Chapter 1. Introduction

INVESTMENT: The sacrifice of certain present value for (possibly uncertain) future values (benefits).

- two attributes: time and risk- this class: investments in financial assets

Real assets:

- tangible: land, building, machine- intangible: patents, goodwill.

Financial assets:

- Equity: common stocks, preferred stocks - Fixed income securities: T. notes, bonds, municipal bonds, corporate bonds,

- Derivative securities: options, futures; their values derive from the price of other assets

TWO MAIN THEMES OF INVESTMENTS

(1) Modern Portfolio theory (MPT):

- risk-return trade off in the securities markets - high risk assets tend to offer high expected return

- efficient diversification

(2) Efficient Market Hypothesis (EMH):

- security price reflects all the information available to investors concerning the value of the securities

ACTIVE AND PASSIVE MANAGEMENTS

(1) Passive: a strategy of holding a well-diversified portfolio without attempting to outperform others through superior security selection & market timing.

(2) Active: the attempt to improve performance either by security selection or market timing

note: the EMH active management should not work very long.

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INVESTMENT PROCESS

A Top-Down Analysis of Portfolio Construction

(1) the Capital Allocation decision

- Choice of safe but low-return money market securities, or risky but higher-return securities (e.g., stocks)

(2) the Asset Allocation decision

- the distribution of risky investments across broad asset classes like stocks, bonds, real estates, foreign assets, and so on.

(3) the Security Selection decision

- the choice of which particular securities to hold within each asset class

- security analysis involves the valuation of particular securities: must forecast dividends and earnings

- fundamental/ technical analysis

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Chapter 2. Financial Markets and Instruments

FINANCIAL MARKETS

(1) the Money market: includes short-term, marketable, liquid, low risk debt securities (cash equivalents)

- Instruments: Treasury bills, CD, CP, Bankers’ acceptances, Eurodollars, Repos & Reverses, Federal Funds, Brokers’ calls.

(2) the Capital market: includes longer-term riskier securities

(a) Fixed income capital markets (longer-term): Treasury bonds & notes, Federal agency debts, Municipal bonds, Corporate bonds, Mortgage-backed securities.

(b) Equity markets: common stocks, preferred stocks

(c) Derivative markets: options, futures.

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Note:

Options: A call (put) option gives its holder the right to purchase (sell) an asset for a specified price—exercise or strike price—on or before a specified expiration date.

ex. A December call (put) option on IBM stock with an exercise price of $90.

e.g., A three-month maturity call option with an exercise price of $70 versus a three-month call on the same stock with an exercise price of $75: which one should sell at a greater price? the former (the lower the exercise price, the greater the price of call options)

Futures contracts: call for delivery of an asset or its cash value at a specified delivery or maturity date for an agreed-upon price (the futures price) to be paid at contract maturity.

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2.1 The Money Market

- a subsector of the fixed-income market

(1) Treasury bills

- most marketable; discount bond - maturities: 91, 182 days, 52-week bills - minimum denomination: $1,000 (recently changed)

- interest (income): exempt from all state and local taxes (not from federal tax)- T.B yields are quoted as the “bank discount yield”

rBD = 10,000 - P x 360 10,000 n

where P = the bond price; n = the maturity in days; rBD = the bank discount yield; $10,000 = par value.

- To determine the T-bill’s true market price: P = 10,000 x [ 1 - rBD x n/360 ]

Ex. T-bill sold at $9,500 with a maturity of a half year (182 days): rBD= (500/10,000) x (360/182) = 0.0989 (9.89%)

- Effective annual yield: reay

( 1 + 500/9,500 )2 - 1 = 0.1080 (10.8%)

6

- The “bond equivalent yield” of the T-bill = APR (annual percentage rate)

rBEY = (10,000 - P)/P x (365/n) = (500/9,500) x (365/182) = 10.555% (< 10.8%)

note: rBD < rBEY < rEAY

(2) Certificate of Deposits (CD):

- a time deposit - denomination > $100,000 are usually negotiable- insured up to $100,000 by the FDIC

(3) Commercial Paper (CP)

- short-term, unsecured debt (promissory) notes issued by large corporations with strong credit ratings

- the biggest source of short-term funding for blue-chip U.S. corporations

- maturities up to 270 days. Bought by money market funds, insurance companies, and any firm needing to park extra cash - issued in multiples of $100,000, about $1.6 trillion market- fairly safe

(4) Banker’s Acceptance

- widely used in foreign trade (creditworthiness)- an order to a bank by a bank’s customer- the bank endorses the order for payment (accepted)

7

How to read Treasury bill yields from the WSJ?

Ex. January 15, 2003__________________________________________________Maturity Days to Mat BID ASKED CHG ASK YLD__________________________________________________July 17 03 183 1.22 1.21 - 1.23

Note: bid (asked) price: at which a dealer is willing to purchase (or sell).

rBD = 1.21%; rBEY = 1.23%; n = 183 days

rBD = 1.21% →

P = 10,000 [ 1 - rBD x (n/360)] = $9,938.492

→ rBEY = (10,000 - 9,938.49)/9,938.49 x (365/n) = 0.01234 (1.23%)

→ reay = (1 + 61.51/9,938.49) (365/183) - 1.0 = 0.0124 (1.24%)

Thus,

rBD < rBEY < reay

8

(5) Eurodollars (CD)

- dollar-denominated deposits at foreign banks or foreign branches of American banks- the liability of a non-US branch of a bank: less liquid, riskier than domestic CDs, offer higher yields, no FDIC protection.

(6) Repos and Reverses

- Repurchase agreement- the dealer sells govt securities to an investor on an overnight basis, with an agreement to buy back these securities the next day at a slightly higher price.

(7) Federal Funds

- member bank maintains reserve requirement in ‘federal funds’- arise as a way for banks to transfer balances to meet reserve requirement- F. F. rate: on very short-term loans among fin. Institutions.

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(8) Brokers’ call

- buy on margin (investors)- brokers borrow the funds from a bank- usually charge 1% higher than short-term T. bill rate.

(9) LIBOR market (London Interbank Offered Rate)

- the rate at which large banks in London are willing to lend $ among themselves- serves as a reference rate, in the European money market.

Note: The risk premium over T-bills (i.e., the spread) increases with economic uncertainty (or crisis) because investors demand a greater premium on debt subject to default risk.

Bankers’ acceptances are negotiable instruments (time draft) drawn to finance the export, import, domestic shipment or storage of goods. A bankers’ acceptance is ‘accepted’ when a bank writes on the draft its agreement to pay it at maturity. A bank may accept the draft for either the drawer or the holder. Banks accept these drafts on behalf of their customers, who are obliged to pay the bank the amount financed on or before the maturity date. The bank becomes the primary obligator of the draft. The acceptance is an outstanding liability of the bank.Letters of credit in foreign transactions are the most common type of acceptance. The most common everyday occurrence of this is when a U.S. firm imports goods from foreign firm and asks a U.S. bank to issue a letter of credit on behalf of the importer to the foreign exporter. The letter authorizes the foreign exporter to draw a time draft upon the U.S. importer’s bank.

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2.2 The Fixed Income Capital Market- longer term borrowing instruments

(1) Treasury Notes and Bonds

maturities: up to 10 years/ 10 - 30 years denominations of $1,000 or more coupon bonds: semiannual paymentsNote: 11/1/2001: The Treasury department would no longer sell 30-year bonds, for years the benchmark for the entire $17.7 trillion U.S. bond market – long-term interest rate will decline. Now 10-year Treasury takes over the benchmark title.

(2) Federal Agency Debt

Home mortgages: FHLB, FNMA (Fannie Mae), GNMA (Ginnie Mae), FHLMC (Freddie Mac)

FHLB: borrow money by issuing sec. and lend this money to S&L to be lent in turn to individual home buyers

Farm Credit related agencies (banks)

(3) Municipal Bonds

issued by state and local governments general obligation bonds and revenue bonds (airport,

hospital, etc) tax-exempt: interest income is exempt from federal income

tax; also is exempt from state & local taxation in the issuing state; capital gains are not exempt

the equivalent taxable yield of the munis: r = rm / (1 - t),

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where rm = the rate on municipal bonds; t = the investor’s marginal tax bracket; r = the total before-tax rate of return on taxable bonds.

Ex. rm = 10%; t = 28% : then r = 13.89%, if t = 36%: then r = 15.625% the higher the bracket, the more valuable the tax-exempt feature of municipals.

Ex. A municipal bond carries a coupon of 6% and is trading at par; to a taxpayer in a 36% tax bracket, this bond would provide a taxable equivalent yield of 9.375%. (4) Corporate Bonds

semiannual coupons default risk secured bonds: collateral unsecured bonds (= debentures) subordinated debentures: lower priority claim callable bonds convertible bonds

(5) Mortgages & Mortgage-backed securities

fixed rate/ adjustable rate securitization of mortgage loans: ex. A 10% coupon GNMA called pass-throughs

2.3 Equity Securities

(1) Common stock

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ownership shares in a corporation

(2) Preferred stock

- hybrid of equity & debt like a bond, pays fixed dividends (perpetuity), but no voting

power like a stock, the failure to pay dividends no bankruptcy;

dividends are cumulative (non-cumulative exists); not tax-deductible expenses for the firm

- corporations (not individuals) may exclude 70% of dividends received from domestic corporations in the computation of their taxable income (advantage over bonds): a firm's preferred stock often sells at yields below its bond

- may be callable (redeemable) by the issuing firm

- may be convertible into common stock

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2.4 Stock Market Indexes

(1) Dow Jones Averages

DJIA: 30 large “blue chip” corporations since 1896 1896: 12 stocks; 1916: 20 stocks; 1928: 30 stocks price-weighted average

DJIAt = Piti

1

30

/30 : simple average of prices

the % in the DJIA measures the return on a portfolio that invests one share in each of the 30 stocks in the index

the divisor : adjusted for stock splits & replacements example: If firm B were to split two for one (*)*A stock split is an event in which a firm decides to divide each share of stock into a multiple of one share.

___________________________________________ firm initial final shares(mil) initial final price(0) price(1) value value A $20 $25 20 $400 $500 B $40 $30 5 $200 $150 B* $20 $15 10 $200 $150

DJIA0 = = 30; DJIA1 =25 30

2

= 27.5

After a split: 20 20

d * = 30 ,

d* = 40

30 = 1.333 (new divisor) After a split:DJIA0 = (20 + 20)/d* = 40/1.333 = 30 (= DJIA0 w/o split)DJIA1 = (25+ 15)/d* = 40/1.333 = 30 ( DJIA1 w/o split)

- current divisor for the DJIA is 0.13561241 (8/30 /04)

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How to understand DJIA = 10,141?

8/30/2004, DJIA = 10,141, and

d* = 0.13561

Originally,

DJIAt = Piti

1

30

/30

→

DJIAt = Piti

1

30

/d*.

→

Piti

1

30

= DJIAt x d*

= 10,141 x 0.13561 = 1,375.22

Thus, average price = Piti

1

30

/30

= 1,375.22 / 30

= $ 45.841

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Dow Jones Averages: 30 industrials, 20 transportation, 15 utilities 65 composite the DJIA: based on small number of firms ; not value-

weighted as of Nov. 1, 1999: Out: Chevron, Goodyear, Sears Roebuck, Union CarbideIn: Microsoft Corp., Intel Corp., Home Depot Inc., and SBC Communications inc.

as of April 1, 2004: Out: AT&T Corp., Eastman Kodak Co., and International Paper, In: Verizon Communications Inc., a company formed after the breakup of the old AT&T, insurer American International Group Inc., and Pfizer Inc., the nation's biggest drugmaker. recognize trends within the U.S. stock market, including the continued growth of the financial and health care sectors,"

Currently: Alcoa, Allied Signal, American Express, American International Group Inc, Boeing, Caterpillar, Citigroup, Coca-Cola, DuPont, Exxon, General Electric, General Motors, Hewlett-Packard, Home Depot, IBM, Intel, Johnson & Johnson, McDonald, Merck, Microsoft, 3M, JP Morgan, Pfizer, Phillip Morris, Proctor& Gamble, SBC Communications, United Technologies, Verizon Communications, Wal-Mart Stores, Walt Disney.

