Negative Lease Rates Revisited

The Gold Lease Rate (GLR) as reported by the London Bullion Market Association (LBMA) turned negative after the peak of the credit crisis in 2008. The GLR over 1,2 and 3 months stayed negative for most of 2009 and 2010.

LBMA Gold Lease Rate 2008-2010

LBMA Gold Lease Rate 2008-2010

Since nobody leases their gold without charging a fee, a negative GLR seems to be nonsense. So how come the LBMA reports consistently negative GLRs?

We show that in an efficient market, the GLR as reported by the LBMA is equal to the risk premium for the case that the leased gold is not returned minus the storage fees for the gold, and so it can indeed come out negative.

Another possible answer is that LIBOR may have been rigged. As of a week ago, US, UK and Japanese authorities were investigating several banks for allegedly having manipulated LIBOR, the London Inter Bank Offered Rate.

How is the GLR calculated? It is derived from the Gold Forward Offered Rate (GOFO) and the London Inter Bank Offered Rate (LIBOR). GOFO is the interest paid on a swap of gold for US$, i.e. the interest paid if one lends gold and borrows US$. In other words, GOFO is the interest payable on a fixed-term US$ loan for which the gold is used as the collateral. GOFO is determined by the LBMA in a survey of the leading market makers.

In order to arrive at the GLR, i.e. the interest received if one lends gold, but does not borrow US$ at the same time, the LBMA assumes that the interest on the US$ portion of the swap is approximately LIBOR, the interest paid on an unsecured loan between some of the major banks. LIBOR is determined by the British Bankers’ Association (BBA) in a survey of a number of the leading banks.

The Gold Lease Rate (GLR) is then calculated as LIBOR minus GOFO.

Let us assume, we ask the same counterparty for two quotes. Firstly, the interest rate on an unsecured US$ loan. For simplicity, let us call it LIBOR:


+ nominal risk-free yield of US$

+ risk-premium for the US$ loan

Secondly, GOFO. In Backwardation in the Case of a Monetary Metal, we have found that in an efficient market, GOFO is determined by


+ nominal risk-free yield of US$

+ risk-premium for US$ loan

+ storage expenses for the gold

– risk-premium for the gold lease

If we compute the GLR as LIBOR minus GOFO (both quotes from the same counterparty), we therefore find


+ risk premium for the gold lease

– storage expenses for the gold

If the lease involves unallocated gold for which there is no storage fee, the GLR is therefore always positive. If the lease involves allocated gold, however, the GLR can turn out to be negative.

In an efficient market in which the GLR is indeed computed for a specific counterparty, we would expect a negative GLR for example in the following situation. There is a bank A with a strong financial position willing to lend US$, but only against collateral. There is a second bank B in a weaker financial position which would like to obtain a US$ loan and which owns allocated gold that can be posted as the collateral for this loan. Now B can enter a swap with A and swap the gold for US$ for a fixed term. If A provides both a LIBOR and a GOFO quote, the GLR calculated as LIBOR minus GOFO will be negative as soon as the risk premium for the gold lease (which is low because A is sound) is less than the storage expenses for the gold.

The GLR as published on the LBMA website, however, is calculated as LIBOR minus GOFO, using the published figures for LIBOR and GOFO that have been determined independently. The problem is that both are sampled from different institutions and potentially at different times of the day. The mismatch of counterparties involved in this calculation can therefore be responsible for the negative lease rate as well.

As of 16 March 2011, we know that there is another possibility: LIBOR may have been rigged by some banks, apparently in order to mask their exceedingly high funding costs:

[3] Libor: investigation by regulators (Financial Times, 16 March 2011)
[4] Big banks investigated over Libor (Financial Times, 16 March 2011)

According to these articles, the authorities in the US, UK, and Japan are investigating UBS, Bank of America, Citigroup, Barclays, and WestLB for allegedly rigging LIBOR:

[UBS] said the regulators were focusing on “whether there were improper attempts by UBS, either acting on its own or together with others, to manipulate Libor rates at certain times”.
Witnesses had been interviewed by investigators from the US Securities and Exchange Commission, the Department of Justice and the UK’s Financial Services Authority, people familiar with the probe said.

Of course, if LIBOR is manipulated down, it is no surprise that the reported GLR comes out negative.

Update (19 April 2011):

The Financial Times writes on 19 April 2011, in the article

[5] Funds accuse banks of manipulation (Financial Times)


Three investment funds have accused a group of US, European and Japanese banks of conspiring to manipulate the benchmark interest rate used to calculate the cost of billions of dollars of debt.
The suit revolves around the London interbank offered rate, or Libor – the estimated cost of borrowing for banks between each other set daily by the British Bankers’ Association.
“We believe the suit is without merit,” Citigroup said.
The other banks named in the suit either declined to comment or spokesmen could not be reached.
They are: Bank of America, Barclays, Credit Suisse, Deutsche Bank, HSBC, JPMorgan Chase, Lloyds Bank, Norinchukin Bank, Royal Bank of Scotland, UBS and West LB.

Update (6 March 2012):

As of March 2012, the enquiry into the possible rigging of LIBOR continues. The Financial Times has a special section on this topic.

Update (27 June 2012):

Barclays was fined $450 million for attemtring to manipulate LIBOR (Financial Times).

3 Responses to Negative Lease Rates Revisited

  1. Michael H says:

    Hello victor,

    1) How far back did the LIBOR manipulation go? Does it extend back to the GOFO peak in 2008?
    2) Was the LIBOR manipulation undertaken to hide stress in the paper markets, or to hide stress in the gold market?

    • I do not know any facts beyond those given in the articles from the Financial Times. From these, I understand that the (alleged) LIBOR manipulation started in 2008 when LIBOR spiked because the commercial banks did not trust each other anymore. I think this alone would be enough motivation to ‘fix’ LIBOR. If I wanted to ‘improve’ the Gold Lease Rate, I would not go via LIBOR, but rather aim straight for GOFO.

      This is precisely my worry. Once you consider the possibility that the banks have colluded to rig LIBOR, why would they not be prepared to rig GOFO as well? GOFO is determined in a fashion very similar to LIBOR: just by phoning the market makers, removing the extremes, and calculating the average.


  2. A lot of contracts use GOFO, so the same motivations can come into play. The negative GLR is a bit of a giveaway, but you can’t also play with GOFO too much as it’s relationship to futures market prices would diverge too much.

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