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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, such as the S&P 500. As a result, most of the financial analysts prefer to use 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 use 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 gives the total return (capital appreciation plus dividends) over 36 months for eight widely traded common stocks and the S&P 500.

The value of beta for the stock market will always be 1; therefore, stocks that tend to rise and fall with the stock market will as well have a beta close to 1. Betas more 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 instance, 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 analyze the risk characteristics of such stocks. Make a report that comprises but 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) Compute 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.

• Reference No.:- M94776

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