hi everyone can somebody explain me how commodity arbitragte works (schweser, book 4, page 67). it says that the investor who does not earn the convenience yield a cash and carry arbirtrage implies taht…future price is lowere than spot plust riskfree rate and storage costs. for the commodity borrower the futures price is greater than the spot price times riskfree rate minus lease rate. whats the difference between the commodity borrower and the investor. don’t understand the roles in this contracts. thanks for your help!!
It is nicely explained in the curriculum.
ok. but still, i am a little confused with the lending rate. in order to obtain the future price in an active lease market i would have the current spot price S0 times riskfree rate minus lease rate times TIME. why do i substract the lease rate from the risk free rate. sorry im totally confused right now. thanks for all your help!
lets put its this way. if the lease rate is greater than the risk free rate, the forward price will be smaller. what does this mean. why do we subtract the lease rate from the risk free rate?
If I own a commodity, I can lease it out to someone and earn lease rate. If I take a long position in a forward contract on same commodity, I cannot earn lease rate. Think of lease rate as dividend on stocks. If you own stocks, you get dividend.
risk free rate is what you spend to borrow money to buy commodities. Lease rate is what you earn when you lend it to a borrower who finds it convenient to have the commodity on hand until he can use it or return it you as part of his operation. So the arb free forward rate is Spot * e^(rf-lease)*T
Risk free rate/Storage Cost are costs, lease rate and/or convenience yield are benefits (negative costs).
alta is correct except for one subtlety convenience yield is really a rather etherous concept…its not something that you can automatically get since you own the commodity…for examply you can lease gold but only jewelers rappers scrooge mcduck etc get a convenience yield for holding gold