Seeking Alpha

Ben Bernanke recently announced QE3. It is estimated by Bank of America that the Federal Reserve balance sheet will go to \$5 trillion in two years from now (end of 2014). If we know that the Federal Reserve balance sheet will go to \$5 trillion in two years from now, I want to point out what this means to the U.S. dollar denominated in gold (GLD). How much depreciation in the U.S. dollar can investors expect due to QE3? For the answer we, need to take a look at the money supply measures of M0 and M1.

 (click to enlarge) Chart 1: Federal Reserve Balance Sheet
 (click to enlarge) Chart 2: Currency in Circulation
 (click to enlarge)

On Chart 1 we see the current Federal Reserve Balance Sheet, and this balance sheet correlates to base money M0 (Chart 3). M0 (or monetary base) is basically the U.S. dollars and coins in your wallet (Chart 2) (biggest part of M0 namely "currency in circulation") (not in the bank) + deposits held by depository institutions at Federal Reserve Banks.

As you can see, currency in circulation was going up very steadily together with the Federal Reserve balance sheet during the period 1985 till 2008. We went from around \$200 billion in 1985 to \$800 billion in 2008. Then suddenly, the Federal Reserve balance sheet exploded by \$2 trillion, while the currency in circulation (your money in your wallet) only went up \$300 billion. That means the Federal Reserve's increase in balance sheet (printing of money) hasn't adequately increased currency in circulation.

The extra \$2 trillion in QE3 recently announced by Ben Bernanke (expansion of the federal reserve balance sheet) is expected to have the same effects. This is because all of the expansion in the federal reserve balance sheet is going to the excess reserves of depository institutions (Chart 4). You can find these excess reserves by simply subtracting Chart 2 (Currency in Circulation) from Chart 3 (M0: Base Money).

This will give Chart 4: Excess Reserves of Depository Institutions. This increase in excess reserves is seen by many to be a sign that inflationary pressure will come to the U.S. economy and the U.S. dollar.

 (click to enlarge) Chart 4: Excess Reserves of Depository Institutions

One simple model for determining the long-run equilibrium exchange rate is based on the quantity theory of money: MV=PT. Money x Velocity = Price x Transaction. A one-time increase in the money supply is soon reflected as a proportionate increase in the domestic price level (everything becomes more expensive). The increase in the money supply is also reflected as a proportionate depreciation of the currency against other foreign currencies.

The question is, how much depreciation will we see in the U.S. dollar against the real currency, gold?

For this we need M1, which is the key monetary aggregate. M1 is the total amount of currency and checking deposits held by households and firms. This number is currently \$2.4 trillion, almost the same as M0. The trend of M1 is almost following the same pattern as the Federal Reserve's balance sheet. The numbers are quantitatively similar.

 (click to enlarge) Chart 5: M1: Monetary Aggregate

So we can basically just look at the Federal Reserve balance sheet and deduct the U.S. dollar exchange rate from it against gold.

In 1988, M1 was \$800 billion, gold was \$500/ounce. In 2008, M1 doubled to \$1600 billion, gold also doubled to \$1000/ounce. The recently announced QE3 will once again triple the federal reserve's balance sheet (which is similar to M1) to \$5 trillion in two years from now, which means gold will again triple to an estimated \$3200/ounce in 2 years from now.

Important to note is that the increase in M1 is increasing at a very rapid pace. This increase in M1 is mostly due to the increase in the federal reserve balance sheet as we can seen in the correlation between the federal reserve balance sheet (Chart 1) and M1 (Chart 5).

Conclusion:

We can quantitatively predict where the gold price will be headed for, just by looking at M1. The quantity theory of money states that the increase in the money supply is reflected as a proportionate depreciation of the currency against other currencies in particular gold. As we know that M0 and M1 are highly correlated to the federal reserve balance sheet, we deduct from this that QE3 will result in a price expectation of gold to \$3200/ounce by end of 2014. This is because the Federal Reserve balance sheet is expected to triple from \$1.6 trillion in 2008 to \$5 trillion at the end of 2014.

Disclosure: I am long PHYS, PSLV, AGQ. (More...)