An Introduction to Interest Rates
It is important that we have a good understanding of what interest rate is before we proceed to discuss some of the key concepts and issues of money and banking. Interest rates represent the prices of credit, which include both borrowing and lending. We are familiar with different uses of credit.
(a)Borrowing: Home mortgages, car loans, credit cards, etc.
(b)Lending: Opening a savings account (i.e. “lending” to the bank), buying a government bond (i.e. “lending” to the government), etc.
Interest rate plays a very important role in the economy because it determines the spending and savings behaviors of individuals and companies.
(1)If interest rate rises, the “cost” of spending increases and hence individuals and companies save more.
(2)If interest rate falls, the “cost” of spending decreases and hence individuals and companies spend more.
When it comes to the definition of interest rate, the most basic definition is the price of credit. However, that does not mean that there is only a single interest rate in an economy.[1] The term (or life) of the credit and the amount of the credit will have an impact on the price of the credit (i.e. interest rate).[2]
In addition, the amount of interest paid/received depends on:
(1)The amount loaned or borrowed (i.e. the principal).
(2)The length of time the amount is loaned or borrowed (i.e. the term of the credit).
(3)The stated (or nominal) interest rate.
(4)The repayment schedule (i.e. how often the interest is paid and how the principal should be paid back).
(5)The method used to calculate the interest payments.
Ways of calculating interest rates
There are many ways of determining the interest payments and some of them can be quite complicated. The following are some of the more common ways of calculating interest payments that you might encounter: (i) simple interest, (ii) bank discount, and (iii) compound interest.
(i) Simple interest
The saver only receives interest payment on the principal for the time period it is in a savings account. In other words, there will be no interest paid on the accumulated interest remaining in the account.
Example: Suppose you deposit $1,000 into a savings account that pay a simple interest rate of 4% for 5 years, assuming that the bank pays its interest once a year. How much interest will you earn at the end of the 5-year period? And how much money is in your account (if you do not withdraw the interest)?
(ii) Bank discount
With the bank discount method, the full interest payment is first determined from the amount of money borrowed, and then the borrower will receive the difference. In other words, the borrower has to pay the interest payments up front when he/she first takes out the loan. This is a very common method used by banks on short-term loans taken out by businesses.[3] It is important to note that the interest rate a borrower effectively paid is different from the nominal interest rate quoted. This is best illustrated with the following example.
Example: Suppose Orange, Inc. took out a $10,000 loan from St. Nick Federal for 1 year at 7% interest and the interest payment is determined on a bank discount method. What is the interest rate Orange, Inc. has effectively paid for that loan?
From the example above, we know that even though Orange, Inc. is quoted an annual rate of 7%, it effectively is paying an interest of 7.53% because it is only “getting” $9,300 from the bank rather than $10,000 (and yet it is paying interest on the full $10,000).
(iii) Compound interest rate
Unlike the simple interest rate, if the saver decides to keep the interest payment received in the savings account, interest will be paid on those interest payments. As a result:
The compound interest rate technique is a more common practice than the simple interest rate technique in the real word.
Example: Suppose the bank decides to pay compound interest rather than simple interest, how would that change your answers to the previous example?
Similar to the bank discount method, the nominal interest rate quoted under a compound interest method usually differs from the interest rate the borrower and lender effectively paid and received, respectively, due to the compounding factor.
We need to look at the effective annual interest rate in order to determine the actual interest rate received or paid for a year.
wherer = quoted annual rate
m = number of times interest is compounded
Example: In the previous example, the bank is compounding its interest once a year. Suppose the bank starts paying its interest once every six months, how much interest will you actually earn?
Interest rate (or return) of money market and fixed-income capital instruments
So far, we have looked at interest as the price of borrowing and lending between individuals, and between an individual and an institution (e.g. a saver and a bank). There are other forms borrowing and lending which involve the exchange of a security. For example, an individual can “lend” the U.S. Federal government by buying a U.S. treasury securities. We will divide such securities into two different categories: (1) money market instruments and (2) fixed income debt instruments.
- Money market instruments
Money market instruments are financial securities that have very short life spans, and they are very homogenous financial instruments, i.e. they share very similar features:
- They are short-term instruments with life spans of less than a year.
- They are very high quality securities, i.e. very low default risk.
- They have very high denominations (or face value).
- They are usually sold at discount, i.e. they are sold for less than their face values.
Quoting prices for the financial instruments
Before we proceed further in discussing the various financial instruments and the interest rates (or returns) associated with them, we need to first understand how their prices are quoted in the newspaper and by the brokers who buy and sell them. When you ask your broker for the price of a particular security, you are usually quoted either the bid price or the ask price (depending on whether you are selling or buying the security).
Bid price: the price that a broker (or dealer) is willing to buy
Ask price: the price that a broker (or dealer) is willing to sell
In this case, you will be paying the ask price when you buy a security and receiving the bid price when you are selling a security.
There are 8 general types of money market instruments:
(i) Treasury bills (T-bills)
The T-bill is the shortest security offered by the federal government. It usually has a life of 91 days (13 weeks or 3 months), 182 days (26 weeks or 6 months), and 52 weeks (1 year); and has a face value of $10,000.
