# Interest Rates for Beginners

For a complete list of Beginners articles, see the Financial Crisis for Beginners page.

One of our regular readers and commenters (and a quite knowledgeable one at that) suggested that we provide an overview of interest rates and the relationship between the Federal Reserve and mortgage rates. So here goes.

An interest rate is the price of money. If you buy a 5-year CD from your bank, it will pay you something like 3% annual interest. You are selling the bank the use of your money for 5 years; in exchange, they are paying you 3% of the money each year. I’m guessing everyone knew that already.

The other basic point you need to understand is how a bond works. A traditional bond is a security with a face value, a coupon, and a maturity.  Let’s take the 10-year U.S. Treasury bond issued on November 17, 2008 as an example. It had a face value of \$100, a coupon of 3.75%, and a maturity of 10 years (a maturity date of 11/15/2018).  If you hold this security, this means that you will get the face value (\$100) back on 11/15/2018, and during the intervening 10 years you will earn 3.75% annual interest on the \$100, or \$3.75 per year. (Treasury bonds pay every 6 months, so you would get \$1.875 every 6 months.) Note however that the price to buy this bond is not necessarily \$100. Treasuries are initially sold at auction, and in this case the 10-year bond sold for \$99.727098. This means that investors valued that bond’s stream of payments (\$1.875 every 6 months for 10 years, then a flat \$100) at about \$99.73, not \$100. The implicit yield is 3.783%, not 3.75%; that means that if you pay \$99.73 and you get that stream of payments, you are earning 3.783% annually on your investment.

Treasury bonds are highly liquid securities, which means that you don’t have to wait 10 years to cash out if you need the money. Instead, you can sell the bond on the secondary market. Right now this bond costs about \$114-10/32, or \$114.31, and the implicit yield is 2.13%. This means that the investor who buys your bond on the secondary market thinks that \$114.31 is the right price for the bond’s stream of payments, and that he will earn a 2.13% yield on his investment. (\$3.75 is more than 2.13% of \$114.31, but after 10 years he will only get \$100 back, not \$114.31.) In the news, you would read that the yield on 10-year Treasuries has fallen over the last month. But this doesn’t affect the Treasury department directly, because Treasury got its money on the day it auctioned the bonds off (11/17/08). However, the next time Treasury issues a 10-year bond, it will probably earn a yield that is pretty close to the yield on the most recent 10-year bond, so changes in yields on the secondary market affect the price at which Treasury can raise money in the future.

In general, the price of a bond (and therefore its yield) depends on three factors: the maturity, or the length of time that you are lending money for; the degree of credit risk, or the risk that you won’t get paid back; and the supply of and demand for money.

OK, that was the introduction. For discussion, I’m going to divide interest rates into three categories: (1) the Federal funds rate; (2) U.S. Treasury yields; and (3) everything else. Within category (3), I’ll spend an extra minute on mortgage rates.

The Federal funds rate

The Federal funds rate is the rate at which U.S. banks lend money to each other overnight. The money in question is the reserves that sit in their bank accounts in the Federal Reserve system. If Bank A has excess reserves at the end of the day and Bank B has a reserve deficit at the end of the day (reserves are the money they have to keep on hand – electronically, at least – in case people ask for it; reserve requirements are set by the Federal Reserve), Bank A will loan the money to Bank B for a period of one day. The rate of interest Bank A will charge is the Federal funds rate.

The Federal funds rate is almost the lowest rate of interest in the economy. (Right now the target for the Federal funds rate is 0.00-0.25%.) This is because the party borrowing the money is a bank that is regulated by the Federal Reserve, and hence unlikely to go bankrupt (put the last few months out of your mind for the moment), especially not in the next 24 hours. Also, there isn’t a lot else Bank A can do with the money, so the opportunity cost is low.

In ordinary times the Federal funds rate is the only rate that is set by the Federal Reserve, and the Fed doesn’t even set it directly; notice that the loan in question is a private transaction between two private entities. Instead, the Fed influences the Federal funds rate by controlling the amount of money in the system (by buying and selling Treasury securities); the more money available, the lower the interest rates that banks will charge each other. Over the last decade or so, the Fed was able to keep the actual Federal funds rate quite close to its target rate, which is the one that gets announced every six weeks. (This has broken down recently, for reasons I won’t get into.)

For more on the Federal funds rate, see Federal Reserve for Beginners.

U.S. Treasury yields

When the Federal Reserve changes the Federal funds rate, its effects ripple out through the economy, but with all sorts of lags and dampening effects. Broadly speaking, interest rates can differ from the Fed funds rate for two reasons:  maturity (the amount of time you are lending money for) and credit risk (the risk that you won’t get paid back). We’ll talk first about U.S. Treasuries, because “by definition” they involve no credit risk.