(2) Standard & Poor’s Indexes (since 1957)

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the S&P 500: improvement over the DJIA(a) a more broadly based index of 500 firms(b) a market-value-weighted index: unaffected by stock splits

400 industrials, 20 transportation, 40 utilities, 40 financial indexes

the S&P index funds provide a low-cost passive investment strategy

S&P 500 Index = [ Pit Qit / O.V. ] x 10where O.V. = original valuation in 1941-1943 (i.e., relative to the average value during the period of 1941-1943, which was assigned an index value of 10) 81% of the mkt value of companies on the NYSE

(3) Other market indexes

the NYSE Index: a mkt value-weighted composite index of all NYSE listed stocks (O.V. as of 12/31/1965 =50.0)

the AMEX Index: also mkt value-weighted the NASDAQ (National Assoc. Sec. Dealers Automatic

Quotations): the Wilshire 5,000 Index: the mkt-value of all NYSE &

AMEX stocks plus actively traded OTC stocks: called ‘total mkt index’includes about 7,000 stocks

Russell 2000: small stock ( mkt capitalization below $1.5 bill) performance

(4) Equally Weighted Index

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places equal weight on each return corresponds to an implicit portfolio strategy that places

equal dollar value on each stock ___________________________Ex. Stocks A B C return 10% -6% 15%

An equally weighted arithmetic avg: rA

rA = (0.10 - 0.06 + 0.15)/3 = 0.06333 An equally weighted geometric avg: rG

rG = [(1.10)(0.94)(1.15)] 1/3 - 1.0 = 0.0594

The Value Line Index: an equally weighted geometrical avg of the performance of about 1,700 firms

(5) Foreign Stock Mkt Indexes

the Nikkei 225: a price-weighted average of the largest Tokyo Stock Exchange stocks

the Nikkei 300 is a value-weighted index Topix: market value -weighted index

The Tokyo Stock Price Index ('TOPIX') is a composite index of all common stocks listed on the First Section of the Tokyo Stock Exchange (TSE).The index is basically a measure of the changes in aggregate market value of TSE common stocks. The base for each of the index is the aggregate market value of its component stocks as of the close on January 4, 1968, the first trading day of the year.

the FTSE 100 (‘footsie’): a value-weighted index of 100 of the largest London Stock Exchange corporations; published by Financial Times of London

the DAX index is the premier German stock index

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MSCI (Morgan Stanley Capital International) stock indexes: computes over 50 country indexes and several regional indexes; market-value weighted indexes of other non-US stock markets

e.g., EAFE (Europe, Australia, Far East), the World Index,

(6) Bond Market Indictors- Merrill Lynch, Lehman Brothers, and Salomon

Smith Barney- Difficult to compute due to infrequent trading- unreliable

Note: After more than two centuries of trading stocks in fractions, the NYSE starting 1/29/2001 began trading all of its 3,525 stock issues in decimals. The much smaller ASE is making the switch at the same time. The Nasdaq stock market converted its nearly 5,200 issues in early April, 2001.

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Chapter 3. How Securities are Traded

3.1 How firms issue securities- Two types of primary market issues

stocks: IPO (Initial public offering) and seasoned new issues * a seasoned equity offering, SEO, is made by a firm whose shares have already been listed.

bonds: public offering and private placement (to a few institutional investors).

- public offerings of both stocks and bonds are marketed via an underwriting by investment bankers:

firm commitment underwriting the best-effort agreement

- some evidence of IPO under-pricing: initial positive abnormal returns in resale- Negative market reactions to SEO: signaling or price pressure

- Several brokerage companies helped form the online investment bank in 2000 to give their customers access to IPO, which has long been dominated by institutional players.

In 1995, Spring Street Brewing Company raised $1.6 mil through internet IPO without investment banker

Internet-based investment banks- Wit Capital, W.R. Hambrecht & Co., DLJ Direct, E*Offering, …..

3.2 Security Markets

(1) The Secondary Markets

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-Organized exchanges

a facility (central physical location) only members may trade The NYSE membership is limited to 1,366 members since 1953,

who collectively own the NYSE memberships (or seats) are valuable assets ($1 mil:1/6/2005, $1.7

mil: 4/3/00, $2 mil in 2003) set of rules and regulations

- nine major stock exchanges in the U.S.

national : NYSE, AMEX regional: local firms and some firms in national exchanges ex. Boston, Chicago, Philadelphia, Cincinnati and so on.

- The NYSE

the largest equities marketplace in the world and is home to 3,042 companies worth more than $15 trillion in global market capitalization. The NYSE represents approximately 80% of the value of all publicly owned companies in America. Average daily volume was 273.5 billion shares or $11.8 trillion in dollar volume through November 1999. Over two-thirds of the roster of NYSE companies have listed here within the last 12 years. These companies include a cross-section of leading U.S. companies, midsize and small capitalization companies. Non-U.S. issuers play an increasingly important role on the NYSE. As of July 1999, 382 non-U.S. companies were listed here - more than triple the number 5 years ago.

initial listing requirements: income, asset, mkt value, shares, shareholders.

Opens 9:30 a.m.-4:00 p.m.

- The AMEX: national, smaller & younger firms

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As the nation's second largest floor-based exchange, the American Stock Exchange has a significant presence in common stocks, index shares and equity derivative securities. On the Amex, trading is conducted through an advanced centralized Specialist system combining the speed of computer delivered orders with the liquidity of customer driven markets.

- dual listing (between national and regional) e.g., regional exchanges trade many NYSE-listed stocks

- most fixed income securities are not traded on the exchanges: Corporate bonds are traded both on the exchanges and OTC, but all federal and municipal government bonds are traded only over the OTC

(2) The Over-the Counter Market (OTC)

no central physical location no membership requirements for trading: brokers register

with the SEC as dealers in OTC dealer market: quote bid & asked prices and execute, over 400 market makers

note: bid (asked) price: at which a dealer is willing to purchase (sell)

about 35,000 issues are traded NASD (National Association of Sec. Dealers) oversees

trading of OTC securities in 1971, the NASDAQ system began

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The Nasdaq composite Index includes about 3,400 companies (about 5,000 companies in 2000) whose weight in the index is based on market capitalizationNasdaq operates two market segments: Nasdaq National Market and Nasdaq SmallCap Market (listing requirements differ)

-Active stocks:Microsoft , Intel, Cisco, Dell, Oracle, Sun Microsystems, Worldcom, 3Com,

- Largest Nasdaq dealers (market makers) by market share, as of August 2000 Knight Trading (13.9%); Schwab (10.5%); Herzog Heine Geduld (11.8%); Spear, Leeds & Kellogg/Goldman (7.5%);Salomon Smith Barney (4.7%); Morgan Stanley Dean Witter (4.6%); Credit Suisse First Boston (3.3%);

- On June 6, 2000, Merrill Lynch decides to buy Herzog Heine.- On Sept. 11, 2000, Goldman Sachs Group decides to buy Spear Leeds & Kellogg for $6.5 bill

(3) The Third and Fourth Markets

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(a) The Third Market refers to trading of exchange-listed securities on the OTC

market (dealers are involved) why exists? Lower commission; trading halts in the NYSE;

off-hour trading (NYSE closes at 4:00 p.m.); confidentiality.

(b) The Fourth Market refers to direct trading between investors in exchange-listed

securities without benefit of a broker avoid brokerage fees; anonymity Instinet or Posit: networks that allow direct trading The fourth market has exploded due to the advent of the

ECN (electronic communication network): it allows members to post buy or sell orders and to have those orders matched up or crossed with orders of other traders in the system (no bid-ask spread): ECNs already have captured about 30% of the trading volume in Nasdaq-listed stocks

e.g., Instinet, Posit, Island ECN, REDIbook, Archipeligo, …

*similarity: trade of exchange-listed securities

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Note: Dual listing between the NYSE and the NASDAQ

- on January 13, 2004, six big companies that are listed on the

NYSE list their shares simultaneously on Nasdaq

- Apache, Cadence Design System, Charles Schwab,

Countrywide Financial, Hewlett-Packard, and Walgreen

Note: After-hours trading

- Institutional investors : instinet

- Individual investors: no access

- Recently

1. Datek (online trading company) : offers after-hour service through Island ECN

2. Discover brokerage, Dreyfus brokerage service: trade the most active Nasdaq and NYSE issues from 6:00-8:00 p.m. Eastern Time.

3. E-trade: Instinet trading available until 6:30 p.m. E.T.

4. Instinet will make itself available to retail investors beyond E-trade

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5. both the NYSE and the Nasdaq markets are considering extending hours.

6. the Chicago stock exchange stays open beginning October 1999 until 5:30 Central Time for a trading in a limited group of issues.

7. Instinet: owned by Reuters group

- seller posts asked price & buyer posts bid prices- may not match, no market makers;- round the clock hours - anonymity- smaller and more volatile

note: foreign currency: trades 24 hours, around the world.

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(4) Market Structure in Other Countries

(a) The London Stock Exchange dealers market like NASDAQ (no specialists) ‘Stock Exchange Automated Quotations’ Computer System as in the U.S., security firms act as both dealers (making

markets) and as brokers (executing trades) 700 foreign firms are traded

(b) The Tokyo Stock Exchange (TSE)

- previously a ‘Saitory’ system (until 2000, but not any more): do not trade for their own account essentially clerical role maintains a public limit order book & matches no specialist system- a long lunch break (one and half hour)- the first section: 1200 the most actively traded stocks the second section: 400 less actively traded stocks the remaining sec. : traded electronically

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3.3 Trading on Exchanges

(1) The Participants

An investor places an order with a broker, who contacts commission broker

the types of membership

(a) commission broker: execute public orderIndividual firms called brokerage houses that are members of the NYSE employ commission brokers. Darting from booth to trading post, these highly trained men and women buy and sell securities for the general public. In return, they earn salaries and commissions.

(b) floor broker: independent member, work for commission broker

Independent floor brokers are brokers who work for themselves. They handle orders for brokerage houses that do not have full-time brokers or whose brokers are off the floor or too busy to handle a specific order. Independent floor brokers are often still referred to as "$2 brokers," a term coined back in the days when they received $2 for every 100 shares they traded.

(c) registered trader (floor trader): trade for own account, performs no public function

(d) specialists:

one and only one specialist for each stock makes a market in one or more listed sec. act as a broker: simply execute other brokers’ orders;

maintain limit order book act as a dealer: may buy or sell shares for their own

portfolio; maintain inventory of stocks and quote bid and asked prices; maintain a ‘fair and orderly market’

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There are 1366 members of the NYSE, of which 455 are specialists (and seven specialist firms) and 911 are floor brokers. Specialists are critical to the auction process. They perform a role that could be compared to that of an air traffic controller. Just as controllers maintain order among aircraft aloft, specialists maintain a fair and orderly market in the securities assigned to them. They manage the auction process, providing a conduit of information -- electronically quoting and recording current bid and asked prices for the stocks assigned to them. This enables current price information to be transmitted worldwide, keeping all market participants informed of the total supply and demand for any particular NYSE-listed stock.

