I'm new here, not sure if this is the forum I need to pose this question to, if not i'd appreciate being pointed in the right direction.

I've been working on the possibility of adjusting U.S. equity option prices for beta (or another measure of systemic risk) for a while know. I've run into this paper by Jin-Chuan Duan and Jason Wei from 2006 (https://www.fdic.gov/bank/analytical/cfr/2006/apr/Duan_paper.pdf). The problem I run into is with their measure of systematic risk to total risk. I am using a shorter rolling window as they did in their paper (90 days vs 1 yr).

The authors define the systemic risk portion of total risk as (Beta^2*Var(market))/Var(equity). I often find the amount of systemic risk is above 1 in my data set, in there examples I do not see any instance where they ran into this.

The authors use this method instead of beta because (as quoted from text):

"The fact that beta is not a good measure of systematic risk for our purpose is not surprising.
A higher beta doesn’t always mean that the systematic risk accounts for most of the total
risk. By the same token, equal betas doesn’t mean equal systematic risk proportions. This
point can be illustrated by a simple example. Suppose the market volatility is ?m = 0.2 and
there are two stocks, A and B, with ?A = 0.4 and ?B = 0.5. If the stocks’ correlations with
the market are ?A = 0.75 and ?B = 0.60, then the two stocks will have the same beta, 1.50,
yet very different systematic risk proportions, 0.563 versus 0.360."

My question(s) to member of this board,

1) Do you agree with this method of measuring systemic risk?

1a) If no, how would you measure systemic risk?

2) Are you aware of any other discussion/writing/text/examples of adjusting option pricing for systemic risk regardless of how systemic risk is measured?

3) Can you offer any insight to why a shorter rolling window of measuring beta would not result in similar results as a 1 yr rolling window?