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. 0 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 (%) 16. 0221. 05 12.
1717. 25 11. 4813.
1 17. 6218. 23 20. 0121. 52 1413. 26 13. 2215. 84 17.
7922. 18 15. 4616. 26 8.
095. 64 1110. 55 18.
5217. 86 14. 0512.
75 8. 799. 13 11.
613. 87 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.
—————————————— 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 0. 018 inch.
The customer will buy only those pins with lengths in the interval inch. In other words, the customer wants the length to be 1. 00 inch but will accept up to 0.
02 inch deviation on either side. This 0. 02 inch is known as the tolerance. . What percentage of the pins will be acceptable to the consumer? In order to improve percentage accepted, the production manager and the engineers discuss adjusting the population mean and the standard deviation of the length of the pins. 2. If the lathe can be adjusted to have the mean of the lengths to any desired value, what should it be adjusted to? why?. 3.
Suppose the mean cannot be adjusted, but the standard deviation can be reduced. What maximum value of the standard deviation would make 90% of the parts acceptable to the consumer? Assume the mean to be 1. 012) 4.
Repeat Question 3, with 95% and 99% of the pins acceptable. 5. In Practice, which one do you think is easy to adjust the mean or the standard deviation? Why? The production manager then considers the cost involved. The cost of resetting the machine to adjust the population mean involves the engineers’ time and the cost of the production time lost. The cost of reducing the population standard deviation involves, in addition to these costs, the cost of overhauling the machine and reengineering the process. .
Assume it costs $150 to decrease the standard deviation by inch. Find the cost of reducing the standard deviation to the values found in Questions 3 and 4. 7. Now assume that the mean has been adjusted to the best value found in Question 2 at a cost of $80. Calculate the reduction in standard deviation necessary to have 90%, 95% and 99% of the parts acceptable.
Calculate the respective costs, as in Question 6. 8. Based on your answers to Questions 6 and 7, what are your recommended mean and standard deviation?