# commodity cash & carry v5 p.203 2b & 2c

Can anyone tell me why they do not multiply the Dec. spot price by the quarterly interest rate (3.00 * 1.015) to get the correct answer as they do in problems #1 & 3? It seems in the other problems they apply an interest rate cost to borrowing the money to buy the current commodity spot price, but in this question they don’t. PLEASE HELP!

I think it is because q2 is a “cash and carry” arbitragy while q1 & q3 are not “cash and carry” arbitragy. In “cash and carry” arbitragy, money is borrowed to purchase at spot price and short at forward price. Storage cost is required here to store the goods purchased.

I am sorry, q1 & q3 are “cash and carry” arbitragy too.

I think the conclusions shall be 2b : The Mar 2005 forward price is fair, no “cash and carry” arbitragy retun (profit). 2c : The Sep 2005 forward price is not fair, there will be a “reverse cash and carry” retun (profit).

I’m going to rephrase your question as “why is there no line ‘borrow @ 6%’ in the table of question 2, to reflect the cost of financing the deal?” The answer is: Because you’re looking for the return on the strategy, and you do not yet care about financing costs. If the return turns out to be above 6% p.a., then the strategy will be profitable because the cost of funding is 6%. You can think of this as calculating the IRR of the cash and carry. When you compute the IRR, the cost of funding should not be included in the cash flows. Also, you can’t even compute a holding period return if you include the financing costs - because the initial investment is zero… Hope this helps.

2b : The Mar 2005 forward price is fair, no “cash and carry” arbitragy retun (profit). The return (near 6%) is almost same as the financing cost 6%, therefore, “cash and carry” makes no arbitragy profit. This means, the Mar 2005 forward price is fair. 2c : The Sep 2005 forward price is not fair, there will be a “reverse cash and carry” retun (profit). The return is negative, therefore, a “reverse cash and carry” arbitragy will make profit. This means, the Sep 2005 forward price is not fair.

About 2c: As is explained on p.206, the mere fact that the “cash and carry” profit is negative does not guarantee that the “reverse c & c” will have a positive benefit. This is due to the fact that there may be a convenience yield, and consequently, instead of a no-arbitrage price, there is a no-arbitrage region. The calculations for 2c show that the forward price is too low to make a positive benefit for the cash and carry strategy. It is possible, however, that it is also too high to make a positive benefit for the reverse cash and carry strategy.

Thank you, that helps. I don’t understand what you mean when you say “you can’t even compute a holding period return if you include the financing costs - because the initial investment is zero”. Seems like the initial investment would be the Dec. spot buy price (\$3). Also, seems to me like the wording on questions 1 vs. 2 (“What is the return on a cash_and_carry” vs. “what is the annualized return on a cash-and-carry”) is the same, so I can’t discern if they asking for the cash flows where borrow cost need to be applied or “IRR” with no borrow cost applied.

If you do include the financing cash flows, then the total cash flows at time 0 will be 0, like for example in the table in 1.B. You then have a net investment of zero (because you are 100% debt financed). About the wording: I do agree that it could be clearer, even though “annualized rate of return” is very clear. I’d expect the wording on the exam clearer.

thank you for the help duck

I think it’s the difference beteween a C&C arbitrage return or simply a C&C return mispriced forward prices can result in risk free arbitrage (from lv.2). If forward price is too high, borrow and buy spot, sell at forward price when contract expires, use it to pay borrowing, and make some risk free profit. hence the emphasis is on the word arbitrage here, whenever taht’s mentioned I think u should include the borrowing. If they simply ask C&C, that’s not the arbitrage strategy, hence no borrowing. the wording on CFAI is MORE THAN CONFUSING. specially the practice problems. in this case they just ignored the term arbitrage all together. Another thing to remember is the metrices used for profits: in C&C arbitrage it will be a CF value, while C&C it will be in % term