Compute an unbiased estimate of the population variance of the Bernoulli random variable Y. Compare this value to the sample variance (i.e. the descriptive/summary statistic discussed in Appendix A). 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 (i.e. for the probability that returns are larger than or equal
to 0.011)? Explain!
4. Compute an unbiased estimate of the population variance of the Bernoulli random variable Y.
Compare this value to the sample variance (i.e. the descriptive/summary statistic discussed in
Appendix A). 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 (i.e. frequency). 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 (i.e. frequency). 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