The Treasury Department raises money by issuing bonds that range in maturity from a few days to 30 years. At the low end, there is virtually no risk of any sort, so the yield is purely a function of supply and demand; if a lot of people have money and nothing else to do with it, yields will be low. There was an auction today for 4-week Treasury bills, and the yield was exactly zero; people are lending money to the government for free.

With a longer maturity, however, there is risk, even when lending to the U.S. government. The main risk is inflation. Because all the payment stream of a bond is fixed in nominal terms, the higher inflation is over the maturity of the bond, the less it will be worth to you in real terms. What matters here is not the current rate of inflation, but investors’ expectations of what inflation will be over the maturity of the bond. If investors expect inflation to go up, they will demand higher yields to compensate; even if they expect inflation to remain steady, they will still demand a higher yield for a longer-maturity bond, because the longer maturity means there is more time in which inflation could increase. There may also be some question of whether, over a longer time horizon, the U.S. government is more likely to default on its debt; however, I don’t want to get into this, because it starts raising some complex issues (like, if the U.S. government defaults on its debt, what kind of world would we be living in?).

Right now, yields range from zero on the 4-week T-bill to 2.60% on the 30-year bond. (These are all at or near historic lows.)

Everything else

In the world of economics and finance, Treasury securities are generally considered risk-free. So for any maturity you want to invest in, you always have the option of buying a Treasury bill or bond. In order to be able to borrow money, entities other than the U.S. government have to offer higher yields. The yield of anything other than the U.S. government can be thought of as having two components: the Treasury yield (with a similar maturity) and the spread over the Treasury yield, which is the risk premium (the additional yield that investors demand to compensate for the additional risk of the borrower).

That spread is determined by a few major factors, of which I’ll mention three: (a) the creditworthiness of the borrower; (b) whether the loan is secured; and (c) the general state of the economy.

(a) The less creditworthy the borrower, the higher the interest rate, since lenders require additional yield to compensate for the risk of default. For bonds issued by governments and businesses, creditworthiness is generally determined by the bond rating agencies, who look at fundamental factors like projected cash flows and debt burdens to estimate the likelihood of a default. Each agency has a scale of ratings that it uses; the top few rungs are considered “investment grade,” and everything else is “junk,” which was recently euphemised into “high yield.” For individuals, creditworthiness is determined based on your credit score (calculated based on factors such as your past payment history, current debt outstanding, current credit available, etc.) and other attributes of your financial situation, such as your income and assets.

(b) A secured loan is one where the borrower pledges collateral to the lender, as in a home mortgage or a car loan. Lenders will accept lower interest rates for these loans than for unsecured loans, such as credit cards.

(c) The same borrower who pays a low interest rate during good economic times will pay a higher interest rate, or will be unable to get a loan at all, during a recession. In a recession, everyone’s risk of default goes up. This is why all sorts of spreads go up in an economic downturn. For example, the spreads on high-yield (junk) corporate debt are far above their previous record levels at over 20 percentage points. That means that if the yield on a 10-year Treasury is about 2%, the yield on a 10-year junk bond is over 22%.

Mortgage rates

For current purposes, I’m just going to talk about traditional, 30-year fixed-rate mortgages.

Even when it has a nominal 30-year maturity, the average mortgage only lives for about 7 years. For every mortgage that is paid off month after month over 30 years, there are many more mortgages that are prepaid, usually because the mortgage holder refinances or sells the house. So when a bank loans money to homeowners, or an investor buys mortgages or mortgage-backed securities, he is thinking that the maturity will be about 7 years.

As a result, people generally think of mortgage rates as the spread over the 10-year Treasury yield. That is, people investing in mortgages, which have some default risk, have the option of buying 10-year Treasury bonds instead, so mortgage rates contain a spread to compensate for that risk.

If you look at this chart comparing 30-year fixed mortage rates to 10-year Treasury yields (among other things), you’ll notice two things. First, on a month-to-month basis, the two seem to move together. Second, however, over longer periods of time, the spread can change. In 2006 and the first half of 2007 the spread was a little less than 2 percentage points, but by early 2008 it had widened to a little over 3 percentage points, where it is today. (Some people argue that this is proof that mortgage rates are not related to 10-year Treasury yields. I think that’s just a product of how you look at things. Because the spread can change, the two are obviously not linked. But conceptually, I think it still makes sense to think of the mortgage rate as being composed of the Treasury yield plus a changing spread.) The spread has gone up for the reasons we’re all familiar with; after a long period of thinking that mortgages were absolutely safe, now lenders and investors think they are risky again, so they are demanding higher yields in exchange for their money.)

