11

Ch 1:Investments & Financial AssetsEssential nature of investment

Reduced current consumptionPlanned later consumptionConsumption TimingAllocation of Risk

Two main themes of investmentsModern Portfolio theory (MPT):

Risk-return trade off in the securities marketsEfficient diversificationCapital asset pricing and valuation

Efficient Market Hypothesis (EMH):security price reflects all the information available to investors

concerning the value of the securities

Real AssetsAssets used to produce goods and services

Financial AssetsClaims on real assets

22

Major Classes of Financial Assets or Securities

Debt Money market instruments

Bonds

EquityCommon stock

Preferred stock

Derivative securities

33

Agency Issues and Crisis in Corporate Governance

Accounting ScandalsExamples – Enron and WorldCom

Analyst ScandalsExample – Citigroup’s Salomon Smith Barney

Initial Public OfferingsCredit Swiss First Boston

44

The Agency Problem

Agency relationshipPrincipal hires an agent to represent their interest

Stockholders (principals) hire managers (agents) to run the company

Two conditions of agency problem:1. Conflict of interest between principal and agent

2. Asymmetric information

Management goals and agency costs

55

The Investment ProcessA Top-Down Analysis of Portfolio Construction

the Capital Allocation decisionChoice of safe but low-return money market securities, or risky

but higher-return securities (e.g., stocks)

the Asset Allocation decisionthe distribution of risky investments across broad asset classes

like stocks, bonds, real estates, foreign assets, and so on.

the Security Selection decisionthe choice of which particular securities to hold within each

asset classsecurity analysis involves the valuation of particular securities:

must forecast dividends and earningsfundamental/ technical analysis

Market efficiency

66

Active vs. Passive Management

Active ManagementFinding undervalued securitiesTiming the market

Passive ManagementNo attempt to find undervalued securitiesNo attempt to timeHolding an efficient portfolio

77

Major Financial Markets and Assets or Securities

Money marketTreasury bills, Certificates of deposits, Commercial

Paper, Bankers Acceptances, Eurodollars, Repurchase Agreements (RPs) and Reverse RPs, Brokers’ Calls, Federal Funds, etc.

Treasury billsmost marketable; highly liquid; discount bond

maturities: 28, 91, 182 days

minimum denomination: $1,000

Issued weekly

88

Costs of Trading

Commission: fee paid to broker for making the transaction

Spread: cost of trading with dealerBid: price dealer will buy from you

Ask: price dealer will sell to you

Spread: ask - bid

Combination: on some trades both are paid

99

Ch 2:Asset classes and financial instruments

Figure 2.2 Treasury Bills

1010

T-billT.B yields are quoted as the “bank discount yield” rBD = 10,000 - P x 360 10,000 nwhere 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%)

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% Effective annual yield: reay

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

note: rBD < rBEY < rEAY

What is the asked price, equivalent yield, and effective yield for the T-Bill marked red in previous slide? RBEY = 365*rBD/(360-n*rBD)

1111

Major Financial Markets and Assets or Securities

Bond marketTreasury Notes and Bonds

MaturitiesNotes – maturities up to 10 years

Bonds – maturities in excess of 10 years

2001 Treasury suspended salesNote: 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. 2005 resume sales

Par Value - $1,000

Quotes – percentage of par

1212

Figure 2.4 Treasury Notes, Bonds and Bills

1313

Example12

1. If a treasury note has a bid price of $982.50, the quoted bid price in the Wall Street Journal would be __________. A) $98:08 B) $98:25 C) $98:50 D) $98:40

2. The price quotations of treasury bonds in the Wall Street Journal show an ask price of 104:16 and a bid price of 104:08. As a buyer of the bond you expect to pay __________. A) $1,041.60 B) $1,045.00 C) $1,040.80 D) $1,042.50

1414

Example 34

3. Suppose you pay $9,800 for a Treasury bill maturing in two months. What is the annual percentage rate of return for this investment? A) 2% B) 12% C) 12.2% D) 16.4%

4. Suppose you pay $9,700 for a Treasury bill maturing in six months. What is the effective annual rate of return for this investment? A) 3.1% B) 6% C) 6.18% D) 6.28%

1515

Municipal Bonds

Issued by state and local governments

Interest income is exempt

TypesGeneral obligation bonds

Revenue bondsIndustrial revenue bonds

Maturities – range up to 30 years

1616

Municipal Bond Yields

Interest income on municipal bonds is not subject to federal and sometimes state and local tax

r = rm / (1 - t),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%

Ex. A municipal bond carries a coupon of 6% and is trading at par; to a taxpayer in a 36% tax bracket, What is the taxable equivalent yield of this bond ?

