Commodity Forwards and Futures

[Nikjam]

Hi David,
I have been reading Derivative Markets by McDonald Chapter 6 on Commodity Forwards and Futures.However I am unable to understand lot of the strategies put forth in the pricing of forwards and the cash and carry arbitrage related tables given in the Chapter.Can you please suggest me an alternative that is more simpler wherein I can read these concepts and understand them better? Also my understanding about commodity market is not great.
Thanx.

 

[David Harper CFA FRM]

Hi Nikjam-

I agree with the difficulty of this chapter in regard to the cash & carry.
For the learning XLS I built for our customers (3.1.arbitrage), I used an example from Kolb's Futures, Options & Swaps
http://books.google.com/books?id=mEQhxvTPdtsC&source=gbs_navlinks_s
...because i think Culp's foray into lease rate, frankly, is unnecessarily complicated (and the testability is low). For what it's worth, i think the reading is about 3 things

1. cost of carry (where you can rely on the assigned John Hull) and which reduces to:
forward = spot * EXP[(rate + storage - income/dividend - convenience yield)*time]
and, the point of Culp is really that lease rate = dividend for purposes of COC

2. the uniqueness of the chapter: the discussion of corn, natural gas, oil, etc ... I would definitely read those (e.g., how does seasonality in corn and natural gas manifest)

3. This important and subtle point, that John hull also makes about the risk premium:
Forward = E[future spot]*EXP(risk free rate - discount rate) Hull 5.2, also
i.e., we don't expect the forward to equal the exp future spot price

So...IMO
* cash and carry: I like Kolb. I couldn't either understand it until i worked the problems (that why i deploy learning XLS). But the testability of cash & carry is low (not cost of carry: this will be tested!); i don't think it deserves much of your time...
* cost of carry: use Hull.
* do study the commodity material in the back of reading

hope that helps, David

 

[Nikjam]

Hi David,
Thanx a ton.One more thing what I can deduce from your reply is that I need to focus on Hull for this topic.Should I read the natural gas,gold etc part from McDonald keeping testability into mind or just for the concepts? I am not clear on this.

 

[David Harper CFA FRM]

Sure thing. More for the concepts as GARP is unlikely to test the specific forward curves (e.g., the text has oil in classic backwardation but I think it's now in contango, so you can't test that...).

I think what you want to do here is connect cost of carry with the forward curves and supply/demand, e.g.,

oil needs to be stored yet has a convenience, how does that manifest in forward curve?
corn is seasonal, how does that show up?
gas is seasonal (demand), what does that do to curve?

It's a really timely topic: there is always discussion about, say, what oil contango means and this gives up a framework to hypothesize that contango/backwardation is due to

1. fundamental (cost of carry) factors, or
2. technical factors (supply/demand, futures speculation)

David

 

[frm_daniel]

Hi David,

I refer to your webinar or the study note page 94(Fin mkt & prod) about the McDonald Commodity Forwards. The Cash and carry arbitrage table, where long commodity at Time 0 is calculated as -9.9 (10e^-1%), why it is not simply the spot (So) ie, $10? Also when borrowing at riskless rate, why the calculation for Time 1 is not simply 9.9*e^4%, but showing the formula as 10e^(4%-1%).

Regards,
Daniel

 

[David Harper CFA FRM]

HI Daniel,

That a great observation .... these implement Culp's tables 6.7 & 6.8, so in regard to cash and carry, please note:
At time 0, buy EXP(-lease*time) commodity units; so it's a fraction purchase of < 100% of the spot. In this case, buy @ 9.90 and sell at expected future spot of $10.513 implies return of 6% = LN(10.513/9.90).

And then borrow the same quantity, in this case
borrow $9.90 and repay $10.305 indeed implies borrow at riskless rate: = 4% = LN ($10.301/9.90);
i.e., the leases washes out: borrow Spot*EXP(-lease*T) and repay at Spot*EXP((riskless - lease)*T) implies riskless return

... so i think if you accept the buy commodity is fractional, you'll see the returns hold up. Why is the buy fractional? So that the future expected spot (St) can be netted out and eliminated: gains on the long spot will exactly offset losses on the short forward as (F - St) - St = F.
(the other really trick idea here, IMO, and it's beyond anything testable is the 6% commodity return is the discount rate such that 6% = 5% growth + 1% lease rate; the lease rate is like a dividend so this is much like total shareholder return of 6% = 5% appreciation + 1% dividend).

Finally, i personally find this very interesting but from solely an exam perspective, this part of McDonald (the lease rate impacting the carry arbitrage) is (IMO) not the best use of your time: I just don't see GARP testing it. So far, the more "basic" cost of carry in Hull has been tested (i.e., without the lease rate)....

Hope that helps ... David

 

[sucheta_isi]

David,

In a Backwardation market , the discount in Forward prices relative to the Spot price represents a positive yield for the commodity consumer or the commodity supplier?

Who is the commodity consumer and who is the supplier in this market?