# A Dash of Chance

The head of the national psychiatry council in the UK recounted a story about her daughter, who was murdered a few years back.

Her daughter was young-ish and the killer had a history of sexual abuse.

The punchline though, was that, we need to be more open to mental disorders.

The problem is the stigma, suppression, and reticence in coming forward for treatment.

Be openminded for the greater good!

A lot of people can jump on board that train.

Until it comes to paedophilia, and everybody scuffles off again.

We bury dark possibilities deep inside; and admitting to mental instability is akin to opening up that internal pandora's box just a little.

The horrific non-determinism of it all.

So in a tangential turn befitting of this blog, let's take our box spreads example, and ever so lightly open up a pandora's box of probability.

Box spreads tame equity volatility and give you a constant return, which is close to a risk free or risk neutral rate.

Now we'll dink the long call in the box spread just a little; replacing it with a call with a slightly lower strike price.

This minor change turns our box spread into something along the lines of a collar.

We lose a constant amount below the lower strike and profit by a constant amount above the higher strike.

We can roughly estimate of landing in either range by calculating dual delta.

That leaves us to estimate the profit and loss areas in between both strikes.

The return here acts like equity. Usually you would resort to Black Scholes to approximate values.

But...

The areas concerned are usually so small (averaging at 2%) that I will use geometry (I like keeping things non-parametric).

The upshot, is that the collars return 0.14% on average with a standard deviation of about 0.16% - about the same as the box spread results from the previous post.

The collar strategy has a return more or less equal to the risk free rate, even though we have opened the door ever so slightly to more risk.

This also means that the dual delta probabilities used to calculate the returns are consistent with risk neutral probabilities.

Which throws up the next question.

The options we used so far have 6 months to expire.

A longer timeframe will result in a larger risk premium, and make for a more robust check of whether the dual delta probabilities are indeed risk neutral.