1717

Corporate Bonds

Issued by private firms

Semi-annual interest payments

Subject to larger default risk than government securities

Options in corporate bondsCallable

Convertible

1818

Figure 2.8 Corporate Bond Prices

1919

Example31

1. The purchase price for a bond is listed as 104 and the annual coupon rate is 4.3%. What is the current yield (annual coupon payment / current price) on this bond? A) 0.00% B) 4.00% C) 4.13% D) 4.30%

2. What is the tax exempt equivalent yield on a 9% bond yield given a marginal tax rate of 28%? A) 6.48% B) 7.25% C) 8.02% D) 9.00%

2020

Equity Markets

Common stockResidual claim

Limited liability

Preferred stockFixed dividends - limited

Priority over common

Tax treatment

Depository receipts

2121

Figure 2.10 Listing of Stocks Traded on the NYSE

2222

Track average returns

Comparing performance of managers

Base of derivatives

Uses of Stock Indexes

2323

Representative?

Broad or narrow?

How is it weighted?

Factors for Construction of Stock Indexes

2424

Examples of Indexes - Domestic

Dow Jones Industrial Average (30 Stocks)

Standard & Poor’s 500 Composite

NASDAQ Composite

NYSE Composite

Wilshire 5000CurrentlyDJIA: 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.

2525

Construction of IndexesHow are stocks weighted?

Price weighted (DJIA) (p40 example 2.2)

Market-value weighted (S&P500, NASDAQ) (p46 example 2.4) S&P 500 Index = [Pit Qit / O.V. ] x 10

where 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

Equally weighted (Value Line Index)

Stock IP FP shares IV FV

ABC 25 30 20 500 600

XYZ 100 90 1 100 90

Total 600 690

2626

Derivatives Securities

Options

Basic PositionsCall (Buy)

Put (Sell)

TermsExercise Price

Expiration Date

Assets

Futures

Basic PositionsLong (Buy)

Short (Sell)

TermsDelivery Date

Assets

2727

Example331. The Chompers Index is a price weighted stock index based on the 3

largest fast food chains. The stock prices for the three stocks are $54, $23, and $44. What is the price weighted index value of the Chompers Index. A) 23.43 B) 35.36 C) 40.33 D) 49.58

2. A benchmark index has three stocks priced at $23, $43, and $56. The number of outstanding shares for each is 350,000 shares, 405,000 shares, and 553,000 shares, respectively. If the market value weighted index was 970 yesterday and the prices changed to $23, $41, and $58, what is the new index value? A) 960 B) 970 C) 975 D) 985

2828

Ch3: Security marketsPrimary vs. Secondary Security Sales

PrimaryNew issueKey factor: issuer receives the proceeds

from the saleSecondary

Existing owner sells to another partyIssuing firm doesn’t receive proceeds and is

not directly involved

2929

How Firms Issue Securities

Investment Banking

Shelf Registration

Private Placements

Initial Public Offerings (IPOs)

3030

Investment Banking Arrangements

Underwritten vs. “Best Efforts”Underwritten: firm commitment on proceeds to

the issuing firm

Best Efforts: no firm commitment

Negotiated vs. Competitive BidNegotiated: issuing firm negotiates terms with

investment banker

Competitive bid: issuer structures the offering and secures bids

3131

Figure 3.1 Relationship Among a Firm Issuing Securities, the Underwriters

and the Public

3232

Initial Public Offerings

Process Road shows:

1. generate interest among potential investors and provide information about the offering.

2. provide price information to the issuing firm and its underwriters.

Bookbuilding: process of polling potential investors

Underpricing Post sale returns

Cost to the issuing firm

3333

Figure 3.4 Long-term Relative Performance of Initial Public Offerings

3434

Stock Market Order Types

Limit order

Buy at best price available, but not more than the preset limit price. Forgo purchase if limit is not met.

Sell at best price available, but not less than the preset limit price. Forgo sale if limit is not met.

Type

Market order

Buy at best price available for immediate execution.

