Netting factor

[Kaiser]

Hi,

Page 65, R46.P2.T6. Gregory Notes it says that the netting factor is given by:

netting factor = NF = sqrt(n + n*(n-1)*rho-bar)/n

While I see that if rho-bar = 1 (no netting benefit) then NF = 100% and of rho-bar=0, then NF = 1/ sqrt (n), I do not see how NF can be 0% with perfect negative correlation rho-bar = -1.

Knowing that "Negative Correlation between MtM values --> High benefit", should we expect NF = 0 if rho-bar = -1 (That would assume that the max benefit is reached when rho-bar= -1) ? This would only be the case if n - n*(n-1) = 0 (hence n = o or n=2).

Rgds,

 

[David Harper CFA FRM]

Hi @Kaiser Good observation, makes sense (candidly, I totally missed it). Gregory has an appendix wherein he clarifies that, in this case of a multivariate normal distribution, the effective lower bound on the correlation, ρ, is -1/(n-1). That is "The maximum negative correlation is bounded by ρ ≥ -1/(n-1) and we therefore obtain: EE[NS]/EE[NN] = sqrt[n - n*(n-1)/(n-1)]/n = 0%." I have attached his appendix, please see 8-E on page 6. Thank you!

 

[Kaiser]

Thanks vm for the confirmation David. Makes sense with this lower bound.

Rgds,