convenience yield Vs lease rate

I was doing a recap of basic concepts in commodity fwds and futures. Perhaps it is too basic… Do you agree with this? a. convenience yield = non-monetary benefit of holding a commodity b. lease rate = monetary benefit = return you would get if you lend the commodity c. Fwd = Spot x EXP [(RFR + Stor.Costs - Conv.Yield - Lease.Rate) x T] d. Arbitrage (with convenience yield): + fwd can not be lower than = Spot x EXP [(RFR + Stor.Costs - Conv.Yield) x T] = “xxx” becaue, if not, we can enter into a fwd contract to buy (receive) the commodity in the future at that “abnormal lower forward price”, and simultaneously now we would borrow the commodity (paying the conv.yield to the original owner, equivalent to paying him the storage costs minus the lease rate), sell it into the spot market, and investing the proceeds in a deposit at the risk free rate. At maturity, we get our money back from the deposit, settle the forward (paying the money and receiving the commodity) and we would give that commodity back to the original lender, obtaining a riskless profit + individual investors do not get any conv.yield (they have no business related non-monetary benefit for holding it), so fwd can not be higher than: = Spot x EXP [(RFR + Stor.Costs) x T] = “yyy” because if fwd is higher than that, they can borrow the money, buy the commodity in the spot market, storage it, and sell it forward with a sure profit + This means fwd should be between “xxx” and “yyy”: xxx <= Fwd <= yyy e. Commodity spread = sum of prices you get for selling each “son” - price of the “mother” thx a lot

typo: in d., convenience yield woud be equivalente to storage costs PLUS the lease rate

I thought the Lease Rate took everything such as CY and Storage Costs into consideration… I could be wrong, but I thought when you use the Lease Rate you ignore all the other costs b/c the Lease Rate accounts for those costs??

according to schweser (i hate to say that), convenience yield = cost + lease rate, so risk free rate + costs - convenience yield = risk free rate + costs - (costs + lease rate) = risk free rate - lease rate so, yes, seems you either use only risk free rate - lease rate, or you just incorporate costs and convenience yield

lease rate is a plug number that equates price of commodity to spot, so lease rate = conviniencey yield - cost

One thing that i dont really understand why cant investor buy and lease and asset with cy, to earn cy - cost? As an example with pencils i can buy pencil and lend them so break even price is Rfr - lease.

Lease rate isn’t a plug number - it’s a real quotable thing for commodities that can be leased. Gold is the poster child and the lease rate is published every day. “convenience yield = cost + lease rate” …huh? The convenience yield is what’s left when you subtract out other costs. Presumably if a commodity can be leased the lease rate is the same as the convenience yield. You can’t lease and slaughter a bunch of hogs for example.

CY = RFR - Lease + Storage Cost. Correct?

Lease Rate = Rf – 1/T * LN(F/S) F = S*e^(Rf *t) + Storage – CY Anyone want to solve :wink:

CY = RFR - Lease + Storage Cost. Correct? I dont think so

CSK, Joey The only way I “understand” this (for exam purposes, and following CFA reasoning) is: Fwd = Spot x EXP [(RFR - Lease Rate) x T] Lease Rate = Convenience Yield - Storage Costs With CFA reasoning, in my own words, for the second one as "I lend you my commodity if my situation does not change, so if I lend you my commodity I will pay your storage costs (which I am already paying as I hold my commodity, so does not change my situation) and you will pay me my convenience yield (which I am currently enjoying because of I hold my commodity, so does not change my situation) The only difference is that, when doing the cash and carry, being an individual with no business related non monetary benefit for holding the commodity, convenience yield = zero, so the upper limit is Spot x EXP [(RFR + Stor.Costs) x T] , while the lower limit, as I do reverse cash and carry borrowing the commodity from an existint owner/producer who does get a convenience yield, is Spot x EXP [(RFR + Stor.Costs - Conv.Yield) x T] But, again, this would only work “in theory”. As Joey said, I don´t know how this fits into real lease rates (for whoever, business or individuals) and what really happens in the market. Actually, CFA formula that lease rate = conv yield - storage costs would imply that, for individual investors, lease rate would be negative and they would just pay the storage costs of the borrower, which does not make a lot of sense… Hope this does not appear in the exam, or only in a multiple choice question where the right answer is just “a) No arbitrage becomes a range instead of a price” :slight_smile:

The Lease rate accordign to CFAI takes the Convenience Yield and Storage costs and any other associated benefits/costs into consideration in the rate. It is not a simple additive formula.

That’s really good madrid. I think theory and reality fit in really well when the commodity is something easily leased, e.g., precious metals, bonds (the bond lease rate is the repo rate), single stocks, and, uh, must be something else.