Reading 36

Is there anyone else out there struggling with the chapter? Better yet, anyone have it down cold? I have been trying to figure this out for hours… (1) I get the gist of Fo=So x e^(r-d)t [Financial Instrument: the future price should be equal to the Spot Price x e ^ (discount minus the dividend yield) x time (2) I also get the fact that for commodities that you cannot store (like electricity), there is little to no chance for arbitrage. Therefore the Expected Spot Price at time T should be the forward rate. Then I hit the darn pencil example and I just lose it (i have trouble grasping commodities). Time Zero - you think a pencil forward is too cheap: (1) Since the FORWARD is deemed to be cheaper, You go LONG on a Pencil Forward (you agree to ‘receive’ a pencil in the future and pay 20 cents from PARTY ‘A’) [ZERO CASH OUT] (2) Then you ‘SHORT’ a pencil from someone (PARTY ‘B’) and agree to pay 10% - THIS IS WHERE I STRUGGLE - I keep thinking - how can you SHORT a pencil? Someone LENDS you a pencil and you do what with it? What do they lend you, the actual pencil or money? [+20 cents in] (3) Then you lend the short sale proceeds at 10% to PARTY 'C"? [-20 cents out] Time 1 (1) You take possession of a pencil from someone at time 1 and pay 20 cents [-20 cents out] (THE FORMULA IS LISTED AS = 0.20 - F(o,1)?) (2) You pay back PARTY ‘B’ [-0.221 cents] (3) You get paid back on the loan to PARTY 'C" from proceeds from the SHORT sale. [+0.221] If no arbitrage exists - profit =0 Then they throw in >Convenience Yield - I don’t get this concept - I don’t get how you ‘lend’ someone corn for example… or what this all means… >Lease Rates (LR = Alpha (discount rate - growth) >Storage Costs BOTTOM LINE - I’ve searched the thread and cant find anything concrete on this. I don’t ever deal with this stuff and cant seem to grasp it. Im sure Volkavv, CSK, et al have this crud down pat… ANYONE HAVE A QUICK OVERVIEW OF WHAT WE SHOULD KNOW AND DO ON THIS STUFF? MUCH APPRECIATED IF YOU DO! Data_Monkey Storage

The pencil example is a little awkward at first… They use it to demonstrate the supply/demand issue with commodities. In this case the commodity is easily produced, available and supply easily meets demands. In this case you can’t arbitrage it by cash and carry because there is no point to carrying it as supply is essentially meeting demand at any point in time and because there is no point to lending it or borrowing it and there is no convenience yield or risk premium (no doubt about the price); the futures curve if there was one is flat.

Essentially it’s a stylized example allowing them to say, this is what happens if all factors in Forward/futures pricing were set to zero.

here is what you need to know as far as storage cost, convinience yield, and lease rate are concerned F = S * e^(r+ storage cost - convinience yield) * T or F = S * e^(r - lease rate) * T What is storage cost? If you would buy actual commodity (and it has to be stored). You would have to physically pay for storage. Now in futures, this implied storage cost becomes a component of the the futures price, hence you add storage. What is convinience yield? Think of it as dividend yield on a stock (its the same concept). If you actually buy a stock, you receive dividends from it, but when you buy futures on a stock you don’t. Similar with commodities if you physically buy a commodity, and it is valuable for you, you receive implicit benefit from holding it (a.k.a. convinience yield). When you buy futures on a stock or a commodity, you neither get your dividends or benefit of convinience yield, hence you deduct the value of convinience yield (or dividend yield if its a stock future) from the futures price. What is lease rate? “Lease rate” is just a term (not to be confused with actual meaning of the lease, since you are not leasing anything here) that just aggregates storage cost and convinience yield into one term, which is called the lease rate. Lease rate = Convinience yield - Storage cost or - Lease rate = Storage cost - Convinience yield So instead of having e^ [r+ (storage cost - convinience yield)] you substitute it with e^ (r - lease rate) When lease rate is higher than risk-free rate, the market is in backwardation. When lease rate is lower that risk-free rate, the market is in cantango. No arbitrage region S * e^(r+ storage cost - convinience yield) * T <= F <= S * e^(r+ storage cost) * T