Sell at best price available for immediate execution.

Buy Sell

Stop orders

convert to a market order to buy when the stock price crosses the stop price from below.

convert to a market order to sell when the stock price crosses the stop price from above

3535

Limited Order and Stop order

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]

Stop-loss (sell) orders [ex. Stop sell @$20]:to sell if price falls a stipulated levelto sell to stop further losses from accumulatingStop-buy orders [ex. Stop buy at @$30]:to buy when price rises above a given limitaccompany short sales, to limit potential losses from the

short position (problem 20, 21)

3636

Order Specification and Trading Mechanisms

Order specificationname of Company

buy or sell

size of order (odd lots = less than 100 shares; round lots = 100 shares)

how long is order to be outstanding (when expires)

types of order

Dealer markets

Electronic communication networks (ECNs)

Specialists markets

3737

U.S. Security Markets

Nasdaq

Small stock OTCPink sheets

Organized Exchanges New York Stock Exchange

American Stock Exchange

Regionals

Electronic Communication Networks (ECNs)

National Market System

3838

OTC (Nasdaq)

No central physical locationNo membership requirements for trading: brokers register with the SEC as

dealers in OTCdealer 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 tradedNASD (National Association of Sec. Dealers) oversees trading of OTC

securitiesin 1971, the NASDAQ system beganThe Nasdaq composite Index includes about 3,400 companies (about

5,000 companies in 2000) whose weight in the index is based on market capitalization

Nasdaq operates two market segments: Nasdaq National Market and Nasdaq SmallCap Market (listing requirements differ)

3939

New York Stock Exchange

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. The NYSE represents approximately 80% of the value of all publicly owned companies in America.

Memberships (or seats) are valuable assets ($1 mil:1/6/2005, $1.7 mil: 4/3/00, $2 mil in 2003)

Member functions Commission brokersFloor brokersSpecialists

4040

Margin Trading

Using only a portion of the proceeds for an investment

Borrow remaining component

Margin arrangements differ for stocks and futures

Margin is the net worth of the investor’s account

4141

Stock Margin Trading

Maximum margin is currently 50%; you can borrow up to 50% of the stock value

Set by the Fed

Maintenance margin: minimum amount equity in trading can be before additional funds must be put into the account

Margin call: notification from broker you must put up additional funds

4242

Margin Trading - Initial Conditions

X Corp $70

50% Initial Margin

40% Maintenance Margin

1000 Shares Purchased

Initial Position

Stock $70,000 Borrowed $35,000

Equity 35,000

4343

Margin Trading - Maintenance Margin

Stock price falls to $60 per share

New Position

Stock $60,000 Borrowed $35,000

Equity 25,000

Margin% = Equity/Asset =$25,000/$60,000 = 41.67%

4444

Margin Trading - Margin Call

How far can the stock price fall before amargin call?

(1000P - $35,000)* / 1000P = 40%

P = $58.33

* 1000P - Amt Borrowed = Equity

4545

Short Sales

Purpose: to profit from a decline in the price of a stock or security

Mechanics

Borrow stock through a dealer

Sell it and deposit proceeds and margin in an account. allowed only after an ‘uptick’ (P > 0)

Closing out the position: buy the stock and return to the party from which is was borrowed

4646

Short Sales

Example: Short SalesYou want to short 100 Sears shares at $30 per

share. Your broker has a 50% initial margin and a 40% maintenance margin on short sales.

Worth of stock borrowed = $30 × 100 = $3,000

Liabilities & Account EquityAssets

Proceeds from sale $3,000 Short position $ 3,000Initial margin deposit 1,500 Account equity 1,500

Total $4,500 Total $4,500

4747

Short SalesExample: Short Sales …continued

Scenario 1: The stock price falls to $20 per share.

Liabilities & Account EquityAssets

Proceeds from sale $3,000 Short position $ 2,000Initial margin deposit 1,500 Account equity 2,500

Total $4,500 Total $4,500

New margin = equity/short position =

$2,500 / $2,000 = 125%

4848

Short SalesExample: Short Sales …continued

Scenario 2: The stock price rises to $40 per share.

Liabilities & Account EquityAssets

Proceeds from sale $3,000 Short position $ 4,000Initial margin deposit 1,500 Account equity (A-L) 500

Total $4,500 Total $4,500

New margin = equity/short position=$500 / $4,000 = 12.5% < 40% Therefore, you are subject to a margin call.

