There are plenty of research notes and opinions around the possible outcome of and how best to position for Britain's upcoming EU referendum on Thursday. They vary from quite pessimistic to quite bullish on Sterling Pound and other risks assets. This piece does not intend to add to that crowd. I do not posses any special knowledge or skills to prognosticate a voting outcome. However, with that in mind, here are few points to note.

Firstly, positioning for the referendum is much less of an issue if it is for hedging. You really do not need to worry about picking a direction. It is about taking the position that reduces risk exposure of existing portfolio. The decision is then to design hedges that are cheap. I have written about some options a while back.

However, for a speculator, positioning for the referendum necessarily means picking a direction and hence having an opinion on the outcome of the vote - which is inherently uncertain. (This is also applicable for volatility trading, or anything else - here the direction is on the second order than underlying for vol trading). But even if you do not have a strong opinion on the possible result on Friday, a few consideration can help to form ideas about potentially profitable positioning.

And that mean picking trades based on 1) subjective probability (or expectation) 2) market prices (implied or average market expectation) and 3) opportunity costs.

The first two are pretty intuitive and commonly practiced - basically compares what an investor expects the price distribution to be based on different outcomes, vs. the actual priced-in distribution. This is essentially a relative value analysis in a broad sense (which usually means a pair strategy in the narrow sense).

The third one, i.e. opportunity costs is arguably the most important consideration for decision under uncertainties. In the context of the referendum, let us assume that we have happened to choose to position of short risks. If the outcome is Brexit, our position will be profitable. But if it is not, we will lose on our short positioning. Worse still, if you assume that given the recent rally in risk assets, the upside is limited, then before we square off and initiate a long position, it is already too late. The upside from Bremain is a relief rally for status quo. The market will adjust upwards quickly and find a stable level.

Now consider the reverse. If you are long and it is a Bremain outcome, again we are in luck. However, the opposite outcome is not same as before. A Brexit outcome will cost us initially. However, a Brexit outcome is far more uncertain than a Bremain outcome, and it is very difficult for risk markets to quickly price in all the consequences and find a proper and stable equilibrium very soon. We will have initial drag from our long position, but plenty of time to reverse that and catch the down-drift.

The explicit assumption here is that from current levels, upside in risks assets are not great and market is more likely to find a stable levels on the upside than on the downside relatively quickly. If this assumption is correct, an analysis of opportunity cost tells us we should have a bias for long positioning.

In addition, the outcome of Thursday's vote will surely have a binary impact. I have written previously about how one should think about distribution when facing a binary outcome. If we believe in the assumption on the market dynamics above, along with the assumption of a binary outcome, we should base our estimates of the first point, i.e. subjective probability, on these assumptions to be consistent. These two assumptions gives rise to an asymmetric bi-modal distribution. Such a distribution will imply a thinner tail for upside outcome along with a heavy-tailed downside. Statistically this means on the upside we will have single jump probability, but multiple jumps allowed on the downside.

Practically this means we cannot use a single volatility model to price across the strikes on both sides of the at-the-money level. This also implies there is no realistic meaning of skew or vol-of-vol parameters as under these assumptions. The volatility dynamics are very different on the two sides and a single group of parameters valid across strikes on both sides does not make much sense. We essentially have to think about two sides as two parallel realities and combine them to arrive at a subjective price and then compare this to what the market is quoting.