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understanding financial

markets and institutions

( H )ow do funds flow throughout the economy? How do financial markets operate and relate to one another? As an individual investor or a financial manager you need to know. Your future decision-making skills depend on it. Investors' funds flow through financial markets such as the New York Stock Exchange and mortgage markets. Financial institutions-commercial banks (e.g., Bank of America), investment banks (e.g., Morgan Stanley), and mutual funds (e.g., Fidelity)-act as intermediaries to channel funds from individual savers or investors through financial markets. This chapter looks at the nature and operations of financial markets and discusses the financial institutions (FIs) that participate in those markets. Bonds, stocks, and other securities that trade in the markets are covered in

Chapters 7 and 8.

In this chapter we also examine how significant changes in the way financial institutions deliver services played a major role in forming the severe financial crisis that began in late 2008. We examine some of the crisis's underlying causes, review some of the major events that occurred during that time, and discuss some resulting regulatory and industry changes that are in effect today in Appendix 6A, which is available in Connect or through your course instructor.

LEARNING GOALS

LG6-

1 Differentiate between primary and secondary markets and between money and capital markets.

LG6-

2 List the types of securities traded in money and capital markets.

LG6-

3 Identify different types of financial institutions and the services that each provides.

LG6-

4 Analyze specific factors that influence interest rates.

LG6-

5 Offer different theories that explain the shape of the term structure of interest rates.

LG6-

6 Demonstrate how forward interest rates derive from the term structure of interest rates.

*See Appendix 6A: The Financial Crisis: The Failure of Financial Institution Specialness in Connect.

viewpoints

business APPLICATION

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DPH Corporation needs to issue new bonds either this year or in two years. DPH Corp. is a profitable firm, but if the U.S. economy were to experience a downturn, the company would see a big drop in sales over the next two years as its products are very sensitive to changes in the overall economy. DPH Corp. currently has $10 million in public debt outstanding, but its bonds are not actively traded. What questions must DPH Corp. consider as its managers decide whether to issue bonds today or in two years? How can DPH Corp. get these bonds to potential buyers and thus raise the needed capital?

FINANCIAL MARKETS

Financial markets exist to manage the flow of funds from investors to borrowers as well as from one investor to another. We generally differentiate financial markets by their primary financial instruments' characteristics (such as bond maturities) or the market's location. Specifically, we can distinguish markets along two major dimensions:

· Primary versus secondary markets.

· Money versus capital markets.

Primary Markets versus Secondary Markets LG6-1

Primary markets provide a forum in which demanders of funds (e.g., corporations such as IBM or government entities such as the U.S. Treasury) raise funds by issuing new financial instruments, such as stocks and bonds. Corporations or government entities continually have new projects or expanded production needs, but do not have sufficient internally generated funds (such as retained earnings) to support their capital needs. Thus, corporations and governments issue securities in external primary markets to raise additional funds. These entities sell the new financial instrument issues to initial fund suppliers (e.g., households) in exchange for the funds (money) that the issuer requires.

In the United States, financial institutions called investment banks arrange most primary market transactions for businesses. Some of the best-known examples of U.S. investment banks include Morgan Stanley, Goldman Sachs, or Merrill Lynch (owned by Bank of America, a commercial bank). These firms intermediate between issuing parties (fund demanders) and investors (fund suppliers). Investment banks provide fund demanders with a number of services, including advising the company or government agency about the securities issue (such as an appropriate offer price and number of securities to issue) and attracting initial public purchasers of the customer's securities offerings. Firms that need funds are seldom expert at raising capital themselves, so they avert risk and lower their costs by turning to experts at investment banks to issue their primary market securities.

The initial (or primary market) sale of securities occurs either through a public offering or as a private placement to a small group of investors. An investment bank serves as a security underwriter in a public offering. In a private placement, the security issuer engages the group of buyers (usually fewer than 10) to purchase the whole issue. Buyers are typically financial institutions. To protect smaller individual investors against a lack of disclosure, publicly traded securities must be registered with the Securities and Exchange Commission (SEC). Private placements, on the other hand, can be unregistered and resold to large, financially sophisticated investors only. Large investors supposedly possess the resources and expertise to analyze a security's risk. Privately placed bonds and stocks traditionally have been among the most illiquid securities in the securities markets; only the very largest financial institutions or institutional investors are able or willing to buy and hold them in the absence of an active secondary market. Issuers of privately placed securities tend to be less well known (e.g., mediumsized municipalities and corporations). Because of this lack of information and its associated higher risk, returns paid to holders of privately placed securities tend to be higher than those on publicly placed securities issues.

Figure 6.1 illustrates a time line for the primary market exchange of funds for a new issue of corporate bonds or equity. We will further discuss how companies, the U.S. Treasury, and government agencies that market primary government securities, such as Ginnie Mae and Freddie Mac, go about selling primary market securities in Chapter 8. Throughout this text, we focus on government securities from the buyer’s, rather than the seller's, point of view. You can find in-depth discussions of government securities from the sellers' point of view in a public finance text.

Primary market financial instruments include stock issues from firms initially going public (e.g., allowing their equity shares to be publicly traded on stock markets for the first time). We usually refer to these first-time issues as initial public offerings (IPOs). For example, on May 17, 2012, Facebook announced a $16 billion IPO of its common stock. Facebook used several investment banks, including Morgan Stanley, JPMorgan, and Goldman Sachs, to underwrite the company's stock. Publicly traded firms may issue additional bonds or stocks as primary market securities. For example, on June 5, 2012, Dollar General announced that it would sell an additional 30 million shares of common stock (at $46.75 per share) underwritten by investment banks such as Citigroup, Goldman Sachs, KKR, Barclays, and JPMorgan. These funds augmented Dollar General's existing capital (equity) of $4,591 million.

personal APPLICATION

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John Adams wants to invest in one of two corporate bonds issued by separate firms. One bond yields 8.00 percent with a 10-year maturity; the other offers a 10.00 percent yield and a 9-year maturity. The second bond seems to be the better deal. Is it necessarily the bond in which John should invest? Once he decides which bond represents the better investment, how can John go about buying the bond?

Should John consider bonds from other countries? Scan the QR code for an extended look. Turn to the back of the book for

solutions to these applications.

Secondary Markets Once firms issue financial instruments in primary markets, these same stocks and bonds are then traded-that

is, bought and resold-in secondary markets. The New York Stock Exchange (NYSE) and the NASDAQ are two well-known examples of secondary markets for trading stocks (see Chapters 7 and 8). In addition to stocks and bonds, secondary markets also exist for financial instruments backed by mortgages and other assets, foreign exchange, and futures and options (i.e., derivative securities, discussed later in the chapter).

( FIGURE 6.1 Primary Market Transfer of Funds )

Buyers find sellers of secondary market securities in economic agents that need funds (fund demanders). Secondary markets provide a centralized marketplace where economic agents know that they can buy or sell most securities quickly and efficiently. Secondary markets, therefore, save economic agents the search costs of finding buyers or sellers on their own. Figure 6.2 illustrates a secondary market transfer of funds. Secondary market buyers often use securities brokers such as Charles Schwab or other brokerage firms to act as intermediaries as they exchange funds for securities (see Chapter 8). An important note: The firm that originally issued the stock or bond is not involved in secondary market transactions in any way-no money accrues to the company itself when its stock trades in a secondary market.

Secondary markets offer benefits to both investors (fund suppliers) and issuers (fund demanders). Investors gain liquidity and diversification benefits (see Chapter 10). Although corporate security issuers are not directly involved in secondary market transactions, issuers do gain information about their securities' current market value. Publicly traded firms can thus observe how investors perceive their corporate value and their corporate decisions by tracking their firms' securities' secondary market prices. Such price information allows issuers to evaluate how well they are using internal funds as well as the funds generated from previously issued stocks and bonds and provides indications about how well any subsequent bond or stock offerings might be received-and at what price.

Secondary market trading volume can be quite large. Trading volume is defined as the number of shares of a security that are simultaneously bought and sold during a given period. Each seller and each buyer actually contract with the exchange's clearinghouse, which then matches sell and buy orders for each transaction. The clearinghouse is a company whose stock trades on the exchange, and the clearinghouse runs on a for-profit basis.

financial markets The arenas through which funds flow.

primary markets Markets in which corporations raise funds through new issues of securities. investment banks Financial institutions that arrange primary market transactions for businesses. initial public offerings (IPOs) The first public issue of financial instruments by a firm. secondary markets Markets that trade financial instruments once they are issued.

trading volume The number of shares of a security that are simultaneously bought and sold during a period.

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( FIGURE 6.2 Secondary Market Transfer of Funds )

( FIGURE 6.3 Money versus Capital Market Maturities )

The exchange and the clearinghouse can process many transactions in a single day. For example, on October 28, 1997, NYSE trading volume exceeded 1 billion shares for the first time ever. On October 10, 2008 (at the height of the financial crisis), NYSE trading volume topped 7.3 billion shares, the highest level to date. In contrast, during the mid-1980s, a NYSE trading day during which 250 million shares traded was considered a high-volume day.

Money Markets versus Capital Markets

We noted that financial markets are differentiated in part by the maturity dates of the instruments traded. This distinction becomes important when we differentiate money markets from capital markets. Both of these markets deal in debt securities (capital markets also deal in equity securities); the question becomes one of when the securities come due.

