INTRODUCTION TO DERIVATIVES MARKETS (INVESTMENTS

BACKGROUND) SPRING 2006

REAL VS. FINANCIAL ASSETS

- A. REAL ASSETS
- Plant and EquipmentPhysical Capital
- Growth Opportunities e.g. RD, Patents, New

Ventures - Human CapitalExpertise, Labor Services
- Contribute Directly to the Productive Capacity of

the Economy (i.e. to GNP Growth)

REAL VS. FINANCIAL ASSETS

- B. FINANCIAL ASSETS
- Stocks, Bonds, Hybrid Securities
- Are Claims to the After-Tax Earnings Streams

Generated by Real Assets - Provide an Incentive to Invest in Real Assets by

Providing Liquidity - Establishes a Pricing (Valuation) Mechanism for

Real Assets - Thereby Contribute Indirectly to the Productive

Capacity of the Economy

CLIENTS OF THE FINANCIAL SYSTEM

- THE HOUSEHOLD SECTOR (INDIVIDUALS)The financial

assets households desire to hold depend on their

tax status, investment horizons, need for

liquidity, cash-flow needs, and risk

preferences. - THE BUSINESS SECTOR (CORPORATIONS) Raises money

by debt and equity issues in primary capital

markets. The business sector raises money

efficiently by using investment bankers and by

keeping securities simple. - THE GOVERNMENT SECTOR (STATE, FEDERAL, AND

MUNICIPAL AGENCIES ) - Can only borrow through debt issues and

taxation,but regulates the financial sector.

FLOW OF CASH BETWEEN CAPITAL MARKETS AND FIRMS

OPERATIONS

2 .CASH INVESTED IN FIRM

1. CASH RAISED FROM INVESTORS

FIRMS OPERATIONS

CAPITAL MARKETS

FINANCIAL MANAGER

5.CASH RE- INVESTED

3. CASH GENERATED BY OPERATIONS

4. CASH RETURNED TO INVESTORS

MONEY MARKET INSTRUMENTS

- U.S. TREASURY BILLS
- FEDERAL FUNDS
- EURODOLLARS
- REPOS AND REVERSES
- BROKER CALLS
- THE LIBOR MARKET
- COMMERCIAL PAPER
- BANKERS ACCEPTANCES

TREASURY BILL PRICING CONVENTIONS

- FOR PURPOSES OF DISCOUNTING, THE TREASURY USES

360 DAYS AS ITS YEAR - BOND YIELDS, ON THE OTHER HAND, ARE QUOTED ON THE

BASIS OF A 365 DAY YEAR - HENCE ADJUSTMENTS MUST BE MADE

TREASURY BILL TERMINOLOGY

- PCURRENT PRICE
- FFACE VALUE
- NNUMBER OF DAYS TO MATURITY
- BDYBANK DISCOUNT YIELD
- BEYBOND EQUIVALENT YIELD

PRICING U.S. TREASURY BILLS

- STEP 1. DETERMINE THE NUMBER OF DAYS TO

MATURITY N. - STEP 2. CALCULATE THE DOLLAR DISCOUNT

CORRESPONDING TO N. THIS IS CALLED THE DOLLAR

BANK DISCOUNT YIELD - D(BDYFN)/360
- STEP 3. THE CURRENT PRICE
- PF-D
- STEP 4. CALCULATE THE HOLDING PERIOD YIELD,
- HPYD/P
- STEP 5 CALCULATE THE BOND EQUIVALENT YIELD,
- BEYHPY365/N

TREASURY BILL PRICING FORMULAE

- CURRENT PRICE,
- PF(1-BDYN/360)
- BOND EQUIVALENT YIELD (BEY)
- BEY365BDY/(360-BDYN)

U.S. TREASURY BILLS PRICE QUOTE (SOURCE

www.bloomberg.com)

MONEY RATES (SOURCE WSJ 01/06/03)