4949

Short Sale - Initial Conditions

Z Corp 100 Shares

50% Initial Margin

30% Maintenance Margin

$100 Initial Price

Sale Proceeds$10,000

Margin & Equity 5,000

Stock Owed 10,000

5050

Short Sale - Maintenance Margin

Stock Price Rises to $110

Sale Proceeds $10,000

Initial Margin 5,000

Stock Owed 11,000

Net Equity 4,000

Margin % (4000/11000) 36%

5151

Short Sale - Margin Call

How much can the stock price rise before a margin call?

($15,000* - 100P) / (100P) = 30%

P = $115.38

* Initial margin plus sale proceeds

5252

Example 23

1. Assume you purchased 200 shares of XYZ common stock on margin at $80 per share from your broker. If the initial margin is 60%, the amount you borrowed from the broker is __________. A) $4000 B) $6400 C) $9600 D) $16,000

2. You short-sell 200 shares of Tuckerton Trading Co., now selling for $50 per share. What is your maximum possible gain ignoring transactions cost? A) $50 B) $150 C) $10,000 D) unlimited

5353

Ch 5: Risk and return: Past and prologue

Holding Period Return

ndCashDivide

eEndingPricP

riceBeginningPP

1

1

0

0

101

D

PDPPHPR

5454

Rates of Return: Single Period Example

Ending Price = 24

Beginning Price = 20

Dividend = 1

HPR = ( 24 - 20 + 1 )/ ( 20) = 25%

5555

Example 43

You purchased a share of stock for $20. One year later you received $2 as dividend and sold the share for $23. Your holding-period return was __________. A) 5 percent B) 10 percent C) 20 percent D) 25 percent

The holding period return on a stock was 25%. Its ending price was $18 and its beginning price was $16. Its cash dividend must have been __________. A) $0.25 B) $1.00 C) $2.00 D) $4.00

5656

Returns Using Arithmetic and Geometric Averaging

Arithmetic

ra = (r1 + r2 + r3 + ... rn) / n

ra =.10 or 10%

Geometric

rg = {[(1+r1) (1+r2) .... (1+rn)]} 1/n - 1

rg = .0829 = 8.29%

5757

Example 12

1. The arithmetic average of 12%, 15% and 20% is _________. A) 15.7% B) 15% C) 17.2% D) 20%

2. The geometric average of 10%, 20% and 25% is __________. A) 15% B) 18.2% C) 18.3% D) 23%

5858

Quoting ConventionsAPR = annual percentage rate

(periods in year) X (rate for period)

EAR = effective annual rate

( 1+ rate for period)Periods per yr - 1

Example: monthly return of 1%

APR =

EAR =

5959

Characteristics of Probability Distributions

1) Mean: most likely value

2) Variance or standard deviation

3) Skewness

* If a distribution is approximately normal, the distribution is described by characteristics 1 and 2

6060

Return Variability: The Second Lesson

1 - 60

6161

Example

What range of return would you expect to see in 95% of time?

Is it possible you can earn 65% return annually at 1% significant level?

6262

Subjective expected returnsSubjective expected returns

p(s) = probability of a stater(s) = return if a state occurs1 to s states

p(s) = probability of a stater(s) = return if a state occurs1 to s states

Measuring Mean: Scenario or Subjective Returns

E(r) = p(s) r(s)s

6363

Numerical Example: Subjective or Scenario Distributions

StateState Prob. of StateProb. of State rrinin State State11 .1.1 -.05-.0522 .2.2 .05.0533 .4.4 .15.1544 .2.2 .25.2555 .1.1 .35.35

E(r) =.15E(r) =.15

6464

Standard deviation = [variance]Standard deviation = [variance]1/21/2

Measuring Variance or Dispersion of Returns

Subjective or ScenarioVariance =

s p(s) [rs - E(r)]2

Var=.01199Var=.01199S.D.= [ .01199] S.D.= [ .01199] 1/2 1/2 = .1095= .1095

Using Our Example:Using Our Example:

6565

Historical mean and standard deviation

)()(

1

))(()(

)(

1

2

1

ii

T

tiit

i

T

tit

i

RVarRSD

T

RERRVar

T

RRE

6666

Risk Premiums and Risk Aversion

Degree to which investors are willing to commit fundsRisk aversion

If T-Bill denotes the risk-free rate, rf, and variance, , denotes volatility of returns then:

The risk premium of a portfolio is:

E(Rp) - Rf

2P

( )P fE r r

6767

Risk Premiums and Risk Aversion

To quantify the degree of risk aversion with parameter A:

E(Rp) – Rf = (1/2) A σp2

2

( )

12

P f

P

E r rA

6868

The Sharpe (Reward-to-Volatility) Measure

Sharpe ratio =

Portfolio risk premium/standard deviation of the excess returns

= (E(Rp) – Rf )/σp

6969

Annual Holding Period ReturnsFrom Table 5.3 of Text

Geom. Arith. Stan.Series Mean% Mean% Dev.%World Stk 9.41 11.17 18.38US Lg Stk 10.23 12.25 20.50US Sm Stk 11.80 18.43 38.11Wor Bonds 5.34 6.13 9.14LT Treas 5.10 5.64 8.19T-Bills 3.71 3.79 3.18Inflation 2.98 3.12 4.35

7070

Figure 5.1 Frequency Distributions of Holding Period Returns

7171

Figure 5.2 Rates of Return on Stocks, Bonds and Bills

7272

Real vs. Nominal RatesFisher effect: Approximation

nominal rate = real rate + inflation premiumR = r + i or r = R - i

Example r = 3%, i = 6%R = 9% = 3% + 6% or 3% = 9% - 6%

Fisher effect: Exactr = (1+R) / (1 + i) - 1

2.83% = (9%-6%) / (1.06)

7373

Figure 5.4 Interest, Inflation and Real Rates of Return

7474

Possible to split investment funds between safe and risky assets

Risk free asset: proxy; T-billsRisky asset: stock (or a portfolio)Risk premium: risk asset return-risk-free rate Issues

Examine risk/ return tradeoffDemonstrate how different degrees of risk aversion

will affect allocations between risky and risk free assets

Allocating Capital Between Risky & Risk-Free Assets

7575

rf = 7%rf = 7% rf = 0%rf = 0%

E(rp) = 15%E(rp) = 15% p = 22%p = 22%

y = % in py = % in p (1-y) = % in rf(1-y) = % in rf

Example:Given:

7676

E(rc) = yE(rp) + (1 - y)rfE(rc) = yE(rp) + (1 - y)rf

rc = complete or combined portfoliorc = complete or combined portfolio

For example, y = .75For example, y = .75E(rc) = .75(.15) + .25(.07)E(rc) = .75(.15) + .25(.07)

= .13 or 13%= .13 or 13%

Expected Returns for Combinations

7777

ppcc ==

SinceSince rfrf

yy

Variance on the Possible Combined Portfolios

= 0, then= 0, then

7878

cc = .75(.22) = .165 or 16.5%= .75(.22) = .165 or 16.5%

If y = .75, thenIf y = .75, then

cc = 1(.22) = .22 or 22%= 1(.22) = .22 or 22%

If y = 1If y = 1

cc = 0(.22) = .00 or 0%= 0(.22) = .00 or 0%

If y = 0If y = 0

Combinations Without Leverage

7979

Using Leverage with Capital Allocation Line

Borrow at the Risk-Free Rate and invest in stock

Using 50% Leverage

rc = (-.5) (.07) + (1.5) (.15) = .19

c = (1.5) (.22) = .33

Reward-to-variability ratio = risk premium/standard deviation

8080

Figure 5.5 Investment Opportunity Set with a Risk-Free Investment

8181

Figure 5.6 Investment Opportunity Set with Differential Borrowing and Lending

Rates

8282

Risk Aversion and AllocationGreater levels of risk aversion lead to larger

proportions of the risk free rate

Lower levels of risk aversion lead to larger proportions of the portfolio of risky assets

Willingness to accept high levels of risk for high levels of returns would result in leveraged combinations

8383

Example 22

1. Consider the following two investment alternatives. First, a risky portfolio that pays 15% rate of return with a probability of 60% or 5% with a probability of 40%. Second, a treasury bill that pays 6%. The risk premium on the risky investment is __________. A) 1% B) 5% C) 9% D) 11%

