Jim’s Mailbox

Posted at 1:28 PM (CST) by & filed under Jim's Mailbox.

Dear Jim,

The following is an analysis of your Mathematics of Gold. The analysis was conducted by our summer intern and we thought it may be of interest to your readers.

Kind Regards
Isaac Matzner

Research Coordinator
Auerbach Grayson & Company
25 West 45th Street
New York, NY 10036 USA
Tel. 1-212-453-3549
Fax. 1-212-557-9066

Case: The Mathematics of Gold

International US dollar debt: $4.4792 trillion (approximately 32% of total US debt of $14.32 trillion)

Portion of international US dollar debt held by China: $1.1449 trillion

90% of total US international debt less portion held by China = 0.90 * ($4.4792 trillion – $1.1449 trillion) = $3.00087 trillion (A)

50% of international US dollar debt held by China = 0.50 * $1.1449 trillion = $0.57245 trillion (B)

Total foreign currency reserves held by People’s Bank of China (Central Bank): $3.045 trillion

Therefore, A + B = $3.57332 trillion (C)

Total US holdings of gold = 8,133.5 tonnes = 8,133.5 * 35,273.9619 = 286.900770 million ounces (D)

Therefore, C/D = $12,454.8986 per ounce ~ $12,455 per ounce

Balance of Payments is an account of financial flows between a country and the rest of the world. It consists of the Current account and the Capital account. Current account consists of the trading account (exports minus imports of good and services), income account (factor payments from abroad minus factor payments to abroad) and the transfer payments account (foreign aid received minus foreign aid disbursed). Capital account, which is in surplus on account of increasing foreign investments in US treasury securities and in deficit for increased US investments in foreign securities and reserves. A surplus in the current account should always be balanced by a deficit in the capital account and vice-versa. That is, the balance of payments must always balance.

Suppose the balance of payments account does not balance. Then there are two options to balance BOP, first, the Central Bank of the country (in this case US Federal Reserve) should increase/reduce its reserves, that is the Central Bank’s holdings of foreign currencies and gold to bring BOP to balance. Second, if the Central Bank cannot increase/decrease its reserves or has decided against changing its existing reserve holdings, then the exchange rate of the country’s currency will be decided by the market and the government will not have any control over its currency.

Now, US has a current account deficit and the BOP is balanced by capital account surplus. If the BOP was not in balance and if US wanted to keep the existing exchange rates fixed, assuming it had a BOP deficit (international debt we calculated above), then it would either have to sell foreign exchange reserves or appropriate amount of gold to the tune of $12,455 per ounce. Thus, to balance the US government balance sheet, its holdings of gold should be valued at $12,455 per ounce.

Present market value of gold = $1,528.80 per troy ounce = $1,528.80 / 1.09714286 per ounce = $1,393.44 per ounce. This means that gold is heavily undervalued at it existing market price. Thus the price of gold has to be raised 8.94 times ($12,455/$1,393.44) ~ 9 times to the present price of gold for US balance sheet to balance.


1. Link: http://en.wikipedia.org/wiki/United_States_public_debt

2. Link: http://www.treasury.gov/resource-center/data-chart-center/tic/Documents/mfh.txt

3. Link: http://en.wikipedia.org/wiki/Foreign_exchange_reserves

4. Link: http://en.wikipedia.org/wiki/Gold_reserve

5. Link: http://finance.yahoo.com/

Ayan Kole,

Michael F. Price College of Business,

University of Oklahoma