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Beta Using Regression Equation

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Think about the risks inherent in your Ficticious Company and how to quantify these risks. Download the data provided and calculate the measure of risk for this company (defined as Beta in the Capital Asset Pricing Model - CAPM) and explain why this calculation is a measure of risk. Discuss when this type of calculation is appropriate, and when the coefficient of variation is an appropriate measure of risk.

The following website might be helpful: Revisiting the Capital Asset Pricing Model http://www.stanford.edu/~wfsharpe/art/djam/djam.htm

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Explain why beta is a measure of risk.  Discuss when this type of calculatin is appropriate, and when the coefficient of variation is an appropriate measure of risk.

In finance risk is defined as the chance that something other than what is expected occurs?that is, variability of returns. When we examine how risky a single investment is by itself, we are examining stand-alone risk; when we examine how risky an investment is when it is combined in a portfolio with other investments, we are examining portfolio risk.

"Measuring Stand-Alone Risk: The Standard Deviation?measures the tightness, or variability, of a set of outcomes?that is, a probability distribution; the tighter the distribution, the less the variability of the outcomes, and the less risk associated with the event; as a result, standard deviation is a measure of risk for a single investment? that is an investment held by itself (alone).
Because standard deviation measures variation, which is associated with risk, we generally say that an investment with a lower standard deviation is considered less risky than an ...

Solution Summary

The solution calculates beta using regression analysis for the data provided. It also discusses why beta is a measure of risk and when this type of calculatin is appropriate, and when the coefficient of variation is an appropriate measure of risk.

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Regression Analysis

A life insurance company wishes to examine the relationship between the amount of life insurance held by a family and family income. From a random sample of 20 households, the company collected the data in the file insur.xls. The data are in thousands of dollars.

(a) Estimate a linear relationship between life insurance (Y) and income (X).
(b) Discuss the relationship you estimated in (a). In particular:

i. What is your estimate of the resulting change in the amount of life insurance when income increases by $1000?

ii. What is the standard error of the estimate in (i), and how do you use this standard error for interval estimation and hypothesis testing?

iii. One member of the management board claims that for every $1000 increase in income, the amount of life insurance held will go up by $5000. Choose an alternative hypothesis and explain your choice. Does your estimated relationship support this claim? Use a 5 percent significance level.

(c) Test the hypothesis that as income increases the amount of life insurance increase by the same amount. That is, test the hypothesis that the slope of the relationship is 1.

(d) Predict the amount of life insurance held by a family with an income of $100,000.

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