Money Markets Money markets feature debt securities or instruments with maturities of one year or less (see Figure 6.3). In money markets, agents with excess short-term funds can lend (or supply) to economic agents who need (or demand) short-term funds. The suppliers of funds buy money market instruments and the demanders of funds sell money market instruments. Because money market instruments trade for only short periods of time, fluctuations in secondary-market prices are usually quite small. With less volatility, money market securities are thus less risky than longer-term instruments. In the United States, many money market securities do not trade in a specific location; rather, transactions occur via telephones, wire transfers, and computer trading. Thus, most U.S. money markets are said to be over-the-counter (OTC) markets.

Money Market Instruments LG6-2 Corporations and government entities issue a variety of money market securities to obtain short-term funds. These securities include:

· Treasury bills.

· Federal funds and repurchase agreements.

· Commercial paper.

· Negotiable certificates of deposit.

· Banker's acceptances.

Table 6.1 lists and defines each money market security. Figure 6.4 graphically depicts the proportion of U.S. money market instruments outstanding across three decades. Notice that, in 2013, Treasury bills commanded the highest dollar value of all money market instruments, followed by negotiable CDs, federal funds and repurchase agreements, and commercial paper.

TABLE 6.1 Money Market Instruments

Capital Markets LG6-1 Capital markets are markets in which parties trade equity (stocks) and debt (bonds) instruments that mature in more than one year (see Figure 6.3). Given their longer maturities, capital market instruments are

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subject to wider price fluctuations than are money market instruments (see the term structure discussion below and in Chapter 7).

Capital Market Instruments LG6-2 Capital market securities include:

· U.S. Treasury notes and bonds.

· U.S. government agency bonds.

· State and local government bonds.

· Mortgages and mortgage-backed securities.

· Corporate bonds.

· Corporate stocks.

Table 6.2 lists and defines each capital market security. Figure 6.5 graphically depicts U.S. capital market instruments outstanding over three decades. Note that corporate stocks (equities) represent the largest capital market instrument, followed by mortgages and mortgage- backed securities and then corporate bonds. The relative size of capital markets depends on two factors: the number of securities issued and their market prices. The 1990s saw consistently rising bull markets; hence the sharp increase in equities' dollar value outstanding. Stock values fell in the early 2000s as the U.S. economy experienced a downturn-partly because of 9/11 and partly because interest rates began to rise-and stock prices fell. Stock prices in most sectors subsequently recovered and, by 2007, even surpassed their 1999 levels. Stock prices fell precipitously during the financial crisis of 2008 and 2009. As of mid-March 2009, the Dow Jones Industrial Average (DJIA) had

fallen in value 53.8 percent in less than 1V year's time. This was greater than the decline during the market crash of 1937 and 1938, when it fell 49 percent. Stock prices recovered along with the economy in the last half of 2009 and first half of 2010, rising 71.1 percent between March 2009 and April 2010. However, it took until March 5, 2013, for the DJIA to surpass its pre-crisis high of 14,164.53, closing at 14,253.77 for the day.

TABLE 6.2 Capital Market Instruments

( FIGURE 6.4 Money Market Instruments Outstanding )

Here we see how the percentage of each money market instrument traded changes across three decades.

Source: Federal Reserve Board, "Flow of Fund Accounts," Statistical Releases, Washington, DC, various issues. www.federalreserve.gov

money markets Markets that trade debt securities or instruments with maturities of less than one year.

over-the-counter market Markets that do not operate in a specific fixed location-rather, transactions occur via telephones, wire transfers, and computer trading.

capital markets Markets that trade debt (bonds) and equity (stock) instruments with maturities of more than one year.

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( FIGURE 6.5 Capital Market Instruments Outstanding )

Source: Federal Reserve Board, "Flow of Fund Accounts," Statistical Releases, Washington, DC, various issues. www.federalreserve.gov

Other Markets

Foreign Exchange Markets Today, most U.S.-based companies operate globally. Competent financial managers understand how events and movements in financial markets in other countries can potentially affect their own companies' profitability and performance. For example, in 2012, IBM experienced a drop in revenue of 3 percent due to foreign exchange trends. Coca-Cola, which gets the majority of its sales from outside the United States, also saw revenues decrease by approximately 5 percent as the U.S. dollar strengthened relative to foreign currencies.

Foreign exchange markets trade currencies for immediate (also called "spot") or some future stated delivery. When a U.S. corporation sells securities or goods overseas, the resulting cash flows denominated in a foreign currency expose the firm to foreign exchange risk. This risk arises from the unknown value at which foreign currency cash flows can be converted into U.S. dollars. Foreign currency exchange rates vary day to day with worldwide demand and supply of foreign currency and U.S. dollars. Investors who deal in foreign- denominated securities face the same risk.

The actual number of U.S. dollars that a firm receives on a foreign investment depends on the exchange rate between the

U.S. dollar and the foreign currency just as much as it does on the investment's performance. Firms will have to convert the foreign currency into U.S. dollars at the prevailing exchange rate. If the foreign currency depreciates (falls in value) relative

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to the U.S. dollar (say from 0.1679 dollar per unit of foreign currency to 0.1550 dollar per unit of foreign currency) over the investment period (i.e., the period between when a foreign investment is made and the time it comes to fruition), the dollar value of cash flows received will fall. If the foreign currency appreciates, or rises in value, relative to the U.S. dollar, the dollar value of cash flows received from the

foreign investment will increase.

Foreign currency exchange rates are variable. They vary day to day with demand for and supply of foreign currency and with demand for and supply of dollars worldwide. Central governments sometimes intervene in foreign exchange markets directly-such as China's valuing of the yuan at artificially high rates relative to the dollar. Governments also affect foreign exchange rates indirectly by altering prevailing interest rates within their own countries. You will learn more about foreign exchange markets in Chapter 19.

Derivative Securities Markets A derivative security is a financial security (such as a futures contract, option contract, or mortgage-backed security) that is linked to another, underlying security, such as a stock traded in capital markets or British pounds traded in foreign exchange (forex) markets. Derivative securities generally involve an agreement between two parties to exchange a standard quantity of an asset or cash flow at a predetermined price and at a specified date in the future. As the value of the underlying security changes, the value of the derivative security changes.

While derivative security contracts, especially for physical commodities like corn or gold, have existed for centuries, derivative securities markets grew increasingly popular in the 1970s, 1980s, and 1990s as traders, firms, and academics figured out how to spread risk for more and more underlying commodities and securities by using derivative contracts. Derivative contracts generally feature a high degree of leverage; that is, the investor only has to put up a very small portion of the underlying commodity or security's value to affect or control the underlying commodity or security.

Derivative securities traders can be either users of derivative contracts (for hedging and other purposes) or dealers (such as banks) that act as counterparties in customer trades for fees. An example of hedging involves commodities such as corn, wheat, or soybeans. For example, suppose you run a flour mill and will need to buy either soft wheat (Chicago) or hard red winter wheat (Kansas City) in the future. If you are concerned that the price of wheat will rise, you might lock in a price today to meet your needs six months from now by buying wheat futures on a commodities exchange. If you are correct and wheat prices rise over the six months, you may purchase the wheat by closing out your futures positions, buying the wheat at the futures price rather than the higher market price. Likewise, if you know that you will be delivering a large shipment to, say, Europe, in three months, you might take an offsetting position in euro futures contracts to lock in the exchange rate between the dollar and the euro as it stands today-and (you hope) eliminate foreign exchange risk from the transaction.

Derivative securities markets are the newest-and potentially the riskiest-of the financial security markets. Losses associated with off- balance-sheet mortgage-backed securities created and held by FIs were at the very heart of the financial crisis. Signs of significant problems in the U.S. economy first appeared in late 2006 and early 2007 when home prices plummeted and defaults began to affect the mortgage lending industry as a whole, as well as other parts of the economy noticeably. Mortgage delinquencies, particularly on subprime mortgages, surged in the last quarter of 2006 through 2008 as homeowners who had stretched themselves to buy or refinance a home in the early 2000s fell behind on their loan payments. As mortgage borrowers defaulted, the financial institutions that held their mortgages and credit derivative securities (in the form of mortgage-backed securities) started announcing huge losses on them. These losses reached $700 billion worldwide by early 2009. The situation resulted in the failure, acquisition, or bailout of some of the largest FIs and a near meltdown of the world's financial and economic systems. More recently, the Finance at Work box above highlights huge losses experienced by JPMorgan Chase from positions in the derivative securities markets.

time out!

6-1 How do primary and secondary markets differ? 6-2 What are foreign exchange markets?

6-3 What are derivatives securities?

foreign exchange markets Markets in which foreign currency is traded for immediate or future delivery.

foreign exchange risk Risk arising from the unknown value at which foreign currency cash flows can be converted into U.S. dollars.

derivative security A security formalizing an agreement between two parties to exchange a standard quantity of an asset at a predetermined price on a specified date in the future.

