Bonds, Borrowing, and Lending

Introduction

A bond is a promise to pay. It is a promise to pay something in the future in exchange for receiving something today.

Promises—that is, bonds—can be bought and sold. The buyer of a bond is a lender. The seller of a bond is a borrower. The bond buyers pay now in exchange for promises of future repayment—that is, they are lenders. The bond sellers receive money now and in exchange for their promises of future repayment—that is, they are borrowers.

Bonds can be traded privately between individuals or in organized markets, called bond markets or credit markets.

You may not realize it, but you buy and sell bonds all the time! Every time you lend someone a few dollars for lunch or borrow your friend’s car in exchange for filling her tank, in economic terms you are buying and selling bonds. Simply remembering that bond buyers are lenders, bond sellers are borrowers, and that they are trading not pieces of paper but promises, can unlock the door to understanding both the vocabulary and the economics of a wide range of economic behavior, from private loans to interest rates to government budget deficits. It’s much easier to understand borrowing and lending than abstract vocabulary like “the bond market”—even though they are the same thing—because we can by think about our own familiar experiences with borrowing and lending.

Interest and interest rates

In addition to repaying the principal, or original amount borrowed, the borrower usually pays interest to the lender. In economics, the interest is a payment for the service of having the money or resources in advance.

When your parents lend you $1000 to help buy a car in exchange for your promise to repay them $100/month, and for your agreeing to keep your room a little cleaner, the $1000 is the principal and the room cleaning is the interest. In economic lingo, your parents bought your $1000 bond. Bonds within families and between friends often trade with the appearance of zero interest. In actuality, interest is usually paid with goods or services, increased courtesy, or an implicit commitment to help each other out similarly in the future. Just because there is no money involved doesn’t always mean a loan comes free!

The interest rate is the amount of the interest expressed as a percentage of the principal. Thus, if someone lends you $100 and you agree to repay him $110 a year later, the interest rate is 10%, which equals the interest divided by the principal, or ($110-$100)/$100.

Interest rates are usually expressed on an annualized basis. If someone lends you $100 and you agree to repay him $110 in six months, the six-month rate of interest is 10%. But 10% every six months is 20% per year. That is, the annualized rate of interest is 20%. (To see this, imagine that in six months you repaid the $110, and that same day borrowed $100 with another agreement to pay $110 in another six months. You’ve essentially borrowed $100 for a year, but paid a total of $20 in interest for the year.) The moral is that you should be careful when comparing interest rates by making sure they are all for the same period of time. Reporting annualized rates is required by law for some kinds of loans, but not all.

Interest rates are also often computed as compound rates of interest. A compound rate of interest pays interest on the interest. For more on this topic, see Compound Interest. From an economic perspective, the ideas are the same as for the simple interest rates we use in our examples. The arithmetic is simply a little more precise.

Interest rates and risk

Let’s look at some more examples of bonds in economics.

When you use your credit cards or buy on installment, you are a borrower. In each case, someone—a bank or business owner—lends you the money by directly paying for the goods up front on your behalf. The lender later sends you a bill, at which time you are responsible to pay the principal and any accumulated interest to the lender. In economic terms, every time you use your credit card, you sell a bond—your promise to repay the credit card company in the future.

When you deposit money in a bank, you are a lender! In economic terms, you buy the bank’s bond—its commitment to repay you when you decide to use the money. The bank acts as an intermediary (a go-between) and pairs you with a borrower. The bank pays some of the interest it earns—by lending out your money—directly back to you, the depositor, and takes the rest as payment for its services in matching you up with a borrower. While checking accounts are usually too small and variable for a bank to do this, other kinds of bank accounts such as savings accounts, money market accounts, and certificates of deposit (CDs) earn interest. The small and erratic amounts of interest earned by a bank for checking accounts are usually shared with the depositor by offering services such as “free” checks, “free” online bank access, “free” toaster ovens, and the like.

A risky borrower usually has to pay more interest to convince someone to lend to him or her. If you borrow from your Mom but repay late and don’t do the laundry like you promised, then probably the next time you’ll have to promise to take out the trash as well as do the laundry to convince her to lend to you again. In organized markets, the age of the borrower, whether or not the borrower has a steady job, and whether or not the borrower has a history of paying bills on time all factor into the interest rate a lender offers. A few agencies collect these data for individuals and provide summaries, called credit ratings. The riskier a borrower is, the lower his credit rating will be, and the higher the interest rate he or she may have to pay to borrow in organized bond markets.

Here’s another example. When you buy a Treasury Bill, you are lending to the government. The government sells its promises to pay in organized markets each week. That $50 U.S. Savings Bond your grandparents gave your parents in your name when you were born to help pay for your college education, was a loan your grandparents made to the government. State and local governments also float bonds—that is, sell their promises to pay. (Governments also hold deposits of tax payments, etc., in banks, and thus are also lenders.)

The U.S. Federal Government has a very good track record of repaying on its loans. (In part, that’s because U.S. citizens reliably pay their taxes, which provides the money the government needs to repay its debts!) Consequently, the T-Bill rate—the interest rate paid by the U.S. Government for selling Treasury Bills—is sometimes considered to be a risk-free rate of interest. Banks offer their best borrowers a rate that is usually only slightly higher, called the prime rate. Other borrowers pay risk premiums—higher interest rates reflecting the market’s assessment of their relative riskiness.

Interest rates and bond prices

The price of a bond is what someone pays today for the promise of future payment. If one person offers to pay $110 a year from now, and someone else buys that bond for $100 today, the price of the bond is $100. (That is, in economic terms, the bond price and the principal refer to the same thing.)

Evidently, the higher the price of the bond, the lower the rate of interest, and vice versa. Someone paying $105 today for a promise of $110 a year from now is paying an interest rate of 4.8% (=[$110-$105]/$105), a lower interest rate than the 10% interest paid by someone who pays $100 for that same bond. Similarly, the lower the bond price, the higher the rate of interest. Bond prices and interest rates are inversely related.

Bonds are often sold in auctions, offering them to the highest bidder. The bond seller promises a stated future payment, and auction participants bid. We can equally well say that the bond seller—the borrower—wants to get the highest possible price, or that he wants the lowest possible rate of interest available in the market.

Classroom activity. To illustrate these concepts in the classroom, I’ve often held a bond auction in class! I offer to pay $1.00 on the last day of class, and ask what students will offer for it. Sometimes the class leaps right in. Other times they sit for a moment in shock, too stunned to participate—but if I joke “You mean no one will even buy my bond for even a penny?!” the action usually gets going pretty briskly. (The going bond price is usually about $.90, though occasionally it goes over a dollar, in which case I have to explain that negative rates of interest, wherein the borrower is paid to borrow, do sometimes occur.) When the auction is completed, we calculate the interest rate, and I ceremoniously write out an IOU—which of course I honor on the last day of class! We talk about risk and how my not honoring my debt would get me in trouble as a teacher, which increases what students are willing to pay for my bond. Occasionally during the semester the buyer even sells the bond to another student, illustrating a secondary bond market in action.

Sometimes people casually say that the interest rate is the cost of a loan. That terminology is correct, but it can get you very confused if you are not careful. The cost of a loan—what you pay to convince someone to lend to you—is the inverse of the price of a bond! Remember that a bond is a promise to pay, so the price of a bond is what you pay to buy someone else’s promise. If the bond price goes up, the interest rate—or cost of the loan—goes down.

Supply and demand in the bond market

Why do interest rates go up and down? For the same reason that prices change in any market! In other markets, when the demand increases, the price rises. If supply increases, the price falls. Bond markets work in exactly the same way. Some people find it easier to think about the underlying borrowing and lending involved. Others find it easier to think about the bond market directly. Both approaches give the same answers.

Let’s give it a try.

Suppose a spate of new ideas spurs an increase in investment. Companies suddenly want to borrow more to develop the new ideas for the future. There is an increase in the demand to borrow. With more people looking to borrow, it makes economic sense to think that they’d have to pay more to borrow. And sure enough, that intuition is correct—they have to pay a higher interest rate.

Another way to predict the same result is to think about the bond market. There is an increased demand to borrow to pay for the increased investment opportunities. Since a borrower is a supplier of bonds, that means the supply of bonds has increased. So, according to economics, the price of bonds should fall. (Bond buyers—lenders—naturally offer only lower bond prices in the face of this increased supply.) So the price of bonds falls. And when the price of a bond falls, the interest rate rises.

When you read in the papers that bond prices rose or fell, you should first think about it in terms of the supply and demand for bonds, and then translate that into the language of borrowing and lending. For example, if bond prices fall, that must mean that either the supply of bonds has increased—i.e., borrowing has increased—or the demand for bonds has fallen—i.e., lending has decreased. No matter which way you prefer to figure it out, the resulting rise in interest rates will make sense.

