You collected 10 years of daily data. Based on that you find first trading day of each month 's average return is 50 bps. Mean return for all days is 4 bps. Stdev across all days is 100 bps. Stdev for first day of each month only is 125 bps. a. What is the mean return for trading days other than first day of the month? b. Take the difference in sample mean for first day vs. other days. This is your point estimate for the difference b/w two types of days. What is that point estimate? What is stdev for the point estimate? c. What is the probability of observing the point estimate above under the null hypothesis that the true difference is zero (this is known as p-value)? d. What is the 95% Confidence interval for the point estimate? At 95% confidence, should you reject or accept that first days’ mean return is not different from other days of the month?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
You collected 10 years of daily data. Based on that you find first trading day of each month 's average return is 50 bps. Mean return for all days is 4 bps. Stdev across all days is 100 bps. Stdev for first day of each month only is 125 bps.
a. What is the mean return for trading days other than first day of the month?
b. Take the difference in sample mean for first day vs. other days. This is your point estimate for the difference b/w two types of days. What is that point estimate? What is stdev for the point estimate?
c. What is the probability of observing the point estimate above under the null hypothesis that the true difference is zero (this is known as p-value)?
d. What is the 95% Confidence interval for the point estimate? At 95% confidence, should you reject or accept that first days’ mean return is not different from other days of the month?
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