Shortfall risk - Normality assumption?

CFA Level III
#1

If a portfolio has bonds with embedded options - will a Shortfall risk measure work?

I want to know if Shortfall risk needs the normality assumption

#2

short fall risk appplies Roy’s Safety ratio right?

Roy’s ratio involves standard deviation, therefore it assumes normality.

#3

Yes, shortfall risk will work. It does not assume normal distriburtion of returns.

Disadvantages of shortfall risk are:

  1. Does not account of magnitude of loss in dollar terms

  2. Not as commonly used as std. dev., thus less familiarity

#4

ShortFall risk does not assume normal distribution. Only VAR calculated using the Analytical method required Normal Distribution. VAR by itself too does not require normality. right?

Drawback of both VAR and SF measure:

Do not provide the magnitude of losses.

#5

Thanks guys

#6

We are saying that shortfall risk doesn’t assume normality of distributions but the curriculum says that SF risk applies Roy Safety First which makes :

Roy Safety First = (Rp - Rl) / Std dev.

Can someone explain me why with a std dev we still don’t have normality distribution?

My answer is that Shortfall risk doesn’t assume normality of distribution in the event we only intend SF risk with a more general rule that is :

Shortfall Risk = Potential loss / Portfolio Value

But Roy Safety First sounds like normal distribution-driven.

Any thoughts?

thanks

#7

I agree with passme

Whenever you use standard deviation you require normal distribution as an assumption in order to draw valid conclusions.

#8

Here is why you guys don’t agree I think.

Shortfall risk does not assume normal distribution. Shortfall risk is simply defined as “the risk that portfolio value will fall below some minimum acceptable level during a stated time horizon.”

Y ou DON’T HAVE to use standard deviation to solve it. You can just look at the historical distribution of returns on a graph, and look how much probably there is to fall below your targeted return for example.

Of course, if you use standard deviation to solve shortfall risk , then you have to wonder if normality really is a relevant assumption. But this issue i s not inherent to shortfall risk. It’s just due to the method you chose.

#9

It’s consistent with my reasoning as well…merci!!