See BKM Text p. 32 Figure 2.1

MEDIUM TO LONG-TERM FIXED INCOME INSTRUMENTS

- U.S. TREASURY NOTES AND BONDS
- FEDERAL AGENCY DEBT
- MUNICIPAL BONDS (MUNIS)
- CORPORATE BONDS
- MORTGAGES
- MORTGAGE-BACKED SECURITIES

TREASURY BOND PRICING CONVENTIONS

- TREASURY BONDS ARE QUOTED IN DOLLARS PLUS 32NDS

PER FACE VALUE. THE LATTER ARE CALLED BOND POINTS - E.G. A BOND POINT (1/32) TRANSLATES INTO

1,000/3231.25 FOR EACH 1,000 OF FACE VALUE - BOND YIELD TO MATURITY (YTM) IS THE BONDS IRR

BASED ON A 365 DAY YEAR

US TREASURY BOND PRICE QUOTATIONS

- (SOURCEWSJ(01/06/03)
- See Text BKM Figure 2.3 Page 37)
- 4.750 Nov08n 10725 10726 1 3.27

U.S. T-BOND CALCULATIONS

- HIGHLIGHTED BOND (06/01/03)
- Coupon Rate 4.75 coupon payment 4.75 of

face value paid annually coupon payments are

paid every six months (i.e. semi-annually) - Maturity November 2008.
- Bid Price 10725
- NOTE this means 107 25/32 per each 100 of face

value. - Ask Price 10726 or107 26/32 per 100 of face

value - 1 ask price up by 1/32 from previous days ask

price. - Ask yield the yield to maturity (IRR) of the

bond based on the asked price3.27

CORPORATE BOND QUOTATIONS

See text BKM Figure 2.7, page 42

READING CORPORATE BOND QUOTATIONS

- HIGHLIGHTED BOND
- Bond ATT, 73/4 coupon, maturing in 2007.
- Interest paid semiannually 77.50 per 1,000 of

face value. - Current yield 77.50/1060 7.3 annual

coupon / current bond price. - Trading volume 54 1000 face value bonds

traded that day. - Closing price 1060 per 1,000 of face value

(i.e. a premium bond). - Net change closing price 1/2 up from closing

price on the previous day.

READING STOCK MARKET QUOTATIONS(SOURCE WSJ

(09/08/97)

See text BKM Figure 2.9, page 46

READING STOCK MARKET QUOTES

- HIGHLIGHTED FIRM (GE CORP.)
- 52 week high and low stock price per share41.24

and 21.40 respectively. - Dollar Dividends .76 /share annually.
- Dividend Yield annual dividend/current price3.0

.76/25.40 - PE price earnings ratio16.
- Volume 100s of shares traded that day 148191
- High and low for that trading day see

www.nyse.com - Closing Price25.40 per share.
- Net change -.08 per share from previous days

close.

STOCK AND BOND MARKET INDICES

- STOCK INDICES
- DJIA
- SP 500
- NYSE
- AMEX
- NASDAQ
- WILSHIRE 5000
- VALUELINE
- CRSP VW
- CRSP EW
- BOND INDICES
- SOLOMON BROTHERS
- LEHMAN BROTHERS
- Center for Research on Security Prices,

value-weighted - Center for Research on Security Prices,

equally-weighted

STOCK MARKET INDICES EXAMPLES

- DJIA 30 blue chip stocks NYSE traded price

weighted divisor adjustment produces a large

number average with large movements overly

influenced by higher priced stocks oldest most

frequently quoted. - SP 500 500 stocks - industrials,

transportation, utilities, financials -- NYSE and

NASDAQ traded, value weighted.. - NYSE All NYSE-listed stocks value weighted.
- NASDAQ All stocks listed on NASDAQ value

weighted.. - WILSHIRE 5000 Value weighted all exchange

listed and NASDAQ listed stocks most

comprehensive, readily available stock index. - VALUELINE 1,700 stocks price weighted, no

divisor manipulation geometric average.

