# Lease rate on commodities..

I’m trying to get an understanding of the lease rate as a rate that a commodity owner charges to lend out the commodity. So is it the higher the lease rate, the lower the forward rate? Why is that in basic terms? I can’t get my head around it. Also, what is even a practical real world example of borrowing a commodity? Don’t commodities get consumed? And does anyone think we’ll have to calculate anything on commodity forwards and futures or will it just be conceptual? Thanks!

This one confused the hell out of me too. But, I finally understand it. If you lease out a commodity you no longer have to pay storage costs, but you (the lender) have to pay the commodity borrower a lease rate which is equal to the storage cost. Which makes sense. That’s exactly the opposite of the way I understood it. The way Schweser set up the equation is extremely confusing and never quite made sense to me. They show the lease rate as being a subtraction that would lower the forward price…but…the lease rate is a negative number because you (the lender) pay the borrower. So if you plug it into the equatoin it adds to the forward rate. To keep it simple in my mind, I’m just viewing the lease rate as a storage cost…same thing. Read CFA text on this one and they make it very clear. Volume 5, page 168. Hope this helps

I still don’t get it. I used to understand this at one point. Why would the lender have to PAY a lease? I am trying to think like in terms of a car where the borrower of the car is paying the lease rate.

because it costs money to store the commodity. Any way you look at it, someone has to pay for the storage of the commodity. If you loan it out to someone (presumably because there is some benefit to them holding it as backup supply or whatever), they have to pay a storage cost…now you have to effectively reimburse them. It’s like a negative lease rate because rather than the lender collecting a lease, the lender pays the lease. This is where the formula gets confusing, but makes sense in light of the above. The lender gets a “benefit” for leasing it out as shown by the fact that you subtract the lease rate. BUT, the lease rate is negative because the lender actually has to PAY the borrower…so in effect, the two negatives make a positive and you’re increasing the futures price. To simplify, look at the lease rate as a positive number and treat it just like a storage cost…you have to pay to loan it out.

mullrich Wrote: ------------------------------------------------------- > because it costs money to store the commodity. > Any way you look at it, someone has to pay for > the storage of the commodity. If you loan it out > to someone (presumably because there is some > benefit to them holding it as backup supply or > whatever), they have to pay a storage cost…now > you have to effectively reimburse them. It’s like > a negative lease rate because rather than the > lender collecting a lease, the lender pays the > lease. Okay. I see what you are saying. > > This is where the formula gets confusing, but > makes sense in light of the above. The lender > gets a “benefit” for leasing it out as shown by > the fact that you subtract the lease rate. BUT, > the lease rate is negative because the lender > actually has to PAY the borrower…so in effect, > the two negatives make a positive and you’re > increasing the futures price. > > To simplify, look at the lease rate as a positive > number and treat it just like a storage > cost…you have to pay to loan it out. Thanks for the help.

Thank you for the discussion on this. Mullrich, I read the CFAI text on this and I guess I kinda get it. I’ll come back to it again a little later rather than kill myself on it now. I can always just regurgitate the text on the exam without knowing why the hell I’m writing it, right!? Anyhow, it doesn’t look like this would be tested as calculations, but more in a conceptual manner. Do you think that’s right?

Mullrich - A sincere thank you for the clear explanation. Very helpful.

Mullrich, I think it is the opposite of what you describe. If you are allowing someone to use your goods, you charge them a rate to “borrow” or lease the good. If you didn’t they would be able to arbitrage the situation and make a profit. The ability to obtain payment of the life of the forward brings the forward price down.

think of gold as an example. You can lend out the physical gold and allow the borrower to earn a return. The lease rate is an estimation of the return they would receive. If there was no lease rate. The borrower would be free to earn a return without any risk.

the lease rate = convenience yield - storage cost hence if lease rate is negative the futures curve is steeper…contango if lease rate is positive and higher than the riskfree rate, we have backwardisation, Also, if lease rate is zero we should have contango, becoz even then the curve will be upward sloping… do u guys agree???

rekooh, I think it comes from the fact that there can’t be a leasing market (and rate - l) without storability, and with storability comes storage costs (s). Also, the borrower earns a convenience yield © from holding the physical. Therefore the borrower earns r+c-s and the lender therefore earns r+l which via no arbitrage I believe must equal r-(c-s). I think this is what the text is getting at since convenience yield is only technically realized by the holder of the physical, the lender gets r-s so they are essentially paying the borrower their storage costs. mullrich, do I have it now? So now comes the bring it all together question. If there is an active lease market for the physical, the text says you don’t earn it with the physical, that’s why you invest through the futures. On thinking about it, I guess this is because you can’t earn a guaranteed return on the physical because the spot price changes, but by buying the commodity, lending it out, and selling it forward, you lock in a return. Since this is a guaranteed return, the reduction of the risk free rate for the storage costs, is the price you have to pay (no free lunch). Does this get the concept right? Opinions?

This thread is blowing my mind.

yeah my bad… it’s not even going to be tested, right?

I am just kidding around. I hope it isn’t tested though. I haven’t looked at this in awhile, but I remember having difficulty with this concept.

mwvt9 Wrote: ------------------------------------------------------- > I am just kidding around. > > I hope it isn’t tested though. I haven’t looked > at this in awhile, but I remember having > difficulty with this concept. I know you were… still, can’t imagine more than 3-6 points if any on this stuff.

rekooh is correct…a lease rate would lower the forward cost, think of it as a benefit to holding the spot position. I know it is confusing but I try not to read into too much and just take it as it is.

ItsAlmostOver Wrote: ------------------------------------------------------- > rekooh is correct…a lease rate would lower the > forward cost, think of it as a benefit to holding > the spot position. > > I know it is confusing but I try not to read into > too much and just take it as it is. Yeah it is confusing, but mullrich’s explanation is the right one per the CFAI text. Essentiallly, you should view the lease rate as a storage cost. It’s weird, and the text kinda hints at that with a nice explanation point on stating this concept, but I know we gotta go with CFAI for better or worse.

If I borrow at the RFR to purchase the commodity and then lend it out, I can’t imagine I would have the pay the RFR + the lease costs and receive no benefits. Arbitrage does not let the lease rate exceed the RFR or this would be a “free lunch” to those who borrow and lease out. Right? Also, can anyone think of a commodity that one can use for their benefit and then return that same commodity in the same condition pre-borrowed? If so then I can understand a lender having to pay the lease rate, but the text claims the convenience yield allows the borrower to use the commodity if necessary - this you would have to pay for minus your storage costs. NO???

Just getting back on, have been watching my two little kids (both under 2) all day. I can’t wait unti this is over because studying for the CFA with kids is impossible. Anyway, I’m sure there is a lot more to lease rates in terms of backwardation, etc…but I’m not taking it any further than my basic understanding. Question 6 in the 2008 exam addresses lease rates and you do need to do a calc, but with a basic understanding you can get it. That question is what made me realize that I didn’t understand lease rates correctly, went back to CFAI text and now it’s clear in my mind. But, again, I’m sure there’s a lot more that determines what lease rates are and why they might differ from storage costs in reality.

Guys, You are reading the text wrong. Lease rate is a benefit, just as convenience yield is. I am not sure where the disconnect is, but it would be ashamed to miss points by having it backwards. The portion you are reading in the book on pg 168 is based on carry markets and spot v. forward. Carry is ONLY used is there are storage needs. Most commodities DONT require storage. Storage is only necessary if there is not a market at a given time for said commodity. Thus with a general commodity the lease rate is a benefit that is paid to the lender for use of the good.