Throughout his text, Mishkin stresses that the evolution of financial markets, both in the U.S. and throughout the world, has resulted from an intricate interplay of three factors: chance, necessity, and design. In short, history matters, and it matters a lot.
In addition, throughout his text Mishkin consistently stresses the importance of information. He argues that it is impossible to understand the special nature of financial markets relative to markets for real goods and services unless one understands the peculiar types of "asymmetric information problems" intrinsically associated with financial assets. He argues that these asymmetric information problems have largely shaped the structure of financial markets in the past, and that the recent surge of innovations in information technology (IT) -- in particular, Internet-related IT -- is leading to a dramatic restucturing of financial markets today.
The notes, below, provide basic background information on financial markets as covered in Mishkin in Chapters 2 and 4. For a more extensive set of notes relating to these and other Mishkin chapters, visit the home page for Econ 353 (Money, Banking, and Financial Institutions)
Lenders are people who have available funds in excess of their desired expenditures that they are attempting to loan out, and borrowers are people who have a shortage of funds relative to their desired expenditures who are seeking to obtain loans. Borrowers attempt to obtain funds from lenders by selling to lenders newly issued claims against the borrowers' real assets, i.e., by selling the lenders newly issued financial assets.
A financial market is a market in which financial assets are traded. In addition to enabling exchange of previously issued financial assets, financial markets facilitate borrowing and lending by facilitating the sale by newly issued financial assets. Examples of financial markets include the New York Stock Exchange (resale of previously issued stock shares), the U.S. government bond market (resale of previously issued bonds), and the U.S. Treasury bills auction (sales of newly issued T-bills). A financial institution is an institution whose primary source of profits is through financial asset transactions. Examples of such financial institutions include discount brokers (e.g., Charles Schwab and Associates), banks, insurance companies, and complex multi-function financial institutions such as Merrill Lynch.
Financial markets serve six basic functions. These functions are briefly listed below:
In attempting to characterize the way financial markets operate, one must consider both the various types of financial institutions that participate in such markets and the various ways in which these markets are structured.
By definition, financial institutions are institutions that participate in financial markets, i.e., in the creation and/or exchange of financial assets. At present in the United States, financial institutions can be roughly classified into the following four categories: "brokers;" "dealers;" "investment bankers;" and "financial intermediaries."
Brokers:
A broker is a commissioned agent of a buyer (or seller) who facilitates trade by locating a seller (or buyer) to complete the desired transaction. A broker does not take a position in the assets he or she trades -- that is, the broker does not maintain inventories in these assets. The profits of brokers are determined by the commissions they charge to the users of their services (either the buyers, the sellers, or both). Examples of brokers include real estate brokers and stock brokers.
Diagrammatic Illustration of a Stock Broker:
Payment ----------------- Payment ------------>| |-------------> Stock | | Stock Buyer | Stock Broker | Seller <-------------|<----------------|<------------- Stock | (Passed Thru) | Stock Shares ----------------- Shares
Dealers:
Like brokers, dealers facilitate trade by matching buyers with sellers of assets; they do not engage in asset transformation. Unlike brokers, however, a dealer can and does "take positions" (i.e., maintain inventories) in the assets he or she trades that permit the dealer to sell out of inventory rather than always having to locate sellers to match every offer to buy. Also, unlike brokers, dealers do not receive sales commissions. Rather, dealers make profits by buying assets at relatively low prices and reselling them at relatively high prices (buy low - sell high). The price at which a dealer offers to sell an asset (the "asked price") minus the price at which a dealer offers to buy an asset (the "bid price") is called the bid-ask spread and represents the dealer's profit margin on the asset exchange. Real-world examples of dealers include car dealers, dealers in U.S. government bonds, and Nasdaq stock dealers.
Diagrammatic Illustration of a Bond Dealer:
Payment ----------------- Payment ------------>| |-------------> Bond | Dealer | Bond Buyer | | Seller <-------------| Bond Inventory |<------------- Bonds | | Bonds -----------------
Investment Banks:
An investment bank assists in the initial sale of newly issued securities (i.e., in IPOs = Initial Public Offerings) by engaging in a number of different activities:
Financial Intermediaries:
Unlike brokers, dealers, and investment banks, financial intermediaries are financial institutions that engage in financial asset transformation. That is, financial intermediaries purchase one kind of financial asset from borrowers -- generally some kind of long-term loan contract whose terms are adapted to the specific circumstances of the borrower (e.g., a mortgage) -- and sell a different kind of financial asset to savers, generally some kind of relatively liquid claim against the financial intermediary (e.g., a deposit account). In addition, unlike brokers and dealers, financial intermediaries typically hold financial assets as part of an investment portfolio rather than as an inventory for resale. In addition to making profits on their investment portfolios, financial intermediaries make profits by charging relatively high interest rates to borrowers and paying relatively low interest rates to savers.
Types of financial intermediaries include: Depository Institutions (commercial banks, savings and loan associations, mutual savings banks, credit unions); Contractual Savings Institutions (life insurance companies, fire and casualty insurance companies, pension funds, government retirement funds); and Investment Intermediaries (finance companies, stock and bond mutual funds, money market mutual funds).
Diagrammatic Example of a Financial Intermediary: A Commercial Bank
Lending by B Borrowing by B deposited ------- funds ------- funds ------- | |<............. | | <............. | | | F |.............> | B | ..............> | H | ------- loan ------- deposit ------- contracts accounts Loan contracts Deposit accounts issued by F to B issued by B to H are liabilities of F are liabilities of B and assets of B and assets of H NOTE: F=Firms, B=Commercial Bank, and H=Households
The costs of collecting and aggregating information determine, to a large extent, the types of financial market structures that emerge. These structures take four basic forms:
Auction Markets:
An auction market is some form of centralized facility (or clearing house) by which buyers and sellers, through their commissioned agents (brokers), execute trades in an open and competitive bidding process. The "centralized facility" is not necessarily a place where buyers and sellers physically meet. Rather, it is any institution that provides buyers and sellers with a centralized access to the bidding process. All of the needed information about offers to buy (bid prices) and offers to sell (asked prices) is centralized in one location which is readily accessible to all would-be buyers and sellers, e.g., through a computer network. No private exchanges between individual buyers and sellers are made outside of the centralized facility.
An auction market is typically a public market in the sense that it open to all agents who wish to participate. Auction markets can either be call markets -- such as art auctions -- for which bid and asked prices are all posted at one time, or continuous markets -- such as stock exchanges and real estate markets -- for which bid and asked prices can be posted at any time the market is open and exchanges take place on a continual basis. Experimental economists have devoted a tremendous amount of attention in recent years to auction markets.
Many auction markets trade in relatively homogeneous assets (e.g., Treasury bills, notes, and bonds) to cut down on information costs. Alternatively, some auction markets (e.g., in second-hand jewelry, furniture, paintings etc.) allow would-be buyers to inspect the goods to be sold prior to the opening of the actual bidding process. This inspection can take the form of a warehouse tour, a catalog issued with pictures and descriptions of items to be sold, or (in televised auctions) a time during which assets are simply displayed one by one to viewers prior to bidding.
Auction markets depend on participation for any one type of asset not being too "thin." The costs of collecting information about any one type of asset are sunk costs independent of the volume of trading in that asset. Consequently, auction markets depend on volume to spread these costs over a wide number of participants.
Over-the-Counter Markets:
An over-the-counter market has no centralized mechanism or facility for trading. Instead, the market is a public market consisting of a number of dealers spread across a region, a country, or indeed the world, who make the market in some type of asset. That is, the dealers themselves post bid and asked prices for this asset and then stand ready to buy or sell units of this asset with anyone who chooses to trade at these posted prices. The dealers provide customers more flexibility in trading than brokers, because dealers can offset imbalances in the demand and supply of assets by trading out of their own accounts. Many well-known common stocks are traded over-the-counter in the United States through NASDAQ (National Association of Securies Dealers' Automated Quotation System).
Intermediation Financial Markets:
An intermediation financial market is a financial market in which financial intermediaries help transfer funds from savers to borrowers by issuing certain types of financial assets to savers and receiving other types of financial assets from borrowers. The financial assets issued to savers are claims against the financial intermediaries, hence liabilities of the financial intermediaries, whereas the financial assets received from borrowers are claims against the borrowers, hence assets of the financial intermediaries. (See the diagrammatic illustration of a financial intermediary presented earlier in these notes.)
Asymmetric information in a market for goods, services, or assets refers to differences ("asymmetries") between the information available to buyers and the information available to sellers. For example, in markets for financial assets, asymmetric information may arise between lenders (buyers of financial assets) and borrowers (sellers of financial assets).
Problems arising in markets due to asymmetric information are typically divided into two basic types: "adverse selection;" and "moral hazard." This section explains these two types of problems, using financial markets for concrete illustration.
Adverse selection is a problem that arises for a buyer of goods, services, or assets when the buyer has difficulty assessing the quality of these items in advance of purchase.
Consequently, adverse selection is a problem that arises because of different ("asymmetric") information between a buyer and a seller before any purchase agreement takes place.
An Illustration of Adverse Selection in Loan Markets:
Moral hazard is said to exist in a market if, after the signing of a purchase agreement between the buyer and seller of a good, service, or asset:
For example, a moral hazard problem arises if, after a lender purchases a loan contract from a borrower, the borrower increases the risks originally associated with the loan contract by investing his borrowed funds in more risky projects than he originally reported to the lender.
Suppose someone promises to pay you $100 in some future period T. This amount of money actually has two different values: a nominal value of $100, which is simply a measure of the number of dollars that you will receive in period T; and a present value (sometimes referred to as a present discounted value), roughly defined to be the minimum number of dollars that you would have to give up today in return for receiving $100 in period T.
Stated somewhat differently, the present value of the future $100 payment is the value of this future $100 payment measured in terms of current (or present) dollars.
The concept of present value permits financial assets with different associated payment streams to be compared with each other by calculating the value of these payment streams in terms of a single common unit: namely, current dollars.
A specific procedure for the calculation of present value for future payments will now be developed.
Present Value of Payments One Period Into the Future:
If you save $1 today for a period of one year at an annual interest rate i, the nominal value of your savings after one year will be
(1) V(1) = (1+i)*$1 ,
where the asterisk "*" denotes multiplication.
On the other hand, proceeding in the reverse direction from the future to the present, the present value of the future dollar amount V(1) = (1+i)*$1 is equal to $1. That is, the amount you would have to save today in order to receive back V(1)=(1+i)*$1 in one year's time is $1.
Notice that this calculation of $1 as the present value of V(1)=(1+i)*$1 satisfies the following formula:
V(1) (2) Present Value = -------- . of V(1) (1+i)
Indeed, given any fixed annual interest rate i, and any payment V(1) to be received one year from today, the present value of V(1) is given by formula (2). In effect, then, the payment V(1) to be received one year from now has been discounted back to the present using the annual interest rate i, so that the value of V(1) is now expressed in current dollars.
Present Value of Payments Multiple Periods Into the Future:
If you save $1 today at a fixed annual interest rate i, what will be the value of your savings in one year's time? In two year's time? In n year's time?
If you save $1 at a fixed annual interest rate i, the nominal value of your savings in one year's time will be V(1)=(1+i)*$1. If you then put aside V(1) as savings for an additional year rather than spend it, the nominal value of your savings at the end of the second year will be
(3)
And so forth for any number of years n.
(4) START --------------------------------/\/\/\-------->YEAR | 1 2 n | Nominal 2 n Value of $1 (1+i)*$1 (1+i) *$1 (1+i) * $1 Savings:
Now consider the present value of V(n) = (1+i)^{n}*$1 for any year n. By construction, V(n) is the nominal value obtained after n years when a single dollar is saved for n successive years at the fixed annual interest rate i. Consequently, the present value of V(n) is simply equal to $1, regardless of the value of n.
Notice, however, that the present value of V(n) -- namely, $1 -- can be obtained from the following formula:
V(n) (5) Present Value = ------------ . of V(n) n (1+i)
Indeed, given any fixed annual interest rate i, and any nominal amount V(n) to be received n years from today, the present value of V(n) can be calculated by using formula (5).
Present Value of Any Arbitrary Payment Stream:
Now suppose you will be receiving a sequence of three payments over the next three years. The nominal value of the first payment is $100, to be received at the end of the first year; the nominal value of the second payment is $150, to be received at the end of the second year; and the nominal value of the third payment is $200, to be received at the end of the third year.
Given a fixed annual interest rate i, what is the present value of the payment stream ($100,$150,$200) consisting of the three separate payments $100, $150, and $200 to be received over the next three years?
To calculate the present value of the payment stream ($100,$150,$200), use the following two steps:
Carrying out Step 1, it follows from formula (5) that the present value of the $100 payment to be received at the end of the first year is $100/(1+i). Similarly, it follows from formula (5) that the present value of the $150 payment to be received at the end of the second year is
$150 (6) ---------- 2 (1+i)
Finally, it follows from formula (3) that the present value of the $200 payment to be received at the end of the third year is
$200 ---------- (7) 3 (1+i)
Consequently, adding together these three separate present value calculations in accordance with Step 2, the present value PV(i) of the payment stream ($100,$150,$200) is given by
(8)
PV(i) = | $100 + |
$150 + |
$200 |
(1 + i)^{1} | (1 + i)^{2} | (1 + i)^{3} |
More generally, given any fixed annual interest rate i, and given any payment stream (V1,V2,V3,...,VN) consisting of individual payments to be received over the next N years, the present value of this payment stream can be found by following the two steps outlined above.
In particular, then, given any fixed annual interest rate, and given any payment stream paid out on a yearly basis to the owner of some financial asset, the present (current dollar) value of this payment stream can be found by following Steps 1 and 2 outlined above. Consequently, regardless how different the payment streams associated with different financial assets might be, one can calculate the present values for these payment streams in current dollar terms and hence have a way to compare them.
By definition, the current annual yield to maturity for a financial asset is the particular fixed annual interest rate i which, when used to calculate the present value of the financial asset's future stream of payments to the financial asset's owner, yields a present value equal to the current market value of the financial asset.
Below we illustrate this calculation for coupon bonds.
