 # 2 futures questions

Since the formula is F = S X e(rf rate+storage costs - conv yield) … one would assume the upper bound includes storage cost but not conv yield, and the lower bound includes conv yield but not storage costs, however the lower bound actually includes both (upper does indeed only include storage costs). I have memorized this but don’t find it intuitive, if you are trying to get an upper bound, you would assume no conv yield, would you not then assume no storage cost for lower bound? Also, as interest rates (rf rate) increase, using the formula it obvious futures will increase. If the rate goes higher and futures therefore increases, it would seem like F is increasing greater than S, but this is not the case as basis is not changed by interest rates, only storage costs, transportation costs, and differences in grade. Why does the basis not change with other factors that affect the futures price, like conv yield and interest rates?

no no no please wait hold up mi amigo …the bound only exist since not every producer is able to reap convenience yield …for example a farmer gets the convenience yield of corn, wheat etc but a watch producer does not vice versa for copper…so in this case the range is thus Se(rf rate+storage costs - conv yield)

Right, i just don’t understand why you incorporate both the conv yield + storage in the lower bound but only storage in the upper bound, from a theoretical standpoint. I think in terms of formulas, and i would just rather imagine an “upper bound” as having no conv yield, i.e. its part of the formula but it equals zero, and the same for the lower bound…

you have to pay to store the commodity. - in either case. so e^(rf + storage) in either case. if you do get a Convenience yield - that lowers your lower bound, since you benefit from it. but if you do not - the upper bound is at (rf+storage).

It depends on whether you can get the conv yield. 1) the form in business(such as manufacturer) can 2) the investor can’t. If the investor buy&hold the commodity, he will request a higher yield(rf+storage) since he can’t take the conv yield.

The convenience yield produces a no-arbitrage region rather than a no-arbitrage price. The observed lease rate will depend upon both storage costs and convenience. Also, bid-ask spreads and trading costs will further expand the no-arbitrage region. The difficulty with the convenience yield in practice is that convenience is hard to observe. The concept of the convenience yield serves two purposes. First, it explains patterns in storage—for example, why a commercial user might store a commodity when the average investor will not. Second, it provides an additional parameter to better explain the forward curve. You might object that we can invoke the convenience yield to explain any forward curve, and therefore the concept of the convenience yield is vacuous. While convenience yield can be tautological, it is a meaningful economic concept and it would be just as arbitrary to assume that there is never convenience. Moreover, the upper bound in Equation 15 depends on storage costs but not the convenience yield. Thus, the convenience yield only explains anomalously low forward prices, and only when there is storage. (Volume 5, p. 185). This is a good question. From the text, we can see it links to 1) bid-ask spread and transaction cost. 2) Is the backwardation caused by a higher convenience yield?(correct me if I’m wrong). L3 topics are INDEED highly correlated…