# Shortfall risk constraint

CFAI 2013 paper Q1.

Shortfall risk of no lower than –10% in any one year = equal to nominal pre-tax expected return minus two times standard deviation

I understand the two-standard-deviation approach resulting in 2 but can’t understand the intuition behind this. Could someone please explain.

return minus 2 * std deviation = left tail of distribution - and the upper limit of that left tail = -10%.

Thanks Cpk123. Howver i still dont get it/ even the intuition of it. Which reading is this?? so that i can re-look at this.

you do not want to run the risk of falling below 2 standard deviations.

read the chapters in order to see where this is. You are unlikely to find this in any one chapter (reading). remember you could get a question in Individual IPS that deals with something from the RIsk Management or Asset Allocation chapters. there is a gradual build up of material in Level III - and the material may either be tested in isolation, in conjunction with some other topic OR not at all.

this is linked to the use of a Safety First concept, if I remember right. (and possibly in the asset allocation chapter).

tjhanks once again CPK123

Confused where this formula came from as well. How do you determine from the question that you don’t want the return to fall below 2, instead of 1 or 3, standard deviations?

Is it because the expected standard deviations of x, y and z are all around 10%?

Thanks.

It means 90% of a normal distribution falls within 2 standard deviations.

Shortfall risk is mean - 1.96 SD, which is 5% that the return will fall short by this, or more than that amount.

Thanks, what in the question prompts you to know you want 90% / 2 standard deviations as opposed to other amounts? I need it broken down as basic as possible haha.

5% shortfall is the standard, if your portfolio falls outside 2 standard deviations, then there is significant shortfall risk, and you adjust accordingly.

3 standard deviations is too conservative, and will likely reject a lot of options, 1 standard deviation is too risky, as it may wall fall below the 1 standard deviation frequently.

Gotcha, I was thrown because I used roys safety first ratio to answer this question and I felt pretty good that I had approached it right. I realize it’s similar concepts but not sure if graders see it same way.

Roys SFR is nothing more than that, a ratio. It’s an ordinal rank, and does not tell you whether you should approach the investment or not.

It’s better to measure shortfall decision making using the above, and to rank shortfall riskiness between several options using RSFR.

And this question was the latter (choosing best amongst 3 options) hence my confusion. Thanks for explanations.

I haven’t seen the question, but if it were an MCQ, then RSFR would be the obvious choice.