FINANCIAL INSTITUTIONS LG6-3

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Financial institutions (e.g., banks, thrifts, insurance companies, mutual funds) perform vital functions to securities markets of all sorts. They channel funds from those with surplus funds (suppliers of funds) to those with shortages of funds (demanders of funds). In other words, FIs operate financial markets. FIs allow financial markets to function by providing the least costly and most efficient way to channel funds to and from these markets. FIs play a second crucial role by spreading risk among market participants. This risk-spreading function is vital to entrepreneurial efforts, for few firms or individuals could afford the risk of launching an expensive new product or process by themselves. Individual investors take on pieces of the risk by buying shares in risky enterprises. Investors then mitigate their own risks by diversifying their holdings into appropriate portfolios, which we cover in Chapters 9 and 10. Table 6.3 lists and summarizes the various types of FIs.

To understand just how important FIs are to the efficient operation of financial markets, imagine a simple world in which FIs did not exist.

In such a world, suppliers of funds (e.g., households), generating excess savings by consuming less than they earn, would have a basic choice. They could either hold cash as an asset or invest that cash in the securities issued by users of funds (e.g., corporations, governments, or retail borrowers). In general, demanders (users) of funds issue financial claims (e.g., equity and debt securities) to finance the gap between their investment expenditures and their internally generated savings, such as retained earnings or tax funds. As shown in Figure 6.6, in a world without financial institutions, we would have direct transfers of funds from fund suppliers to fund users. In return, financial claims would flow directly from fund users to fund suppliers.

TABLE 6.3 Types of Financial Institutions

In this economy without FIs, the amount of funds flowing between fund suppliers and fund users through financial markets would likely be quite low for several reasons:

· Once they have lent money in exchange for financial claims, fund suppliers would need to continually monitor the use of their funds. Fund suppliers must ensure that fund users neither steal the funds outright nor waste the funds on projects that have low or negative returns, since either theft or waste would lower fund suppliers' chances of being repaid and/or earning a positive return on their investments (such as through the receipt of dividends or interest). Monitoring against theft, misuse, or underuse of their funds would cost any given fund supplier a lot of time and effort, and of course each fund supplier, regardless of the dollar value of the investment, would have to carry out the same costly and time-consuming process. Further, many investors do not have the financial training to understand the necessary business information to assess whether a securities issuer is making the best use of their funds. In fact, so many investment opportunities are available to fund suppliers, that even those trained in financial analysis rarely have the time to monitor how their funds are used in all of their investments. The resulting lack of monitoring increases the risk of directly investing in financial claims. Given these challenges, fund suppliers would likely prefer to delegate the task of monitoring fund borrowers to ensure good performance to others.

· Many financial claims feature a long-term commitment (e.g., mortgages, corporate stock, and bonds) for fund suppliers, but suppliers may not wish to hold these instruments directly. Specifically, given the choice between holding cash or long-term securities, fund suppliers may choose to hold cash for its liquidity. This is especially true if the suppliers plan to use their savings to finance consumption expenditures before their creditors expect to repay them. Fund suppliers may also fear that they will not find anyone to purchase their financial claim and free up their funds. When financial markets are not very developed, or deep, in terms of the number of active buyers and sellers in the market, such liquidity concerns arise.

· Even though real-world financial markets provide some liquidity services by allowing fund suppliers to trade financial securities among themselves, fund suppliers face price risk when they buy securities-fund suppliers may not get their principal back, let alone any return on their investment. Trading securities on secondary markets involves various transaction costs. The price at which investors can sell a security on secondary markets such as the New York Stock Exchange (NYSE) or NASDAQ may well differ from the price they initially paid for the security. The investment community as a whole may change the security's valuation between the time the fund supplier bought it and the time the fund supplier sold it. Also, dealers, acting as intermediaries between buyers and sellers, charge transaction costs for completing a trade. So even if an investor bought a security and then sold it the next day, the investor would likely lose money from transaction and other costs.

( FIGURE 6.6 Flow of Funds in a World without FIs )

financial institutions Institutions that perform the essential function of channeling funds from those with surplus funds to those with shortages of funds.

direct transfer The process used when a corporation sells its stock or debt directly to investors without going through a financial institution.

Unique Economic Functions Performed by Financial Institutions

Because of (1) monitoring costs, (2) liquidity costs, and (3) price risk, most average investors may well view direct

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investment in financial claims and markets as an unattractive proposition and, as fund suppliers, they will likely prefer to hold cash. As a result, financial market activity (and therefore savings and investment) would likely remain quite low. However, the financial system has developed an alternative, indirect way for investors (or fund suppliers) to channel funds to users of funds: financial intermediaries indirectly transfer funds to ultimate fund users. Because of monitoring, liquidity risk, and price risk costs, fund suppliers often prefer to hold financial intermediaries' financial claims rather than those directly issued by the ultimate fund users. Consider Figure 6.7, which more closely represents the way that funds flow in the U.S. financial system than does Figure 6.6. Notice how financial institutions stand-or intermediate-between fund suppliers and fund users. That is, FIs channel funds from ultimate suppliers to ultimate fund users. Fund suppliers and users use these FIs to channel funds because of financial intermediaries' unique ability to measure and manage risk, and thus reduce monitoring costs, liquidity costs, and price risk.

Monitoring Costs As we noted above, a fund suppler who directly invests in a fund user's financial claims faces a high cost of comprehensively monitoring the fund user's actions in a timely way. One solution to this problem is that a large number of small investors can group their funds together by holding claims issued by an FI. In turn, the FI will invest in direct financial claims that fund users issue. Financial institutions' aggregation of funds from fund suppliers resolves a number of problems:

· First, large FIs now have much greater incentive to collect information and monitor the ultimate fund user's actions, because the FI has far more at stake than any small individual fund supplier would have.

· Second, the FI performs the necessary monitoring function via its own internal experts. In an economic sense, fund suppliers appoint the FI as a delegated monitor to act on their behalf. For example, full-service securities firms such as Bank of America Merrill Lynch carry out investment research on new issues and make investment recommendations for their retail clients (investors), while commercial banks collect deposits from fund suppliers and lend these funds to ultimate users, such as corporations. An important part of these FIs' functions is their ability and incentive to monitor ultimate fund users.

( FIGURE 6.7 Flow of Funds in a World with FIs )

Financial institutions stand between fund suppliers and users.

liquidity The ease with which an asset can be converted into cash.

price risk The risk that an asset's sale price will be lower than its purchase price.

indirect transfer A transfer of funds between suppliers and users of funds through a financial institution.

delegated monitor An economic agent appointed to act on behalf of smaller investors in collecting information and/or investing funds on their behalf.

finance at work II: markets

JP Morgan's $2 Billion Blunder

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JP Morgan Chase & Co. is reeling after a huge trading bet backfired and left the bank with at least $2 billion in losses from the bad trade. This may be the end of chief executive James Dimon's run as the so-called "King of Wall Street." The bank's Chief Investment Office (CIO), responsible for managing the New York company's risk, placed a series of risky bets and trades. In an article published last month, The Wall Street Journal reported that "large positions taken in that office by a trader nicknamed 'the London whale' had roiled a sector of the debt markets. The bank, betting on a continued economic recovery with a complex web of trades tied to the values of corporate bonds, was hit hard when prices moved against it starting last month, causing losses in many of its derivatives positions. The losses occurred while J.P. Morgan tried to scale back that trade."

Mr. Dimon held a conference call with investors and analysts on May 10, stating, "In hindsight, the . . . strategy was flawed, complex, poorly reviewed, poorly executed, and poorly monitored. The portfolio has proven to be riskier, more volatile and less effective . . . than we thought." Dimon resolves, "We will learn from it, we will fix it, we will move on, hopefully in the end, it will make us a better company." Though JP Morgan Chase came through the financial crisis better off than many other financial institutions, this trading loss certainly tarnishes their reputation. Mr. Dimon reports that the loss is "slightly more than $2 billion" in the second quarter of this year.

In April of 2012, The Wall Street Journal reported that investors and hedge funds were trying to take advantage of trades made by Chase's London whale, Bruno Iksil, who worked out of the Chief Investment Office, by making bets in the market on credit default swaps (CDSs). The CIO group

previously had stopgaps in place to protect and prevent the company from significant losses during periods of downturn in the economy. However, the Journal reports that earlier in 2012, "it began reducing that position, [taking] a bullish stance on the financial health of certain companies and selling protection that would compensate buyers if those companies defaulted on debts. Mr. Iksil was a heavy seller of CDS contracts tied to a basket, or index, of companies." In April of 2012, these protection costs began to go up, which further contributed to the bank's losses.

According to JP Morgan Chase company filings, Mr. Iksil's group had approximately $350 billion in investment securities, about 15% of the bank's total assets, on December 31, 2011. Mr. Dimon said the bank has an extensive review under way of what went wrong. "These were grievous mistakes, they were self-inflicted, we were accountable and we happened to violate our own standards and principles by how we want to operate the company. This is not how we want to run a business."

Want to know more?

Key Words to Search for Updates: JPMorgan, London whale, derivative trading losses

Sources: Dan Fitzpatrick, Gregory Zuckerman, and Liz Rappaport, "J.P. Morgan's $2 Billion Blunder," The Wall Street Journal Online, May 11, 2012. JP Morgan Chase & Co. Business Update Call, May 10, 2012.

