NEW YORK (Fortune) -- There are two things you may have heard about the Federal Reserve Board, both of which are wrong.

The first is that the Fed controls U.S. interest rates.

The second is that the Fed has made so many commitments that it's in danger of running out of cash or Treasury securities. Which would mean it couldn't carry out its declared policy of putting cash into the world financial system or its undeclared policy of keeping institutions that it deems worthy afloat. Let me show you why both of these beliefs are myths, not reality.

Let's do interest rates first. It's the more common myth, created partly by sloppiness among people in my business who write (and say) things like, "The Fed cut interest rates today."

In fact, we should always insert "short-term" before "interest rates" when we talk about the Fed's control. That because the Fed controls only some short-term rates, primarily the so-called Federal funds rate that financial institutions charge each other for overnight loans. The financial markets set long-term rates, which often don't move in the same direction as the Fed funds rate.

The case in point: the relationship - or lack of one - between the Fed funds rate and the interest rate on long-term mortgages.

Since September, the Fed has reduced the Fed funds rate by 62% - to 2% from the previous 5.25%. But long-term mortgage rates are higher than on Sept. 18, when the Fed began its rate cuts, as you can see from the adjacent graphic, which is based on numbers from mortgage experts HSH Associates.

The rate on a 30-year fixed-rate conforming mortgage - "conforming" means that the mortgage is eligible for sale to mortgage guarantors Fannie Mae (FNM, Fortune 500) or Freddie Mac (FRE, Fortune 500) - was 6.44% the week before the Fed's first cut, and was recently 6.51%. Jumbo mortgages - mortgages too big to be considered conforming - were going for 7.63%, up from 7.26%. (All of these numbers include up-front points that borrowers pay, in addition to their basic interest rate.)

The Fed and Treasury - along with many of the world's big financial players - would love to have U.S. mortgage rates decline, because that would lend support to home prices, which could use it.

Falling home values - what we have in most U.S. housing markets - increase foreclosures, which increase borrowers' pain and lenders' losses. The declining value of houses as collateral for mortgages makes mortgage lenders less eager to lend, and makes potential home purchasers far less eager to buy. It's a vicious cycle that will end sooner or later - everything does - but it's not something that the Fed (or any individual regulator or player) can control.

The Fed cut short-term rates to help mitigate the panics that have been sweeping the world financial markets for more than a year. In addition, those lower rates - in theory, at least - help prop up the U.S. economy.

But you can also argue that the Fed's lowering of short-term rates has raised inflation fears and contributed to the decline of the dollar in international markets, which in turn has affected commodities prices, whose massive increases are a major factor in U.S. inflation. So repeat after me: the Fed can set only short-term rates. Which may contribute to having long-term rates act in ways that the Fed didn't intend, and doesn't particularly like.

Can the Fed afford it?

There's an idea out there that the Fed may run out of money or government securities as a result of the huge, high-dollar programs that it and the Treasury have launched, or could end up having to launch, to keep financial markets afloat.

Fed chief Ben Bernanke and his crew have recently embarked on two programs that have raised questions about how it can afford its commitments. First, it will now lend directly not just to commercial banks, but also to institutions, like investment banks. Second, it will now lend selected borrowers Treasury securities (which they can then sell or borrow against) in return for securities (like some mortgage-backed bonds) that can't be sold or borrowed against for anything close to their stated value.

The worry is that the Fed owns only about $800 billion of Treasury securities, and all these existing programs, not to mention possibly helping arrange huge loans to Fannie Mae and Freddie Mac under a bailout plan now being kicked around, would consume a total of more than $800 billion.

But that worry overlooks the Fed's amazing power to create as much money as it needs - out of nothing, as it were.

Here's how it works. If an institution borrows, say, $50 billion from the Fed, the Fed can just post a $50 billion credit to the bank's account at the Fed, and the borrower can spend that balance on whatever it wants. It is indeed as if the Fed created cash out of nothing.

And if the Fed somehow needed more than $800 billion of Treasury securities, it could buy them in the open market, and deposit the payment for them in the seller's Fed account. That way, the Fed could lay its hands on however many Treasury securities it needed.

Yes, I'll grant you that this sounds odd. But if you ask a Fednik how this all works, he (or she) would tell you what I've just told you. Except that it would be dressed up in fancier language, with all sorts of explanations of how the Fed can do all this and still carry out its monetary policy.

Why am I bothering you with this stuff in mid-summer, a time when I'd rather be off drinking something cold than trying to deal with the Fed?

Because myths get in the way of understanding. And if there were ever a time when understanding the Fed's powers - and limitations - matters, that time is now.