Cash and Carry

Hey guys, More commodity stuff I am struggling on…sorry but this stuff is a pain. In CFAI volume 5 page 203 question 2b I cant get my head around the answer. They ask you to do a cash and carry including storage costs. However, in the solution they show no borrowing and thus assume you are simply buying the spot with cash. So in the solution they have that you buy spot at $3 store it at .03 and sell the forward at 3.075. In the end you have 3.045 (3.075-.03) for a return of 1.5% (3.045/3). Isn’t the whole point of cash and carry that you borrow to buy the spot. With a rate of 1.5% you would borrow $3 and owe $3.045. Storage costs cancel since you have to pay them, however you would receive this amount from the lender. Thus you sell the commodity from the future at $3.075 and pay $3.045 for a return of .03 which is a return of 1% (.03/3). Am I completely missing something here? Thanks

even in your case - you borrowed 3, need to pay 3.045. so you are paying .045 on the 3$ which is 1.5%… the difference between 3.075 and 3.045 is the 0.03 (storage) - which is what you seem to be regarding the profit from the deal. On the borrow side - borrowed 3, need to pay 3.045 (1.5%) on the sell side - 3.075 sold, pay the 0.03 storage – still pay 3.045 so 3.045/3 - 1 = 1.5%…

Isn’t the whole point of a cash and carry that you borrow the initial cash? If so then you would borrow $3 at 1.5%, buy the commodity at $3, and short the forward at 3.075. Net cash flow is 0 At expiry, you deliver the commodity against the forward 3.075, pay storage costs of .03, and pay off the loan of 3.045. Net cash flow is 0. Thus, you will have earned 0 return. In fact the future price seems to me to be at the no arb price (ignoring convenience yield) 3e^(.015+(.03/3)) = 3.075 I don’t get it why they exclude the borrowing.

with cash and carry, at the no-arb price - your rate of return is the risk free rate of 1.5%. 3.045 is what you paid back, 3 is what you borrowed - so 1.5%. if you had a higher futures price - you get more than the risk free rate.

Sorry to keep bugging you, but your logic only seems to make sense to me if you do not borrow. If you borrow you pay 1.5%. With the future you gain 1.5%…thus you earn net 0%. Without borrowing, then I see you could earn the 1.5% buy simply buying the spot and selling the forward.

the idea is if the future cost = what it is supposed to be - you can earn no more than the risk free rate… so the cash+carry=Future cost - no gain/loss in the transaction. any gain/loss can only happen if your future cost > what is predicted by the So*e^(rt+x) is - then you get more than the risk free rate by using the future with the cash and carry option. If it is less than the future cost - you do a reverse cash and carry - and make money in that way.

OK yes that makes sense. I keep focusing on the fact that it was $0 cash flows at time 0 and $0 at expiry, which thus made me think 0 return. Also, what can be useful to people when they come across this question (found this by digging through the boards): For question 2b and 2c they do not use borrowing and for question 3 they do use borrowing. The reason is that in 2b and 2c they asked for an annualized return. You cannot calculate an annualized return when you include borrowing costs because your initial cost is $0, thus you do not include borrowing. In question 3 they asked what the arbitrage profit would be. Here you would use the borrowing rate. From,979149,983151#msg-983151: If you are calculating arbitrage profits, then consider the borrowing/lending costs. If calculating annualized rates of return, do not consider borrowing/Lending costs.