New issues of the T-bills are auctioned off at the Federal reserve banks, and individual and institutional investors can bid for them. 3 months and 6 months T-bills are auctioned off every week (on Monday), and 1 year T-bills are auctioned off every month (on the fourth Thursday). Existing issues of T-bills can be purchased directly from the Fed or from brokers (that are government securities dealer).
Pricing of a T-bill
Since T-bills do not pay interest, you buy the T-bills on discount (i.e. paying a price less than the face value), and you receive the face value on maturity. Since T-bills are bought and sold at discount, their prices are not quoted directly. You are quoted the discount that you will receive/pay for the T-bills. In addition, the discount is quoted on an annual basis so you will need to adjust the discount based on the life of the T-bill. To actually determine the bid or asked price of the T-bill, you need to use the following formula:
where= bid discount rate if selling or asked discount rate if buying
n = number of days to maturity
Example: The following table is taken from the Feb 19, 1997 Treasury Bills table in the Wall Street Journal. As an investor, you are interested in buying one Jun 5, 1997 T-bill and selling one Jun 19, 1997 T-bill from your portfolio. What price will you pay for the Jun 5, 1997 T-bill? And what price will you receive for the Jun 19, 1997 T-bill?
Maturity / Days to mat. / Bid / Asked / Chg. / Ask Yld.Jun 05 ’97 / 106 / 4.96 / 4.94 / +0.01 / 5.08
Jun 12 ’97 / 113 / 4.95 / 4.93 / +0.01 / 5.08
Jun 19 ’97 / 120 / 4.98 / 4.96 / +0.03 / 5.11
Jun 26 ’97 / 127 / 4.98 / 4.96 / +0.03 / 5.12
(i) Price paid for Jun 5, 1997 T-bill (asked price)
(ii) Price received for Jun 19, 1997 T-bill (bid price)
The return (or yield) of a T-bill
As an investor, you are interested in the return earned by a particular T-bill you have bought (hence the asked yield). However, you have to make certain adjustments before you can compare the T-bill’s yield rate to another financial instrument’s yield rate for the following two reasons:
(i) T-bill does not pay interest payment. The “interest payment” receives by an investor comes in the form of the discount receives.
(ii) The price of a T-bill is computed using a 360-days calendar year rather than a 365-days calendar year, which is common in computing the yield of most financial instruments.
In order to compare the return of a T-bill to other financial instruments, we need to compute the T-bill’s bond equivalent yield () using the following formula:
The above formula is very tedious because we need to first solve for the T-bill’s asked price. We can simplify it by substituting the formula for P we have discussed earlier. As a result, the bond equivalent yield is computed as follows:
Example: Using the same T-bill price sheet, verify that the asked yield (i.e. bond equivalent yield) of a Jun 19, 1996 T-bill is 5.11%.
(ii) Federal funds
All commercial banks and depository institutions are required by law to hold reserves for the deposits at its branches with its district Federal Reserve Bank. Each institution is required to keep a certain percentage of its total deposits as reserves. This is like keeping a non-interest-bearing checking account with a Federal Reserve Bank.
If a bank is temporarily short of its required reserve, it can borrow from other banks that have excess reserves. In other words, the banks can trade reserves among themselves. The amount of money traded for this purpose is known as federal funds. They are usually traded (or borrowed) for a very short period of time: overnight to 3 days.
(iii) Commercial paper
One of the short-term financing sources for a firm to meet its current obligations is the commercial paper. They are short-term (usually less than 270 days) unsecured (i.e. not backed by any asset) promissory notes with a fixed maturity. Commercial papers usually have a very large face value (with the smallest denomination at $100,000), and they are traded at discount (i.e. selling at less than the face value).
(iv) Negotiable certificates of deposits (CD)
Most of you have some experience dealing with CDs at a local bank. That is when you put aside a certain amount of money for a fixed period of time (and there is a penalty for early withdrawal). Such CDs are non-negotiable, i.e. you cannot sell this CD to another person.
The CDs which can be classified as money market instruments are those issued by banks and S&Ls. They have a very large denomination (or face value) in the amount of $1 million per CD. Unlike most other money market instruments, such CDs do pay interest to their holders on the maturity date. In addition, they are negotiable, i.e. they can be sold to another person. These negotiable CDs have a maturity date of at least 14 days. However, most of them are issued at 30 and 60 days.
(v) Eurodollar deposits
Eurodollar deposits are US dollar-denominated deposits kept at banks outside the United States. These are large time deposits with a maturity of less than 6 months. Most of these deposits are concentrated in London, which is one of the world’s and Europe’s largest financial market.
(vi) Banker’s acceptance
Banker’s acceptance dates back to the 12th century when they are used to finance international trades. It is simply a promissory note issued by a credit worthy bank guaranteeing the exporter will make the payment once the shipment has been received. Banker’s acceptances are usually traded at discount once it is issued. The last holder of the banker’s acceptance will receive the face value from the exporter’s bank.