THREE TYPES OF STOCK MARKET INDICES

- PRICE-WEIGHTED
- implies one share of each stock is purchased,
- therefore overweights the higher priced stocks in

the index, - VALUE-WEIGHTED
- implies that stocks are held in the index in

proportion to their relative market values, - EQUALLY-WEIGHTED
- implies that equal dollar amounts of each stock

are purchased.

IN-CLASS PROBLEM ON THE TYPES OF INDICES

- Use the following information to answer questions

1-4 - BASE YEAR
- Stock Price Shares
- A 40 10,000,000
- B 50 20,000,000
- C 60 30,000,000

CONTINUED

- CURRENT YEAR
- Stock Price Shares
- A 22 20,000,000 B

55 20,000,000 - C 66 30,000,000
- 1. What is the percentage change in a

price-weighted index ? - 2. What is the percentage change in a market

value-weighted index ? - 3. What is the percentage change in an

equally-weighted index ? - 4. What is the geometric average of the returns?

SOLUTION TO IN-CLASS PROBLEM

- 1. A price-weighted index simply adds up the

prices of the individual stocks underlying the

Indexs construction and divides by the number

of such stocks. - Therefore, the initial value of the Index is
- 405060/350.
- If we did the same in the current year we would

obtain - 225566/347.67
- which represents a -4.67 decline
- in the index. But did it decline ?

IN-CLASS SOLUTION (CONT.)

- Since there are double the number of shares

outstanding in the current year compared to the

base year, the stock must have split 2 for 1.

Part of the decline in the Index was caused by

this stock split and therefore does not represent

a true decline in the market. To account for

this, the divisor used in calculating the Index

must be adjusted let x be the new value of the

divisor. Then x is given as the solution to - 205060/x405060/3
- x2.6

IN-CLASS SOLUTION (CONT.)

- In computing the new value of the Index we use

the adjusted divisor 2.6 instead of 3.0 - Index in current year
- 225566/2.655
- The percentage change in the Index (representing

the true increase in the market) is - 55-50/5010

IN-CLASS SOLUTION (CONT.)

- 2. A value-weighted Index multiplies each price

by the number of shares outstanding and therefore

automatically adjusts for stock splits. - Value of the Index in the base year
- 4010mm5020mm60303200mm
- Usually, this is set to a standard number in the

base year, e.g. 100 Index points by dividing by

32. The value of the Index in the base year is

100.

IN-CLASS SOLUTION (CONT.)

- Value of the Index in the current year
- 2220mm5520mm66303520mm
- Note the automatic adjustment for the stock

split. The value of the Index in the base year is

3520/32110 - Clearly the Index increased by
- 110-100/10010

IN-CLASS SOLUTION (CONT.)

- 3. An equally- weighted Index requires that the

same dollar investment be placed in each stock

in the Index. The least common divisor of the

stock prices in the base-year 40, 50, and 60

is 2400. - 2400 purchases 60 shares of stock A

(60402400), 48 shares of stock B

(48502400), and 40 shares of stock C

(40602400). - The adjustment for stock splits
- occurs naturally because in the current year you

own 120 shares

IN-CLASS SOLUTION (CONT.)

- The value of the Index in the base-year is just

the value of the dollars invested in it - 2400240024007200
- Normalize to 100 Index points by dividing by 72 .
- The value of the Index in the current year is

12022485540667920 - Divide by 72 to obtain 110.
- This represents a 10 increase as before.
- 4. Stock A increased by 10 after adjusting for

the stock split (20 to 22), Stock B by 10 (50

to 55) and Stock C by 10 (60 to 66). The

geometric average is 10.

MARGINING OF LONG EQUITY POSITIONS

- INITIAL MARGINS
- SET BY THE FEDERAL RESERVE
- CURRENTLY EQUALS 50
- INITIAL MARGININVESTORS EQUITY/MARKET VALUE OF

SECURITIES HELD - E.G. AN INVESTOR PURCHASES 10,000 WORTH OF

COMMON STOCK BY PUTTING 6,000 DOWN AND BORROWING

4,000 - HIS INITIAL MARGIN6,000/10,00060.

