## Descriptive statistics for every stock, Applied Statistics

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Simple Linear Regression

One calculate of the risk or volatility of an individual stock is the standard deviation of the total return (capital appreciation plus dividends) over various periods of time. Although the standard deviation is simple to compute, it does not 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, more financial analysts prefer to use another 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 using monthly data.
You have been assigned to examine the risk characteristics of these stocks. List a report that contains but is not limited to the following items.

a.    Compute descriptive statistics for every stock and the S&P 500. Comment on your results. Which stocks are the most volatile?

b.    Compute the value of beta for every stock. Which of these stocks would you expect to perform best in an up market? Which would you expect to hold their value best in adown market?

c.    Comment on how much of the return for the individual stocks is detailed by the market.

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