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## Statistics

One measure of the risk or volatility of an individual stock is the standard deviation of the total return (capital appreciation plus dividends) over some periods of time. Though the standard deviation is simple to find out, it doesn’t take into account the extent to which the price of a given stock varies as a function of a standard market index, like the S&P 500.

As an outcome, most of the financial analysts prefer to use the other measure of risk referred to as beta. Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock and the independent variable is the total return for the stock market. For this case problem we will utilize the S&P 500 index as the measure of the total return for the stock market, and an estimated regression equation will be developed by using monthly data. The beta for the stock is the slope of the estimated regression equation (b1). The data contained in the file named Beta provides the total return (capital appreciation plus dividends) over 36 months for eight broadly traded common stocks and the S&P 500.

The value of beta for stock market will always be 1; therefore, stocks which tend to increase and drop with the stock market will as well have a beta close to 1. Betas greater than 1 point out that the stock is more volatile than the market and betas less than 1 point out that the stock is less volatile than the market. For ex, if a stock has a beta of 1.4, it is 40% more volatile than the market, and if a stock has a beta of .4, it is 60% less volatile than the market.

Managerial Report:

You have been assigned to examine the risk characteristics of these stocks. Prepare a report that includes however is not limited to the given items.

A) find out descriptive statistics for each stock and the S&P 500. Comment on your results. Which stocks are the most volatile?

B) find out the value of beta for each stock. Which of such stocks would you expect to perform best in an up market? Which would you expect to hold their value best in a down market?

C) Comment on how much of the return for the individual stocks is described by the market.

Applied Statistics, Statistics

• Category:- Applied Statistics
• Reference No.:- M9739
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