Forward Prices
- Thread starter peter333
- Start date
Hi Peter,
I can, only b/c this has been a source of much confusion...
our cost of carry model, in most of Hull, gives the forward an *unbiased* estimate of future spot price:
F0 = S0*exp[(r + u - q - convenience)(T)] = E[(St)]
this is just a fundamental pricing framework, as you know. Lots of ink spent trying to fit it to observed forward curves. But, as a simple model, it omits many things. Start with supply/demand which will manifest as investors (market consensus) risk premium.
So, say the model above, after we plug in the values for oil says the forward price (F0) should by $180. Given rate, storage/transport, convenience yield, the current spot of oil "predicts" a no-arbitrage expected future spot of $180. That's the unbiased.
But investors, in their price implied consensus, bid it down to $170. They've added a risk premium. Now it is biased (i.e., by investor risk preference/aversion): the expected future spot is 180 but the forward is 170. This bias is *normal backwardation.* At F0 = 190, the bias would be *normal contango*. The bias you mention underlies notions of normal contango/backwardation (versus contango/backwardation which merely refer to the slope of the observed forward curve)
At the end of Hull, he shift from the unreal world to the real world with F0 = E(St)*[EXP(r-k)T]. If r=k, F0 = E(St) = unbiased. But if k different than r, biased ("real"). Inconveniently, it is hard/impossible to parse out the (k), that's why i've long written that *normal* backwardation/contango cannot be observed (ie., because the k can't be quantified).
For what it's worth, the fallacy, IMO, of interfluidity argument is he omits investor preference, k (or, if you like, supply/demand) so he puts the entire burden of oil contango on the convenience yield. And surely that is most of it, but it's hard to parse out convenience from investor risk.
David
I can, only b/c this has been a source of much confusion...
our cost of carry model, in most of Hull, gives the forward an *unbiased* estimate of future spot price:
F0 = S0*exp[(r + u - q - convenience)(T)] = E[(St)]
this is just a fundamental pricing framework, as you know. Lots of ink spent trying to fit it to observed forward curves. But, as a simple model, it omits many things. Start with supply/demand which will manifest as investors (market consensus) risk premium.
So, say the model above, after we plug in the values for oil says the forward price (F0) should by $180. Given rate, storage/transport, convenience yield, the current spot of oil "predicts" a no-arbitrage expected future spot of $180. That's the unbiased.
But investors, in their price implied consensus, bid it down to $170. They've added a risk premium. Now it is biased (i.e., by investor risk preference/aversion): the expected future spot is 180 but the forward is 170. This bias is *normal backwardation.* At F0 = 190, the bias would be *normal contango*. The bias you mention underlies notions of normal contango/backwardation (versus contango/backwardation which merely refer to the slope of the observed forward curve)
At the end of Hull, he shift from the unreal world to the real world with F0 = E(St)*[EXP(r-k)T]. If r=k, F0 = E(St) = unbiased. But if k different than r, biased ("real"). Inconveniently, it is hard/impossible to parse out the (k), that's why i've long written that *normal* backwardation/contango cannot be observed (ie., because the k can't be quantified).
For what it's worth, the fallacy, IMO, of interfluidity argument is he omits investor preference, k (or, if you like, supply/demand) so he puts the entire burden of oil contango on the convenience yield. And surely that is most of it, but it's hard to parse out convenience from investor risk.
David
I have one more question on Basis. In your slides you use May08 and May09 prices. Now in May08 the spot is 4 and the futures prices is 3.8. The question is what future period should we use i.e. one month futures, one year etc.
I have presumed we use 1 year futures in this example as we compare it to May09 prices. In May09 shouldn't the spot price converge with the futures price?
I have presumed we use 1 year futures in this example as we compare it to May09 prices. In May09 shouldn't the spot price converge with the futures price?
rdcunha,
Great point. That slide is trying to illustrate *unexpected* strengthening/weaking of the basis, and to illustrate *unexpected* basis change, i didn't always show convergence. I should have said, to your point, "the futures contract is longer than one year"; i.e., as of May 08, the purchase is one year and the futures contract is (for illustrative purposes only!) further out beyond one year. That would explain/reconcile their non-convergence (i.e., implies their convergence is still in the future).
But, to your question, if we disgard the unexpected strenghtening/weakening for a moment, if it's May 2008 and the manufacturer has a May 2009 copper purchase to hedge, the obvious hedge is to go long a one-year OTC *forward* contract as it will minimize basis risk (incl. synch the timing). And, yes, under the one-year forward/future, no arbitrage suggests they should converge as May 09 approaches. (in theory, lately cash and futures markets have not necessarily proven been comporting to this trusted theory! There is *always* some basis risk!).
But there is no "right" answer here, on the maturity. For the companies that use the futures market, it is partly of a function of liquidity (what is available?). Very common to "stack and roll," as we see in the Metallgesellshaft Case Study: to stack a bunch of short term (e.g., one month futures) and roll each forward. So, in the copper example, i don't really know copper futures, but maybe for example only 6 months are really liquid so they could be used and rolled over, too.
David
Great point. That slide is trying to illustrate *unexpected* strengthening/weaking of the basis, and to illustrate *unexpected* basis change, i didn't always show convergence. I should have said, to your point, "the futures contract is longer than one year"; i.e., as of May 08, the purchase is one year and the futures contract is (for illustrative purposes only!) further out beyond one year. That would explain/reconcile their non-convergence (i.e., implies their convergence is still in the future).
But, to your question, if we disgard the unexpected strenghtening/weakening for a moment, if it's May 2008 and the manufacturer has a May 2009 copper purchase to hedge, the obvious hedge is to go long a one-year OTC *forward* contract as it will minimize basis risk (incl. synch the timing). And, yes, under the one-year forward/future, no arbitrage suggests they should converge as May 09 approaches. (in theory, lately cash and futures markets have not necessarily proven been comporting to this trusted theory! There is *always* some basis risk!).
But there is no "right" answer here, on the maturity. For the companies that use the futures market, it is partly of a function of liquidity (what is available?). Very common to "stack and roll," as we see in the Metallgesellshaft Case Study: to stack a bunch of short term (e.g., one month futures) and roll each forward. So, in the copper example, i don't really know copper futures, but maybe for example only 6 months are really liquid so they could be used and rolled over, too.
David
Similar threads
- Sticky