(vii) Repurchasing agreements (Repos)
A repurchasing agreement is simply the sale of securities (usually treasury securities) with the promise of buying them back at a higher price at a later date. They are usually issued by corporations, state and local governments, and some other big non-bank institutions. The concept of a repurchasing agreements market is very similar to a federal funds market. In that case, why does a repurchasing agreements market exist? That is because the federal funds market is only open to depository institutions.
(viii) Broker’s calls
As an investor, you do not have to pay the full amount for the securities you purchased through a broker. You can set up a margin account. In other words, you can borrow part of the money from your broker. In other to loan you the money, the broker can borrow the money from a bank. The amount borrow is the broker’s call.
As we have discussed earlier, money market instruments are very homogenous financial securities. As a result, the rates (or yields) for each type of money market instruments are pretty standardized regardless of the issuers. You can find the rates for the different money market instruments in the Money Rate table of WSJ’s Credit Markets section.
2. Fixed income capital market instruments
Unlike money market instruments, fixed income capital market instruments do pay interest payment on a regular basis. That is why they are called fixed income instruments, because holders of these instruments receive a fixed amount of interest payments on a regular basis and a known face value on the maturity date. They are capital market instruments because they have a maturity of more than a year (and some go up to 30 years). There are 5 general types of fixed income capital market instruments:
(i) T-notes and T-bonds
T-notes and T-bonds have longer life spans than T-bills: T-notes are usually 2 to 10 years, and T-bonds are usually 10 to 30 years. Unlike T-bills, T-notes and T-bonds pay interest periodically on a semi-annual basis.
You have to be very careful when reading the price quotes for T-notes and T-bonds. Their “prices” are quoted as a percentage of the face value (which is usually $1000). In addition, they are quoted in 1/32, e.g. 100: 16 is 100 16/32. Do not confuse the colon with a period. Why is this the case? That is because 1/32 used to be the Spanish dollar units.
As a result, the actual bid or asked price is determined as follows:
wherer = “price” quoted as percentage of face value
Example: The following table is taken from the Nov 6, 1995 Govt. Bonds & Notes table in the Wall Street Journal. As an investor, you are interested in buying one 7 7/8 % Aug 2001 T-bond and selling one 7½% Nov 2001 T-bond from your portfolio. What price will you pay for the Aug 2001 T-bond? And what price will you receive for the Nov 2001 T-bond?
Rate / MaturityMth/Yr. / Bid / Asked / Chg. / Ask
Yld.
7 7/8 / Aug 01n / 110:09 / 110:11 / -4 / 5.74
8 / Aug 96-01 / 101:24 / 101:28 / +1 / 5.49
13 3/8 / Aug 01 / 136:31 / 137:03 / -5 / 5.74
7 1/2 / Nov 01n / 108:23 / 108:25 / -2 / 5.75
(i) Price paid for 7 7/8 % Aug 2001 T-bond (asked price)
(ii) Price received for 7½% Nov 2001 T-bond (bid price)
(ii) Agency debts
There are a number of federally sponsored agencies (which are privately owned entities) that make loans to a certain class of borrowers. The reason such agencies exist is because the Congress believes that the supply of credit is too limited, too variable or too expensive for certain class of borrowers. These agencies are set up to provide dependable sources of credit at the lowest possible cost. These agencies issue their own debt instruments to raise money to make various types of loans.
The following are examples of some federally sponsored agencies:
1. Agencies issuing mortgage related debt
a. Federal Home Loan Bank (FHLB)
b. Federal National Mortgage Association (FNMA) or Fannie Mae
c. Government National Mortgage Association (GNMA) or Ginnie Mae
d. Federal Home Loan Mortgage Corporation (FHLMC) or Freddie Mac
2. Agencies issuing farm related debt
a. Farm Credit Financial Assistance Corporation
b. FederalLand Banks
c. Federal Intermediate Credit Banks
Pricing of agency debts
The pricing of agency debts is very similar to the pricing of T-notes and T-bonds: it uses the “:” to represent 1/32.
(iii) Municipal bonds
In addition to the federal government, there are other governmental units in the United States which can be group as states, counties, municipalities, townships, school districts and special districts. Many of these governmental units raise money by issuing municipal bonds (or Munis).
There are three different types of municipal bonds:
1. Revenue bonds: These are bonds issued to financed a particular project. Revenues generated by the project will be used to pay the interest payments and repay the principal.
2. General Obligation bonds (GOs): These are bonds that are backed simply by the full faith and credit of the governmental units that they will make the interest payments and repay the principal.
3. Industrial Development bonds (IDBs): These are bonds used to finance the purchase or construction of industrial facilities that will be leased to firms at favorable rates.
(iv) Corporate bonds
As we have discussed earlier, a firm can raise money by issuing debt instruments. They will issue commercial papers for short-term needs, and corporate bonds for long-term needs. Issuing corporate bonds is more complicated than issuing commercial papers because the firm needs to prepare a lengthy legal document and seek approval from the Securities and Exchange Commission (SEC).