# Futures on Commodities, Fixed Income and Equities

Discussion in 'P1.T3. Financial Markets & Products (30%)' started by intuit2k2, Nov 18, 2010.

1. ### intuit2k2New Member

David, I am a bit overwhelmed by all of the different formulas for futures and forward pricing. I see that commodity futures are positively related to cost while fixed income futures deduct the continuous yield to maturity and there are many forms. Do you have a concise consolidated study sheet that would clear things up?

2. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Hi intuit,

We have the 17-page formula sheet for L1.T3 @
http://www.bionicturtle.com/how-to/note/2010-markets-products-formulas/

... which includes Hull's chapter. I don't have new stuff other than that (for upcoming exam anyway)

But, you know, most of it (IMO) is covered by Hull's generalized cost of carry:
F0 = S0*EXP[(riskfree rate + storage - dividend/income yield - convenience yield)*T]

David

3. ### intuit2k2New Member

David: thanks for the prompt response. With regards to the generalized formula F = Se^(rf + storage - dividend yield - convenience yield)*T.

Risk Free rate is applicable to all futures. Storage costs are applicable only to commodities, dividend yield only applies to Coupon paying bonds and equities while convenience yield only applies to commodities)

Now I am confused as to the difference between Storage and convenience yield. Storage costs are the costs that the buyer of the futures would have needed to incur in order to hold the spot - I understand why thats added since this should increase the price of the future relative to spot). Convenience Yield from what I understand is a function of the commodity futures curve. Please correct me If I am wrong.

Will the convenience yield be given to us or would we ever have to calculate and if so how?

4. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Hi intuit,

Excellent summary. While my COC generalizes, you have rightly parsed the investment (dividend) versus consumption commodity (storage, convenience, maybe income) factors .

Convenience has, somewhere, been called "negative storage." Take oil (e.g.). Storage cost, as you say, is a burden on the oil (spot commodity) owner, a cost the futures holder forgoes but must pay for in a way similar to, when buying retail, we must pay the wholesaler for additional costs. Convenience is just the inversion but intangible; convenience is the intangible sibling of tangible dividend/income. Maybe, as spot owner of the oil, you enjoy the "optionality" of holding onto oil (ready to consume if you need it). Convenience yield gives a number to this benefit (negative storage) that is economically like a dividend but not explicit/cash.

Re: "Convenience Yield from what I understand is a function of the commodity futures curve. "
This is true. Precisely b/c the convenience yield tends to unobserved (unlike the others), it tends to be assumed and "solved for" as the plug variable. In the formula, we observe F0 and the others, so this approach is solving for the all variables except convenience yield. Note that still treats convenience as economically identical to dividend/income and therefore, negative storage.

Re: Will the convenience yield be given to us or would we ever have to calculate and if so how?
If you focus on the formula, it is just another factor … it tends to be treated as such ….

David