MARGINS (CONT.)

- MAINTENANCE MARGINS
- SET BY BROKERS
- CURRENTLY 30
- E.G. SUPPOSE THAT THE MARKET VALUE OF THE STOCKS

HELD FALLS TO 5,000. - THE LOSS COMES OUT OF THE CUSTOMERS

EQUITY, HENCE THE ACTUAL MARGIN1,000/5,00020 - THIS REQUIRES AN ADDITIONAL 5,00 FROM THE

INVESTOR TO RESTORE THE MAINTENANCE MARGIN LEVEL

TO 30 - OR THE BROKER CAN SELL OFF 1,667 OF THE

INVESTMENT

THE MECHANICS OF SHORT SALES

- The way its supposed to work
- STEP 1 BORROW STOCK FROM BROKER,
- STEP 2 SELL STOCK AT CURRENT PRICE (SAY, 100

DOLLARS A SHARE), - STEP 3 HOPEFULLY, BUY BACK STOCK AT LOWER PRICE

(SAY, 80 DOLLARS PER SHARE, - STEP 5 ENJOY 20 DOLLAR PROFIT.
- The way it could work
- STEP 1 BORROW STOCK FROM BROKER,
- STEP 2 SELL STOCK AT CURRENT PRICE (SAY, 100

DOLLARS A SHARE), - STEP 3. THE STOCK PRICE KEEPS GOING UP. SO YOU

GIVE UP AND BUY STOCK AT HIGHER PRICES (SAY, 120

DÓLLARS PER SHARE), - STEP 4 .RETURN SHARES TO BROKER,
- STEP 5. WEEP OVER 20 DOLLAR LOSS.

THE MARGIN CALL PRICE ON LONG POSITIONS

- How low can the security price fall before the

investor receives a margin call ? - Let L the amount borrowed from the broker.
- Let N the number of shares purchased
- Let M the maintenance margin level
- Then Pm(L/N(1-M))
- E.g. Pm(4000/(100x(1-0.30))57.14

THE MARGIN CALL PRICE ON SHORT POSITIONS

- Let N the number of shares sold short,
- P0the price per share at the time of the short

sale, - P1the price per share when the short sale is

covered, I.e. the shares are bought back. - IMthe initial margin
- M the maintenance margin level
- Then Pm(Nx P0IM)/(Nx(M1))

THE MARGIN CALL PRICE ON SHORT POSITIONS EXAMPLE

- Suppose that you sell short 100 shares at 100

dollars per share. You post 5,000 in initial

margin, - The maintenance margin requirement is 30 ,
- Then the margin call price is
- (10,0005000)/(100x(0.31))
- 115.38

DEFINING INVESTMENTS A GENERAL DEFINITION

- We need a definition of investment

sufficiently general to encompass investments in

real assets and investment in financial assets.

Further, it should apply to explaining the

connection between the two. The following

definition serves - THE SACRIFICE OF (CERTAIN) PRESENT CONSUMPTION

FOR FUTURE (GENERALLY UNCERTAIN) CONSUMPTION

THE PROBLEM SOLVED BY INVESTMENTS

- Re-allocating consumption claims (certain and

uncertain) across time and under conditions of

uncertainty

ONE MAIN REASON FOR INVESTING

- IN ORDER TO REALLOCATE CONSUMPTION CLAIMS IN THE

PRESENT AND IN THE FUTURE FROM GIVEN PATTERNS

INTO PREFERRED PATTERNS. - THE PRICING MECHANISM GIVES THE RATES AT WHICH

THIS IS POSSIBLE IN THE MARKET THROUGH A VARIETY

OF FINANCIAL VEHICLES.