Liquidity and Price Risk In addition to providing more and better information about fund users' activities, financial intermediaries provide additional liquidity to fund suppliers, acting as asset transformers as follows: FIs purchase the financial claims that fund users issue-primary securities such as mortgages, bonds, and stocks-and finance these purchases by selling financial claims to household investors and other fund suppliers as deposits, insurance policies, or other secondary securities. The secondary securities- packages or pools of primary claims-that FIs collect and then issue are often more liquid than are the primary securities themselves. For example, banks and thrift institutions (e.g., savings associations) offer draft deposit accounts with fixed principal values and (often) guaranteed interest rates. Fund suppliers can generally access the funds in those accounts on demand. Money market mutual funds issue shares to household savers that allow the savers to maintain almost fixed principal amounts while earning somewhat higher interest rates than on bank deposits. Further, savers can also withdraw these funds on demand whenever the saver writes a check on the account. Even life insurance companies allow policyholders to borrow against their company-held policy balances with very short notice.

The Shift away from Risk Measurement and Management and the Financial Crisis

Certainly, a major event that changed and reshaped the financial services industry was the financial crisis of the late 2000s.

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As FIs adjusted to regulatory changes brought about in the 1980s and 1990s, one result was a dramatic increase in systemic risk of the financial system, caused in large part by a shift in the banking model from that of "originate and hold" to "originate to distribute." In the traditional model, banks take short-term deposits and other sources of funds and use them to fund longer term loans to businesses and consumers. Banks typically hold these loans to maturity, and thus have an incentive to screen and monitor borrower activities even after a loan is made. However, the traditional banking model exposes the institution to potential liquidity, interest rate, and credit risk. In attempts to avoid these risk exposures and generate improved return-risk tradeoffs, banks have shifted to an underwriting model in which they originate or warehouse loans, and then quickly sell them. Figure 6.8 shows the growth in bank loan secondary market trading from 1991 through 2012. Note the huge growth in bank loan trading even during the financial crisis of 2008 and 2009. When loans trade, the secondary market produces information that can substitute for the information and monitoring of banks.1 Further, banks may have lower incentives to collect information and monitor borrowers if they sell loans rather than keep them as part of the bank's portfolio of assets. Indeed, most large banks are organized as financial service holding companies to facilitate these new activities.

"Money market mutual funds issue shares to household savers that allow the savers to maintain almost fixed principal amounts while earning somewhat higher interest rates than on bank deposits."

More recently activities of shadow banks, nonfinancial service firms that perform banking services, have facilitated the change from the "originate and hold" model of commercial banking to the "originate and distribute" banking model. Participants in the shadow banking system include structured investment vehicles (SIVs), special purpose vehicles (SPVs), asset-backed commercial paper (ABCP) conduits, limited-purpose finance companies, money market mutual funds (MMMFs), and credit hedge funds. In the shadow banking system, savers place their funds with money market mutual2 and similar funds, which invest these funds in the liabilities of other shadow banks. Borrowers get loans and leases from shadow banks such as finance companies rather than from banks. Like the traditional banking system, the shadow banking system intermediates the flow of funds between net savers and net borrowers. However, instead of the bank serving as the middleman, it is the nonbank financial service firm, or shadow bank, that intermediates. Further, unlike the traditional banking system, where the complete credit intermediation is performed by a single bank, in the shadow banking system it is performed through a series of steps involving many nonbank financial service firms.

These innovations remove risk from the balance sheet of financial institutions and shift risk off the balance sheet and to other parts of the financial system. Since the FIs, acting as underwriters, are not exposed to the credit, liquidity, and interest rate risks of traditional banking, they have little incentive to screen and monitor activities of borrowers to whom they originate loans. Thus, FIs' role as specialists in risk measurement and management is reduced.

Adding to FIs' move away from risk measurement and management was the boom ("bubble") in the housing markets, which began building in 2001, particularly after the terrorist attacks of 9/11. The immediate response by regulators to the terrorist attacks was to create stability in the financial markets by providing liquidity to FIs. For example, the Federal Reserve lowered the short-term interest rate that banks and other financial institutions pay in the federal funds market and even made lender of last resort funds available to nonbank FIs such as investment banks. Perhaps not surprisingly, low interest rates and the increased liquidity provided by central banks resulted in a rapid expansion in consumer, mortgage, and corporate debt financing. Demand for residential mortgages and credit card debt rose dramatically. As the demand for debt grew, especially among those who had previously been excluded from participating in the debt markets because of

their poor credit ratings, FIs began lowering their credit quality cutoff points. Moreover, to boost their earnings in that part of the mortgage market now popularly known as the "subprime market," banks and other mortgage-supplying institutions often offered relatively low "teaser" rates on adjustable rate mortgages (ARMs). These ARMs allowed for substantial step-ups in rates after the initial rate period expired two or three years later and if market rates rose in the future. Under the traditional banking structure, banks might have been reluctant to so aggressively pursue low credit quality borrowers for fear that the loans would default. However, under the originate to distribute model of banking, asset securitization and loan syndication allowed banks to retain little or no part of the loans, and hence the default risk on loans that they originated. Thus, as long as the borrower did not default within the first few months after a loan's issuance and the loans were sold or securitized without recourse back to the bank, the issuing bank could ignore longer term credit risk concerns. The result was deterioration in credit quality, at the same time as there was a dramatic increase in consumer and corporate leverage.

asset transformer Service provided by financial institutions in which financial claims issued by an FI are more attractive to investors than the claims directly issued by corporations.

secondary securities Packages or pools of primary claims.

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( FIGURE 6.8 Bank Loan Secondary Market Trading )

Bank loan sales have increased dramatically over the last 20 years.

Eventually, in 2006, housing prices started to fall. At the same time, the Federal Reserve started to raise interest rates as it began to fear inflation. Since many subprime mortgages originated in the 2001 to 2005 period had adjustable rates, the cost

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of meeting mortgage commitments rose to unsustainable levels for many low-income households. The confluence of falling house prices, rising interest rates, and rising mortgage costs led to a wave of mortgage defaults in the subprime market and foreclosures that only reinforced the downward trend in house prices. The number of subprime mortgages that were more than 60 days behind on their payments was 17.1 percent in June 2007 and over 20 percent in August 2007. As this happened, the poor quality of the collateral and credit quality underlying subprime mortgage pools became apparent, with default rates far exceeding those apparently anticipated by the rating agencies in setting their initial subprime mortgage securitizations ratings. In 2007, the percentage of subprime mortgage-backed securities delinquent by 90 days or more was 10.09 percent, substantially higher than the 5.37 percent rate in May 2005. The financial crisis began. Appendix 6A to this chapter (available in Connect or through your course instructor) provides a detailed discussion of the causes of, major events during, and regulatory and industry changes resulting from the financial crisis.

The economy relies on financial institutions to act as specialists in risk measurement and management. The importance of this was demonstrated during the global financial crisis. When FIs failed to perform their critical risk measurement and management functions, a crisis of confidence that disrupted financial markets ensued. The result was a worldwide breakdown in credit markets, as well as an enhanced level of equity market volatility.

time out!

6-4 List the major types of financial institutions.

6-5 What three main issues would deter fund suppliers from directly purchasing securities?

6-6 What events resulted in banks' shift from the traditional banking model of "originate and hold" to a model of "originate and distribute"?

INTEREST RATES

We often speak of "the interest rate" as if only one rate applies to all financial situations or transactions. In fact, we can list tens or hundreds of interest rates that are appropriate in various conditions or situations within the U.S. economy on any particular day. Let's explore a bit how the financial sector sets these rates and how the rates relate to one another. We actually observe nominal interest rates in financial markets-these are the rates most often quoted by financial news services. As we will see in Chapters 7 and 8, nominal interest rates (or, simply, interest rates) directly affect most tradable securities' value or price. Since any change in nominal interest rates has such profound effects on security prices, financial managers and individual investors spend a lot of time and effort trying to identify factors that may influence future interest rate levels.

Of course, interest rate changes influence investment performance and trigger buy or sell decisions for individual investors, businesses, and governmental units alike. For example, in 2008 and 2009, the Federal Reserve, in an effort to address the severe financial crisis, unexpectedly announced that it would drop its target fed funds rate to a range between 0 and 0.25 percent and lowered its discount window rate to 0.5 percent, the lowest level since the 1940s. These rates remained at historically low levels into 2013.

Figure 6.9 illustrates the movement of several key U.S. interest rates over the past 41 years:

· The prime commercial loan rate.

· The 3-month T-bill rate.

· The home mortgage rate.

· The high-grade corporate bond rate.

Figure 6.9 shows how interest rates vary over time. For example, the prime rate hit highs of over 20 percent in the early 1980s, yet fell as low as 4.75 percent in the early 1970s. The prime rate stayed below 10 percent throughout much of the 1990s, fell back further to 4.00 percent in the early 2000s, then rose to as high as 8.25 percent in the mid-2000s. During the financial crisis of 2008 and 2009, the Fed took aggressive actions to stimulate the economy, including dropping interest rates to historic lows. As a result, the prime rate fell to 3.25 percent and stayed there through 2013.

Factors That Influence Interest Rates For Individual Securities LG6-4

Specific factors that affect nominal interest rates for any particular security include:

· Inflation.

· The real risk-free rate.

· Default risk.

· Liquidity risk.

· Special provisions regarding the use of funds raised by a particular security issuer.

· The security's term to maturity.

nominal interest rates The interest rates actually observed in financial markets.

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( FIGURE 6.9 Key U.S. Interest Rates, 1972-2013 )

Source: Federal Reseve Board, website, various dates. www.federalreserve.gov

We will discuss each of these factors after summarizing them in Table 6.4.

