Tom, thanks. Most of the work in the portfolio optimization space was done on asset classes where the word “risk” is used interchangeable with volatility. Anyone who owned mortgage backed securities in 2008 found out that risk and volatility are two different creatures. You can often measure volatility historically but the risk of being wiped out is something that can often never be seen in backtests. I assume that most if not all of the portfolio optimization strategies that you mentioned aim to minimize volatility or to minimize the Sharpe or equivalent. That’s fine as far as it goes. But buying the XIV ETN has the additional ‘risk’ of going to zero that almost no other asset class has because if the VIX spikes by 80% or more within one day then XIV will terminate. The VIX has spiked by far more on Black Monday and I have to assume that it will happen again at some point in the future. Therefore it seems prudent to add additional measures of safety such as position sizing to limit the maximum loss, and only buying XIV when the ‘insurance premium’ is good enough to compensate for the risk (as Tom C pointed out). My question is if the maximum position size for the wipeout risk can be mathematically estimated or should I use a rule of thumb such as 5%. Rules of thumb are generally convenient and often approximately right but sometimes they can be totally off.