CONSUMPTION CHOICES

Consumption later

2.5

2.2

Invest in tennis facility

1.4

1.1

Invest in the bank

Consumption now (millions)

Villa in Spain

2.0

2.3

2.5

BORROWING AND LENDING ENLARGE CHOICES

Dollars, period 1

H

Interest rate lines shows cash flows from

borrowing or lending

F

O

Dollars, period 0

B

D

By borrowing OF, an individual can consume an

extra BD today by lending OB, he can consume an

extra FH tomorrow.

THE EFFECT OF INVESTMENT IN REAL ASSETS

Consumption, period 1

Investment opportunities line shows cash flows

from investing in real assets

Consumption, period 1

Notice the diminishing return on additional units

of investment

HOW INVESTMENT IN REAL ASSETS IMPROVES WELFARE

Consumption, period 1

The miser can spend more today and the next period

M

H

L

G

... and so can the prodigal

O

J

D

K

Consumption, period 0

The miser and prodigal have initial wealth of

OD. Both are better off if they invest JD in

real assets and then borrow or lend in the

capital markets.

KEY QUESTIONS ADDRESSED BY INVESTMENT ANALYSIS

- 1. WHAT TYPES OF RE-ALLOCATIONS ARE AVAILABLE IN

THE MARKETS FOR FIXED INCOME, EQUITIES, HYBRIDS,

ETC. ? - 2. WHAT ARE THE RISK/EXPECTED RETURN

CHARACTERISTICS OF THESE MECHANISMS (OPPORTTUNITY

COSTS) ? - 3. HOW CAN THESE INVESTMENT VEHICLES BE

RISK-MANAGED ? - E.G. THROUGH PORTFOLIO DIVERSIFICATION, AND THE

CORRECT USES OF DERIVATIVES .

DEFINING VIABLE INVESTMENT PROGRAMS

- 1. THE SET OF AVAILABLE RISK-FREE INVESTMENT

ALTERNATIVES. - 2. THE SET OF AVAILABLE RISKY INVESTMENT

ALTERNATIVES. - 3. SUBJECTIVE PREFERENCES FOR THE RISK/EXPECTED

RETURN TRADEOFFS EMBODIED IN FINANCIAL

INSTRUMENTS AS INVESTMENT VEHICLES.

OBJECTIVES OF INVESTMENT ANALYSIS

- 1. MAP OUT THE RISK/RETURN CHARACTERISTICS OF

ALTERNATIVE INVESTMENT STRATEGIES. - 2. SIFT OUT WHAT CAN ACTUALLY BE DONE BY

PORTFOLIO MANAGERS FOR THEIR CLIENTS FROM WHAT

CANT BE DONE SO AS TO SATISFY THEIR SUBJECTIVE

RISK/RETURN PREFERENCES.

TYPES OF INVESTMENT STRATEGIES

- 1. MARKET TIMING.
- 2. STATIC PORTFOLIO DIVERSIFICATION.
- 3. DYNAMIC PORTFOLIO DIVERSIFICATION.
- 4. ASSET ALLOCATION.

BASIC ASSET ALLOCATION STRATEGIES

- ALLOCATING FUNDS BETWEEN CASH EQUIVALENTS, BONDS,

AND EQUITIES. - E.G. CAPITAL ALLOCATION LINE STRATEGIES--HOW MUCH

IN THE BANK , HOW MUCH IN A SINGLE RISKY ASSET

MUTUAL FUND

CAPITAL ALLOCATION LINES

E

p

E

1

R

F

p

1

THE EQUATION OF THE CAL

- E(RP ) RF(E1-RF ) /s1xsp
- WHERE E(RP ) IS THE EXPECTED RATE OF RETURN OF

THE PORTFOLIO. - AND sp IS THE STANDARD DEVIATION OF THE RATE OF

RETURN OF THE PORTFOLIO.