Inflation The first factor that influences interest rates is the economywide actual or expected inflation rate. Specifically, the higher the level of actual or expected inflation, the higher will be the level of interest rates. We define inflation of the general price index of goods and services (or the inflation premium, IP) as the (percentage) increase in the price of a standardized basket of goods and services over a given period of time. The U.S. Department of Commerce measures inflation using indexes such as the consumer price index (CPI) and the producer price index (PPI). For example, the annual inflation rate using the CPI index between years t and t + 1 would be equal to:

The positive relationship between interest rates and inflation rates is fairly intuitive: When inflation raises the general price level, investors who buy financial assets must earn a higher interest rate (or inflation premium) to compensate for continuing to hold the investment. Holding on to their investments means that they incur higher costs of forgoing consumption of real goods and services today, only to have to buy these same goods and services at higher prices in the future. In other words, the higher the rate of inflation, the more expensive the same basket of goods and services will be in the future.

TABLE 6.4 Factors Affecting Norminal Interest Rates

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Real Risk-Free Rates A real risk-free rate is the rate that a risk-free security would pay if no inflation were expected over its

holding period (e.g., a year). As such, it measures only society's relative time preference for consuming today rather than tomorrow. The higher society's preference to consume today (i.e., the higher its time value of money or rate of time preference), the higher the real risk- free rate (RFR) will be.

Fisher Effect Economists often refer to the relationship among real risk-free rates (RFR), expected inflation (expected IP), and nominal risk-free rates (i), described previously, as the Fisher effect, named for Irving Fisher, who identified these economic relationships early last century. The Fisher effect theorizes that nominal risk-free rates that we observe in financial markets (e.g., the 1-year Treasury bill rate) must compensate investors for:

· Any inflation-related reduction in purchasing power lost on funds lent or principal due.

· An additional premium above the expected rate of inflation for forgoing present consumption (which reflects the real risk-free rate issue discussed previously).

Thus, the nominal risk-free rate will equal the real risk-free rate only when market participants expect inflation to be zero: Expected IP = 0. Similarly, the nominal risk-free rate will equal the expected inflation rate only when the real risk-free rate is zero. We can rearrange the nominal risk-free rate equation to show what determines the real interest rate:3

It needs to be noted that the expected inflation rate is difficult to estimate accurately, so the real risk-free rate can be difficult to measure accurately. Investors' expectations are not always realized either.

The 1-year T-bill rate in 2012 was 0.17 percent, while the CPI for the year was 1.70 percent, which implies a real risk-free rate of 21.53 percent-that is, the real risk-free rate was actually negative. Thus, the real value of investments actually decreased in that year.

Figure 6.10 shows the nominal risk-free rate (1-year T-bill rate) versus the change in the CPI from 1962 through 2012. Note that generally the T-bill rate is greater than the CPI, that is, the real risk-free rate earned on securities is positive. It is during periods of economic slowdowns that the T-bill rate is less than the CPI, that is, real risk-free rates are negative.

Default or Credit Risk Default risk is the risk that a security issuer may fail to make its promised interest and principal payments to its bondholders (or its dividend in the case of preferred stockholders). The higher the default risk, the higher the interest rate that security buyers will demand to compensate them for this default (or credit) risk relative to default-risk-free U.S. Treasury securities. Since the U.S. government has taxation powers and can print currency, the risk of its defaulting on debt payments is practically zero. But some borrowers, such as corporations or individuals, have less predictable cash flows (and no powers to tax anyone to raise funds immediately). So investors must charge issuers other than the U.S. government a premium for any perceived probability of default and the cost of potentially recovering the amount loaned built into their regular interest rate premium. The difference between a quoted interest rate on a security (security j) and a Treasury security with similar maturity, liquidity, tax, and other features is called a default or credit risk premium (DRPj). That is:

where ijt = Interest rate on a security issued by a non-Treasury issuer (issuer j) of maturity m at time t. iTt = Interest rate on a security issued by the U.S. Treasury of maturity m at time t.

Various rating agencies, including Moody's and Standard & Poor's, evaluate and categorize the potential default risk on many corporate bonds, some state and municipal bonds, and some stocks. We cover these ratings in more detail in Chapter 8. For example, in 2013, the 10- year Treasury rate was 1.97 percent. Moody's Aaa-rated and Baa-rated corporate debt carried interest rates of 3.90 percent and 4.84 percent, respectively. Thus, the average default risk preminums on the Aaa-rated and Baa-rated corporate debt were:

inflation The continual increase in the price level of a basket of goods and services.

real risk-free rate The interest rate that would exist on a default-free security if no inflation were expected.

default risk The risk that a security issuer will default on that security by being late on or missing an interest or principal payment.

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( FIGURE 6.10 Nominal Interest Rates versus Inflation )

Notice the difference between the nominal risk-free rate and the change in CPI over the last several decades.

Source: Federal Reserve Board and U.S. Department of Labor websites, various dates. www.federalreserve.gov and www.states.bls.gov/cpl/home.htm

Figure 6.11 presents these risk premiums for the stated credit-worthiness categories of bonds from 1977 through 2013. Notice from this figure and Figure 6.10 that default risk premiums tend to increase when the economy is contracting and decrease when the economy is expanding. For example, from 2007 to 2008, real risk-free rates (T-bills - CPI in Figure 6.10) increased from 0.43 percent to 1.73 percent. Over the same period, default risk premiums on Aaa-rated bonds increased from 1.39 percent to 1.97 percent. Baa-rated bonds showed a default risk premium increase from 2.55 percent to 3.78 percent.

Liquidity Risk A highly liquid asset can be sold at a predictable price with low transaction costs. That is, the holder can convert the asset at its fair market value on short notice.

EXAMPLE 6-

1 Calculating Real Risk-Free Rates LG6-4

Scan the code or log in to Connect for access to the interactive guided examples

One-year Treasury bill rates in 2007 averaged 4.53 percent and inflation (measured by the consumer price index) for the year was 4.10 percent. If investors had expected the same inflation rate as that actually realized, calculate the real risk-free rate for 2007 according to the Fisher effect.

SOLUTION:

4.53% - 4.10% = 0.43%

Similar to Problems 6­1, 6­2, self­test problem 1

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( FIGURE 6.11 Default Risk Premiums on Corporate Bonds )

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Source: Federal Reserve Board website, various dates. www.federalreserve.gov

The interest rate on a security reflects its relative liquidity, with highly liquid assets carrying the lowest interest rates (all other characteristics remaining the same). Likewise, if a security is illiquid, investors add a liquidity risk premium (LRP) to the interest rate on the security. In the United States, most government securities sell in liquid markets, as do large corporations' stocks and bonds. Securities issued by smaller companies trade in relatively less liquid markets.

A different type of liquidity risk premium may also exist if investors dislike long-term securities because their prices (present values, as discussed below and in Chapters 4 and 7) react more to interest rate changes than short-term securities do. In this case, a higher liquidity risk premium may be added to a security with a longer maturity because of its greater exposure to price risk (loss of capital value) on the longer-term security as interest rates change.

Interest rates change as the maturity of a debt security changes; in general, the longer the term to maturity, the higher the required interest rate buyers will demand.

Special Provisions or Covenants Sometimes a security's issuing party attaches special provisions or covenants to the security issued. Such provisions affect the interest rates on these securities relative to securities without such provisions attached to them. Some of these special provisions include the security's taxability, convertibility, and callability. For example, investors pay no federal taxes on interest payments received from municipal securities. So a municipal bond holder may demand a lower interest rate than that demanded on a comparable taxable bond-such as a Treasury bond (which is taxable at the federal level but not at the state or local levels) or a corporate bond (the interest on which is taxable at the state, local, and federal levels).

Another special covenant is convertibility: A convertible bond offers the holder the opportunity to exchange the bond for another type of the issuer's securities-usually preferred or common stock-at a preset price (see Chapter 7). This conversion option can be valuable to purchasers, so convertible security buyers require lower interest rates than a comparable nonconvertible security holder would require (all else equal). In general, special provisions that benefit security holders (e.g., tax-free status and convertibility) bring with them lower interest rates, and special provisions that benefit security issuers (e.g., callability, by which an issuer has the option to retire, or call, the security prior to maturity at a preset price) require higher interest rates to encourage purchase.

Term to Maturity Interest rates also change-sometimes daily-because of a bond's term to maturity. Financial professionals refer to this daily or even hourly changeability in interest rates as the term structure of interest rates, or the yield curve. The shape of the yield curve derives directly from time value of money principles. The term structure of interest rates compares interest rates on debt securities based on their time to maturity, assuming that all other characteristics (i.e., default risk, liquidity risk) are equal. Interest rates change as the maturity of a debt security changes; in general, the longer the term to maturity, the higher the required interest rate buyers will demand. This addition to the required interest rate is the maturity premium (MP). The MP, which is the difference between the required yield on long- versus short-term securities of the same characteristics except maturity, can be positive, negative, or zero.