Thanks Volvovv - that made a ton more sense than the book! So -given the full equation: F = S * e^(r+ storage cost - convenience yield) * T Inputs: S= 100 e = 2.717281 r = 5% t = 6 months (0.5) Storage = ??? (Where do they get this # from?) Convenience Yield ??? = To me this is some arbitrary number - Convenience could be different between the types of commodities as well as the holder of the future - example Convenience Yield for Corn for ADM would be > than that for General Motors (extreme example). Also does convenience yield bounce around due to supply and demand? - not sure where this figure comes from and when and who uses it. DO you only include it if you are shorting/selling a forward and have the commodity in house? Fo =100 * (2.718281)^[(5% + 0 - 0) (.5)] = 102.53 [If market value of the actual F < 102.53 you would buy long corn forward and then sell short corn in the spot market - invest the proceeds from the short sell,. At close, use the payment on the investment to buy the long at 102.53 and then close out the short sale with the actual commodity?] NOW Add in convenience Yield (2%) and Storage Cost (6%): Fo =100 * (2.718281)^[(5% + 6% - 2%) (.5)] = 104.60

it looks like the formula to really know are these: Just plug them with what you know and shoot for partial points! (1) S * e^[(r+ storage cost - convinience yield) * T] <= Fo <=So * e ^ [(r + storage) * T] - if the Futures price falls within this range, there is no arbitrage. (2) Lease Rate = R - 1/t x [ln (F/S)] (3) Basis Risk = the risk that the commodities are not the exact same type/grade

> NOW FLIP IT - Add in convenience Yield (6%) and > Storage Cost (2%): > Fo =100 * (2.718281)^[(5% + 2% - 6%) (.5)] = > 164.81 value of having the commodity (or at lease access > to it in the future - i dont physically own it). > > > It appears that similar Convenience Yield has more > impact on the pricing vs storage costs. you have your math wrong here Fo =100 * (2.718281)^[(5% + 2% - 6%) (.5)] = 100.50 Convinience yield and storage cost, affect forward price in the same way, they are just numbers in e^(…) formula, so 2% storage will have e^(.02) increase effect same as 2% convinience yield will have e^(.02) decrease effect Convinience yield and storage cost are driven by underlying commodities, some are expensive to store and others are not, similiraly holding some commodities may give the holder implicit value for holding (i.e., convinience yield) and others may have no value at all. As far as exam is concerned, the storage cost and convinience yield will be provided. All you need to know is how to plug them in the formula, and how they affect futures price (i.e., increase in storage cost will increase the futures price, etc) Also, you would need to know no arbitrage formula. Lease Rate = R - 1/t x [ln (F/S)] (this one you don’t have to remember, but if you do it certainly won’t hurt; it can be easilly derived from F = S * e^(r - lease rate) * T by taking natural log of both side, ofcourse if you are not math chalenged :slight_smile:

how likely do you think this is for the exam?..i would love to punt this.

It says no calcs I thought. I think this would be tested as a "Pick the formula that best corresponds with a commodity with X as the lease rate Y as the storage cost etc…

If lease rate increase, Futures price Increases or Decreases… Those types of questions i think.

LOL cfacfacfa - as I was writing this post, i used the word PUNT to myself! I thought - man, just give me some bullschiznit partial points and then PUNT! I’ve read and re-read, this crap just isn’t sticking… Then I was destroyed by the end of chapter questions… Fo =100 * (2.718281)^[(5% + 2% - 6%) (.5)] = 100.50

None of the LOS’s in the reading ask you to calculate this stuff. Know the concepts, don’t get stuck up in memorizing the formulas.

What about the arbitrage stuff ? You guys think it’s important ? I do not understand it ???

You have to game the test a little derswap, especially at this point. Read it, try to understand it, but don’t go overboard on it. Very few people are going to walk into the exam with a strong understanding of all the concepts. Take last year for example. I know a few for sure who were on this board that I know going in were probably in a stronger position than I was. Unfortunately they didn’t make it and I did for the simple fact I got a little lucky and the questions that were asked for the most part were in regards to my strong areas. For a large number of people that pass these tests, there is an element of luck.