Forums  > Basics  > Combining different expiries in a futures vs underlying cash and carry arbitrage.  
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Total Posts: 2
Joined: Aug 2019
Posted: 2019-09-20 17:16
Consider these three assets:

- StockA
- StockA NOV19 futures
- StockA DEC19 futures

Say I buy 100 StockA and sell 100 NOV19 futures in an arbitrage.

Current portfolio:

- +100 StockA
- -100 NOV19 futures
- 0 DEC19 futures

Now I spot an arbitrage in StockA vs NOV19 futures. I sell 50 StockA and buy 50 DEC19 futures.

Current portfolio:

- +50 StockA
- -100 NOV19 futures
- +50 DEC19 futures

Now when NOV19 expiry comes, I don't have enough stock to cover my futures position.

How does one handle cash and carry when mixing futures of different expiration dates?

{do just enough to get things done well}


Total Posts: 124
Joined: May 2016
Posted: 2019-09-20 23:26
So you’re assuming something like:

Stock = $101

Nov = $103

Dec = $102

In which case you should just put the risk in the shorter term and more profitable arb position and avoid Dec altogether


Total Posts: 2
Joined: Aug 2019
Posted: 2019-09-21 10:48
That's not quite the scenario I'm imagining. I'm thinking about an HFT context, trying to figure out how HFTs do cash and carry with futures of different expiries.

So my scenario starts with a market that is perfectly in line, say

- StockA @ 100 USD
- StockA NOV19 futures @ 101 USD
- StockA DEC19 futures @ 102 USD

where i assume the cost of carry is 1 USD per month, to keep it simple.

In this case, if momentarily NOV19 futures are trading at 101.2 USD, you can go

- +100 StockA
- -100 NOV19 futures
- 0 DEC19 futures

Then everything goes back in line. A few hours afterwards, DEC19 futures are trading at 101.7, so HFTs go

- +50 StockA
- -100 NOV19 futures
- +50 DEC19 futures

Now when NOV19 expiration date comes, I don't have enough stock.
I assume they just roll half of the NOV19 futures in this case, but I'm wondering if there are other solutions.

This is the kind of scenario I'm considering.

{do just enough to get things done well}


Total Posts: 1126
Joined: Jun 2005
Posted: 2019-09-21 12:52
Given that you keep delta ~ 0 (neglecting tail risk) rolling seems the only solution.

Imagine you lower your arb threshold to zero PnL (= no loss, no gain) for StockA/DEC19 pair and refill StockA upto +100. But then DEC19 is zero again. Which means that after every single maturity your portfolio must be empty!

Rolling can be done with similar arbitrage algorithm, like you do Stock/Fut, just set the goal and "drive" into wanted position. Your arb.threshold and bid-ask shift are those steering parameters to make this happen.


Total Posts: 103
Joined: Apr 2018
Posted: 2019-09-21 14:32
You can short the stock by borrowing it. If you can't find borrows, then it's not really an arbitrage.


Total Posts: 585
Joined: May 2006
Posted: 2019-09-23 03:49

That is some confused thinking.

First of all, most of these single stock futures have zero daily volume and zero open interest. They only 'exist' in some metaphysical sense, as data containers on some server.

Even when you do see some volume and open interest, it is only ever on the front contract. You see a bit of leakage into the second and third contract from people starting to roll early, but that's it.

If you see some numbers that don't add up, it's because you are comparing a liquid contract to an illiquid contract. You won't be able to trade one against the other. Look at the actual orderbooks and try to paper-trade your perceived arbitrage. It won't take long to work out that it isn't actually there.

> Now when NOV19 expiry comes, I don't have enough stock to cover my futures position.

That doesn't matter. Most of these contracts are cash settled. And even if your contract is physically settled, you will only have to buy enough stock at delivery.

Bottom line, there are assets for which it is possible to trade different parts of the curve against each other. But equities aren't one of them.

"There is a SIX am?" -- Arthur
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