How to Calculate Arbitrage: Bid Ask Spread Arbitrage Examples

Question

An unhelpful test prep provider answer has confused me about triangular arbitrage...Can I please double check with someone, which of the below situations is triangular arbitrage possible, and when is it impossible? For an e.g. I'm going to presume the quoted dealer spread is 65-66.

1) the fair market arbitrage quote has to either be nowhere near the dealer spread i.e. dealer = 64-66 and arb spread is 67-68

or 2) have one figure an improvement on the dealer quote and another not an improvement (possibly a worse quote or just the same): dealer = 64-66; arb = 64-65

or 3) completely inside the dealer quote? dealer = 64-66; arb = 64.5-65

I understand that if both arb prices 'straddle' the dealer spread: dealer = 64-66; arb = 63-67, there is no arb opportunity. But is there another option above or elsewhere which is an example of triangular arbitrage not being possible?

mikey · Accepted Answer

Maybe I'm misunderstanding here. Are you referring to 'regular' (2 trades) arbitrage, or triangular (3 trades) arbitrage?

Here is an example and discussion of triangular arbitrage.

The example you're giving seems to be for just 2 parties/trades:

Dealer 64-66, market spread 67-68

Arbitrage opportunity: Buy from dealer at 66, sell at market at 67

Dealer 64-66, market spread 64-65

No arbitrage opportunity

Dealer 64-66, market spread 64.5-65

No arbitrage opportunity

The governing concept behind all this:

The idea is that you need to 'buy low and sell high', but the dealer and market will also, from their perspective, 'buy low and sell high'. If you can find a way to make money by transacting around, then there is an arbitrage opportunity.

So in your example 1, you do two transactions:

Buy from the dealer at their ask (i.e. sell price, i.e. the higher price, because they're 'selling high') of 66.
 	Sell it to the market at their bid (i.e. buy price, i.e. the lower price, because they're 'buying low') of 67.
 	You profit by 1 from the two trades.

cfyay · Answer

Sorry, you're right - this is just regular arbitrage! Apologies for any confusion to you Mikey and anyone reading.

So, just to make sure I've got this right, in my head the rule is: there is only an arb opp if there is some 'price improvement' in the arb or dealer spread for the opposite transaction, i.e. if you can buy cheaper in the market but cannot sell for a better price to the dealer (either the dealer bid is worse or the same as the market bid), then there is no arbitrage; but if you can also sell at a better bid to the dealer, then there is an opp? Opposite of course for selling in the market/buying from the dealer.

And is an 'outside spread' completely outside the dealer spread or can it be straddling one end of the dealer spread range?

Zee Tan · Answer

@cfyay:

So, just to make sure I’ve got this right, in my head the rule is: there is only an arb opp if there is some ‘price improvement’ in the arb or dealer spread for the opposite transaction, i.e. if you can buy cheaper in the market but cannot sell for a better price to the dealer (either the dealer bid is worse or the same as the market bid), then there is no arbitrage; but if you can also sell at a better bid to the dealer, then there is an opp? Opposite of course for selling in the market/buying from the dealer.
Yes - buy from either party to sell to the other. If you profit, then you're profiting from price differences, i.e. arbitrage.

@mikey has got the right idea on how to think about arbitrage.

The outside spread is the 'widest range', the prices at which value-based traders are willing to buy and sell, since value-based traders are the ultimate buy-low-and-sell-high counterparties. So it will be outside the dealer spread.