Relative volatility and cat tax

I was thinking in the weekend a bit about how to measure volatility relative to median feed price (which is used when you convert HBD to HIVE). This would give information on when to convert HBD to HIVE as opposed to using the market.

Volatility is defined as the variance which is in terms of mean sqrt(E( (X-E(X))^2)) with X the random variable. Substituting the E(X) by the median feed price will give you something like volatility relative to the median feed price. Just to illustrate this see the graph below:

Here the red line is median feed price, the blue line is close price for the internal market and the bars are the relative volatility on a day scale. When the close prices move close to the red line the relative volatility becomes smaller.

Note, that this volatility in a sense measures distance to the median feed price. This means that it doesn't care if the close is above the median feed price or below. Hence, it usefulness as an indicator when to convert HBD to HIVE is limited.

Anyway, enough complicated words. Here is cat tax: