## Posts Tagged ‘lease rate’

### Pricing of gold forward rate

Wednesday, April 8th, 2009

Back in Pricing of futures, we discussed about the theoretical pricing of futures. But the futures price (or more technically correct, the forward price) of gold is calculated differently. This is because there is a lease rate for gold. As we mentioned before in Get paid to borrow gold and silver?,

But for a certain class of gold owners, they DO earn interests on gold. Right now, instead of receiving interest for lending out gold, they are paying people to borrow gold.

The best way to explain gold forward pricing is to use an example. To understand this, we assume that you have already read and understood Pricing of futures beforehand. Let’s suppose the spot price of gold is \$1000 per ounce. The lease rate for 180 days is 2 percent per annum while the carry cost (which includes storage and interests) is 5% per annum.

So, we borrow \$1000 for 180 days. At the carry cost of 5%, we have to repay \$1000 * (1+.05(180/365)) = \$1024.66 in 180 days time. With the borrowed \$1000, we buy 1 ounce of gold and lease it out. At the end of the 180 days lease period, we expect to get back 1 * (1+.02(180/365) = 1 (1.01) = 1.01 ounce of gold.

Therefore, 1 ounce of gold has grown to 1.01 ounce in 180 days time at a value of \$1024.66. Therefore, the forward price of gold will have to be \$1024.66/1.01 = \$1014.51. If the 180-day forward price of gold is not at \$1014.51, then an arbitrage opportunity exists (see How futures price affect market price for more details).

To sum it all up with an equation, if the spot price is S, the forward price is F(T) for a time-horizon of T days, the carry cost is r, and the gold lease rate is r*, we have:

F(T) = S [1 + r (T/365)] / [1 + r* (T/365)]

### How are gold lease rates quoted?

Sunday, August 31st, 2008

Back in Get paid to borrow gold and silver?, we mentioned that

But for a certain class of gold owners, they DO earn interests on gold. Right now, instead of receiving interest for lending out gold, they are paying people to borrow gold. Who are these gold owners?

They are the central banks. The ?interest rates? on gold is the gold lease rates…

One of our readers alerted us to this forum discussion, Anybody like to explain the negative lease rates:

Many people, even those that seem to understand the gold market seem to get confused on how the gold least rate is quoted… It is the LIBOR rate minus the gold lending rate for the duration quoted. Normally gold is loaned at less than LIBOR and that results in a positive figure for the lease rate (designated as GOFO by the LBMA).

Actually, that explanation from the forum is not accurate too. So, what are the gold lease rates all about and how are they quoted? We did some digging and found this commentary. To explain lease rates, we will start off with the definitions:

GOFO– according to the London Bullion Metal Association, the GOFO is the

Gold Forward Offered Rate. These are rates at which contributors are prepared to lend gold on a swap against US dollars. Quotes are made for 1-, 2-, 3-, 6- and 12-month periods.

GOFO is basically the interest rate for borrowing money using gold as collateral. For example, a central bank will enter a swap position with a bank by swapping its gold for US dollars with the bank. At the end of the period, the swap has to be reversed with the central bank paying an additional certain percentage above the original amount of US dollars. That “certain percentage” is the GOFO rate. The GOFO rate is related to the gold futures price. This is because if the GOFO rate is too much higher than the gold futures price, then the central bank will be better off selling the gold in the spot market and simultaneously buy gold futures.

LIBOR– this is the London inter-banking lending rate

Derived Lease Rate (DLR)– this is the lease rate that you see quoted at Kitco.com. The DLR is defined as LIBOR – GOFO.

Now, this is where it is getting complicated. So, we’ll use an example. Let us suppose, this is the current situation:

LIBOR- 5%
GOFO- 1%
DLR- 5 – 1 = 4%
Gold price- \$1000/oz

Let’s say Bank A has 100 oz of gold. It then enters a swap with Bank B. So, Bank A will end up with \$100,000 and Bank B has 100 oz of gold. At the end of the period, Bank A has to pay \$101,000 to get back its gold. Now Bank A invests the \$100,000 in the market markets and receives LIBOR interests. At the end of the period, it will have \$105,000. Then it pays \$101,000 to Bank B to get back its gold. The net ‘profit’ in this transaction is \$4000, which is 4% of the original total gold purchase price.

The net effect of these transactions is this: Bank A lend gold at 4% lease rate. To end it all, the lease rate, as explained in Kitco.com is:

The lease rate is the cost of borrowing gold. In much the same way that individuals borrow dollars, pay an interest charge, and then return dollars to the lendor, gold bullion participants will borrow ozs of gold, pay a borrowing cost, and return the ozs of gold to the lendor. The debt is measured in terms of ozs as opposed to dollars. The value of the metal when it is being borrowed or returned is not a factor.

### Get paid to borrow gold and silver?

Wednesday, April 2nd, 2008

For the vast majority of us, gold is a lump of metal that does nothing. As we said before in Is gold an investment?,

… since gold is a boring, inert metal that does not have much pragmatic use and does not pay dividends, income or interests, it is completely unfit for ?investment.?

But for a certain class of gold owners, they DO earn interests on gold. Right now, instead of receiving interest for lending out gold, they are paying people to borrow gold. Who are these gold owners?

They are the central banks. The ‘interest rates’ on gold is the gold lease rates. Typically, central banks lend out gold through bullion banks, which then pass them on to the market. Eventually, the gold has to be repaid with ‘interest’ paid with more gold. Sometimes gold producers pre-sell their gold by borrowing them from central banks first and then repaying those borrowed gold (with interests, of course) later through their own production.

Right now, at this point of writing, the gold lease rate for 1 month is -0.0483%. This negative lease rate has been going on since last week. For silver, the lease rate for 1 month and 2 month is -0.04% and -0.0379% respectively.  This is a very curious phenomenon. In other words, central banks are paying for others (e.g. bullion banks, gold miners,  hedge funds, etc) to borrow gold to sell to the market. In other words, central banks are paying for others to ‘short’ gold.

That could be the reason why gold prices had been falling recently.