# Risk Neutral != Risk Free Rates(!?)

Box spreads are option strategies which return a constant rate.

Risk neutral rates of return are fudge factors used so that derivative valuations give us the 'right' price.

The old joke is funny because it's true:

Want to value an option? See the last price it traded at on Bloomberg

Until now the risk free rate has coincided with the risk neutral rate of return retrieved from box spreads.

But I just calculated the risk neutral rate over all expiries and saw this -

which means if the bid ask spreads were thin enough we could make a small constant arbitrage profit by trading box spreads on options expiring far off in the future.

Specifically we could earn a sure 1.35% from a box spread on options expiring in December 2017 - which is 0.55% more than what you would earn on treasury bills.

These calculations are all based on mid prices, and wouldn't be the prices that you can actually buy and sell at, nevertheless the spread is pretty darn large.

Moreover, as the expiries lengthen, the standard deviation of the box spread returns lower drastically as a ratio to the rates of return.

This is a very unusual occurrence in finance - our estimates seem to get more sure as we peer further into the future!

The morale of then story is that the risk neutral rate does *not* have to equal the risk free rate!

The next step would be to check whether any of these differences are large enough to be truly tradable (spoiler alert - probably not) nevertheless food for thought.

Also I want to see how the Rn curve looks when we add a drop of chance across the term structure.