2. Consider the following two investment alternatives. First, a risky portfolio that pays 20% rate of return with a probability of 60% or 5% with a probability of 40%. Second, a treasury that pays 6%. If you invest $50,000 in the risky portfolio, your expected profit would be __________. A) $3,000 B) $7,000 C) $7,500 D) $10,000

8484

Example 41

3.You have $500,000 available to invest. The risk-free rate as well as your borrowing rate is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should __________. A) invest $125,000 in the risk-free asset B) invest $375,000 in the risk-free asset C) borrow $125,000 D) borrow $375,000

4.The Manhawkin Fund has an expected return of 12% and a standard deviation return of 16%. The risk free rate is 4%. What is the reward-to-volatility ratio for the Manhawkin Fund? A) 0.5 B) 1.3 C) 3.0 D) 1.0

8585

Example 4225.You invest $100 in a complete portfolio. The complete portfolio is composed of a risky asset with an

expected rate of return of 12% and a standard deviation of 15% and a treasury bill with a rate of return of 5%. __________ of your money should be invested in the risky asset to form a portfolio with an expected rate of return of 9% A) 87% B) 77% C) 67% D) 57%

6.An investor invests 40% of his wealth in a risky asset with an expected rate of return of 15% and a variance of 4% and 60% in a treasury bill that pays 6%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively. A) 8.0%, 12% B) 9.6%, 8% C) 9.6%, 10% D) 11.4%, 12%

7.The expected return of portfolio is 8.9% and the risk free rate is 3.5%. If the portfolio standard deviation is 12.0%, what is the reward to variability ratio of the portfolio? A) 0.0 B) 0.45 C) 0.74 D) 1.35

8686

Ch 6

Efficient Diversification

8787

Diversification and Portfolio Risk

Total risk:Market risk

Systematic or Nondiversifiable Firm-specific risk

Diversifiable or nonsystematic or unique

8888

Figure 6.1 Portfolio Risk as a Function of the Number of Stocks

8989

Figure 6.2 Portfolio Risk as a Function of Number of Securities

9090

Exercise 42

1. Risk that can be eliminated through diversification is called ______ risk. A) unique B) firm-specific C) diversifiable D) all of the above

2. The risk that can be diversified away is ___________. A) beta B) firm specific risk C) market risk D) systematic risk

9191

Two Asset Portfolio Return – Stock and Bond

ReturnStock

htStock Weig

Return Bond

WeightBond

Return Portfolio

rwrwr

S

S

B

B

p

rwrwr SSBBp

9292

Covariance

1,2 = Correlation coefficient of returns

1,2 = Correlation coefficient of returns

Cov(r1r2) = 12Cov(r1r2) = 12

1 = Standard deviation of returns for Security 12 = Standard deviation of returns for Security 2

1 = Standard deviation of returns for Security 12 = Standard deviation of returns for Security 2

9393

Correlation Coefficients: Possible Values

If If = 1.0, the securities would be = 1.0, the securities would be perfectly positively correlatedperfectly positively correlated

If If = - 1.0, the securities would be = - 1.0, the securities would be perfectly negatively correlatedperfectly negatively correlated

Range of values for 1,2

-1.0 < < 1.0

9494

Two Asset Portfolio St Dev – Stock and Bond

Deviation Standard Portfolio

Variance Portfolio

2

2

,

22222 2

p

p

SBBSSBSSBBp wwww

9595

rp = Weighted average of the n securitiesrp = Weighted average of the n securities

p2 = (Consider all pair-wise

covariance measures)p

2 = (Consider all pair-wise covariance measures)

In General, For an n-Security Portfolio:

9696

Numerical Example: Bond and Stock

ReturnsBond = 6% Stock = 10%

Standard Deviation Bond = 12% Stock = 25%

WeightsBond = .5 Stock = .5

Correlation Coefficient (Bonds and Stock) = 0

9797

Return and Risk for Example

Return = 8%

.5(6) + .5 (10)

Standard Deviation = 13.87%

[(.5)2 (12)2 + (.5)2 (25)2 + …

2 (.5) (.5) (12) (25) (0)] ½

[192.25] ½ = 13.87

9898

Figure 6.3 Investment Opportunity Set for Stock and Bonds

9999

Minimum variance portfolio

Ws = [σB

2 - Cov(rS, rB)] / (σs2 + σB

2 -2Cov(rS, rB))