Specialists act as agents, executing orders entrusted to them by a floor broker -- orders to be executed if and when a stock reaches a price specified by a customer. In instances when there is a temporary shortage of buyers or sellers, NYSE specialists will buy or sell for their own accounts, against the trend of the market. They are not, however, required to fund all the liquidity for the market at any time. These transactions serve to manage volatility and represent a small portion of trading. The vast majority of NYSE volume is a result of public order meeting public order -- individuals, institutions and member firms interacting directly with each other. Each stock listed on the NYSE is allocated to a specialist, a broker who trades only in specific stocks at a designated location. All buying and selling of a stock occurs at that location, called a trading post. Buyers and sellers -represented by the floor brokers - meet openly at the trading post to find the best price for a security.

The people who gather around the specialist's post are referred to as the trading crowd. Bids to buy and offers to sell are made by open outcry to provide interested parties with an opportunity to participate, enhancing the competitive determination of prices. When the highest bid meets the lowest offer, a trade is executed.

To a large degree the specialist is responsible for maintaining the market's fairness, competitiveness and efficiency. Specifically, the specialist performs five vital functions.

Act as Agents One of the specialist's jobs is to execute orders for floor brokers in their assigned stocks. A floor broker may get an order from a customer who only wants to buy a stock at a price lower than the current market price - or sell it at a price higher than the current market price. In such cases, the broker may ask the specialist to hold the order and execute it if and when the price of the stock reaches the level specified by the customer. In this role the specialist acts as an agent for the broker.

Act as Catalysts Specialists serve as the contact point between brokers with buy and sell orders in the NYSE's two-way auction market. In this respect, the specialists act as catalysts, bringing buyers and sellers together, so that offers to

29

buy can be matched with offer to sell.

Act as Auctioneers At the start of each trading day, the specialists establish a fair market price for each of their stocks. The specialists base that price on the supply and demand for the stock. Then, during the day, the specialists quote the current bids and offers in their stocks to other brokers.

Stabilize Prices Specialists are also called upon to maintain "orderly markets" in their assigned stocks. That is, they ensure that trading in the stocks moves smoothly throughout the day, with minimal fluctuation in price. Provide Capital Finally, if buy orders temporarily outpace sell orders in a stock - or if sell orders outpace buy orders - the specialist is required to use his firm's own capital to minimize the imbalance. This is done by buying or selling against the trend of the market, until a price is reached at which public supply and demand are once again in balance. In this role the specialist acts as a principal or dealer. Specialists participate in only about 10 percent of all shares traded. The rest of the time, public order meets public order, without specialist participation.

30

* Some push market reforms that will replace specialists and market makers with a single electronic market (e.g., Goldman Sachs)* Spear, LeBranche (AT&T, Exxon Mobile, Morgan Stanley) and FleetBoston Financial Corp.'s Fleet Specialists (GE, Coca-Cola, Sprint): largest* Goldman buys Spear Leeds & Kellogg, which is the specialists for many companies including American International Group, General Mills, Verizon. Bear Stearns co-owns a specialist unit.

(2) Types of Orders

(a) market orders: to be executed immediately at current market prices (about 80% of orders)

(b) limit orders: specify limit price; execution is uncertain

Ex. Stock A selling $25: a limit buy @ $23 [instruct the broker to buy when price falls below $23]; a limit sell @$27 [to sell when price goes above $27]

(c.1) stop-loss (sell) orders [ex. Stop sell @$20]: to sell if price falls a stipulated level to sell to stop further losses from accumulating

(c.2) stop-buy orders [ex. Stop buy at @$30]: to buy when price rises above a given limit accompany short sales, to limit potential losses from the

short position

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(3) order specification(a) name of Company (b) buy or sell

(c) size of order (odd lots = less than 100 shares; round lots = 100 shares) (d) how long is order to be outstanding (when expires) (e) types of order

(4) special procedures: the DOT and Super DOT system

Designated Order Turnaround system exchange members send orders directly to the specialist

over computer lines (25 seconds)Member firms may send orders electronically from the floor directly to the specialist through the NYSE SuperDot system. The specialist represents these orders as an agent in the trading crowd.

3.4 Trading on the OTC Market

the decentralized dealer market each dealer maintains an inventory of selected securities sells from their inventories at asked prices and buy at bid

prices trades negotiated directly through dealer brokers must search directly for best trading opportunities.

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3.5 Buying on Margin

margin account (vs. Cash account) borrow part of purchase price from brokers, who

borrow money from bank at the “call money rate” street name: securities purchased on margin must be left

with the brokerage firm in street name; used as collateral

margin requirements:- The Board of Governors of the Fed. Res. System : 50%- The Exchange and broker may set higher margin requirements (55% and 60%)- margin = Equity / Asset ; equity = net worth

Ex. Initial margin: im = 60%; 100 sh @ $50 = $5,000 x 0.6 = $3,000 down ($2,000 loan)

B/SAsset $5,000 Loan $2,000(P x SH) Equity $3,000 (A – L)

**loan amount fixed.

If price falls to $40: B/SAsset $4,000 Loan $2,000 Equity $2,000

Then, actual margin (AM) = Equity/Asset = 2,000/4000 = 50%.

the broker sets a MM (maintenance margin)

33

- if AM < MM, the broker will issue a ‘margin call’ daily ‘marking to market’: investor should add new cash or sec to the margin account.

(i) undermargined: AM < MM(ii) overmargined: AM > im (unrestricted) (> MM)(iii) restricted: MM < AM < im

undermargined margin call

Ex. MM (maintenance margin) = 30% (minimum margin)Suppose price falls to $25 (from $50): AM = (2,500-2,000)/2,500 = 500/2,500 = 20% < 30% = MM

* Formula: How far could stock price fall before the investor should get a margin call?

AM = Equity/Asset = (P x sh - Loan)/(p x sh) MM

Ex. P = ?, sh = 100; Loan = $2,000; MM = 0.30(100 x P - 2,000)/ (100 x P) = 0.30

P = 2,000/70 = $28.57.

overmargined:Ex. Price goes up to $60 AM = 4,000/6,000 = 67% > IM (= 60%)

B/S

34

Asset $6,000 Loan $2,000 Equity $4,000

you can withdraw cash from your account until AM = 60%Ex. AM = (6,000 - 2,000 - x)/6,000 = 0.60 = im

x = $400 (can borrow $400 from the account)

B/SAsset $6,000 Loan $2,400 Equity $3,600

Why buy stocks (or bonds) on margin?

to achieve greater upside potential but expose themselves to great downside risk

Ex. Start with $5,000; P0 = $50; expect P1 = $65 borrow $5,000 and buy sh = 200; an interest rate on the margin loan = 9% (i.e., pay $5000(1+0.09) = $5,450) return = [65 x 200 - (5,000+5,450)]/5,000 = 51% If p1 = $35: return = [35 x 200 - (5,000+5,450)]/5,000 = -69%

35

3.6 Short Sales

sell first and then buy the shares later to profit from a decline in price

Investors who sell securities "short" borrow stock and sell it, betting that the stock's price will decline and that they will be able to buy the same shares back later at a lower price for return to the lender.

borrow shares from a broker and sell them later the short-seller must purchase the same stock to

replace the borrowed shares ‘covering the short position’

also pay the lender of the security any dividends paid during the short sale:

profit in short sales = initial price - (ending price + dividend) in practice, brokerage firm takes care of this: street name allowed only after an ‘uptick’ (P > 0) proceeds from a short sale must be kept on account with

the broker and cannot be invested Short interest reflects the number of shares that have yet

to be repurchased to give back to lenders. Short interest ratio: the number of trading days at the

exchange's average daily volume required to convert the total short interest positions.

e.g., 4.7 4.4 : the level of negative sentiment (or a contrarian indicator) is down.

need to deposit margin requirement (i.e., collateral)

36

Ex. P0 = $100; short 100 sh; im = 50%; MM = 30%; im = Equity/Loan = 5,000/10,000 = 50% B/S

Asset $15,000 Loan $10,000 (P x SH) Equity $5,000 (A – L)

- Suppose P1 = $70; can close out your position at a profit. To cover the short sale, you buy 100 sh to replace the ones you borrowed

- Suppose P1 = $130. You get a margin call from broker AM = Equity/ Loan = 2,000/13,000 < MM = 30%

B/SAsset $15,000 Loan $13,000 Equity $2,000

**Loan amount changes

Formula: How far can price go up before you get a margin call?

Equity/Loan = (asset-Loan)/Loan = (15,000 - sh x P1)/(sh x P1) = 0.3 (= MM) 15,000 = 1.3 x 100 x P1 P1 = $115.38

37

Second board Markets:

The success of NASDAQ prompted the development of second board markets around the world. In Asia, Singapore (SESDAQ, 1987), Japan (JASDAQ, 1991), Taiwan (TAISDAQ, 1994), and South Korea (KOSDAQ, 1996) set up or formalized their own over-the-counter markets in the 1980s and early 1990s. In 1999, Malaysia (MESDAQ) and Hong Kong (GEM) also set up their secondary markets, consecutively. In Europe, EASDAQ, a Brussels-based system that trades stocks from across Europe, was founded in 1996. Most recently, NASDAQ-JAPAN was launched in June 2000, and NASDAQ-CANADA was commenced in November 2000.

The main reason that many stock exchanges have established their own second board markets is to provide a place for fund-raising for small firms and venture capitals, most of which are high-tech related and have the potential for high growth. The second board markets also provide a new venue for investors so that they can adopt a broader investment strategy and enjoy business opportunities outside the main board market. NASDAQ has become an important source of information for stock markets around the world. In the absence of appropriate benchmarks, investors around the world look to NASDAQ to set valuations for home-grown technology and Internet issues. Global companies like Microsoft Corporation, Oracle Corporation, Intel Corporation, Cisco Systems, Inc., and Sun Microsystems, Inc. are all listed on the NASDAQ market and play the role of benchmarks for similar companies or industries in other countries.

38

EASDAQ:

In 1994 the European Association of Securities Dealers (EASD), created a European counterpart to Nasdaq, called Easdaq. After securing the necessary approvals, the Easdaq market opened for trading in November 1996. Nasdaq helped to create Easdaq, and it also took a small stake in the Easdaq market. In April 2000, Nasdaq acquired a majority stake in Easdaq, renaming it Nasdaq Europe, and revealing plans for using it as a stepping-stone towards a global, integrated marketplace.During 1999, the Easdaq market was open from 09:30 to 16:30 Central European Time corresponding to 03:30 to 10:30 EST (except for the period from the last Sunday of March through the first Sunday of April, when this corresponds to the period from 02:30 to 09:30 EST). Quotes and trade prints were disseminated in real time through Easdaq’s own system as well as through information vendors such as Bloomberg, Bridge, Datastream and Reuters; however, all trading was done by telephone.Nasdaq is open from 9:30 to 16:30 EST, and the pre-opening is from 8:00 to 9:30(although the first quotes are disseminated around 8:15 EST).