You’ll note that that chart was intended to make a different point: that the Federal funds target rate does not affect mortgage rates. That’s because the Fed funds rate has only a limited impact on the 10-year Treasury. Remember, the 10-year Treasury yield is primarily determined by inflation expectations, and a lower Fed funds target rate is not going to by itself reduce inflation expectations (arguably it would increase them). This is why the conventional wisdom is that the Fed has limited ability to affect long-term interest rates. Recently, however, Bernanke has started talking about the Fed buying hundreds of billions of dollars’ worth of mortgage-backed securities in an effort to push mortgage rates down. This isn’t guaranteed to work, because the Fed is only a small part of the global market for U.S. mortgage-backed securities, but simply announcing the intention has already brought mortgage rates down significantly.

Mortgage rates are an unusual case because the government has another lever it can use to influence them. Fannie Mae and Freddie Mac make up a large part of the secondary market for home mortgages, in two ways. First, they buy mortgages from lenders. Second, they bundle together mortgages from lenders into mortgage-backed securities, which they then issue back to the lenders (who typically sell the securities to investors). Therefore, the price that Fannie and Freddie are willing to pay for mortgages plays a large role in setting the interest rates that lenders charge borrowers. The Hubbard-Mayer mortgage proposal that I reviewed a while back is predicated on the observation that the mortgage spread is unusually high (as mentioned above), and it’s high because the spread for Fannie and Freddie bonds (their cost of money) is unusually high.

Clarification: Fannie and Freddie want to make profits, which means that the interest rate they charge on mortgages (I know they don’t lend directly, but by purchasing mortgages they are effectively doing the same thing as far as interest rates are concerned) has to be higher than the interest rate they pay on their own bonds. Since the credit crisis began, but especially since July, there has been a tremendous “flight to quality” in the bond markets: that is, investors have been selling everything that has even the slightest risk, and buying Treasuries instead. This pushes the yields of Treasuries down and the yields of everything else – including Fannie/Freddie debt- up, widening the spread.

If the Treasury Department can bring down the Fannie/Freddie spread to where it should be, given that Fannie and Freddie are more or less backed by the government anyway, then they will be able to pay more for mortgages, lowering the interest rates that lenders have to charge borrowers.

Clarification: There are at least two ways that Treasury can bring down the Fannie/Freddie spread. The first, which Krugman recommends, is simply to announce that debt issued by Fannie and Freddie is backed by the “full faith and credit” of the U.S. government. That will make it equivalent to Treasuries from a risk perspective. Right now, although Fannie and Freddie are government-chartered and in a government conservatorship (meaning the government is calling the shots), their debt is still not explicitly guaranteed by the government. The second, which Hubbard and Mayer recommend, would be for Treasury to issue additional debt themselves, and then lend the proceeds to Fannie/Freddie at a lower interest rate than they currently have to pay on the open market. Note that either one of these would reduce the spread, but not solely by bringing down the yields for Fannie/Freddie; Treasury yields would also go up somewhat. First, by increasing demand for Fannie/Freddie debt, this would reduce demand for Treasuries. Second, because Fannie/Freddie debt would be explicitly guaranteed, some people would think that this increases the overall riskiness of the U.S. government as a borrower. Some people would also think that it increases the risk that the government will choose to print money to pay off the debt, which would create inflation – and higher inflation expectations mean higher Treasury yields.

As always, if you see any mistakes I made, please point them out.

Update: Krugman has a nice chart with the recent spread between mortgages and 10-year Treasuries. He thinks that the spread is too high and that the government can bring it down.

Update: Thanks to the corrections by Jim W and Durable Investor, I changed my incorrect usage of “duration” to “maturity.”

Update: Simon Johnson talked to the Planet Money guys about the Fed funds rate and other interest rates. The segment starts about 2 minutes in.

### 20 responses to “Interest Rates for Beginners”

1. anon

Thank you. Good basic stuff. You covered it very well.

2. Larry

Hi James, Thanks for the primer. I’m one of the beginners for whom you wrote it, and there were just a couple of things I didn’t follow. If you can help me, I’d appreciate it.

In your example of how a bond works, the table shown, http://www.treasurydirect.gov/RI/OFNtebnd , calls the 10 year security a “note”, the only ones identified as “bonds” have a 29 year, 6 or 9 month term (which raises a second question, why not an even 30 years?). What’s the distinction between a “note” and a “bond”?

Then, in the section on mortgage spread, in the last paragraph, you say “the mortgage spread is unusually high (as mentioned above), and it’s high because the spread for Fannie and Freddie bonds (their cost of money) is unusually high.” Why is that?

Then you go on to say “If the Treasury Department can bring down the Fannie/Freddie spread to where it should be,….”. How do they do that?

Thanks, read your blog every day, and have learned a lot and hope to learn a lot more.

3. James Kwak

Offhand I’m not sure what a note is. Short-duration Treasury securities are called “bills,” and long-duration Treasuries are called “bonds,” for no good reason that I know of.

