Q2. You collected 500 weeks of data (2500 days total). Based on that you find Tuesday's mean return is 12 bps. Mean return of all days is 2 bps. Stdev across all days is 100 bps. There is no noticeable difference b/w Tuesday stdev vs other weekdays' stdev.question c Q2b. What is the z-score (t-stat) for the difference b/w Tuesday's mean return and other weekdays's mean return? Q2c. What is the stdev for the difference above? What is the 95% Confidence interval?

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Asked Apr 8, 2019
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Q2. You collected 500 weeks of data (2500 days total). Based on that you find Tuesday's mean return is 12 bps. Mean return of all days is 2 bps. Stdev across all days is 100 bps. There is no noticeable difference b/w Tuesday stdev vs other weekdays' stdev.

question c 

Q2b. What is the z-score (t-stat) for the difference b/w Tuesday's mean return and other weekdays's mean return?
 
Q2c. What is the stdev for the difference above? What is the 95% Confidence interval?

 

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Expert Answer

Step 1

Given tuesday mean return = 12bps

Mean return of all days = 2 bps

Standard deviation across all days = 100 bps

Sample size = total number of weeks = 500

There is no noticeable difference in standard deviation between tuesday standard deviation and other days standard deviation. So the distribution of difference in tuesday mean returns and other days mean return will have same sd =100 bps.

Step 2

The formula to calculate the confidence interval is shown below

Mean difference = Tuesday mean returns - Mean return of all days  = 12-2 = 10

Standard deviation = σ = 100

Sample size = n = 500 (number of weeks or tuesdays)

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Step 3

We need to find 95% confidence interval. So α = 1-0.95 = 0.05.

So 1 - α/2 = 1- 0.05/2 = 1 - 0.025 = 0.975.

So we need to look in the ...

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