Both markets are of the same type: they are continuous, quote-driven, and screen-based. Both allow for independent price discovery, given that each market, for most of its opening hours, is the primary trading venue in most of its listed securities. Order forms available to investorson both markets include market, limit, and stop orders. Pre-trade transparency for quotes on both markets consists of side, size, price and market maker identity (although on Nasdaq, ECNs allow market makers to place what amounts to anonymous quotes).For trades done over the telephone, dealers on both markets know the identity of the broker placing the order – in the case of institutional trades this often means knowing the identity of the trader (however, the SOES facility on Nasdaq allows for automatic execution of small trades). Post-trade, transactions have to be reported to the market (within 90 seconds on Nasdaq and within 180 seconds on Easdaq) and the transaction price and volume are disseminated as soon as the report is received. The exact trading protocols differ across the two markets, with perhaps the most notable difference being the price grid. During the period of our study, on Nasdaq the grid was in multiples of $1/32 or $1/16, while on Easdaq (for stocks traded in U.S. dollars) it is $0.01.4

39

Chapter 5. Interest Rates and Risk Premium

5.1 Determinants of interest rates

among the most important input

factorssupply of funds : savingdemand for funds: investment (real assets)govt and the Fed. Res. Bank

(1) Real and Nominal rates of interest

R = nominal; r = real int rate; = inflation rate

1 + r = (1 + R)/ (1 + ) (1 + r) (1 + ) = 1 + R r + r + = R r R - because r 0.

ex-ante: 1 + r e = (1 + R)/ (1 + e)

40

(2) The equilibrium real rate of interest

r (real)

demand

Funds ($)

As r increases, supply increases (upward sloping) demand decreases (downward sloping)

govt: as budget deficits , borrowing r (Demand curve shifts out) expansionary monetary policy r (Supply curve shifts out)

(3) The equilibrium nominal rate of interest

Irving Fisher (1930): Fisher equation

R = r + e

If real rates, r, are stable, the R should predict . Debated the real, after-tax rate: R (1 - t) - , where t = tax rate

41

Supply

5.2 Risk and risk premiums

Holding-period return (HPR) = (P1 - P0 + D1)/ P0

= capital gains yield + dividend yield

the expected (mean) return:

E [r] = s ps rs, where ps = probability in state s;

rs = the HPR in state s.

risk = uncertainty about future rates of return

a measure of risk : (standard deviation of r)

2 = s ps [ rs - E[r]]2 : with probability, or = s [rt - r ]2 /(T-1) : with past data, T = # of obs

the risk premium = the expected excess return

= the expected HPR - the risk-free rate

Example: see Section 6.1

42

5.3 The Historical record_________________________________________ series avg return std. Dev__ Treasury Bills 3.8% 3.3% long-term T. Bonds 5.1% 8.1% Long-term Corp. bonds 6.1% 8.7% large co. stocks 11.1% 20.2% small co. stocks 12.6% 39.7% inflation 3.1% 4.5%____

1926-1999 [Ibbotson p.33].

evidence of the risk-return trade-off

small-firm effect in the long-term

43

Example:

State 1 2 Probability 0.6 0.4 Return 10% 15%

E(r) = (0.6 x 0.10) + (0.4 x 0.15)

= 0.06 + 0.06 = 0.12 (12%)

var(r) = 2 = [0.6 x (0.10 – 0.12)2 ] + [0.4 x (0.15 – 0.12)2]

= (0.6 x 0.0004) + (0.4 x 0.0009)

= 0.00024 + 0.00036 = 0.00060

= 0.024495 ( 2.45 %)

44

Chapter 6. Risk and Risk Aversion

6.1 Risk with simple prospects

(1) A: risky investment

W0 W1

$1,000 (a) p = 0.6 : $1,500 (b) 1-p = 0.4: $ 800

E(W1) = pa W1 a + pb W1 b = (0.6)(1,500) + (0.4)(800) = $1,220

2 = pa [W1 a - E(W1)] 2 + pb [W1 b - E(W1)] 2

= 0.6 [1,500-1,220] 2 + 0.4 [800-1,220] 2 = 117,600

= $342.93

B: risk-free T-bill; W0 = $1,000, W1 = $1,050

risk premium = 1,220 - 1,050 = $ 170.

Ex. Expected value of a risky portfolio = $ 11,200 T-bill rate = 5%If you require a risk premium of 7%, how much will you be willing to pay for the portfolio?

$11,200/ (1.0 + 0.05 + 0.07) = $10,000

45

(2) Risk aversion and utility values

risk averse investors demand investment portfolio with a positive risk premium

utility = f ( E(r ), ) + -

Assume U = E (r ) - 0.005 A 2

where U : the utility value A : degree of risk aversion

0.005: a scaling convention for %

as E (r ) U

as 2 U (when A > 0) as A more risk averse penalize risky inv. more severely

If A > 0, risk-averse investor If A = 0, risk-neutral investor U = E( r ) If A < 0, risk-lover.

46

Note that : U = E (r ) - 0.005 A 2

Two assets: risky and risk-free

(a) E (r ) = 20%; = 30%(b) E (rf) = 7% ( = 0).

Ex. Investor 1: Suppose A = 3, and

Then U a = 20 - (0.005)(3)(30) 2 = 20 - 13.5 = 6.5 Ub = 7.

Thus, U a < U b.

Ex. Investor 2: Suppose A = 2 (less risk averse, or more risk tolerant)

U a = 20 - (0.005) (2) (30) 2 = 20 - 9 = 11, Ub = 7.

Thus, U a > U b.

Ex. Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 20%. T-bills offer a risk-free 6% rate of return. What is the maximum level of the degree of risk aversion (i.e., A) for which the risky portfolio is still preferred to bills?→ 12 – 0.005 A (20)2 > 6

47

(3) The Mean-Variance Criterion (M-V)

- ‘A dominates B’ if E(r A) E(r B) and A B, and at least one inequality is strict. - the preferred direction is ‘northwest’ N E(r) W E S

The Indifference Curve: set of portfolios that offer identical utility: U = E( r ) - 0.005 A 2

E (r) = U + 0.005 A 2; y = a + b x2

E(r)

U

6.2 Portfolio Risk

48

E (r) = U + 0.005 A 2

(1) hedging: investing in an asset with a payoff pattern that offsets your exposure to a particular source of risk ()

Ex. Insurance contract, sun tan lotion co. and umbrella co.- diversification: another means to control portfolio risk

(2) A review of portfolio mathematics

an asset

E(r) = s ps rs , and 2 = s ps [rs - E( r)]2

a portfolio E( rp) = i wi E[ ri ] , and p

2 = i j wi wj cov(ri, rj),

where wi = weight on asset i, and i wi = 1.0

cov (ri, rj) = s ps [ ris - E (ri)][rjs - E(rj)]

when n = 2,

E (rp) = w1 E(r1) + w2 E(r2): weighted average

p2 = w1

2 12 + w2 2 2

2 + 2 w1 w2 cov(r1, r2)

correlation = (r1, r2) = cov (r1, r2)/ [1 2].

observations

49

(1) portfolio variance: the effect of ‘cov’ on portfolio risk a positive cov port. variance a negative cov port. variance

(2) hedging involves the purchase of a risky asset that is negatively correlated with the existing portfolio (risk-reducing)

(3) note: when n = 2 and one asset is rf, then p = w1 1

50

Chapter 7. Capital Allocation

7.1 Capital Allocation Across Risky & Risk-Free Portfolio

recall top-down analysis

(i) capital allocation decision(ii) asset allocation decision(iii) security selection decision

Ex. Complete portfolio ( c ), $500,000:

F: money market fund, $150,000; P: risky asset fund, $350,000; Stocks: $200,000 IBM, $70,000 (35% = w1) GM, $130,000 (65% = w2) Bonds: $150,000 y = the weight of P = 350/500 = 0.7 1-y = the weight of F = 150/500 = 0.3 Stocks: 200/500 = 0.4 Bonds: 150/500 = 0.3

7.2 The Risk-Free Asset

a perfectly price-indexed bond (e.g., inflation indexed Treasury securities)

in practice, Treasury bills, money market instruments (T.B., CD. CP)

7.3 Portfolio of One Risky Asset and One Risk-Free Asset

51

notation: proportion return risk risky portfolio P : y rp , E(rp) p

risk-free asset F : 1-y rf 0 complete portfolio C : 1 rc , E(rc) c

rc = y rp + (1-y) rf [e.g., E(rp) = w1 E(r1) + w2 E(r2) ]

E (rc) = y E(rp) + (1-y) rf = rf + y [E(rp) - rf],

where y = investor’s exposure to P; E(rp) - rf = risk premium.

note: c = y p y = c / p [e.g., p = w1 1]

E(rc) = rf + (c / p ) [E(rp) - rf]: CAL

note: y = a + b x

52

Capital Allocation Line: the investment opportunity set with a risky asset and a risk-free asset. E(r) CAL E(rp) PE(rc) C E(rp) - rf

rf c p

E(rc) = rf + c [E(rp) - rf] / p : CAL

Intercept = rf

slope = S = rise/run = [E(rp) - rf]/ p = the reward-to-

variability ratio measures extra return per extra risk

CAL : It depicts all the risk-return combinations available to investors

Ex. Suppose that E(rp) = 15%; p = 22%; rf = 7%; Then, the CAL will be given by

E(rc) = 7 + (8/22) c

Ex. Suppose that you manage a risky portfolio with an E(rp) = 12% and a p = 25%; and rf = 5%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected return and standard deviation of your client’s portfolio?

53

- A Leveraged Position in the Risky Asset

borrow at rf (= 7%) Ex. Investment budget = $300,000; borrow $120,000,

and invest the total inv. funds in the risky asset, P. y = 420/300 = 1.4; (1-y) = -0.4 (i.e., a short position in rf) E(rc) = rf + y [E(rp) - rf] = 7% + (1.4)(8%) = 18.2% c = y p = (1.4) (22%) = 30.8% (> p = 22%) S = slope = [ E(rc) - rf]/ c = (18.2-7)/30.8 = 0.36 (same) 18.2%=E(rc) C CAL

15%=E(rp) P

7%=rf

p (22%) c(30.8%) Suppose the borrowing rate rf B = 9% slope of CAL = [E(rp) - rf]/ p = 6/22 = 0.27 the CAL will be ‘kinked’ at point P. CAL P slope = 0.27 (y>1):

9%= rfB borrowing

slope = 0.36 (y<1): lending 7%= rf

L

p (=22%)

7.4. Risk Tolerance and Capital Allocation

54

A. Algebraic way:

investor’s problem (choose y*)

maximize U = E(rc) - 0.005 A c 2

subject to E(rc) = rf + y [E(rp) - rf] , and c 2 = y2 p

2

max U = {rf + y [ E(rp) - rf]} - 0.005 A y2 p2

dU /dy = 0 [ E(rp) - rf] - 0.01 A y p2 = 0

y* = [E(rp) - rf] / [0.01 A p 2 ]

Observation: the optimal position in the risky asset y* = f ([E (rp) - rf], A, p ) + - -

Ex. rf = 7%; E(rp) = 15%; p = 22%; A = 4

y* = (15 - 7)/ [(0.01)(4)(22)2] = 0.413 (invest 41% in P, 59% in rf)

E(rc) = 7 + (0.41) (15 - 7) = 10.28%c = (0.41) (22) = 9.02%

slope = [E(rc) - rf]/ c = (10.28 - 7)/9.02 = 0.36

Note: With A = 3, y* = 0.551 and 1-y* = 0.449

B. Graphic Way: use indifference curve

55

indifference curve: U = E(r) - 0.005 A 2

E(r) = U + 0.005 A 2

the intercept of indifference curve ( = U) = the certainty equivalence

graph:

E(r) A=4 E(r) ΔU ΔA A=2 U2

U4 U (A fixed)

observations: (1) ‘A’ determines the slope of the indifference curve

(2) the less risk averse (A), the higher the certainty equivalence for a risky portfolio

(3) as we move northwest, the higher the level of utility

The Graphic Solution to Capital Allocation

56

Two steps:

(1) determine CAL; (2) find C (the point of highest utility along the CAL) graph: E(r) CAL E(rp) P E(rc) C

rf

σc σ p σ

7.5 Passive Strategies

a portfolio decision that avoids any direct or indirect security analysis

invest in ( 1) risk-free short-term T-bills (a money mkt fund), and (2) a mkt index fund (the S&P 500)

the Capital Market Line (CML): CAL with P being a mkt index (M)

history: risk premium = 8.6%; SD = 20.9%; Slope = 0.41; y* = 0.8; A 2.46 [usually between 2 & 4]

57

●

Chapter 8. Optimal Risky Portfolios

* capital allocation between P and F* how to construct P asset allocation and security selection

8.1 Diversification & Portfolio risk σ

B

A 20 n = # of sec.

observations: portfolio risk falls as the number of securities increases, but it cannot be reduced to zero

A: market [systematic, non-diversifiable] risk; e.g., business cycle, inflation, interest rates, macroeconomic factors

B: unique [non-systematic, diversifiable] risk; e.g., personal changes, success in R&D.