4. Tyler

James, what do you mean when you say that Fannie and Freddie are essentially backed by the government? I was under the impression that the government has fully taken over both entities. Thanks for all the good info.

5. Bill W.

10 year and shorter debt maturities are defined as notes. Greater than 10 years are technically bonds.

Functionally, as debt instruments, there are no differences except their duration.

6. D.H.LIM

The difference between bills, notes and bonds are the length until maturity:

Treasury bills are issued for terms less than a year.
Treasury notes are issued in terms of 2, 3, 5, and 10 years.
Treasury bonds are issued in terms of 30 years, and have just recently been reintroduced in February 2006.
—————————————————-

Probably, bonds with maturity of 29.x are considered as “bonds”.
Anyway, thank you for your great posting, Mr.Kwak.

7. Jim W

Very nice intro, but please do not use “duration” for maturity or tenor of the bond. Duration is the name for measures of bond’s price sensitivity to changes in interest rates. A bond with a duration of 3 years would see its price change by about 3 percent if rates move by 100 basis points. As might be expected, duration is a function of a bond’s maturity (or time to reset for variable rate bonds) and other factors.

8. Tom K

James, this is excellent. I now have a much better understanding of the relationship between 10 year Treasury rates and mortgage rates.

You, Simon, and Peter are to be commended. You have provided a great service for the public with this website.

9. Bill W.

Anything with a maturity longer than 10 years is a bond, regardless of the length of maturity from when it was issued. EX: the treasury issued a 30 bond in 1986, maturing in 2016. It is now a note since it matures in less than 10 years.

Bills, by definition, have no coupon. They are issued at a discount and mature at par, the differnce is considered “interest.” Therefore, a note or a bond could never be considered a bill, since notes and bonds pay regular coupon interest payments.

10. I was holding money in Freddie Mac and they called the note. Is that because of the buy out by the government of Freddie Mac?

11. Trung Ly

Thanks for the post. I just want to ask a quick question. If the Fed has been quite successful to keep the federal funds rate close to its target, why is the TED Spread so high? As the interest rate on the 3-month Treasury bill is around 0.01 and the federal funds rate is somewhere between 0.00 and 0.25, I think the TED Spread should be lower than it actually is. Please explain or correct me if I misunderstand something about these rates. They’re kind of confusing.

12. Jim W

Pete – You invested in a “callable” bond. In exchange for a slightly higher coupon rate, you gave Freddie the right to call the bond. They will do so when interest rates fall. Freddie uses the bond to fund their portfolio. When rates decline, they can call existing callable bonds and issue new bonds at the now lower rate. This reduces their funding costs. The call decision had nothing to do with being in a govt conservatorship.

13. Durable Investor

I want to echo Jim W’s comment: duration and maturity are not the same thing. There is a very important difference for investors. The post consistently uses “duration” when maturity is what is being discussed. Otherwise, excellent info as usual.

14. Jimbo

Trung,

The TED spread is a different beast – it is the spread between t-bills and Libor (the “ED” comes from the symbol for eurodollar futures on the CME, which track the Libor) The Libor is the interest rate paid on dollar deposits by non-U.S. banks (Hence the name: “London inter-bank offered rate”) For a primer on Eurodollars, go here: http://wfhummel.net/eurodollars.html The Libor is a dollar interest rate that is of the exact same duration as a T-bill, but that is not guaranteed by the govt. Thus, the spread between the 2 rates is a measure of the “fear factor” in the markets.

As to the main post: good overall, but you miss the main determinant of T-note yeilds: it’s not inflationary espectations, etc, but simply projections about what the Fed will do. Since the U.S. is a sovereign currency issuer, it (through it’s central bank) can set interest rates on it’s debt at any level it chooses (in point of fact, the only real purpose for a currency issuer to sell debt is to support non-zero interest rates) Thus, since in our current arrangment the Fed closely controls short term rates while allowing long rates to float, longer rates must necessarily be set by expectations about future Fed action. If the Fed set the FF rate at 1% and announced it’s intention to keep it there for 30 years, long term rates would have to come down. See: http://www.moslereconomics.com/mandatory-readings/the-natural-rate-of-interest-is-zero/

15. James Kwak

Thanks to Jim W and Durable Investor for catching my mistake with duration and maturity. I just fixed it. And thanks to Jim W and Jimbo for answering other readers’ questions.

To Tyler’s question: Fannie and Freddie are in a government conservatorship, which means that the government is running them. But they have not been absorbed into the Treasury department, so their debt is not equivalent to Treasuries.

16. Ash

On the secondary market, how is \$114.31 calculated and not a different number. Is there a formula that determines this number. Also, how is yield 2.13% is calculated. What happens to the spread between \$100 the origin value and \$114.31.