# Safety-first rules, comfused

In Notes, Book 1, Page 214. “professor’s notes: Using a measure of two standard deviations places a 95% confidence interval around the expected return. If the client’s minimum allowable return falls at least two standard devations below the expected return(i.e., it falls in the 2.5% lower tail of the distribution), the clients can be 95% confident the minimum allowable return will not be violated.” I think because of one tail distribution, here should be 97.5% confident interval. Any one helps?

2.5% on downside …2.5% on upside …its a two tail distribution not one tail

Your quote answers your own question. It’s a distribution with two tails, 2.5% on each tail, so 95% confidence interval. This is level 1.

mik82 Wrote: ------------------------------------------------------- > Your quote answers your own question. It’s a > distribution with two tails, 2.5% on each tail, so > 95% confidence interval. This is level 1. Why it is two-tail? I think If the client’s minimum allowable return falls more than two standard devations below the expected return, it is a violent. while If the client’s minimum allowable return rise more than two standard devations above the expected return, it is ok. so it is one tail. please point out my misunderstand, thanx a lot!!!

The distribution is two tails, but the advisor is only concerned about the left tail, the negative returns, so the 2.5% in a two tail distribution is 5% or 95% confidence interval.

mik82 Wrote: ------------------------------------------------------- > The distribution is two tails, but the advisor is > only concerned about the left tail, the negative > returns, so the 2.5% in a two tail distribution is > 5% or 95% confidence interval. then why not choose a one tail distribution? becasue it only concerns the left tail.

We are talking about normal distribution here, so two tails.

even if its normal distribution, it is actually 97.5% confidence interval that the minimum allowable return will not falls more than two standard devations below the expected return. is it right?

baifan Wrote: ------------------------------------------------------- > even if its normal distribution, it is actually > 97.5% confidence interval that the minimum > allowable return will not falls more than two > standard devations below the expected return. > > is it right? Technically yes but literally no.

Thanx guys!!!

baifan Wrote: ------------------------------------------------------- > even if its normal distribution, it is actually > 97.5% confidence interval that the minimum > allowable return will not falls more than two > standard devations below the expected return. > > is it right? No. Please go back and read level 1 books about normal distribution.

I’m sorry to ask this L1 question again “If the client’s minimum allowable return falls at least two standard deviations below the expected return(i.e., it falls in the 2.5% lower tail of the distribution), the clients can be 95% confident the minimum allowable return will not be violated.” I think the clients can be 97.5% confident the minimum allowable return will not be violated. --no “interval” here.

mik82 Wrote: ------------------------------------------------------- > > No. Please go back and read level 1 books about > normal distribution. I get through that material, but still miss the point. please explain detailly, thanx!!!

go back - refer to level I – check 2 tailed test for 5% Level of Significance - what it really means… that is what mik82 is referring to.

it is 95% confidence of a one-tailed distribution. Loss is one-sided ( always below mean) . That would be 2-stdev below mean. What you may be confusing is looking at the 95% of a two-tailed distribution which would mean 1-stdev on the negative side( the other 1-stdev or 2.5% is on the upper side )

Hi, guys. This Q is very similar to VAR. For a 2.5% VAR, we use z-value=1.96, which is about 2. For Roy’s Safety-first rule, we also focus on lower tail, which is 2.5% in this case. So, the clients can be 97.5% confident…actually, the clients shall be slightly higher than 97.5% confident the minimum allowable return will not be violated. --I’m 95% confident that the Q is valid.

Hi, guys. I get this one. "it is 95% confidence of a one-tailed distribution. Loss is one-sided ( always below mean) . That would be 2-stdev below mean. " this is the key. Thanx!