# shortfall risk

shortfall risk = exp.return - 2 x st.dev, I know the formula, but regarding “the concept behind”: + if exp.return - 1.65% = return that my portfolio will experience (or lower) with 5% probability + and exp.return - 2.33% = return that my portfolio will experience (or lower) with 1% probability what is exactly shortfall risk? is it some kind of VaR figure? thx

(sorry, I mean - 1.65 x st.dev ; and - 2.33 x st.dev)

yeah. shortfall risk is the risk that the portfolio won’t meet a certain required return.

thx but what is the purpose of substracting 2 x st.dev? get some “probabilistic” concept?

subtracting 2 standard deviations is considered by many to be a “worst-case scenario” should the markets go against you. You can illustrate to the client what the “worst case” would be. It was covered in Schweser.

Shortfall risk is a “two-tail” concept, the Z value for .025 level of significance is 1.96, you have .025 on both sides, thus you say with 95% confidence the return will be within 1.96 std (you round up and just use 2) of the mean.

volkovv Wrote: ------------------------------------------------------- > Shortfall risk is a “two-tail” concept, the Z > value for .025 level of significance is 1.96, you > have .025 on both sides, thus you say with 95% > confidence the return will be within 1.96 std (you > round up and just use 2) of the mean. i always thought short fall is one-tail concept

I think a one-tail concept is always a two-tail concept, it only depends if you only care about the % to the left… So, in this case, shortfall risk is the minimum return that you will get with 97.5% confidence, right? thx

Isn’t a two-tailed test whenever you have “NOT EQUAL TO” in the null hypothesis? for example: Ho = Sample Mean not equal to 0. And a one-tailed test is the probably of being <= to some number or >= to some number? could be wrong but this is what I remember from my L1 days… again, my memory ain’t the best and haven’t covered this material in a while. Pathetic because I should know this lol

you will use different z values for 95% for 1 vs 2 tailed tests, that is the diff

yes, agree, but I mean that the value that you will get for a 1 tailed at 97.5% will be the same the one you will get for a 2 tailed at 95%

hala, that is correct

hala_madrid Wrote: ------------------------------------------------------- > I think a one-tail concept is always a two-tail > concept, it only depends if you only care about > the % to the left… > > So, in this case, shortfall risk is the minimum > return that you will get with 97.5% confidence, > right? > > thx Yeah, you are as liley to experience positive surprise (+2 std from the mean) as you are to experience possibility of shortfall (-2 std from the mean). The area under the bell curve between -2 std and +2 std region, covers 95%, and corresponding Z value at 2 std is 1.96, So if you add the 95% region and positive surprise, then you can conclude that you are 97.5 confident that you won’t expirience shortfall risk. You can also say that theres is 95% chance that you won’t experince an extreme event (as measured by 2 std), including both positive surprise and shortfall.

that looks look like the formula of VaR to me, isn’t shortfall risk the probability of not achieving some specified return target?