Yield to Maturity for Coupon Bonds:
The basic contractual terms of a coupon bond are as follows:
Seller Purchase Receives: Price Pb | MATURITY START |_______________________ /\/\/\ _____ DATE | | | | | | Coupon Coupon ... Coupon Buyer Payment C Payment C Payment C Receives: + Face Value F
Consider a coupon bond whose purchase price is Pb=$94, whose face value is F = $100, whose annual coupon payment is C = $10, and whose maturity is 10 years.
The payment stream to the buyer (new owner) generated by this coupon bond is given by
(9)
For any given fixed annual interest rate i, the present value PV(i) of the payment stream (9) is given by the sum of the separate present value calculations for each of the annual payments in this payment stream as determined by formula (5). That is,
(10)
The current value of the coupon bond is its current purchase price Pb = $94. It then follows by definition that the yield to maturity for this coupon bond is found by solving the following equation for i:
(11)
The calculation of the yield to maturity i from formula (11) can be difficult, but tables have been published that permit one to read off the yield to maturity i for a coupon bond once the purchase price, the face value, the coupon rate, and the maturity are known.
More generally, given any coupon bond with purchase price Pb, face value F, coupon payment C, and maturity N, the yield to maturity i is found by means of the following formula:
(12a)
where the present value PV(i) of the coupon bond is given by
(12b)
Given any asset A held over any given time period T, the return to A over the holding period T is, by definition:
The return rate on asset A over the holding period T is then defined to be the return on A over period T divided by the market value of A at the beginning of period T.
More precisely, suppose that an asset A is held over a time period that starts at some time t and ends at time t+1. Let the market value of A at time t be denoted by P(t) and the market value of A at time t+1 be denoted by P(t+1). Finally, let V(t,t+1) denote the sum of all payments accruing to the holder of asset A from t to t+1, assumed to be paid out at time t+1.
Then, by definition, the return rate on asset A from t to t+1 is given by the following formula:
(13) Return Rate on V(t,t+1) + P(t+1) - P(t) Asset A From = --------------------------- time t to t+1 P(t) V(t,t+1) P(t+1) - P(t) = --------- + ------------- P(t) P(t) = payments + Capital Gain (if +) received as or Loss (if -) as percentage percentage of P(t) of P(t)
Formula (13) holds for any asset A, whether physical or financial. The question then arises: For financial assets, what is the connection between the return rate defined by formula (13) and the interest rate on the financial asset defined by the yield to maturity?
The return rate on a financial asset is not necessarily equal to the yield to maturity on the financial asset. Starting at any current time t, the return rate is calculated for some specified holding period from t to t', whether or not this holding period coincides with the maturity of the financial asset. Moreover, the return rate takes into account any capital gains or losses that occur during this holding period, in addition to any payments received from the financial asset during this holding period. In contrast, starting at any current time t, the yield to maturity takes into account the payment stream generated by the financial asset over its entire remaining maturity, plus the overall anticipated capital gain or loss that will be incurred when the financial asset is held to maturity.
The yield to maturity measure of an interest rate, as examined to date, has been "nominal" in the sense that it has not been adjusted for expected changes in prices. What actually concerns a "rational" saver considering the purchase of a financial asset is not the nominal payment stream he or she expects to earn in future periods but rather the command over purchasing power that this nominal payment stream is expected to entail. This purchasing power depends on the behavior of prices.
Let inf^{e}(t) denote the expected inflation rate at time t, and let i(t) denote the (nominal) yield to maturity for some financial asset at time t. Then the real interest rate associated with i(t) is defined by the following "Fisher equation:"
(14)
That is, the real interest rate is the nominal interest rate minus the expected inflation rate.
Note:The real interest rate defined by (14) is more precisely called the ex ante real interest rate because it adjusts for expected changes in the price level. If the expected inflation rate in (14) is replaced by the actual inflation rate, one obtains the ex post real interest rate.
Real interest rates provide a more accurate measure of the true costs of borrowing and the true gains from lending than nominal interest rates, and hence provide a better indicator of the incentives to borrow and lend. In particular, for any given nominal interest rate i on a debt instrument D, the incentive to borrow (issue D) will be higher if the real interest rate associated with i is lower (i.e., the expected inflation rate is higher). This is so since a higher expected inflation rate means the borrower (issuer of D) can expect to pay off his future nominal debt obligations using cheaper dollars than he borrowed. For this same reason, the incentive to lend (purchase D) will be lower if the real interest rate associated with i is lower.
A similar distinction is made between the (nominal) return rate defined by (13), which has not been adjusted for expected changes in prices, and the "real return rate" which is subject to such adjustment. More precisely, the real return rate on any asset A over any holding period from t to t+1 is defined to be the (nominal) return rate (13) minus the expected inflation rate inf^{e}(t).