CAPITAL ALLOCATION LINES(REWARD TO RISK RATIO)

- THE SLOPE OF THE CAPITAL
- ALLOCATION LINE IS THE (EXCESS) REWARD TO

RISK RATIO (E1-RF ) /s1 - NOTE THAT (E1-RF ) IS THE EXCESS EXPECTED RETURN

OFFERED BY SECURITY OR PORTFOLIO 1 ABOVE THAT

OFFERED BY CASH EQUIVALENTS REPRESENTED BY THE

SURE RATE OF RETURN, - s1 IS A MEASURE OF RISK

CAPITAL ALLOCATION LINES

E

p

CAL

2

E

CAL

1

2

E

1

R

F

s

s

p

1

MORE EFFICIENT CALS

- THE REWARD TO RISK RATIO OF CAL2 IS GREATER THAN

THE REWARD TO RISK RATIO OF CAL1. - THEREFORE CAL2 PROVIDES MORE EFFICIENT

RISK-RETURN OPPORTUNITIES THAN DOES CAL1.

ROLE OF THE PORTFOLIO MANAGER

- OFFER MORE AND MORE EFFICIENT CAPITAL ALLOCATION

LINES TO INVESTORS RATHER THAN - ATTEMPTING TO SATISFY THEIR SUBJECTIVE

RISK/RETURN PREFERENCES DIRECTLY.

DIFFERENT INVESTORS HAVE DIFFERENT INDIFFERENCE

CURVES

E

p

Investor As indifference curves

Investor Bs indifference curves

NOTE B IS LESS RISK-AVERSE THAN A.

?

p

PORTFOLIO CHOICES FOR DIFFERENT INVESTORS ARE

DIFFERENT

E

p

Investor As indifference curves

Investor Bs indifference curves

Bs choice

CAL

As choice

NOTE since B is less risk-averse than A, B will

choose a riskier portfolio from the CAL.

?

p

PORTFOLIO ANALYSIS

- 1. What is a portfolio ?
- 2. Calculating two parameters of paramount

importance to risk-averse investors - (a) Expected rate of return of a portfolio E(RP

). - (b) Standard deviation of the rate of return of

a portfolio ?P.

PORTFOLIO ANALYSIS (CONT.)

- Suppose that there are N securities traded in the

market. - A portfolio is an asset allocation scheme for

distributing your capital among the available

securities traded in the market. - In order to define a portfolio, you need to have

- 1. A list of the securities that you want to

include in the portfolio. - An asset allocation scheme defined by a set of

portfolio weights x1, x2, x3, .,xN.

PROPERTIES FOR PORTFOLIO WEIGHTS

- 1. xigt0 for i1,2,N
- (No short sales allowed.)
- 2. ? xi1.0
- (Portfolio wealth is fully allocated.)

THE SP 500 UNDERLYING PORTFOLIO

- 1. The list of securities is all current Fortune

500 companies. - xithe market value of company is equity divided

by the aggregate market value of all companys

equities. - xiNi P i/? Ni P i
- Checking the properties is easy
- (a) Insofar as companies have equity, the weights

are positive, - (b) If we add up the portfolio weights, we get

the sum of the equity values of all companies

divided by aggregate market value which is

clearly 1.0.

NUMERICAL EXAMPLE OF WHAT A PORTFOLIO DOES

GRAPHICAL ILLUSTRATION OF WHAT A PORTFOLIO DOES

11

10

60

50

00

00

100

118

30

34.5

00

00

10

12.5

CALCULATING THE RATE OF RETURN OF A PORTFOLIO

- The holding period rate of return of the

portfolio in the last example is clearly - 118-100/10018
- But it is also x1 R1 x2 R2 x3 R3 x4R4

x5 R5 x6 R6 - The general formula emerges
- A portfolios rate of return is the

portfolio-weighted average of the individual

securities returns.

CALCULATING THE EXPECTED RATE OF RETURN OF A

PORTFOLIO

- Calculating the expected rate of return of any

portfolio, in general, is easy - Just take the expected value of the random rate

of return - E(Rp)
- x1 E(R1) x2 E(R2). xNE(RN)

PORTFOLIO RISK

Portfolio variance is the sum of the boxes

where ?12 is the correlation coefficient between

the return on security 1 and the return on

security 2, ?1 is the standard deviation of the

rate of return of security 1 and ?2 is the

standard deviation of the rate of return of

security 2.

