# Operation Twist: More Details

Several people have mentioned that my previous entry about operation twist was a little terse.  Let me see if I can be more expansive this time.

First, everyone should understand that the net change in the U.S. money supply will be zero.  The Fed will sell \$400 billion in short-term government securities.  Then they will quickly pass those funds into their other hand, using it immediately to buy \$400 billion in long-term government securities.  No change in the money supply.

The effect of this is also straightforward.  \$400 billion is a lot, even in U.S. government securities markets.  When the Fed sells short-term securities, that will increase the supply of those securities, causing their price to fall and their yield to maturity (interest rate) to rise.  (If you don’t get that, read on.)  Similarly, buying \$400 billion in long-term securities will cause their price to increase and their yield to fall.  Thus, the Fed is trying to twist the yield curve (aka term structure of interest rates).

## Introduction to Yield Curves

A bond is simply a promise to make one or more future payments on specified future dates.  Some promises are more trustworthy than others.  If the U.S. government, IBM, or General Electric makes a promise like that, there’s a pretty good chance they’ll keep their promise.  On the other hand, if I have a great idea for a new product and try to raise funds in the bond market to finance my startup, … well, let’s just say I wouldn’t buy one of those bonds myself (unless the promised interest rate was very, very high, in which case the bonds would have junk status).

The price of any bond (and most assets) is the present value of its future payments.  Present value is easy.  Let’s take a minute to learn about it.

The present value of a dollar today is one dollar.  That’s what “present” means.  But what about the present value of a dollar you will receive a year from now?  Let’s make it \$100 instead and see how this works.  Assume that you can earn 2% interest on your \$100.  If you have \$100 and put it in a savings account earning 2% per year for one year, you will have \$102 at the end of the year.  (That’s \$100 + (2%)(\$100) = \$102.)   More generally, if the amount you have today is PV (the present value) and the interest rate is r, the future value one year from now (FV) will be FV = PV(1 + r).

If you believe that — and, frankly, I’ve never met anyone who doesn’t believe it — then you also have to believe the present value of \$102 to be paid a year from now is \$100.  I’m still assuming the interest rate is 2%.  The present value must be \$100.  You can see this with a little algebra.  If FV = PV(1 + r) then PV = FV/(1 + r).  Always remember, the laws of both physics and mathematics are more powerful than the laws of economics!

The point of all this is that the price of any asset will move in a direction opposite to the change in the interest rate.  For example, suppose the interest rate rose to 5% but we were still going to receive \$102 a year from now.  The present value would be PV = \$102/1.05 = \$97.14.  At five percent, the \$102 a year from now is only worth \$97.14 today, not \$100.  The price of an asset and its interest rate (technically called the yield to maturity) always change in opposite directions.

Oh, yeah, the yield curve.  This is a graph with time to maturity on the horizontal axis.  (A bond matures when it makes the final promised payment, usually including a large amount commonly called the maturation value).  The vertical axis is the interest rate on securities of varying times to maturity.  Here’s the yield curve for September 23, 2011:

U.S. Yield Curve, Sept. 23, 2011

## Back to Operation Twist

Now it should be clear what the Fed is trying to do.  By selling short-term government securities, short-term interest rates should rise.  Buying long-term bonds should cause their interest rates to fall.  And the yield curve will rotate clockwise (for those of you old enough to remember what that means).

It’s traditional to include the yield curve one year earlier for comparison purposes.  As you might expect, longer-term securities have higher interest rates than shorter-term securities.  The reason is simple.  A lot more things can go wrong in 10 years than in 3 months.  Intuitively, the longer the promised stream of payments, the more likely something very bad will happen that disrupts the cash flow.

Here’s what the Fed is trying to do:

U.S. Yield Curve Twisted

OK, so my artistic skills aren’t the greatest.  But the point is clear.  Drive up short-term interest rates and drive down long-term interest rates.

Will it work?  Probably not, but no one can accuse the Fed of not giving it their best shot.

Share if you feel like it

## About Tony Lima

Retired after teaching economics at California State Univ., East Bay (Hayward, CA). Ph.D., economics, Stanford. Also taught MBA finance at the California University of Management and Technology. Occasionally take on a consulting project if it's interesting. Other interests include wine and technology.

## 4 Replies to “Operation Twist: More Details”

1. Zhi Huang

Since this scheme would drive up short term interest rate, would that not hurt short term borrowing? We are at a time when banks’ exposure to European debt is at a focal point, would rising short term rate (even by a little) further discourage banks to lend to each other? How is this going to help the market and the economy in general? I am baffled.

The Fed is trying to stimulate business investment and mortgage borrowing. Those activities depend on the long-term interest rate. But they also don’t want to look like they’re encouraging inflation, so they need a policy that does not affect overall monetary policy. With that objective and the constraint, I think this is about the best they could do. But I don’t think it will help the economy very much.

Perhaps we should call this “monetary policy theater.”

3. Zhi Huang

Just as you pointed out before, businesses don’t invest today not because of high interest rate, but an uncertain legislative environment. Many big corporations are hoarding cash, so there’s little need for them to borrow. On the other hand, banks are still reluctant to lend, especially when the Euro crisis is unfolding and the stock market crashing. It seems from both demand and supply side, lending and borrowing remains weak.

Just a side note, the new prime minister of Thailand is trying to distort market price of rice by setting up a price floor, just as president of Venezuela is making it illegal to charge “outrageous” prices of everyday produce, i.e. fair market price. Your teachings in economics 101 comes to mind…

4. Touc

“…they also don’t want to look like they’re encouraging inflation…”

even though that has been a mandate of the fed all along (inflation, but not at a rate that is alarming).