58

8.2 Portfolio of Two Risky Assets

debt (D) and equity (E)

rp = wD rD + wE rE

E(rp) = wD E(rD) + wE E(rE) (weighted avg)

p2 = wD

2 D2 + wE

2 E2 + 2 wD wE cov(rD, rE)

= wD2 D

2 + wE2 E

2 + 2 wD wE corr(rD, rE) D E

= (* )

note: a2 x2 + b2 y2 ± 2 a b x y = (ax ± by)2

the relation between 1 ,2, and p : three cases,

(1) when corr = 1, then p 2 = (wD D + wE E )2, or

p = (wD D + wE E ) : weighted avg

(2) when corr = -1, then p 2 = (wD D - wE E )2, or

p = wD D - wE E : weighted avg = wD D + wE (-E )

(3) when -1 < corr < 1, p 2 = (* ).

59

- Observations: (1) E(rp) : weighted avg

p = weighted avg when corr = 1.0; otherwise, less than weighted avg whenever corr < 1.0 the less correlation, the greater the gain.

(2) when corr = -1, a perfectly hedged position (p = 0) is possible by choosing

wD = E /[ D + E ], and wE = 1 - wD = D /[ D + E ].

Proof:

when corr = -1, p = wD D - wE E . Set P = 0 with wE = 1 - wD.

0 = wD D – (1 – wD ) E

= wD D – E + wD E

= wD (D + E ) – E wD = E /[ D + E ], and wE = 1 - wD = D /[ D + E ].

(3) when corr = +1, P = 0 is possible by choosing

60

wD = -E /[ D - E ] , wE = 1 - wD = D /[ D - E ] : this may require short sales

Proof:

when corr = 1, p = wD D + wE E. Set P = 0 with wE = 1 - wD. 0 = wD D + (1 – wD ) E

= wD D + E - wD E

= wD (D - E ) + E wD = -E /[ D - E ], and wE = 1 - wD = D /[ D - E ].

graph: E(r) E ρ = -1 ρ = 0.4 ρ = 1 D

σ

ρ = correlation. The role of ρ ?

Examples:

61

E(rD) = 6%; D = 10%, E(rE) = 10%; E = 20%,

(1) Suppose correlation = -1. What will be risk-free rate (rf)?

wD = E /[ D + E ] = 20/(10+20) = 2/3, and wE = 1 - wD = D /[ D + E ] = 1/3.

Check: p = wD D - wE E = (2/3)(10) – (1/3)(20) = 0.

E(rp) = rf = wD E(rD) + wE E(rE) = (2/3)(6) + (1/3)(10) = 22/3 = 7.333 % (2) Suppose correlation = 1. What will be risk-free rate (rf)?

wD = -E /[ D - E ] = -20/(10-20) = 2, and wE = 1 - wD = - 1.

Check: p = wD D + wE E = (2)(10) + (-1)(20) = 0.

E(rp) = rf = wD E(rD) + wE E(rE) = (2)(6) + (-1)(10) = 2 %.

62

8.3 Asset Allocation with Stocks, Bonds, and Bills- the optimal risky portfolio with two risky assets and a risk-free asset graph:

E(r) E(r) E(r) IC2 IC1

E p E C’ rf p C D D rf D

Ex. y = 0.74; 1-y = 0.26; wD = 0.4; wE = 0.6 [invest 74% of wealth in P and 26% in T-bills, P consists of 40% in bonds and 60% in stocks]

Summary: “Portfolio Construction Problem”

1. Specify the return characteristics of all securities [E(ri), i

2, Covi j, and correlations]

2. Establish the risky portfolio P (given rf) [E(rp), p

2 , slope, wi…]

3. Allocate funds between the risky port. P and the risk-free asset: [y, 1-y, E(rc), c

2, …..]

63

●

●

●●

8.4 The Markowitz Portfolio Selection

(1) Security Selection

Markowitz (1952): a formal model of portfolio selection embodying diversification principles (1990 Nobel prize)

identification of the efficient frontier of risky assets 1st step of portfolio selection:

graph E(r) efficient frontier • • • • • • • MVP (minimum variance port. ) Minimum variance frontier σ

- individual assets minimum variance frontier efficient frontier : the set of portfolio that are not dominated (above m.v.p.)

2nd step: search for the CAL with the steepest slope and P. 3rd step: choose the appropriate mix of P and rf

graph:E(r) E(r) IC2

64

CAL IC1 CAL EF P C2

C1

rf rf

σ σ (2nd step) (3rd step)

The first step input list: n number of E(ri) Covariances n variances ( i 2) ; n2 - n covariances (Cov i j) [one half different]

(2) Capital Allocation & Separation Property

In step 2, a portfolio manager offers the same risky portfolio P to all clients regardless of their degree of risk aversion

Separation Property1. determination of P: purely technical2. allocation to T-bills vs. P (determination of C):

depends on personal preference

note: theories of Security Selection and Asset allocation are the same

65

●

●●

8.5 Optimal Portfolios with Restrictions on the risk-free Asset

Case 1. When a risk-free asset is not available IC4

E(r) IC3 EF

R P Q

σ

P: optimal portf. ; Q: more risk-averse investor R: more risk-tolerant investor note: with rf, both lenders and borrowers are better off.

Case 2. Different rates for borrowing and lending E(r)

IC1 IC2 A: optimal port. of P2 B defensive (risk-averse) rf

B A P1 investors B: aggressive investors rf

L (borrow at rfB to invest

in P2) σ

66

●

●

●

●●

●●

8.5 The Power and Limitation of diversification

Assume an equally weighted portfolio wi = (1/n) for each security

p2 = i j wi wj Covij

= i wi2 vari + ij wi wj covij

= (1/n2) i vari + (1/n2) ij covij

[ n variance terms & n(n-1) covariance terms]

= (1/n2) ( n 2 ) + (1/n2) [n(n-1) cov]

= (1/n) 2 + [(n-1)/n] cov

where 2 = avg var = (1/n) i i2

cov = avg cov = [1/n(n-1)] ij covi,j

the effect of diversification

lim p2 = cov as n

[i.e., firm specific risk i2 is diversified away and

portfolio risk converges to average covariance]

67

Chapter 9. The Capital Asset Pricing Model (CAPM)

a precise prediction of the relationship between the risk of an asset and its expected return

a benchmark rate of return for evaluating possible investment (fair return)

Harry Markowitz: the foundation of modern portfolio management (1952)

CAPM : by William Sharpe (1964), John Lintner (1965), and Jan Mossin (1966)

9.1 Simplifying Assumptions

A.1. many investors (perfect competition)

A.2. one holding period

A.3 publicly traded fin. Assets

A.4 no tax on returns, no transaction cost

A.5 mean-variance optimizers

A.6. homogeneous expectations (belief)

68

9.2 The Resulting Equilibrium

(1) All investors will hold the market portfolio (M) as a risky portfolio: A.2, A3, A.5, and A.6

all investors hold an identical risky portfolio, & this port. has to be M [note: all assets have to be included in M]

graph: E(r ) CAL→CML E(rM) P→M EF

rf

σM σ

(2) M will be on the efficient frontier

the passive strategy of investing in M is efficient in the simple world of the CAPM, M is the optimal

tangency portfolio on the efficient frontier.

9.3 The Risk Premium of the Market Portfolio

69

Recall y (= a proportion allocated to the risky optimal portfolio M) :

y* = [E (rp) - rf] / [0.01 A p 2 ]

In the simple CAPM, net borrowing & lending across all investors must be zero y * = 1

with y * = 1,

[E (rp) - rf] = [0.01 A p 2 ] : the risk premium on the market portf. depends on average degree of risk aversion and p 2

70

9.4 The CAPM

the expected return-beta relationship

E(ri) = rf + i [E(rM) - rf] , where i = cov(ri, rM) /M2.

or i = ri / rM

M = 1; i > 1: aggressive, i < 1: defensive

the beta of a stock measures the stock’s contribution to the variance of the market portfolio;

measures only systematic risk

CAPM: the security’s risk premium is directly proportional to both the beta & the risk premium of the market port.

The Security Market Line (SML):

graph: E(ri) E(ri) = rf + i [E(rM) - rf] SML ME(rM) E(rM)-rf

rf

M = 1 i

SML: E(ri) = rf + i [E(rM) - rf]

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E(ri) - rf = i [E(rM) - rf]

individual asset risk premium as a function of asset risk i

is valid for both efficient port. and individual assets

USE: to compute ‘required (fair) rate of return’

(1) a benchmark for the evaluation of inv. performance

fairly priced assets: plot on the SML under-priced assets: plot above the SML over-priced assets: plot below the SML

alpha ( ) : actual - fair expected rate of return Ex. = 1.2; rf = 5%; E(rM) - rf = 8%; E(ri) = 16% SML : E(ri) = 5 + 1.2 (8) = 14.6% : fair return

= 16 - 14.6 = 1.4% > 0. graph: E(ri) E(ri) = rf + i [E(rM) - rf] 16% SML 14.6% M

5% 1.0 1.2 i

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(2) capital budgeting: required (or fair) discount rate

NPV = C0 + PV

PV = i Ci/ (1+ ri)i

E(ri) = rf + i [E(rM) - rf]

(3) utility rate decision (regulated)

Ex. i = 0.6; rf = 5%; E(rM) - rf = 8%;

fair return = 5 + 0.6 (8) = 9.8%

the firm is allowed to set prices at a level expected to generate these profits

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- Comparison of the SML with the CML

SML: E(ri) = rf + i [E(rM) - rf]

CML : E(rc) = rf + c [E(rM) - rf] /M

graph: E(r) CML

M

rf

σM

note: beta measures only systematic risk, while SD measures total risk.

Differences:1. measure of risk2. well-diversified or not

Ex. Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 12%. I am buying a firm with an expected perpetual cash flow of $1 million but am unsure of its risk. If I think the beta of the firm is 0.6, when in fact the beta is really 1.2, how much more will I offer for the firm than it is truly worth?

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Ch. 10 & 11. Index Models & Arbitrage Pricing Theory

Ch. 10. Index model

(1) Systematic risk versus firm-specific risk

the Markowitz portfolio selection model requires E(ri): N var(ri): N need (N2 + 3N)/2 estimates cov(ri, rj): (N2 - N)/2

Ex. If N = 100, we need 10,300/2 = 5,150 estimates. = 500, = 125,750

distinguish between macro(common economic) factors and micro (firm specific) factors

factor model: return = expected + unexpected

ri = E(ri) + (ri - E(ri)) = E(ri) + (i F + ei),

where E(ri) = the expected return; F = the unanticipated components of the macro factor, with E(F) = 0; ei = the unanticipated firm-specific events, with E(ei) = 0; and

cov(F, ei) = 0 and cov(ei, ej) = 0 for i j.

