole.) The rate of return Yt in period t on a security is hypothesized to be related to the rate of return mt on a market portfolio by the equation

Yt = a + bmt + et

Here, a is the risk-free rate of return, b is the security's systematic risk, and et is an error term.

a) Using the output below, estimate the systematic risk of the common stock of Nicklaus Electronics.
b) Would you say that Nicklaus stock is a "risky" investment? Why or why not?

Results of multiple regression for Stock_Return

Summary measures
Multiple R 0.8045
R-Square 0.6473
Adj R-Square 0.6369
StErr of Est 0.0549

Source df SS MS F p-value
Explained 1 0.1878 0.1878 62.3944 0.0000
Unexplained 34 0.1023 0.0030

Regression coefficients
Coefficient Std Err t-value p-value
Constant 0.0221 0.0197 1.1242 0.2688
Market_Return 1.4328 0.1814 7.8990 0.0000

4. State the steps that you should follow when conducting a regression analysis.
5. What is a residual in a regression analysis?
6. How many residuals are there in a regression analysis?
7. What information can you discover when analyzing residuals?

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