The financial industry most often reports and analyzes the yield curve for U.S. Treasury securities. The yield curve for U.S. Treasury securities has taken many shapes over the years, but the three most common shapes appear in Figure 6.12. In graph (a), the yield curve on February 26, 2013, yields rise steadily with maturity when the yield curve slopes upward. This is the most common yield curve. On average, the MP is positive, as you might expect. Graph (b) shows an inverted, or downward-sloping, yield curve, reported on November 24, 2000, in which yields decline as maturity increases. Inverted yield curves do not generally last very long. In this case, the yield curve inverted as the U.S. Treasury began retiring long-term (30-year) bonds as the country began to pay off the national debt. Finally, graph (c) shows a flat yield curve, reported on June 4, 2007, when the yield to maturity is virtually unaffected by the term to maturity.

liquidity risk The risk that a security cannot be sold at a predictable price with low transaction costs on short notice.

term structure of interest rates A comparison of market yields on securities, assuming all characteristics except maturity are the same.

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( FIGURE 6.12 Common Shapes for Yield Curves on Treasury Securities )

Three common yield curve shaps are (a) upward sloping, (b) downward sloping, and (c) a flat slope.

Source: U.S. Treasury, Office of Debt Management, Daily Treasury Yield Curves, various dates. www.ustreas.gov

Note that yield curves may reflect factors other than investors' preferences for the maturity of a security. In reality, liquidity differences may arise among the securities traded at different points along the yield curve. For example, newly issued 20-year Treasury bonds offer a lower rate of return than previously issued Treasury bonds (so-called seasoned issues), all else being equal. Ten-year Treasury bonds may be more liquid if investors prefer new ("on the run") securities to previously issued ("off the run") securities. Specifically, since the U.S. Treasury has historically issued new 10-year notes and 20-year bonds only at the long end of the maturity spectrum, a seasoned 10-year Treasury bond would have to have been issued 10 years previously (i.e., it was originally a 20-year bond when it was issued 10 years previously). Increased demand for previously issued (and thus more liquid) 20-year Treasury bonds relative to the newly issued but less liquid 10-year Treasury bonds can be large enough to push the equilibrium interest rate on the 20-year Treasury bonds below that for the 10-year Treasury bonds and even below short-term rates. In the next section, we will review three major theories that financial analysts often use to explain the shape of the yield-to-maturity curve (or the shape of the term structure of interest rates).

Putting together the factors that affect interest rates in different markets, we can use the following general equation to note the influence of the factors that functionally impact the fair interest rate-the rate necessary to compensate investors for all security risks-(ij*) on an individual (jth) financial security.

EXAMPLE 6-

2

Determinants of Interest Rates for Individual Securities LG6-4

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Scan the code or log in to Connect for access to the interactive guided examples

Morningstar Corp.'s 8-year bonds are currently yielding a return of 6.85 percent. The expected inflation premium is 1.15 percent annually and the real risk-free rate is expected to be 2.25 percent annually over the next 8 years. The default risk premium on Morningstar's bonds is 1.35 percent. The maturity risk premium is 0.50 percent on 2-year securities and increases by 0.05 percent for each additional year to maturity. Calculate the liquidity risk premium on Morningstar's 8-year bonds.

SOLUTION:

Similar to Problems 6­3, 6­4, self­test problem 2

where IP = Inflation premium. RFR = Real risk-free rate.

DRPj = Default risk premium on the jth security. LRPj = Liquidity risk premium on the jth security. SCPj = Special covenant premium on the jth security. MPj = Maturity premium on the jth security.

The first two factors, IP and RFR, are common to all financial securities, while the other factors can uniquely influence the price of a single security.

time out!

6-7 What is the difference between nominal and real risk-free rates? 6-8 What does "the term structure of interest rates" mean?

6-9 What shape does the term structure usually take? Why?

Theories Explaining the Shape of the Term Structure of Interest Rates LG6-5

We just explained the necessity of a maturity premium, the relationship between a security's interest rate and its remaining term to maturity. We can illustrate these issues by showing that the term structure of interest rates can take a number of different shapes. As you might expect, economists and financial theorists with various viewpoints differ among themselves in theorizing why the yield curve takes different shapes. Explanations for the yield curve's shape fall predominantly into three categories:

1. The unbiased expectations theory.

2. The liquidity premium theory.

3. The market segmentation theory.

Look again at Figure 6.12 (a), which presents the Treasury yield curve as of February 26, 2013. We see that the yield curve on this date reflected the normal upward-sloping relationship between yield and maturity. Now let's turn to explanations for this shape based on the three predominant theories noted above.

Unbiased Expectations Theory According to the unbiased expectations theory of the term structure of interest rates, at any given point in time, the yield curve reflects the market’s current expectations of future short­term rates. As illustrated in Figure 6.13, the intuition behind the unbiased expectations theory is this: If investors have a 4-year investment horizon, they could either buy current 4-year bonds and earn the current (or spot) yield on a 4-year bond (1R4, if held to maturity) each year, or they could invest in four successive 1- year bonds [of which they know only the current 1-year spot rate (1R1)]. But investors also expect what the unknown future 1-year rates [E(2r1), E(3r1), and E(4r1)] will be. Note that each interest rate term has two subscripts, e.g., 1R4. The first subscript indicates the period in which the security is bought, so that 1 represents the purchase of a security in period 1. The second subscript indicates the maturity on the security. Thus, 4 represents the purchase of a security with a 4-year life. Similarly, E(3r1) is the expected return on a security with a 1-year life purchased in period 3.

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( FIGURE 6.13 Unblased Expectations Theory of the Term Structure of Interest Rates )

Return from buying four 1-year maturity bonds versus buying one 4-year maturity bond.

According to the unbiased expectations theory, the return for holding a 4-year bond to maturity should equal the expected return for investing in four successive 1-year bonds (as long as the market is in equilibrium). If this equality does not hold, an arbitrage opportunity

exists. That is, if investors could earn more on the 1-year bond investments, they could short (or sell) the 4-year bond, use the proceeds to buy the four successive 1-year bonds, and earn a guaranteed profit over the 4-year investment horizon. So, according to the unbiased expectations theory, if the market expects future 1-year rates to rise each successive year into the future, then the yield curve will slope upward. Specifically, the current 4-year T-bond rate or return will exceed the 3-year bond rate, which will exceed the 2-year bond rate, and so on. Similarly, if the market expects future 1-year rates to remain constant each successive year into the future, then the 4-year bond rate will equal the 3-year bond rate. That is, the term structure of interest rates will remain constant (flat) over the relevant time period. Specifically, the unbiased expectation theory states that current long-term interest rates are geometric averages of current and expected future short-term interest rates. The mathematical equation representing this relationship is:

therefore:

where 1RN = Actual N-period rate today (i.e., the first day of year 1).

N = Term to maturity.

1R1 = Actual 1-year rate today.

E(ir1) = Expected 1-year rates for years 2, 3, 4, . . ., N in the future.

Notice that uppercase interest rate terms, 1Rt, are the actual current interest rates on securities purchased today with a maturity of t years. Lowercase interest rate terms, tr1, represent estimates of future 1-year interest rates starting t years into the future.

Liquidity Premium Theory The second popular explanation-the liquidity premium theory of the term structure of interest rates

-builds on the unbiased expectations theory. The liquidity premium idea is as follows: Investors will hold long-term maturities only if these securities with longer term maturities are offered at a premium to compensate for future uncertainty in the security's value. Of course, uncertainty or risk increases with an asset's maturity. This theory is thus consistent with our discussions of market risk and liquidity risk, above.

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EXAMPLE 6-

3

Calculating Yield Curves LG6-5

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Scan the code or log in to Connect for access to the interactive guided examples

Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bond rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

1R1 = 2.94% E(2r1) = 4% E(3r1) = 4.74% E(4r1) = 5.10%

Construct a yield curve using the unbiased expectations theory.

SOLUTION:

Using the unbiased expectations theory, current (or today's) rates for 1-, 2-, 3-, and 4-year maturity Treasury securities should be:

and the current yield to maturity curve will be upward sloping as shown:

This upward-sloping yield curve reflects the market's expectation of persistently rising 1-year (short-term) interest rates over the future horizon.4 Similar to Problems 6­5, 6­6, 6­7, 6­8, self­test problem 3

Specifically, in a world of uncertainty, short-term securities provide greater marketability (due to their more active secondary markets) and have less price risk than long-term securities do. As a result (due to smaller price fluctuations for a given change in interest rates), investors will prefer to hold shorter-term securities because this kind of paper can be converted into cash with little market risk. Said another way, investors face little risk of a capital loss, i.e., a fall in the price of the security below its original purchase price. So, investors must be offered a liquidity premium to buy longer-term securities that carry higher capital loss risk. This difference in market and liquidity risk can be directly related to the fact that longer-term securities are more sensitive to interest rate changes in the market than are shorter-term securities- Chapter 7 discusses bond interest rate sensitivity and the link to a bond's maturity. Because longer maturities on securities mean greater market and liquidity risk, the liquidity premium increases as maturity increases.

