Going in a bit of a circle jerk in another thread. If I am buying gold at spot and shorting the forward, CFAI claims I want lease rate to be less than storage costs.
Trying to reconcile with text. Is the lender in a cash and carry the one who bought gold spot and loans it out? Who sold it forward at the forward rate. I would think if I lend it out, I earn the lease rate less storage (since I am only vitually loaning it, I still have it in possession).
I’m no commodity expert but this is how I reason it out. Lengthy but I try to break it up into simple steps.
If you buy commodity at spot, you own the commodity. If this commodity can be leased out, it must be factored into the forward price. Normally, the forward price would be spot + what you can earn risk free, just to prevent arb. Why? because had you not put the money into buying this commodity, at the very least you could’ve bought a government bond and earned the risk-free. In other words, by buying the commodity, you gave up chance to buy a risk-free asset… that is your opportunity cost, and that’s why the forward price you charge must reflect that.
However, knowing the owner can lease it out in the meantime, that will take away from your compensation. If I agree to buy the commodity at the forward price, your opportunity cost isn’t entirely the risk free rate because you can recoup some of that investment by leasing it out.
So what does this all mean? The lower the lease rate, the higher the forward. If you are shorting the forward, you are selling the forward commodity. You are selling the commodity at the forward price, and you want that price to be high as possible. That is wh you want the lease rate to be low.
Now why do you want it lower than the storage cost? Because the storage cost is the cost you have to pay to keep this sucker in good condition. So this is a cost you would ADD on as part of your compensation (in addition to the risk-free rate mentioned above). So base case, you earn risk-free. If there’s a storage cost, you add that on and increase your forward price. But if we know you can lease it out in the meantime, that will lower your forward price.
If lease rate = storage cost, then you’d earn just the risk free. If lease rate < storage cost, net / net you’re earning slightly more than the risk free.
Btw, the last leg which I didn’t mention is the convenience yield, which is the non-monetary benefit you receive for owning the asset. The classic example being you’re some manufacturer and by having this commodity in-stock, your production stays on schedule. This benefit, like the lease rate, is something that would reduce your forward price.
Hence, conceptually…
Forward = Spot + (Rf) + (Storage Cost) - (Convenience Yield)
also, if there’s a lease “market” available
Forward = Spot + (Rf) - (Lease Rate)
Therefore, Lease Rate = Convenience Yield - Storage Cost [they are opposites, ie one is the negative of the other since the first equation, you add the net benefit of Storage - Convenience, and in the bottom equation you subtract the Lease Rate)
Andy Trader:
You are not “virtually” loaning it . You are really lending it to someone who is paying for storage cost to get immediate possession of the gold.
He is providing you with “virtual storage” because he will return you the gold in the future , and you didn’t have to pay storage. In return you pay the guy who borrows it a lease rate .
In the cash and carry with storage , the lender buys the gold , shorts the forward , lends the spot gold he owns to save storage . In return to balance the equation he pays the lease rate . The borrower pays the bank the storage costs for the physical gold and earns the lease rate from the lender .
the CFAI text is horrible in explaining all this . No equations , no example , just work it out by yourself
I really appreciate these comments but I see a contradiction. Yabba said I, who owns the gold, receive a lease rate for loaning it out which lowers the forward price. This offsets the risk freet rate return I earn for buying gold rather than buying a Treasury.
J: you said I pay a lease rate to the borrower who borrowed my gold. In lieu of having to pay storage,
I think Yabba is confusing the issue when he writes this:
However, knowing the owner can lease it out in the meantime, that will take away from your compensation. If I agree to buy the commodity at the forward price, your opportunity cost isn’t entirely the risk free rate because you can recoup some of that investment by leasing it out.
The owner cannot lease gold to someone when he doesn’t have phyical possession of the gold. By lending out the gold he has foregone physical possession ( as well as reduced his expense of storage ) and still kept the advantage of an appreciating commodity asset ( when he delivers on the forward , he should be getting more in the appreicated spot price ) . In return all he needs to pay the borrower a lease rate. The borrower is the one who has physical possession and so he can earn the lease rate
Who would borrow a commodity? Geez. Stop being cheap, people! Either buy it, or don’t! Don’t you hate it when your friends ask you to borrow stuff from you? In this case, the guy is not even my friend. In fact, I don’t even know the guy!
Some confusion might arise because of the fact that the lease rate is earned by different parties depending on whether or not there are storage costs.
If there are no storage costs, the lender earns the lease rate (he must be compensated for loaning it out).
However, if there are storage costs, the lender pays the borrower the lease rate (in this case, the borrower must be compensated for bearing the storage costs).