PORTFOLIO RISK AN EXAMPLE

.4

.6

.6

.4

where ?12 .30, ?1 20 ?2 30 X1 .6 and

X2 .4 ?PSQRT(144144(2x43.2))19.35

EFFECT OF DIVERSIFICATION

For a correlation coefficient of ?120.3

E

p

20

10

p

30

20

THE DIVERSIFICATION EFFECT IN AN EXTREME CASE

PORTFOLIO VARIANCE THE GENERAL CASE ADD UP ALL

THE BOXES

Portfolio Weights

x 3

x 2

x N

x 1

x 1

THE SHADED BOXES CONTAIN VARIANCE TERMS

THE REMAINDER CONTAIN COVARIANCE TERMS

1

x 2

2

x 3

3

x 4

4

x 5

A typical variance term x i2 ?i2

5

x 6

6

A typical COvariance term x i x j ?i?j ?ij

x N

N

1

2

3

4

5

6

N

STOCK

PORTFOLIO VARIANCE AS A FUNCTION OF THE NUMBER OF

SECURITIES IN THE PORTFOLIO

Portfolio

standard

deviation

UNIQUE RISK

MARKET RISK

Number of

5

10

securities

FOUNDATIONS OF PORTFOLIO ANALYSIS

- The efficient frontier of risky assets
- Identify the efficient risk-expected return

combinations from among the simply feasible ones, - Choosing the optimal risky asset portfolio from

the efficient frontier - Find the optimal portfolio that supports the

highest CAL.

SINGLE-INDEX MODELS

- The objective here is to define a

return-generating model for security returns. - The simplest way to do this is in terms of a

single factor which can be thought of as an

aggregate stock market index e.g. the SP500

Index. - Riaibi RMei
- Here Ri is the random holding period rate of

return of the security over a chosen holding

period, RM is the random holding period rate of

return of the Market over a chosen holding

period.

SINGLE-INDEX MODELS (CONT.)

- ai is the actual rate of return that the security

can earn on its own, i.e. independently of the

Market, - bi is the beta of the securitys rate of return,

i.e. a measure of its comovement with the market

as a percentage of the total volatility of the

market, - ei is a pure noise term, I.e. a random variable

that is independent of the Markets rate of

return.

SINGLE-INDEX MODELS (CONT.)

- KEY PROPERTIES OF ei
- a. E(ei)0 (zero mean, I.e no systematic bias in

any direction) - b.Cov(ei, RM )0 (noise is not a fundamental

economic factor, it is not correlated with any

such factor).

SINGLE FACTOR INDEX MODELS VS. THE CAPM

- The first note is that the CAPM in the form of

the Security Market Line (SML) describes expected

rates of return (not actual rates of return). - The Index model describes actual rates of return.
- However, the two types of models are consistent

with each other.

SINGLE FACTOR INDEX MODELS VS. THE CAPM

- By taking expected values of the single-factor

index model one notes that - E(Ri)aibi E(RM)E(ei)
- aibi E(RM)
- by property(a) of the noise term.
- Then equating corresponding terms in the SML one

notes that the following equality must hold - ai (1- bi)RF
- Thus the CAPM is a significantly stronger
- statement than the single factor Index model.

PORTFOLIO CHOICES OF DIFFERENT INVESTORS

- The optimal final portfolio and the Separation

Property - Mix the optimal risky portfolio with cash

equivalents to get the final portfolio for the

given investor.

SINGLE-PERIOD CAPM ASSUMPTIONS

- 1. There is a risk-free rate, RF at which

investors can borrow and lend as much as they

wish without affecting that rate (e.g. T-Bills). - 2. All investors make their investment decisions

solely on the basis of the mean and the variance

of their portfolios. Further, in making their

portfolio decisions, they maximize the expected

utility of their final wealth positions. - 3. All investors have homogenous expectations

regarding the relevant parameters underlying

their portfolio decisions.

