BR formula when stepping down

[Angel]

I was discussing the formula for determining one's needed bankroll [-(SD^2/2*hourly win rate)ln(risk of ruin)] recently and was asked if there was a formula if one was willing to step down to a smaller game if one lost half their bankroll. I have seen a couple of estimates for this - most notably I believe Malmuth said you could cut your needed bankroll to 2/3's of the formulaic total if you were willing to step down if you lost a significant portion of your bankroll. But playing with the numbers I came up with [-(SD^2/2*hourly win rate)ln(SQRT risk of ruin)] which calculates a bankroll size of 1/2 the original.

Could someone explain where this formula fails - if in fact it does?