The liquidity premium theory states that long-term rates are equal to geometric averages of current and expected short-term rates (like the unbiased expectations theory), plus liquidity risk premiums that increase with the security's maturity (this is the extension of the liquidity premium added to the unbiased expectations theory). Figure 6.14 illustrates the differences in the shape of the yield curve under the unbiased expectations theory versus the liquidity premium theory. For example, according to the liquidity premium theory, an upward- sloping yield curve may reflect investors' expectations that future short-term rates will be flat, but because liquidity premiums increase with maturity, the yield curve will nevertheless slope upward. Indeed, an upward-sloping yield curve may reflect expectations that future interest rates will rise, be flat, or even fall as long as the liquidity premium increases with maturity fast enough to produce an upward-sloping yield curve. The liquidity premium theory can be mathematically represented as

EXAMPLE 6-

Calculating Yield Curves Using the Liquidity Premium

4 Theory LG6-5

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Scan the code or log in to Connect for access to the interactive guided examples

Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bond rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

1R1 = 2.94%, E(2r1) = 4.00%, E(3r1) = 4.74% E(4r1) = 5.10%

In addition, investors charge a liquidity premium on longer-term securities such that:

L2 = 0.10% L3 = 0.20%, L4 = 0.30%

Using the liquidity premium theory, construct the yield curve.

SOLUTION:

Using the liquidity premium theory, current rates for 1-, 2-, 3-, and 4-year maturity Treasury securities should be:

and the current yield to maturity curve will be upward sloping as shown:

Similar to Problems 6­9, 6­10, self­test problem 3

where Lt = Liquidity premium for a period t and L2 > L3 > LN.

Let's compare the yield curves in Examples 6-3 (using the unbiased expectations theory) and 6-4. Notice that the liquidity premium in year 2(L2 = 0.10%) produces a 0.05 (= 3.52% - 3.47%) percent premium on the yield to maturity on a 2-year T-note, the liquidity premium for year 3 (L3 = 0.20%) produces a 0.10 (= 3.99% - 3.89%) percent premium on the yield to maturity on the 3-year T-note, and the liquidity premium for year 4 (L4 = 0.30%) produces a 0.15 (= 4.34% - 4.19%) percent premium on the yield to maturity on the 4-year T-note.

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( FIGURE 6.14 Yield Curve Using the Unbiased Expectation Theory (UET) versus the Liquidity Premium Theory (LPT) )

Notice the differences in the shape of the yield curve under the UET and the LPT.

Market Segmentation Theory The market segmentation theory does not build on the unbiased expectations theory or the liquidity premium theory, but rather argues that individual investors and FIs have specific maturity preferences, and convincing them to hold securities with maturities other than their most preferred requires a higher interest rate (maturity premium). The main thrust of the market segmentation theory is that investors do not consider securities with different maturities as perfect substitutes.

"The market segmentation theory assumes that investors and borrowers generally do not want to shift from one maturity sector to another without adequate compensation- that is, an interest rate premium."

Rather, individual investors and FIs have distinctly preferred investment horizons dictated by the dates when their liabilities will come due. For example, banks might prefer to hold relatively short-term U.S. Treasury bonds because their deposit liabilities also tend to be short-term

-recall that bank customers can access their funds on demand. Insurance companies, on the other hand, may prefer to hold long-term U.S. Treasury bonds because life insurance contracts usually expose insurance firms to long-term liabilities. Accordingly, distinct supply and demand conditions within a particular maturity segment-such as the short end and long end of the bond market-determine interest rates under the market segmentation theory.

The market segmentation theory assumes that investors and borrowers generally do not want to shift from one maturity sector to another without adequate compensation-that is, an interest rate premium. Figure 6.15 demonstrates how changes in supply for short- versus long- term bond market segments result in changing shapes of the yield to maturity curve. Specifically, as shown in Figure 6.15, the higher the demand for securities is, the higher the yield on those securities.5 Further, as the supply of securities decreases in the short-term market and increases in the long-term market, the slope of the yield curve becomes steeper. If the supply of short-term securities had increased while the supply of long-term securities had decreased, the yield curve would have a flatter slope and might even have sloped downward. Indeed, the U.S. Treasury's large-scale repurchases of long-term Treasury bonds (i.e., reductions in supply) in early 2000 has been viewed as the major cause of the inverted yield curve that appeared in February 2000.

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( FIGURE 6.15 Market Segmentation and Determination of the Slope of Yield Curve )

The higher the demand for securities, the higher the yield on those securities.

time out!

6-10 What three theories explain the shape of the yield curve?

6-11 Explain how arbitrage plays a role in the unbiased expectations explanation of the shape of the yield curve.

Forecasting Interest Rates LG6-6

We noted in the time value of money (TVM) chapters (Chapters 4 and 5) that as interest rates change, so do the values of financial securities. Accordingly, both individual investors and public corporations want to be able to predict or forecast interest rates if they wish to trade profitably. For example, if interest rates rise, the value of investment portfolios of individuals and corporations will fall, resulting in a loss of wealth. So, interest rate forecasts are extremely important for the financial wealth of both public corporations and individuals.

Recall our discussion of the unbiased expectations theory in the previous section of this chapter. That theory indicated that the market's expectation of future short-term interest rates determines the shape of the yield curve. For example, an upward-sloping yield curve implies that the market expects future short-term interest rates to rise. So, we can use the unbiased expectations theory to forecast (short-term) interest rates in the future (i.e., forward 1-year interest rates). A forward rate is an expected, or implied, rate on a short-term security that will originate at some point in the future. Using the equations in the unbiased expectations theory, we can directly derive the market's expectation of forward rates from existing or actual rates on spot market securities.

To find an implied forward rate on a 1-year security to be issued one year from today, we can rewrite the unbiased expectations theory equation as follows:

where 2f1 = expected 1-year rate for year 2, or the implied forward 1-year rate for next year.

Saying that 2f1 is the expected 1-year rate for year 2 is the same as saying that, once we isolate the 2f1 term, the equation will give us the market's estimate of the expected 1-year rate for year 2. Solving for 2f1 we get:

forward rate An expected rate (quoted today) on a security that originates at some point in the future.

EXAMPLE 6-

5

Estimating Forward Rates LG6-6

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Scan the code or log in to Connect for access to the interactive guided examples

In the mid-2000s, the existing or current (spot) 1-, 2-, 3-, and 4-year zero coupon Treasury security rates were as follows:

Using the unbiased expectations theory, calculate 1-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4. SOLUTION:

Similar to Problems 6­15, 6­16, self­test problem 4

In general, we can find the forward rate for any year, N, into the future using the following generalized equation derived from the unbiased expectations theory:

time out!

6-12 What is a forward rate?

6-13 How can we obtain an implied forward rate from current short- and long-term interest rates? 6-14 Why is it useful to calculate forward rates?

Log in to your Connect course to access Appendix 6A: The Financial Crisis: The Failure of Financial Institution Specialness.

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Your Turn...

Questions

1. Classify the following transactions as taking place in the primary or secondary markets (LG6­1):

a. IBM issues $200 million of new common stock.

b. The New Company issues $50 million of common stock in an IPO.

c. IBM sells $5 million of GM preferred stock out of its marketable securities portfolio.

d. The Magellan Fund buys $100 million of previously issued IBM bonds.

e. Prudential Insurance Co. sells $10 million of GM common stock.

2. Classify the following financial instruments as money market securities or capital market securities (LG6­2):

a. Federal funds

b. Common stock

c. Corporate bonds

d. Mortgages

e. Negotiable certificates of deposit

f. U.S. Treasury bills

g. U.S. Treasury notes

h. U.S. Treasury bonds

i. State and government bonds

3. What are the different types of financial institutions? Include a description of the main services offered by each. (LG6­3)

4. How would economic transactions between suppliers of funds (e.g., households) and users of funds (e.g., corporations) occur in a world without FIs? (LG6­3)

5. Why would a world limited to the direct transfer of funds from suppliers of funds to users of funds likely result in quite low levels of fund flows? (LG6­3)

6. How do FIs reduce monitoring costs associated with the flow of funds from fund suppliers to fund users? (LG6­3)

7. How do FIs alleviate the problem of liquidity risk faced by investors wishing to invest in securities of corporations? (LG6­3)

8. What are six factors that determine the nominal interest rate on a security? (LG6­4)

9. What should happen to a security's equilibrium interest rate as the security's liquidity risk increases? (LG6­4)

10. Discuss and compare the three explanations for the shape of the yield curve. (LG6­5)

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11. Are the unbiased expectations and liquidity premium theories explanations for the shape of the yield curve completely independent theories? Explain why or why not. (LG6­5)

12. What is a forward interest rate? (LG6­6)

13. If we observe a 1-year Treasury security rate that is higher than the 2-year Treasury security rate, what can we infer about the 1-year

rate expected one year from now? (LG6­6)

Problems

BASIC PROBLEMS

6-1 Determinants of Interest Rates for Individual Securities A particular security's default risk premium is 2 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. The security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the security's equilibrium rate of return. (LG6­4)

6-2 Determinants of Interest Rates for Individual Securities You are considering an investment in 30-year bonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Journal reports that 1-year T-bills are currently earning 1.25 percent. Your broker has determined the following information about economic activity and Moore Corporation bonds:

Real risk-free rate = 0.75% Default risk premium = 1.15% Liquidity risk premium = 0.50% Maturity risk premium = 1.75%

a. What is the inflation premium? (LG6­4)

b. What is the fair interest rate on Moore Corporation 30-year bonds? (LG6­4)

6-3 Determinants of Interest Rates for Individual Securities Dakota Corporation 15-year bonds have an equilibrium rate of return of 8 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.50 percent. The security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the bond's default risk premium. (LG6­4)

6-4 Determinants of Interest Rates for Individual Securities A 2-year Treasury security currently earns 1.94 percent. Over the next two years, the real risk-free rate is expected to be 1.00 percent per year and the inflation premium is expected to be 0.50 percent per year. Calculate the maturity risk premium on the 2-year Treasury security. (LG6­4)