CAPM EQUILIBRIUM CONDITIONS

- 1. The market portfolio will be on the efficient

frontier and will be the optimal risky asset

portfolio to be combined with riskless borrowing

or lending in building their final, personal,

optimal portfolios. - That is, all investors hold the same risky

portfolio(M), adding T-bills to their portfolios

to obtain desired risk levels. - 2. The CML is therefore the best obtainable CAL.
- 3. The risk premium on individual assets is

proportional to the risk premium on the market

portfolio and to the b of the security. b

measures the extent to which the stock returns

respond to the market returns.

DERIVATION OF THE CAPM

- The Reward-to-Variability Ratio of the CML
- E(RM) - RF / sM
- The risk premium for security I is in proportion

to its contribution of the risky asset portfolio

in which it is held. This is the Market portfolio

according to the CAPM. - Setting the two values equal to each other

produces the SML - E(Ri) RF bi ( E(RM ) -RF)

The Number of Estimates Needed for Standard

Portfolio Analysis Vs. the Single Factor Index

Model

- STANDARD ANALYSIS (50 Stocks)
- N 50 Estimates of expected returns
- N 50 Estimates of variances
- (N2 - N)/2 1,225 Estimates of covariances
- 1,325 Estimates in Total

The Number of Estimates Needed for Standard

Portfolio Analysis Vs. the Single Factor Index

Model

- SINGLE-INDEX ANALYSIS (50 Stocks)
- N 50 Estimates of expected excess returns
- N 50 Estimates of betas
- N 50 Estimates of firm-specific variances
- 1 Estimate of the variance of the common

macro-economic factor - 151 Estimates (3n 1) in Total

THE CAPM VS. THE APT

- 1. The CAPM assumes an unobservable market

portfolio, - 2. The APT is based on the assumption of no

arbitrage profits in well-diversified portfolios, - 3. However, the APT admits the possibility of

arbitrage profits on a few individual

securities, - 4. The APT provides no guidance for

identification of the various market factors and

appropriate risk premiums for these factors

PERFORMANCE ATTRIBUTION PROCEDURES

- First, decide on the proportions of equity, fixed

income, and money market funds in the portfolio. - Secondly, decide on the proportions of particular

industries (sectors) within each market. - Third, decide on the particular securities in an

industry to be included in the portfolio. - Use a benchmark or bogey portfolio as the

standard of a passive strategy.

PERFORMANCE ATTRIBUTION PROCEDURES (CONT.)

- For allocation comparisons, compare the bogey

portfolio returns to the returns on your

portfolio which has different allocations. - Subtract the allocation differential returns from

the total return differential to get the security

return difference.

PERFORMANCE ATTRIBUTION PROCEDURES (CONT.)

- Compare your equity performance to the SP 500

Index. - Compare your fixed income performance to the

Shearson-Lehman Index . - Compare sector weights in your portfolio to the

sector weights in the SP 500 Index.

RISK-ADJUSTED MEASURES OF PORTFOLIO PERFORMANCE

- SHARPE MEASURE
- E(RP) - RF / sP
- TREYNOR MEASURE
- E(RP) - RF / bP
- JENSEN MEASURE
- aP
- E(RP) -RF bi ( E(RM ) -RF)
- APPRAISAL RATIO
- aP/s(eP)

INVESTOR ClASSIFICATIONS

- INDIVIDUAL INVESTORS
- PERSONAL TRUSTS
- MUTUAL FUNDS
- PENSION FUNDS
- ENDOWMENT FUNDS
- LIFE INSURANCE COMPANIES
- NONLIFE INSURANCE COMPANIES
- BANKS

CONSTRAINTS ON INVESTING

- LIQUIDITY
- INVESTMENT HORIZON
- REGULATIONS
- TAX CONSIDERATIONS
- UNIQUE NEEDS