100100

Figure 6.4 Investment Opportunity Set for Stock and Bonds with Various

Correlations

101101

Extending to Include Riskless Asset

The optimal combination becomes linear

A single combination of risky and riskless assets will dominate

102102

Figure 6.5 Opportunity Set Using Stock and Bonds and Two Capital Allocation

Lines

103103

Dominant CAL with a Risk-Free Investment (F)

CAL(O) dominates other lines -- it has the best risk/return or the largest slope

Slope = (E(R) - Rf) / E(RP) - Rf) / PE(RA) - Rf) /

Regardless of risk preferences combinations of O & F dominate

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Figure 6.6 Optimal Capital Allocation Line for Bonds, Stocks and T-Bills

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Figure 6.7 The Complete Portfolio

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Figure 6.8 The Complete Portfolio – Solution to the Asset Allocation Problem

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Extending Concepts to All Securities

The optimal combinations result in lowest level of risk for a given return

The optimal trade-off is described as the efficient frontier

These portfolios are dominant

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Figure 6.9 Portfolios Constructed from Three Stocks A, B and C

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Figure 6.10 The Efficient Frontier of Risky Assets and Individual Assets

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Exercise 22

1. Adding additional risky assets will generally move the efficient frontier _____ and to the _______. A) up, right B) up, left C) down, right D) down, left

2. Rational risk-averse investors will always prefer portfolios ______________. A) located on the efficient frontier to those located on the capital market line B) located on the capital market line to those located on the efficient frontier C) at or near the minimum variance point on the efficient frontier D) Rational risk-averse investors prefer the risk-free asset to all other asset choices.

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Exercise33

1. The standard deviation of return on investment A is .10 while the standard deviation of return on investment B is .05. If the covariance of returns on A and B is .0030, the correlation coefficient between the returns on A and B is __________. A) .12 B) .36 C) .60 D) .77

2. Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return 10% and a standard deviation of return of 30%. The weight of security B in the global minimum variance is __________. A) 10% B) 20% C) 40% D) 60%

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Exercise42

1. Which of the following correlations coefficients will produce the least diversification benefit? A) -0.6 B) -1.5 C) 0.0 D) 0.8

2. The expected return of portfolio is 8.9% and the risk free rate is 3.5%. If the portfolio standard deviation is 12.0%, what is the reward to variability ratio of the portfolio? A) 0.0 B) 0.45 C) 0.74 D) 1.35

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Single Factor Model

ri = E(Ri) + ßiF + e

ßi = index of a securities’ particular return to the factor

F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns

Assumption: a broad market index like the S&P500 is the common factor

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Single Index Model

Risk PremRisk Prem Market Risk PremMarket Risk Prem or Index Risk Premor Index Risk Prem

ii= the stock’s expected return if the= the stock’s expected return if the market’s excess return is zeromarket’s excess return is zero

ßßii(r(rmm - r - rff)) = the component of return due to= the component of return due to

movements in the market indexmovements in the market index

(r(rmm - r - rff)) = 0 = 0

eei i = firm specific component, not due to market= firm specific component, not due to market

movementsmovements

errrr ifmiifi

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Let: RLet: Ri i = (r= (rii - r - rff))

RRm m = (r= (rmm - r - rff))Risk premiumRisk premiumformatformat

RRi i = = ii + ß + ßii(R(Rmm)) + e+ eii

Risk Premium Format

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Figure 6.11 Scatter Diagram for Dell

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Figure 6.12 Various Scatter Diagrams

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Components of RiskMarket or systematic risk: risk related to the

macro economic factor or market indexUnsystematic or firm specific risk: risk not

related to the macro factor or market indexTotal risk = Systematic + Unsystematic

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Measuring Components of Risk

i2 = i

2 m2 + 2(ei)

where;

i2 = total variance

i2 m

2 = systematic variance

2(ei) = unsystematic variance

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Total Risk = Systematic Risk + Unsystematic Risk

Systematic Risk/Total Risk = 2

ßi2

m2 / 2 = 2

i2 m

2 / (i2 m

2 + 2(ei)) = 2

Examining Percentage of Variance

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Ch 7 Capital asset pricing model and arbitrage pricing model

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Capital Asset Pricing Model (CAPM)

Equilibrium model that underlies all modern financial theory

Derived using principles of diversification with simplified assumptions

Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

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Assumptions

Individual investors are price takers

Single-period investment horizon

Investments are limited to traded financial assets

No taxes, and transaction costs

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Assumptions (cont.)Information is costless and available to all

investors

Investors are rational mean-variance optimizers

Homogeneous expectations

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Resulting Equilibrium Conditions

All investors will hold the same portfolio for risky assets – market portfolio

Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

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Risk premium on the market depends on the average risk aversion of all market participants

Risk premium on an individual security is a function of its covariance with the market

Resulting Equilibrium Conditions (cont.)