6-5 Unbiased Expectations Theory Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

1R1 = 6%, E(2r1) = 7%, E(3r1) = 7.5%, E(4r1) = 7.85%

Using the unbiased expectations theory, calculate the current (long-term) rates for 1-, 2-, 3-, and 4-year-maturity Treasury securities. Plot the resulting yield curve. (LG6­5)

6-6 Unbiased Expectations Theory Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the

following three years (i.e., years 2, 3, and 4, respectively) are as follows:

1R1 = 1%, E(2r1) = 3.75%, E(3r1) = 4.25%, E(4r1) = 5.75%

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Using the unbiased expectations theory, calculate the current (long-term) rates for 1-, 2-, 3-, and 4-year-maturity Treasury securities. Plot the resulting yield curve. (LG6­5)

6-7 Unbiased Expectations Theory One-year Treasury bills currently earn 1.45 percent. You expect that one year from now, 1-year Treasury bill rates will increase to 1.65 percent. If the unbiased expectations theory is correct, what should the current rate be on 2-year Treasury securities? (LG6­5)

6-8 Unbiased Expectations Theory One-year Treasury bills currently earn 2.15 percent. You expect that one year from now, 1-year Treasury bill rates will increase to 2.65 percent and that two years from now, 1-year Treasury bill rates will increase to 3.05 percent. If the unbiased expectations theory is correct, what should the current rate be on 3-year Treasury securities? (LG6­6­5)

6-9 Liquidity Premium Theory One-year Treasury bills currently earn 3.45 percent. You expect that one year from now, 1-year Treasury bill rates will increase to 3.65 percent. The liquidity premium on 2-year securities is 0.05 percent. If the liquidity premium theory is correct, what should the current rate be on 2-year Treasury securities? (LG6­5)

6-10 Liquidity Premium Theory One-year Treasury bills currently earn 2.25 percent. You expect that one year from now, 1-year Treasury bill rates will increase to 2.45 percent and that two years from now, 1-year Treasury bill rates will increase to 2.95 percent. The liquidity premium on 2-year securities is 0.05 percent and on 3-year securities is 0.15 percent. If the liquidity premium theory is correct, what should the current rate be on 3-year Treasury securities? (LG6­5)

6-11 Liquidity Premium Theory Based on economists' forecasts and analysis, 1-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows:

Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (LG6­5)

6-12 Liquidity Premium Theory Based on economists' forecasts and analysis, 1-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows:

Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (LG6­5)

INTERMEDIATE PROBLEMS

6-13 Determinants of Interest Rates for Individual Securities Tom and Sue's Flowers, Inc.'s, 15-year bonds are currently yielding a return of 8.25 percent. The expected inflation premium is 2.25 percent annually and the real risk-free rate is expected to be 3.50 percent annually over the next 15

years. The default risk premium on Tom and Sue's Flowers' bonds is 0.80 percent. The maturity risk premium is 0.75 percent on 5-year securities and increases by 0.04 percent for each additional year to maturity. Calculate the liquidity risk premium on Tom and Sue's Flowers, lnc.'s, 15-year bonds. (LG6­4)

6-14 Determinants of Interest Rates for Individual Securities NikkiG's Corporation's 10-year bonds are currently yielding a return of

6.05 percent. The expected inflation premium is 1.00 percent annually and the real risk-free rate is expected to be 2.10 percent annually over the next 10 years. The liquidity risk premium on NikkiG's bonds is 0.25 percent. The maturity risk premium is 0.10

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percent on 2-year securities and increases by 0.05 percent for each additional year to maturity. Calculate the default risk premium on NikkiG's 10-year bonds. (LG6­4)

6-15 Unbiased Expectations Theory Suppose we observe the following rates: 1R1 = 8%, 1R2 = 10%. If the unbiased expectations theory of the term structure of interest rates holds, what is the 1-year interest rate expected one year from now, E(2r1)? (LG6­5)

6-16 Unbiased Expectations Theory The Wall Street Journal reports that the rate on 4-year Treasury securities is 1.60 percent and the rate on 5-year Treasury securities is 2.15 percent. According to the unbiased expectations theories, what does the market expect the 1-year Treasury rate to be four years from today, E(5r1)? (LG6­5)

6-17 Liquidity Premium Theory The Wall Street Journal reports that the rate on 3-year Treasury securities is 5.25 percent and the rate on 4-year Treasury securities is 5.50 percent. The 1-year interest rate expected in three years is, E(4r1), is 6.10 percent. According to the liquidity premium hypotheses, what is the liquidity premium on the 4-year Treasury security, L4? (LG6­5)

6-18 Liquidity Premium Theory Suppose we observe the following rates: 1R1 = 0.75%, 1R2 = 1.20%, and E(2r1) = 0.907%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2, L2? (LG6­5)

6-19 Forecasting Interest Rates You note the following yield curve in The Wall Street Journal. According to the unbiased expectations theory, what is the 1-year forward rate for the period beginning one year from today, 2f1? (LG6­6)

6-20 Forecasting Interest Rates On March 11, 20XX, the existing or current (spot) 1-, 2-, 3-, and 4-year zero coupon Treasury security rates were as follows:

Using the unbiased expectations theory, calculate the 1-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4 as of March 11, 20XX. (LG6­6)

ADVANCED PROBLEMS

6-21 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 10-year Treasury bonds is 7.25 percent, on 20-year Treasury bonds is 7.85 percent, and on a 20-year corporate bond issued by MHM Corp. is 8.75 percent. Assume that the maturity risk premium is zero. If the default risk premium and liquidity risk premium on a 10-year corporate bond issued by MHM Corp. are the same as those on the 20-year corporate bond, calculate the current rate on MHM Corp.'s 10-year corporate bond. (LG6­4)

6-22 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 8-year Treasury

bonds is 5.85 percent, the rate on 15-year Treasury bonds is 6.25 percent, and the rate on a 15-year corporate bond issued by MHM Corp. is 7.35 percent. Assume that the maturity risk premium is zero. If the default risk premium and liquidity risk premium on an 8-

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year corporate bond issued by MHM Corp. are the same as those on the 15-year corporate bond, calculate the current rate on MHM Corp.'s 8-year corporate bond. (LG6­4)

6-23 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 5-year Treasury bonds is 1.85 percent and on 10-year Treasury bonds is 3.35 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 5-year Treasury bond purchased five years from today, E(5r5). (LG6­4)

6-24 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 10-year Treasury bonds is 2.25 percent and the rate on 20-year Treasury bonds is 4.50 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 10- year Treasury bond purchased 10 years from today, E(10r10). (LG6­4)

6-25 Unbiased Expectations Theory Suppose we observe the 3-year Treasury security rate (1R3) to be 8 percent, the expected 1-year rate next year

-E(2r1)-to be 4 percent, and the expected one-year rate the following year- E(3r1)-to be 6 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the 1-year Treasury security rate, 1R1? (LG6­5)

6-26 Unbiased Expectations Theory The Wall Street Journal reports that the rate on 3-year Treasury securities is 1.20 percent and the rate on 5-year Treasury securities is 2.15 percent. According to the unbiased expectations theory, what does the market expect the 2-year Treasury rate to be three years from today, E(3r2)? (LG6­5)

6-27 Forecasting Interest Rates Assume the current interest rate on a 1-year Treasury bond (1R1) is 4.50 percent, the current rate on a 2-year Treasury bond (1R2) is 5.25 percent, and the current rate on a 3-year Treasury bond (1R3) is 6.50 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the 1-year forward rate expected on Treasury bills during year 3, 3f1 ? (LG6­6)

6-28 Forecasting Interest Rates A recent edition of The Wall Street Journal reported interest rates of 1.25 percent, 1.60 percent, 1.98 percent, and 2.25 percent for 3-, 4-, 5-, and 6-year Treasury security yields, respectively. According to the unbiased expectation theory of the term structure of interest rates, what are the expected 1-year forward rates for years 4, 5, and 6? (LG6­6)

1 Gande and Saunders, "Are Banks Still Special When There Is a Secondary Market for Loans?" Journal of Finance, 2012, pp. 1649-1684, find that equity of borrowers whose bank loans trade on secondary markets for the first time receive positive announcement period returns. Further, the announcement by a bank of new loans to a borrower after the borrower's loans begin trading in the secondary markets show positive announcment period returns.

2 Recent regulatory proposals recognize that MMMFs are operating as "banks," including requirements that MMMFs maintain capital levels similar to banks

and/or be backed by a private deposit insurance scheme.

3 Often the Fisher effect formula is written as (1 + i) = (1 + IP) x (1 + RFR), which, when solved for i, becomes: i = Expected IP + RFR + (Expected IP x RFR), where Expected IP x RFR is the inflation premium for the loss of purchasing power on the promised nominal interest rate payments due to inflation. For small values of Expected IP and RFR this term is negligible. The approximation formula used here assumes these values are small.

4That is, E(4r1) D E(3r1) D E(2r1) D 1R1.

5 In general, the price and yield on a bond are inversely related. Thus, as the price of a bond falls (becomes cheaper), the demand for the bond will rise. This is the same as saying that as the yield on a bond rises, it becomes cheaper and the demand for it increases. See Chapter 7.

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