Calculating confident intervals for the expected daily returnsSV=1n−1⋅∑i({DR}i−SM)2

Question

elxanaijm · Accepted Answer

Step 1What you calculated as:SE=SVnis known as the standard-error of your estimate of the mean. It&#039;s basically the standard deviation of your estimator.Let&#039;s assume the true mean were μ. What&#039;s referred to the t-stat is:t=SM−μSEfollows a t-distribution with n−1 degrees of freedom. By the CLT, the distribution of estimator SM converges to the normal distribution but there&#039;s a bit of extra complexity for the t-stat here in that we&#039;re dividing by the square root of our estimate of the variance, which is a random variable too. The t-distribution is basically the standard normal distribution with somewhat fatter tails.Where does the 1.96 etc... come from? A t distributed random variable with greater than approximately 1000 degrees of freedom will lie between -1.96 and 1.96 about 95 percent of the time. This can be seen using the inverse of the t-cdf.Ft−1(0.975,1000)≈1.9623 and Ft−1(0.025,1000)≈−1.9623

Calculating confident intervals for the expected daily returns

Answered question

Answer & Explanation

New Questions in College Statistics