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A single Index Model:

use the mkt index return to proxy for F: F rM

ri - rf = i + i [rM - rf] + ei, or

Ri = i + i RM + ei,

where Ri = ri - rf, RM = rM - rf

each security has two sources of risk: mkt risk and firm-specific risk

for the index model:

E(ri): N i : N var(ei): N need (3N + 1) estimates M

2: 1

Ex. If N= 100, we need 301 estimates (vs. 5,150)

note:

var(Ri) = i2 = i

2 M2 + 2(ei)

because cov (RM, ei)= 0,

cov(Ri, Rj) = cov (iRM, jRM) = i j M2.

Because cov (ei, ej) = 0.

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(2) Estimating the index model

the security characteristic line: Rit = i + i RMt + eit

graph: slope=i= ΔRi/ ΔRM

Ri Rit CL eit

i + i RMt

αi

RM

eit = measures the impact of firm-specific events

= difference between the actual stock return & the return predicted from the regression equation.

R2 = coefficient of determination = the ratio of the explained variance of the stock’s return to total variance (market risk) = squared correlation coefficient

1 - R2 = unique risk (firm-specific risk)

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Ex. Suppose that the correlation coefficient between company A and the S&P 500 Stock Index is 0.80.

What percentage of company A’s total risk is specific?

The R2 of the regression is (0.8)2 = 0.64, leaving 36% of total variance unexplained by the market, and therefore, interpreted as firm-specific.

(3) The CAPM and the Index Model

the CAPM is impractical for two reasons: E(ri) = rf + i [E(rM) - rf]

1. expectations are unobservable2. the theoretical mkt portfolio includes every risky asset

& is in practice unobservable

in the single index model, we replace the (theoretical) mkt portfolio of the CAPM with the well-specified and observed mkt index

Ri = i + i RM + ei, single index model

cov(Ri, RM) = i var(RM) = i M2

i = cov(Ri, RM)/ M2 = Ri/ RM

= Slope of the CL

i.e., i of the index model = i of the CAPM

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the index model

ri - rf = i + i [rM - rf] + ei,

take expectation:

E(ri) - rf = i + i [E(rM ) - rf] ,

CAPM:

E(ri ) - rf = i [E(rM ) - rf]

the CAPM predicts i = 0:

expected return in excess of (or below) the fair expected return as predicted by the CAPM is zero.

Ex. Assume that security returns are generated by the single-index model,

Ri = i + iRM + ei,where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose that security A is characterized by following data:

A = 0.6, E(RA) = 14%, and (eA) = 20%. If M = 12%, calculate the variance of returns of security A.

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10. Arbitrage pricing Theory (APT)

An arbitrage opportunity: when an investor can construct ‘a zero investment portfolio’ that will yield a sure profit

a zero investment portfolio: an investor sells short assets and uses proceeds to purchase (go long) other assets [borrowing may be considered as a short position in the risk-free asset]

the APT uses a single factor security mkt assumption & arbitrage arguments to obtain ‘the E(R)- relationship’ for well-diversified portfolio.

Ross developed the APT in 1976.

- In contrast to the CAPM, the APT does not require the restrictive assumptions concerning the market portfolio.

- In contrast to the single factor CAPM, the APT recognizes multiple systematic risk factors.

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11.1 Betas and expected returns

portfolios with equal betas: must have equal expected returns in mkt eqm. Or arbitrage opportunities exist

portfolios with different betas: their risk premium must be proportional to beta. Or arbitrage opportunities exist

RPi /i = RPj /j = RPk /k

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Ex. A: E(rA) = 10%, A = 1.0 B: rf = 4%, = 0

C: E(rC) = 6%, C = 0.5

graph: E(r ) 10% A 7% D

6% C

B (4%)

0 0.5 1.0

Then, consider D with ½ of B and ½ of A:

D = (0.5 x 0) + (0.5 x 1) = 0.5.

E(rD) = (0.5 x 4 ) + (0.5 x 10) = 7%.

Now D = C = 0.5 but E(rD) > E(rC)

Conclusion: [E(rP) - rf]/ P = [E(rQ) - rf]/ Q

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Ex. _____________________________ portfolio E( r) beta A 10% 1.0 B 4% 0 E 9% 2/3

A: (10 - 4)/1 = 6%; E: (9 - 4)/(2/3) = 7.5%

arbitrage opportunity existsgraph: E(r ) 11.5% G 10% A 9% E

B (4%)

0 2/3 1.0

create portfolio G with = 1.

E(rG) = (-0.5) E(rB) + (1.5) E(rE) = (-0.5) (4) + (1.5) (9) = 11.5%

G = (1.5) E = (1.5) (2/3) = 1.0

G has the same beta & a higher return[a long position in E and a short position in B] Now consider portfolio H, which includes a short position

in A and a long position in G:

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H = (-1) A + (1) G = (-1 x 1) + (1 x 1) = 0

E(rH) = (-1) E(rA) + (1) E(rG) = -10% + 11.5% = 1.5%

a zero investment portf. With a zero risk results in a positive return of 1.5% H is an arbitrage portfolio.

Ex. Consider the following three portfolios.

Portfolio E ( r) beta

A 10% 1.0 B 3% 0 C 8% 0.6

a. (1 pts) Discuss how to show there is an arbitrage opportunity

b. (3 pts) Discuss how to form an arbitrage portfolio that involves a zero investment portfolio [hint: drawing a graph may help].

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Chapter 12. Market Efficiency

12.1 Random Walks and the Efficient Mkt Hypothesis

EMH: stock prices reflect “all available information”

random walk: prices change only in response to new information, which by definition, must be unpredictable:

Pt = Pt-1 + et, with Et-1(et) = 0. Or Pt = et

in 1953, Maurice Kendall: no predictable patterns in stock prices competition among analysts may contribute

three versions of the EMH

(i) the weak form: information about mkt trading data (past prices, trading volume)

(ii) the semi-strong form: all publicly available information regarding prospects of a firm (earnings forecasts, accounting practices, firm’s product line, quality of management)

(iii) the strong form: all information relevant to the firm even including information available only to

company insiders.

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Note: Inside Information

Ex. In the summer of 1994, Intuit’s (the maker of Quicken financial software program) chief fin. officer shared some exciting news with his wife: The company was going to be bought out by Microsoft Corp. She shared the secret with her son and daughter. The children, together with three others, used the merger news to buy Intuit stock options ahead of the Microsoft announcement. And then they bailed out a year later when she warned them of the merger’s imminent collapse: the SEC charged them for an insider trading case (except the CEO) and they paid $$ to settle the federal securities fraud charges.

Jaffe (1974), Seyhun (1986), Givoly and Palmon (1985): Insiders tend to make superior profits trading in their firm’s stock: stock prices tend to rise (fall) after insiders intensively bought (sold) shares.

Can other investors benefit by following insiders’ trade?- the SEC requires all insiders to register their trading

activity and the SEC published these trades in an ‘Official Summary of Insider Trading.’

- Seyhun (1986): carefully tracked the public release dates of the Official Summary, and found that following insider transactions would be of no avail, although there is some tendency for stock prices to increase: abnormal returns are too small to overcome transaction costs.

12.2 Implications of the EMH for Investment policy

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( a) Technical analysis

the search for recurrent & predictable patterns in stock prices using publicly available information; believe security prices adjust gradually to new information. called ‘chartists’ the EMH implies that technical analysis is without merit: the past history of prices & trading volume is publicly available & their information has already been reflected in stock prices continual search for yet undiscovered rules

(b) Fundamental analysis

uses information on fundamental factors to determine proper stock prices (the PDV) e.g., earnings and dividend prospects, interest rate forecasts, prospects for the industry & the firm’s standing within the industry the EMH predicts that most fundamental analysis is doomed to failure only if your analysis is better than that of your competitors

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(c) Active versus Passive portfolio management

the EMH implies that active mgmt is largely wasted effort & unlikely to justify the expenses incurred advocate a ‘passive investment strategy’ makes no attempt to outsmart the mkt invest in an index fund

(d) the Role of Portfolio Mgmt in an Efficient Mkt

to tailor the portfolio to meet the needs of investors rather than to beat the market, which requires identifying the client’s return requirements and risk tolerance. Rational portfolio management also requires examining the investor’s constraints, such as liquidity, time horizon, laws and regulations, tax bracket, risk aversion, age and employment

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12.3 Event Studies

a technique of empirical financial research that enables an observer to assess the impact of a particular event on a firm’s stock price under the EMH, price changes must reflect new information due to an event

Ex. dividend (earnings) change announcement, merger, stock repurchase

to estimate abnormal returns (AR) around the date that new information is released:

- from the index model: rt = a + b rMt + et

- ARt = rt - (a + b rMt)

to handle possible leakage of information, use cumulative AR (CAR)

Ex. dividend increase announcementgraph: CAR CAR 0.15%

0%

-0.13% -8 -4 -2 AD 2 4 8

12.4 Are Markets Efficient?

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tests of predictability in stock market returns (using correlations): Pt = Pt-1 + et, with Et-1(et) = 0. Pt = et

(i) Returns over short horizon

weekly returns of NYSE stocks reveal (small) positive serial correlation : small firms not necessarily trading opportunities Conrad & Kaul (1988), Lo and MacKinlay (1988).

(ii) Returns over long-horizon

negative long-term (3- 5 years) serial correlation Fama & French (1988), Poterba & Summers (1988) underreaction leads to positive correlation (momentum) over short-horizon, and subsequent correction leads to negative correlation over long horizon: related to excess volatility a fad hypothesis

Alternative interpretation:- need not be fads- market risk premiums vary over time: a rational response of market prices to changes in discount rates

Statistical problem- few observations of long-horizon returns- the great depression period

(iii) Predictors of broad mkt returns

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Fama/French (1986): dividend yields (D/P) Campbell/Shiller (1988): earnings yields (E/P) Keim/Stambaugh (1986): corporate bond yield spread (high & low grade)- interpretation: either in violation of the EMH or proxying for variation in the market risk premium.

12.5 Market Anomalies

evidence that seems inconsistent with the EMH joint tests of the efficient market hypothesis and the risk adjustment procedure (or techniques)

(a) The small firm (size) effect - Banz (1981)

both total and risk-adjusted rates of return tend to be larger for small firms (size effect) later studies: it occurs virtually entirely in January (in the first two weeks) ‘small-firm-in-January’ effect.

explanations:

( i) tax-loss selling hypothesis(ii) the neglected firm effect: information deficiency(iii) liquidity effect: spread

(b) Market-to-Book ratio (M/B ratio): Fama/French (1992)

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after controlling for the size and market-to-book effects, beta seems to have no power to explain security returns

‘Is beta dead?’

M/B ratio is a powerful predictor of returns across securities (inverse relationship)

(c ) Reversals: losers rebound and winners fade back

De Bondt & Thaler (1985)

the loser portfolio in five-year base period outperforms the winner portfolio in the following three year period a contrarian investment strategy: investing in recent losers should be profitable

Criticism by Ball, Kothari, and Shanken (1995):(i) using mid-year rather than December as ending

period substantially weakens the reversal effect(ii) concentrated in very low-priced stocks (e.g., less

than $1 per share)(iii) the risk-adjusted return of the contrarian strategy

is close to zero

for intermediate horizon (3 to 12-months), Jegadeesh and Titman (1993) found that stocks exhibit a momentum property: good or bad recent performance continues the opposite of a reversal phenomenon.