Discount rates and discounted present value (DPV)

Another word associated with interest rates is the discount rate. A discount is similar to interest, but it is paid in advance instead of at the end or over the course of the loan. Thus, if you promise to pay $100 a year from today at an interest rate of 10%, then a year from today you’d fork over $110. An alternative is that you might agree to pay the interest up front, in which case out of the $100 you receive, you immediately pay $10 back to the lender. So, you receive only $90 in cash today, but the day the loan is due you’d only hand over $100 (because you already paid the $10 interest up front). In essence, the lender bought your $100 bond “at a discount”—it only cost him $90 today. You can read more about the details in a book on interest rates.

Economists talk more often about interest rates than about discount rates. However, in the news you sometimes hear things about how the Fed lowered or raised the Discount Rate. What this means is that the Federal Reserve Bank, the issuer of U.S. dollars, changed how much it’s willing to pay to buy certain kinds of bonds. We’ve capitalized “D” and “R” in “Discount Rate” to emphasize that in this case it is a discount rate on a particular kind of bond that the Fed is allowed to buy. The custom in that particular bond market is to pay the interest up front, or to buy the bonds at a discount. You can read more about this in the Federal Reserve System.

A more common use in economics of the word “discount” is in the term discounted present value or DPV. The discounted present value of an amount you have been promised to receive in the future is its value today. It is the amount you’d have to put in a bank today in order to have exactly that promised amount when the future arrives. It’s always less than what you’ll receive in the future because you get interest.

Let’s see this in an example. Suppose your father promises you $100 a year from now if you get an A on your economics final. Your Dad is confident that you will succeed, so he decides to put the cash aside in a bank savings account so he will have enough to pay you a year from now. If he puts $100 in the savings account, and if the savings account pays 10% interest per year, he’ll have $110 at the end of the year. That’s more than he’ll need! How much does he have to put in the account to have exactly $100 at the end of the year? Hmmm. If he puts $90 into the account, he’ll only get $9 in interest, so he’ll only have $99 at the end of the year. It must be more than $90 but less than $100. In fact, the amount he has to put into the account today is $90.91 (rounded to the nearest penny). [It’s the solution to x(1+.10)=$100, or x=$100/(1+.10).] You can check this easily: If he puts $90.91 into the account today, he’ll receive interest of $9.09, for a total of $100 a year from now.

To describe this, we say that, at an interest rate is 10%, the discounted present value of $100 is $90.91. If the interest rate were higher, the discounted present value would be less. (Similarly, at a lower interest rate, the discounted present value would be more.)

Happily, in economics you do not ever have to make these calculations! Economists leave these calculations to bankers, accountants, and actuaries. (I can’t promise your teacher won’t ask you to calculate the present value of some amount, though. That depends on the course you are taking.)

What economists care about is only one fundamental principle: The discounted present value is always less than the promised future amount. The amount you’d have to set aside today in order to have a given amount tomorrow is always less than that future amount because you can get some interest on the amount you set aside. (If you don’t get the interest because you put your money under your mattress instead of in the bank, that’s a somewhat foolish choice on your part, but it doesn’t change the fact that you could have gotten the interest!)

Just by understanding that one principle of discounting and discounted present value can get you very far in understanding financial matters.

Application: Winning the lottery

Why is it that when someone wins a million dollar lottery she can’t just have the million dollars right now? It’s because the fine print probably read that the winnings would be distributed not as $1,000,000 today, but as $100,000 a year for 10 years. But, the discounted present value of those future promises—what they are worth today—is less than a million dollars!

In practice, the lottery sponsor or group that pays out the million dollars in installments of $100,000 a year puts into an account today only the exact amount necessary to get interest payments that will just exactly cover the promised stream of payments. And as we’ve seen, that amount today is always less than the future payment will be, because of the interest that will be earned.

If the prize winner prefers, she can usually receive the discounted present value up front. She could then put that money into an interest-paying account herself, in theory distributing to herself the $100,000 each year. Of course, most people who take their winnings up front don’t have that kind of self-discipline. They may have even better ideas about what to do with it; or they may squander it; but how people decide what to consume or how much to save is a different economic question from how much they have in total to allocate among different uses. The important economic point is just to notice that it’s not an injustice that the prize-winner doesn’t get to have the whole million up front. She’s not being cheated. It’s just a consequence of the opportunity to earn interest. It’s an application of discounted present values.

Lauren F. Landsburg

March 2007