Case Study 3
According to the capital Asset pricing model (CAPM), the risk associated with a capital asset is proportional to the slope obtaining by regressing the asset’s past returns with the corresponding returns of the average portfolio called the market portfolio. (The return of the market portfolio represents the return earned by the average investor. It is a weighted average of the returns from all the assets in the market). The larger the slope of an asset, the larger is the risk associated with that asset. A of 1.00 represents average risk. The return from an electronics firm’s stock and the corresponding returns for the market portfolio for the past 15 years are given below. Market Return (%)Stock’s Return (%)

1.Carry out the regression and find the for the stock. What is the regression equation?

2.Does the value of the slope indicate that the stock has above average risk? (For the purpose of this case assume that the risk is average if the slope is in the range , below average if it is less than 0.9 and above average if it is more than 1.1).

3.Give a 95% confidence interval for this . Can we say the risk is above average with 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.

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Case Study 1.
A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Due to many causes- vibration, temperature, wear and tear and the like-the length of the pins made by the machines are normally distributed with a mean of 1.012 inches and a standard deviation of...

...CAPMCAPM provides a framework for measuring the systematic risk of an individual security and relate it to the systematic risk of a well-diversified portfolio. The risk of individual securities is measured by β (beta). Thus, the equation for security market line (SML) is:
E(Rj) = Rf + [E(Rm) – Rf] βj
(Equation 1)
Where E(Rj) is the expected return on security j, Rf the risk-free rate of interest, Rm the expected return on the market portfolio and βj the...

...REGRESSION
1. Prediction Equation
2. Sample Slope
SSx= ∑ x2- (∑ x)2/n
SSxy= ∑ xy- ∑ x*∑ y/n
3. Sample Y Intercept
4. Coeff. Of Determination
5. Std. Error of Estimate
6. Standard Error of 0 and
1
7. Test Statistic
8. Confidence Interval of 0 and 1
9. Confidence interval for mean value of Y given x
10. Prediction interval for a randomly chosen value of Y given x
11. Coeff. of Correlation
12....

...Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean...

...
The Capital Asset Pricing Model commonly known as CAPM defines the relationship between risk and the return for individual securities. CAPM was first published by William Sharpe in 1964. CAPM extended “Harry Markowitz’s portfolio theory” to include the notions of specific and systematic risk. CAPM is a very useful tool that has enabled financial analysts or the independent investors to evaluate the risk of a specific investment while...

...Linear Regression deals with the numerical measures to express the relationship between two variables. Relationships between variables can either be strong or weak or even direct or inverse. A few examples may be the amount McDonald’s spends on advertising per month and the amount of total sales in a month. Additionally the amount of study time one puts toward this statistics in comparison to the grades they receive may be analyzed using the...

...Regression Analysis: A Complete Example
This section works out an example that includes all the topics we have discussed so far in this chapter.
A complete example of regression analysis.
PhotoDisc, Inc./Getty Images
A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.
Driving Experience (years) Monthly...

...the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.
The Standard 3 class is where the transition from junior to senior level occurs where...

...BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens....

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