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Depends on time horizon of the investment

(d) The Day of the week effect (the weekend effect)

Using the mean return of the S&P 500, 62/6-78/12

Mon Tu Wed Thur Fri-.134% .002 .096 .028 .084

not nearly large enough to offset the transaction costs involved in short selling avoid purchases on Friday, delaying them until Monday

(e) Post-Earnings Announcement Price Drift

Foster, Olsen, and Shevlin (1984): - a large cumulative abnormal return on the earnings

announcement day: positive (negative) for positive (negative) earnings surprise

- However, the CAR of positive (negative) earnings surprise stocks continue to grow even after the earnings information becomes public

- the market appears to adjust to the earnings information only gradually, resulting in a sustained periods of abnormal returns (up to four quarters).

12.6 Risk premiums or Anomalies?

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A common feature to small size, low market-to-book, and recent losers: suffer from a recent drop in stock prices – distressed firms

Fama & French (1993): risk premium hypothesis- propose a three factor model in the spirit of the APT: risk is determined by the sensitivity of a stock to three factors: (i) the mkt portfolio returns, (ii) the relative returns of small versus large firms, and (iii) the relative returns of firms with high versus low ratios of book value to market value - size and B/M ratios might act as proxies for more

fundamental determinants of risk- so consistent with the EMH

Lakonishok, Shleifer, and Vishney (1995): Systematic errors in forecasts of stock analysis

- analysts extrapolate past performance too far into the future. Ultimately when market participants recognize their errors, prices reverse.

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12.7 Mutual fund performance

no evidence of professionally managed portfolios consistently beating the market the evidence on the risk-adjusted performance of professional managers is mixed at best.

12.8 Are Markets Efficient?

1. the magnitude issue: How efficient are markets?2. the selection bias issue: winning strategy will not be

reported and only failed ones will be reported.3. the lucky event issue: Can they repeat their

performance?

12.9 Behavioral finance models and Accounting model

- Psychologists have identified several ‘irrationalities’ that seem to characterize complex decision making

- Cutler, Poterba, and Summers (1990): introduce some irrational traders such as feedback traders and the market’s slow adjustment to fundamentals [see also Delong, Shleifer, Summers, and Waldmann (1990)].

- Daniel, Hirshleifer, and Subrahmanyam (1998) develop a theory based on investor overconfidence and on changes in confidence resulting from biased self-attribution of investment outcomes.

- Barberis, Shleifer, and Vishny (1998): a learning model in which actual earnings follow a random walk,

95

but individuals believe that earnings either follow a steady growth trend or are mean-reverting.

- Odean (1998): overconfident traders

- in Accounting: an alternative valuation model, the discounted residual income model (RIM), become more popular- by Ohlson (1991, 1995) and Feltham and Ohlson (1995)

- The RIM assumes an accounting identity, the clean surplus relation (CSR), which posits that the change in book value of equity is equal to the difference between accounting earnings and dividends. The residual income (RI) (or abnormal earnings) is defined as the difference between accounting earnings and the previous period book value multiplied by the cost of equity. The residual income model (RIM) maintains that the current stock price equals the current book value of equity plus the present discounted value of expected future residual income.

- Clean Surplus Relation: Bt = Bt-1 + Xt - Dt ,

- Residual Income: RIt = Xt - r Bt-1 ,

- Residual Income Model: ,

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Chapter 17. Macroeconomic and Industry Analysis

17.1 The Global Economy

the international environment (factor) exchange rate, export prospects, price competition, political risk

17.2 The Domestic Macroeconomy

key economic statistics for macroeconomy- GDP, IP- employment, unemployment rate, (factory) capacity utilization rate- inflation (trade-off between inflation and unemployment)- interest rates investment, housing, durable demand- budget deficits/surpluses- consumers’ & producers’ sentiment

17.3 Demand and Supply Shocks

a demand shock: an event that affects the demand for goods and services AD = C + I + G + (X-M) Ex. Tax rate, MS, G, X (export)

a supply shock: an event that influences production capacity and costs; AS = f (K, L, technology) Ex. Imported oil price; freezes, floods, droughts; educational level; wage rate.

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Note on Euro: - The euro is the unit of currency that replaced most of Europe’s money

-Timetable: On January 1, 1999, (practically on Jan. 4, the first business day of the new year) the foreign-exchange rate of the currencies of 11 European countries was irrevocably fixed against one another and against the euro. The dollar exchange from then on is made against the euro, not individual currencies.

-But they still used national currencies for at least three more years. Euro coins and bills were put into circulation on Jan 1, 2002. National currencies continued to be used until six months beyond that date. After that (On July 1, 2002), only the euro exists and national currencies for participating countries were no longer legal tender.

-the 11 European nations that agreed to adopt the euro: Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal and Spain.-Three European Union countries opted not to participate at this time, though they may join in later: Britain, Denmark and Sweden.-Greece, another EU member, didn’t meet the fiscal and economic standards mandated in the Maastricht Treaty, the basis for the monetary change – joined later in June 2000- Now 12 nations

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- Non-EU members such as Norway, Switzerland and Iceland are not using euros unless they choose to join the union. Nor are Eastern European countries, though the EU is considering expanding into that region.

- With the advent of the euro, the European union became a major economic force. The new 12-member “Euroland (or Eurozone)” have a gross domestic product close to that of the United States. With such economic clout, some are predicting the euro could eventually topple the dollar as the preferred international currency.

- EU-11 U.S.

GDP $6.3 tril (21%) $7.8 tri (26%) Population 290 mil 250 mil Exports $ 823 bil (20%) $689 bil (17%) Inflation (’98) 1.6% 1.5%

- The exchange rate between the U.S. dollar and the euro: around $1.18 to 1 euro in 1999.

- A new bank, the Frankfurt-based European Central Bank, takes on a role similar to the U.S. Federal Reserve beginning Jan. 1, setting interest rates in the euro zone.

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Datast ream Exchange Rates

Recent Values:

Latest Value

High over 12 M thsLow over 12 M thsAvg over 12 M ths

Perform ance:

Actual Value% Change

-1M -3M -12M

Background Inform at ion:

S tart Date

Base Currency

Datatype

09/11/04 17.29

U S $ TO E U R O (W M R )

31/12/1998

E

ER

1.24155 4.31

1.29505

1.29505 1.14740 1.22650

1.22575 5.65

USEURSP

EXCHANG E RAT E

08/11/04

08/11/0407/11/03

1.14740 12.87

EXCHANG E RAT E

94 95 96 97 98 99 00 01 02 03 040.80

0.90

1.00

1.10

1.20

1.30

USEURSP

Source: DAT AST REAM

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17.4 Federal Government Policy

(a) Fiscal policy: Tax/ G budget deficit

part of demand-side management much of post-war history directly stimulate or slow the economy formulation & implementation: slow & involved much of govt spending: non-discretionary (medicare,

social security, interest payment)

(b) Monetary policy: Ms

the other leg of demand-side policy through its impact on interest rates (indirect) in the short run: Ms r Inv , Cons AD in the long run: Ms P (inflation) ; no permanent effect on income the stimulation-inflation trade-off formulation & implementation: fast

Monetary Policy tools

(i) the open mkt operation: buy Ms r (ii) the discount rate(iii) the reserve requirement

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(C ) Supply-side policies

the goal: to create environment in which workers and owners of capital have maximum incentive & ability to produce & develop goods lower tax rate Inv , improve incentive to work economic growth national policy on education, infrastructure (communication & transportation system)

17.5 Business Cycles

recurring patterns of recession and recovery periods of expansion & contraction peak/trough the NBER: designator (the official timekeeper for American business cycles)

- Recessions past and present Between February 1945 and March 1991, the U.S. experienced 10 recessions. A recession is the period between a peak in business activity and

a bottoming-out point at which the economy resumes its expansion.

Peak - bottom length of recession (in months)2/45 - 10/45 811/48 - 10/49 117/53 - 5/54 108/57 - 4/58 84/60 - 2/61 1012/69 - 11/70 1111/73 - 3/75 161/80 - 7/80 67/81 - 11/82 167/90 - 3/91 8 3/01 - ?

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cyclical industries: above-average sensitivity to the business cycle high beta stocksEx. Producers of durable goods (cars, washing machines) and capital goods (steels)

defensive industries: little sensitivity low beta stocksEx. food companies, public utilities, pharmaceutical firms outperform others during recession

leading economic indicators: economic series that tend to rise or fall in advance of the rest of the economy

Ex. stock prices; Ms; housing starts; manufacturers’ new orders; index of consumer expectations.

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17.6 Industry Analysis

- performance can vary widely across industries

(a) Defining an industry

by SIC codes (Standard Industry Classification) four or five digits: xx xxx [first two: broad, the second three: narrow]

ex.

0 (Agriculture, Forestry, Fishing)

1 (Mining, Construction)

2 (Manufacturing)

3 (Manufacturing)

4 (Transportation & Utilities)

5 (Whole Sale & Retail Sale)6 (Finance, Insurance, Real estate)

7 (Services)

8 (Services)

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(b) Sensitivity to the Business Cycle (Earnings)

three factors( i) the sensitivity of sales: little sensitivity - necessities [food, drug, medical services] and low budget items [movies, tobacco]high sensitivity - autos, transportation, steel, machine tools

(ii) operating leverage - Fixed cost/Variable cost low O.L. firms will be less sensitive

(iii) financial leverage- low F.L. (low debt) firms will be less sensitive

* Investors need not always prefer industries with lower sensitivity to the business cycle.

* the issue: whether the expected return on the investment is fair compensation for the risk borne.

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(c ) Industry Life Cycle

graph: sales

I II III IV time

I: Start-up: a new technology or products, ex. genetic engineeringII: Consolidation stage: grows faster than the rest of economy, ex. computer softwareIII: Maturity stage: ‘cash cow’ IV: Relative decline, ex. railroad

- At what stage to invest? conventional wisdom: seek firms in high-growth industry Peter Lynch: he prefers to invest in a low-growth industry

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Chapter 18. Equity Valuation Models

models used by fundamental analysts to uncover mis-priced securities

18.1 Balance Sheet Method

(1) Book Value: a common valuation measure

the net worth of a company as shown on the B/S B/S

Assets Liabilities Common Equity

b. v. : result of accounting rules to spread the acquisition cost of assets over a period market value (price): the PV of its expected future cash flows

(2) the Liquidation Value

by breaking up the firm, selling its assets, repaying its debt, and distributing the remainder to the shareholders a better measure of a floor than the book value If a mkt price < liqui. value, then a takeover target

(3) the ‘Replacement Cost’ of assets less liabilities Tobin’s q = mkt price/replacement cost If q > 1, competitors try to replicate the firm in the long run, q 1.

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18.2 Intrinsic Value versus Market Price

the expected HPR = E(r) = [E(D1)+ E(P1)]/P0 - 1

Ex. E(P1) = $60; E(D1) = $0.5; P0 = $55

E( r) = [60 + 0.5]/55 - 1 = 5.5/55 = 10%

E(r) = E(D1)/P0 + [E(P1) - P0]/P0

= the expected dividend yield + the expected capital gains yield

k = mkt capitalization rate (fair return)

= Investor’s required rate of return (based on CAPM)

A. Return comparison:

CAPM: k = rf + [E(rM) - rf] = 6% + 1.2 [5%] = 12%

E( r) < k, then over-priced

B. Price comparison

Intrinsic Value : V0

V0 = [E(D1) + E(P1)]/(1+k) = [0.5 + 60]/1.12 = $54.02

V0 < P0 = $55, then over-valued

18.3 Dividend Discount Models (DDM)

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V0 = j E(Dj)/(1+k)j = E(D1)/(1+k) + E(D2)/(1+k)2 +

E(D3)/(1+k)3 + ………

derivation: use E(Dj) = Dj and E(Pj) = Pj

from V0 = [D1 + P1]/(1+k) V1 = [D2 + P2]/(1+k) and set

Vj = P j (i.e., assume stock is selling for its intrinsic value)

then V0 = D1/(1+k) + D2/(1+k)2 + P2/(1+k)2

= D1/(1+k) + D2/(1+k)2 + D3/(1+k)3 + ….

