# Cash-and-carry arbitrage

My answer is also 2.21. IMO, the solution to 2008 AM Q6 is mathmatically wrong because e^(A-B) is different from e^A - e^B.

Specifically, 316x[e^(0.05-0.06)x3/12] is different from 316x[e^(0.05x3/12)]-316xe^[(0.06 x3/12)]

I think I have understood and practiced pretty much everything except this. Does anyone have a shortcut to remember the formula for cash and carry and reverse cash and carry? thanks

I just remember SBB for c-and-c and LBL for rev-c-and-c SBB = Short Futures, Buy at spot, borrow cash LBL = Long Futures , Borrow Commodity , Lend it

I thought it was a matter of rounding errors!

bell99 Wrote: ------------------------------------------------------- > I thought it was a matter of rounding errors! It’s a matter of tailing the position by PV of lease costs which should be done from a theoretical landscape.

janakisri Wrote: ------------------------------------------------------- > I just remember SBB for c-and-c and LBL for > rev-c-and-c > > SBB = Short Futures, Buy at spot, borrow cash > LBL = Long Futures , Borrow Commodity , Lend it Thanks for that. I also watched this, it helped me understand even though it doesn’t apply 100% http://www.youtube.com/watch?v=2vT77NE9Bks&feature=related The spreadsheet that goes with this is here: http://www.bionicturtle.com/how-to/video/cash-and-carry-arbitrage-video/

Paraguay Wrote: ------------------------------------------------------- > bell99 Wrote: > -------------------------------------------------- > ----- > > I thought it was a matter of rounding errors! > > It’s a matter of tailing the position by PV of > lease costs which should be done from a > theoretical landscape. Can you explain what is “tailing” ? I am also confused by the “tailed gold” in the solution to EOC Q1C.

I also think 2.19 is wrong. The lease rate, like dividend, could be reinvested. So one unit of commodity at the begining grow to 1*exp(l*t) units at the end. Then the value of this should be timed by the spot price at the end. i.e., 1*exp(l*t)*spot_T. Total gain/loss from lease is: (exp(l*t) -1) * spot_T. Instead of (exp(l*t) -1) * spot_0 the answer used and many people here agreed.

Paraguay, can you help on this?

glacier88 Wrote: ------------------------------------------------------- > Paraguay, can you help on this? It’s a question that has been beat to death. Either the position is tailed by the PV of lease costs such as the gold example or it isn’t such as the exam question. The obvious answer would be it should be “tailed” based on both of the examples. I am not going to get into this one again though.

what in the world is ‘tail’? Anyway I am not going to bother about this. The objective is to pass the exam and not to get 100% score.

I am confused too. Conceptually, cost (interest) & benefit (lease payment) shall be treated/integrated as one transaction rather than 2 separate transactions, and the FAIR future price shall be So x e^[(5%-6%)x0.25] rather than So x [e^(5%x0.25) - e^(6%x0.25)] If not so, are those equations in the text wrong ?

bell99 Wrote: ------------------------------------------------------- > what in the world is ‘tail’? > > Anyway I am not going to bother about this. The > objective is to pass the exam and not to get 100% > score. Tailed according to google is when you subtract out the PV of lease costs exactly like they are doing in the book. You tail the position size. On a side note, we don’t know what the curriculum looked like in 2008, we do know what the curriculum looks like today.

Paraguay Wrote: ------------------------------------------------------- > On a side note, we don’t know what the curriculum > looked like in 2008, we do know what the > curriculum looks like today. I checked 2008 text got from a friend of mine, completely same as 2011.

alta168 Wrote: ------------------------------------------------------- > Paraguay Wrote: > -------------------------------------------------- > ----- > > On a side note, we don’t know what the > curriculum > > looked like in 2008, we do know what the > > curriculum looks like today. > > I checked 2008 text got from a friend of mine, > completely same as 2011. Then I have no idea. Apparently they don’t tail the position and there is room for another \$.002 of arbitrage.

my two cents: 1, Implied by spot price: FP=316*e^[(0.05-0.06)*3/12]=315.21 > F0=313 2, So it’s profitable to: short spot and long future. 3, Profit=315.21-313=2.21 Hope CFAI won’t reject the answer as OP…