# Market neutral strategy with quarterly futures and perpetual swaps?

## What is a "perpetual swap"?

• In cryptocurrency exchanges, there is a financial product called "perpetual swap". (It is also called as "perpetual futures" or "perpetual contracts" as well)
• It is a kind of futures, except the fact that it does not have a delivery date. That is why it is "perpetual".
• To make the perpetual swap follow the price of that of spot market, we have "funding rate", which is an exchange of interest between long side and short side based on how much futures price deviates from that of spot market. For more detailed explanation, you can refer to Bitmex's information page.

## Can I achieve 'market neutrality' with perpetual swaps and quarterly futures?

• If I buy 1 BTC from a spot market and short it in a perpetual swap market, my position to BTC is neutral because the 1 BTC long and 1 BTC short cancel out. Can I do the same thing with quarterly futures (instead of spot) and perpetual swap?
• The first problem that came to my mind was that the basis between quarterly futures and that of perpetual futures will gets smaller as time passes by. And at the maturity date of the quarterly futures, the basis would be the smallest. (The assumption is that the price of perpetual futures closely follows that of spot.) So if I long quarterly futures, the loss from quarterly futures' long position seems to make it impossible to have 'market neutrality'. One example is provided below.
• Is there a way to be neutral to market by long quarterly futures (instead of spot) and shorting perpetual swap? The reason that I would like to short perpetual swaps is that if you long perpetual swaps, you usually need to pay the funding fee, which is expensive.
• Why would the Futures go down in price as time goes by? With constant interest rates the Futures price is given by $F(t,T)=e^{-r(T-t)}\mathbb{E}^{\mathbb{Q}}[S(T)]$. Given a constant spot, this increases with time. In Black-Scholes $\mathbb{E}^{\mathbb{Q}}[S(T)]=e^{r(T-t)+\frac{1}{2}\sigma^2(T-t)}S(t)$, so the Futures price is $F(t,T)=e^{\frac{1}{2}\sigma^2(T-t)}S(t)$, which also increases with time. So I have a hard time seeing why the Futures price should decrease with time. – mmencke May 2 at 11:51
• The rate of increase on a long Futures should be the same as the interest paid on a short perpetual swap - otherwise you can earn the interest rate differential "for free". But remember that there are transaction costs involved in roll-over of the Futures. – mmencke May 2 at 11:53
• @mmencke.The reason that the price of futures goes down is pretty simple. Speculators are "willing to pay more for a commodity to be received at some point in the future than the actual expected price of the commodity at that future point. This may be due to people's desire to pay a premium to have the commodity in the future rather than paying the costs of storage and carry costs of buying the commodity today. You can refer to it more in the contango page of wikipedia. – Eiffelbear May 2 at 12:51
• @mmencke To put it simply, in normal market situation, which is contango, the future price is higher than that of spot. However, as the maturity of the futures approach, the spot price and futures price converge and the futures are cleared by a clearing house at the exactly same price with that of spot. – Eiffelbear May 2 at 12:54
• @mmencke To put it more precisely, the basis will decrease as the maturity gets closer. I edited my question as well. Sorry for the confusion. – Eiffelbear May 2 at 12:54

Recall that the daily pnl for a CFD is $$\Delta S_{t_i} - r S_{t_{i-1}} \Delta t$$ and for a tailed future is $$e^{-r(T-t_i)} \Delta F_{t_i}$$ where $$\Delta F_{t_i} = e^{r(T-t_i)}S_{t_i} - e^{r(T-t_{i-1})}S_{t_{i-1}}$$ and so the pnl is $$S_{t_i} - e^{r\Delta t}S_{t_{i-1}} \approx S_{t_i} - S_{t_{i-1}} - r S_{t_{i-1}} \Delta t$$
So a dynamic portfolio consisting of $$e^{-r(T-t_i)}$$ futures contracts and 1 CFD hedges out.
• A perpetual swap is not just $\Delta S_t$ it includes a cost of carry which you are missing. – river_rat May 3 at 6:51