Capital Gain is included in the DDM PH = DH+1/(1+k)1 + DH+2/(1+k)2 + …..

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( a) The Constant Growth DDM

Assume Dj+1 = Dj (1+g): g = a constant growth rate V0 ( or P0) = D1/(k-g)

Ex. V0 (or P0) = $2/(0.12-0.04) = $25.0

price in this case will grow at the same rate as dividend (g)

[assume PH = VH]

P1 = D2/(k-g) = D1(1+g)/(k-g) = P0 (1+g)

E(r) = dividend yield + capital gains yield

= D1/P0 + [P1 - P0]/P0 = D1/P0 + g = k ( if P0 = V0)

rate hearing for regulated public utilities

use k = D1/P0 + g

many stock analysts assume Pj Vj gradually over time.

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(b) Stock Prices & Investment Opportunities

Case 1. No growth

Expected earnings = $5/share ( accounting earnings) (net of economic depreciation)

payout ratio = 1 ( plowback ratio = 0) k (market capitalization rate) = 12.5%

E1 = D1 and P0 = D1/k = E1/k = 5/0.125 = $40 (non-growing perpetuity)

Case 2 . With growth

Suppose ROE (return on equity or investment) = 15%;

k = 12.5%; p.b. ratio (= earnings retention ratio) = 60%

D1 = E1 x p.o. = $5 x (1 - 0.6) = $2.00

the growth rate of the dividends: g = ROE x p.b. = 0.15 x 0.60 = 0.09

P0 = D1/(k-g) = $2/(0.125-0.09) = $57.14

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price = no growth price + PVGO (PV of growth opportunities) P0 = E1/k + PVGO

= 40 + 17.14 , PVGO > 0 because ROE > k

Suppose ROE = k = 12.5%

Then g = ROE x p.b = 0.125 x 0.60 = 0.075

P0 = D1/(k-g) = $2/(0.125-0.075) = $2/(0.050) = $40

= price of no-growth strategy

Note: ROE > k ROE < k ROE = k

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(c) Life Cycles and Multi-stage Growth Models

firms typically pass through life cycles with different dividend profiles in different phases:

in early years: p.o. ratio low, growth is rapid in later years: p.o. ratio high, growth is slow

- a multistage version of the dividend discount model (in 2004)

year 05 06 07 08 dividend $.54 $.66 $.78 $.90

Assume the dividend growth rate levels off in 2008

g = ROE x pb = 14% x (1 - .18) = 11.5%

k = rf + [E(rM) - rf] = 3% + 1.2 [10.75-3] = 12.3%

P08 = D09/(k-g) = D08 x (1+g)/(k-g) = $.90 (1.115)/(.123 - 0.115) = $125.44

V04 = D05/(1+k) + D06/(1+k)2 + D07/(1+k)3 +

D08/(1+k)4 + P08/(1+k)4

V04 = .54/1.123 + .66/(1.123)2 + .78/(1.123)3 +

.90/(1.123)4 + 125.44/(1.123)4 = $80.99

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V = $80.99 < actual price = $102 our intrinsic value analysis indicates this stock is overpriced.

- evaluation:

advantages: solid theoretical framework; ease in adjusting for risk levels; flexible and more realistic than constant growth model

disadvantages: Need to forecast well into the future; problem with non-dividend paying companies;

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18.4 Price/Earnings Ratio

(a ) The P/E ratio and growth opportunities

much of the real world discussion of stock mkt valuation concentrates on the P/E ratio

from P0 = E1/k + PVGO

P0/E1 = (1/k) [1 + PVGO/(E1/k)]

observations:

(i) if PVGO = 0, P0 = E1/k : a non-growing perpetuity value

(ii) as PVGO , P/E

(iii) PVGO/(E1/k) = component due to growth/nongrowth price: the ratio matters

Ex. EPSA = EPSB, but (P/E)A > (P/E)B A has a higher growth opportunity

- using the constant growth DDM:

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P0 = D1/(k-g) = E1(1 - pb)/[k - (ROE x pb)]

P0/E1 = (1 -pb)/[k - (ROE x pb)]

P0/E1 = f (k, ROE, pb) - + ?

observations

(i) as ROE , P/E [high ROE projects give the firm good opportunities for growth]

(ii) the effect of p.b. on P/E:

(P/E)/ (p.b) = [ROE - k]/[k - ROE x p.b]2

as p.b , P/E when ROE > k (the firm offers superior investment opportunity)

as p.b , P/E when ROE < k

as p.b , P/E unaffected when ROE = k (the firm offers break-even investment opportunity with a fair rate of return)

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(b) Pitfalls in P/E analysis: Evaluation

- advantages:

(i) widely used by investors(ii) easy to compare with market and other companies in specific industries

- pitfalls and disadvantages

(i) E : accounting earnings- influenced by somewhat arbitrary accounting rules –effect of accounting differences (depreciation, inventory)(ii) the earnings in P/E ratio in newspaper: most recent past accounting earnings should be earnings net of economic depreciation: the maximum flow of income that the firm could pay without depleting its productive capacity or the ‘normal’ P/E ratio: E = the trend value of future earnings, E1 (hard to project earnings).

(ii) difficult with volatile earnings(iii) problems with companies with no (or negative)

income(iv) does not address quality of earnings Analysts must be careful in using P/E ratios P/E vary across industry.

18.5 Inflation and Equity Valuation

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Conventional wisdom: stocks are inflation-neutral investment

i.e., expected or unexpected inflation has no effect on the expected real rate of return on common stocks based on Fisher Equation idea common stocks are claims to real assets

- Empirical Research: real rates of return and inflation are negatively correlated during the post-war period

- Explanations

(i) Proxy hypothesis (Fama):

stock return higher economic activity inflation lower economic activity negative correlation : e.g. stagflation (oil price hike)

(ii) uncertainty: higher inflation is associated with greater uncertainty about the economy require high k a lower stock prices and returns

(iii) tax: higher inflation lower real dividends (& after-tax earnings)(iv) money illusion: Investors mistake the rise in nominal interest rate for a rise in real interest rate undervalue stocks in a period of higher inflation

(v) supply shocks vs. nominal shocks:

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supply shocks (e.g., lower oil price) lower inflation, higher stock return a negative correlation demand shocks (e.g., higher MS ) higher inflation, higher stock return a positive correlation prewar period: a positive correlation postwar period: a negative correlation relative importance of supply/demand shocks will determine the correlations

18.6 Inflation and Real Interest Rates

supply shocks vs. demand shocks: supply shock (e.g., lower oil price): lower inflation, higher real interest rate negative correlation demand shock(i) monetary shock (e.g., higher MS ): higher inflation, lower real interest rate negative correlation(ii) fiscal shock (e.g., higher G, lower Tax) : higher inflation, higher real interest rate positive correlation relative importance of shocks will determine the correlations.

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CHAPTER 15. The Term Structure of Interest Rate

- the pattern of interest rates for different-term assets.

- T.S.I.R.: the structure of interest rates for discounting

cash flows of different maturities.

- Observation: longer-term bonds offer higher yields to

maturity.

Reason: 1. a risk premium.

2. high interest rates in later years.

15.1 The Term Structure under Certainty

- (future interest rates known)

1. Bond Pricing

- Short interest rate: the interest rate for a given time

interval for that period.

- Assume a zero-coupon bond paying $1,000 in n years.

where ri is the one-year interest rate that will prevail in

year i.

- example:

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- The yield (to maturity): the single interest rate that

equates the PV of the bond's payments to the bond's

price.

note: Although interest rates may vary over time, the yield

to maturity is calculated as one "average" rate that is

applied to discount all of the bond's payments.

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- the Yield Curve: A graph of the yield to maturity on

bonds as a function of time to maturity.

See P.438. Figure 15.2:

A: upward sloping B: a hump-shaped curve

C: flat

Yield %

A

B

C

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Maturities

- the Spot Rate: the yield to maturity on zero-coupon

bonds.

i.e., yi ri

Figure 15.3

∣ ∣ ∣ ∣

- relation:

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- Forward Rates

Reality: short interest rate quotations not available

only bond prices and YTM are available on newspaper.

Example: two strategies:

1. a three-year bond.

2. a two-year bond and rollover.

- In general: for the certainty case, a future short interest

rate from the yield curve of zero-coupon bonds can be

inferred from

- Interpretation:

The numerator is total growth factor of an investment in

an n-year zero held until maturity.

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- Uncertainty case:

i.e., the forward rate is defined as the break-even interest

rate that equates the returns on an n-period zero-

coupon bond to that of an (n-1)-period zero-coupon

bond rolled over into a one-year bond in year n.

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15.2 Measuring the Term Structure

- so far on default-free zero-coupon bonds.

- majority of bonds pay coupons.

Complication:

(i) coupons are paid and reinvested.

(ii) bonds with different coupons rates can have different

yields even with equal maturities.

Example. Two coupon bonds: Each with a two year time to

maturity and annual coupon payments: 3%

and 12% coupon, r1 = 8% and r2 = 10%.

Because bond B makes a greater share of its payments in

the first year when the interest rate is lower, its yield to

maturity is slightly lower.

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- the pure yield curve: the yield curve for zero-coupon

bonds.

- the yield curve on coupon bonds: to treat each coupon

payment as a separate "mimi"-zero-coupon bond A

coupon bond then becomes a "portfolio" of many zeros.

Example:

(i) An 8% coupon bond making semiannual payments with

one year maturity, selling at $986.10.

(ii) An 10% coupon bond making semiannual payments

with one year maturity, selling at $1,004.78.

where

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Generalization:

From this, we can calculate the yields on pure zero-coupon

bonds. We use treasury securities to avoid complications

arising from default risk.

15.3 Interest Rate Uncertainty and Forward Rates

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— Interest rates are uncertain:

The forward rate is the interest rate that would need to

prevail in the second year to make the long- and short-term

investments equally attractive, ignoring risk [i.e.,

When we account for risk, it is possible that investors will

require a risk premium to hold the longer-term bond.

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15.4 Theories of The Term Structure

- The forward rate equals the market consensus expectation

of the future short interest rate,

i.e., liquidity premium = 0.

— Example:

— An upward-sloping yield curve would be clear

evidence that investors anticipate increase in interest

rates.

- The expectation hypothesis and liquidity hypothesis: view

bonds of different maturities as potential substitutes for

each other So yields on short and long bonds are

determined jointly in market equilibrium

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3. The Market Segmentation Theory:

- Long- and short-maturity bonds are traded in essentially

distinct or segmented markets, each of which finds its own

equilibrium independently.

4. The Preferred Habitat Theory:

- Investors prefer specific maturity ranges but can be

induced to switch if premiums are sufficient.

15.5 Interpreting the Term Structure

- Under certainty

- Under uncertainty of future rates

Note:

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- Two reasons for a rising yield curve:

Note: Although it is true that expectations of increases in

future interest rates can result in a rising yield curve, the

converse is not true.

Two problems:

Still

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