Compare this value to the sample variance . Are the two values different and – if yes – how do they differ?

Financial econometrics Ex 3
Complete the following set of exercises.
1. From the data provided, select/generate a random sample of 355 companies. From now on, forget about the raw data set, and work only with the companies in this sample.
2. Generate a data series with the same number of observations as the return-data series. Each observation of the new series corresponds to the outcome of a Bernoulli random variable, Y.
The outcome is 1 if the holding-period stock return in the same month is larger than or equal to
0.011 and zero otherwise.
3. Based on your random sample of Bernoulli variables, compute the sample average/sample mean of the outcomes in question 2. above. Is this value an unbiased estimate for the population’s probability of success ? Explain!
4. Compute an unbiased estimate of the population variance of the Bernoulli random variable Y.
Compare this value to the sample variance . Are the two values different and – if yes – how do they differ?
5. Now consider the 355 observations on holding-period returns. Make a histogram that summarizes the distribution of returns in your sample by counting the number of observations in each bin . Let Excel automatically generate the bins.
6. Make a histogram that summarizes the distribution of returns in your sample by counting the number of observations in each bin . Plot the distribution in 25 bins of equal size.
7. For the same 25 bins as in question 6. above, make a histogram that summarizes the distribution of returns in your sample by reporting the proportion of outcomes that fall into each bin.
8. Based on your random sample of holding-period returns, which is assumed to represent the population well, would you be inclined to conclude that returns are normally distributed? Explain

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