Using daily and monthly returns data for the equal- and value-weighted CRSP market indexes

(VWRETD and EWRETD), perform the following statistical analysis. Note that some stocks do

not have complete return histories, so be sure to use only valid observations for the entire 1962 to

2022 sample period. Also, for subsample analysis, split the available observations into equal

subsamples.

1. Compute the sample mean p, standard deviation o, and first-order autocorrelation

coefficient p(1) for daily simple returns over the entire sample period for the two

indices. Split the sample into four equal subperiods and compute the same statistics

each sub-period - are they stable over time?

2. Compute the sample mean p, standard deviation a, and first-order autocorrelation

coefficient p(1)dr continuously compounded daily returns over the entire sample

period, and for each of the four equal sub periods. Compare these to the results for

simple returns-

can continuous compounding change interences substantially?

3. Plot histograms of daily simple returns for VWRETD and EWRETD over the entire

sample period. Plot another histogram of the normal distribution with mean and

variance equal to the sample mean and variance of the returns plotted in the first

histograms, Do daily simple returns look approximately normal? Which looks closer

to normal: VWRETD or EWRETD? Perform the same analysis for continuously

compounded daily retums and compare these results to those for simple returns.

4. Using daily simple returns for the entire sample period, construct 994 confidence

intervals for u for the two series under consideration, Construct the 999 confidence

intervals in cach of the four subperiods-

- do they shift a great deal?

Compute the skewness, kurtosis, and studentized range of daily simple returns for the

two series over the entire sample period and in each of the 4 subperiods. Which of the

estimates are statistically dilferent from the corresponding statistics of a normal

random variable at the 5% level? For these two series, pertorm the same calculation

using monthly data. What do you conclude about the normality of these return series.

and why?