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Figure 7-1 The Efficient Frontier and the Capital Market Line

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M = Market portfoliorf = Risk free rate

E(rM) - rf = Market risk premium

E(rM) - rf = Market price of risk

Slope and Market Risk Premium

MM

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Expected Return and Risk on Individual Securities

The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio

Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

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Figure 7-2 The Security Market Line and Positive Alpha Stock

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SML Relationships

= [COV(ri,rm)] / m2

Slope SML = E(rm) - rf

= market risk premium

SML = rf + [E(rm) - rf]

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Sample Calculations for SML

E(rm) - rf = .08 rf = .03

x = 1.25

E(rx) = .03 + 1.25(.08) = .13 or 13%

y = .6

e(ry) = .03 + .6(.08) = .078 or 7.8%

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E(r)E(r)

RRxx=13%=13%

SMLSML

mm

ßß

ßß1.01.0

RRmm=11%=11%RRyy=7.8%=7.8%

3%3%

xxßß1.251.25

yyßß.6.6

.08.08

Graph of Sample Calculations

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Estimating the Index Model

Using historical data on T-bills, S&P 500 and individual securities

Regress risk premiums for individual stocks against the risk premiums for the S&P 500

Slope is the beta for the individual stock

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Table 7-1 Monthly Return Statistics for T-bills, S&P 500 and General

Motors

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Figure 7-3 Cumulative Returns for T-bills, S&P 500 and GM Stock

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Figure 7-4 Characteristic Line for GM

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Table 7-2 Security Characteristic Line for GM: Summary Output

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Multifactor Models

Limitations for CAPM

Market Portfolio is not directly observable

Research shows that other factors affect returns

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Fama French Research

Returns are related to factors other than market returns

Size

Book value relative to market value

Three factor model better describes returns

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Table 7-4 Regression Statistics for the Single-index and FF Three-factor Model

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Arbitrage Pricing Theory

Arbitrage - arises if an investor can construct a zero beta investment portfolio with a return greater than the risk-free rate

If two portfolios are mispriced, the investor could buy the low-priced portfolio and sell the high-priced portfolio

In efficient markets, profitable arbitrage opportunities will quickly disappear

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Figure 7-5 Security Line Characteristics

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APT and CAPM Compared

APT applies to well diversified portfolios and not necessarily to individual stocks

With APT it is possible for some individual stocks to be mispriced - not lie on the SML

APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio

APT can be extended to multifactor models

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Exercise241

1. Stocks A, B, C and D have betas of 1.5, 0.4, 0.9 and 1.7 respectively. What is the beta of an equally weighted portfolio of A, B and C? A) .25 B) .93 C) 1.00 D) 1.13

2. The market portfolio has a beta of __________. A) -1.0 B) 0 C) 0.5 D) 1.0

3. According to the capital asset pricing model, a well-diversified portfolio's rate of return is a function of __________. A) market risk B) unsystematic risk C) unique risk D) reinvestment risk

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Exercise 42

1. According to the capital asset pricing model, fairly priced securities have __________. A) negative betas B) positive alphas C) positive betas D) zero alphas

2. Consider the single factor APT. Portfolio A has a beta of 1.3 and an expected return of 21%. Portfolio B has a beta of 0.7 and an expected return of 17%. The risk-free rate of return is 8%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio __________. A) A, A B) A, B C) B, A D) B, B

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Exercise221. Security X has an expected rate of return of 13% and a beta of 1.15. The risk-free rate is

5% and the market expected rate of return is 15%. According to the capital asset pricing model, security X is __________. A) fairly priced B) overpriced C) underpriced D) None of the above

2. If the simple CAPM is valid, which of the situations below are possible? Consider each situation independently.

A) Situation A B) Situation B C) Situation C D) Situation D