Hi @shivanin Setting aside the usual caveat about VaR (ie, VaR confidence is always one-tailed, being only concerned with the loss tail; e.g., 1.645 @ 95% and 2.33 @ 99% under a normal distribution), if it doesn't say or your aren't sure, I'd suggest assuming two-tail because it's the more common significance test. A well-written question should not leave it in doubt. Keep in mind the null must contain the equals sign ("="). So your typical situation is an alternative hypothesis that is "in either direction of the null;" i.e., less than or greater than. Below is an example of a one-sided test (from https://www.bionicturtle.com/forum/threads/p1-t2-317-continuous-distributions-topic-review.7227/ ). My question is explicit, I went out of my way to identify one tailed . But it would be fair game to have written something like the following: "... His hypothesis is that the true hedge fund return is greater than zero .... " and that would be enough to signal that the alternative hypothesis is one-tailed rather than two-tailed (the alternative hypo is usually what you are trying to prove...). I hope that helps!
317.1. For a sample of ten (n = 10) market-neutral hedge funds, analyst Peter finds their sample average monthly excess return to be +0.890% with a sample standard deviation of 1.00%. He wants to conduct a one-tailed test of significance, specifically: his null hypothesis is that the true excess return is equal to, or less than, zero. Here is a snippet of the student's t lookup table:
Which is nearest to his p-value? (bonus: use the p-value in a sentence)
@shivanin Right, i think you are referring to question 2 ("2. Using the prior 12 monthly returns, an analyst estimates the mean monthly return of stock XYZ to be -0.75% with a standard error of 2.70%."). The confidence interval is generally (almost always?) two-sided, although it can be one-sided. It's so common that they don't need to explicitly say two-sided. Thanks!