capm & indices

Comm 324 --- W. SuoSlide 1Slide 1

CAPM & IndicesCAPM & Indices


Investment Opportunities in Risk-Return Space

Markowitz Efficient Portfolios

Individual assets

Efficient Frontier—these

portfolios contain only

undiversifiable risk


Borrowing and Lending at the Risk-Free Rate


The Market Portfolio

Portfolio M is known as the market portfolio Equilibrium portfolio containing all the assets in the world in the

proportions they are supplied Represents the single portfolio all rational investors want to own

Because it can be used to create the dominant CML

A useful theoretical concept Return that security market indexes approximate


The Separation Theorem

All investors desiring Markowitz diversification will select Portfolio M

The next question is: How should the investment in Portfolio M be financed? The decision to invest in portfolio M is separate from the

decision as to whether the investor will be a borrower or a lender


Assumptions Underlying Portfolio Theory

Four assumptions underlie all portfolio theories based on the efficient frontier

Rate of return is the most important investment outcome Investor’s risk estimates are proportional to the standard deviation or

variance they perceive Investors are willing to base their decisions on only the expected

return and variance (or standard deviation) of the expected return For any risk class, investors desire a higher rate of return to a lower

one


Assumptions Underlying the CML, SML and CAPM

Investors are price takers: prices are unaffected by individual’s decisions Investors plan for one identical holding period Investments are limited to publicly traded financial assets, and all

investments are infinitely divisible No tax/transaction costs Homogeneous belief: All investors visualize the same expected return,

risk and correlation for any specified asset (homogeneous expectations) No inflation or changes in interest rates exist Capital markets are a static equilibrium (supply equals demand) The market portfolio contains all assets in the proportions in which they

exist


Assumptions Underlying the CML, SML and CAPM

Assumptions are unrealistic But provide a concrete foundation

Final test should be the theory’s predictive power, not the realism of its assumptions


Implications

All investors hold the same risky portfolio Market portfolio on the efficient frontier It is also the tangent portfolio

Security Market Line

SML can also be stated in terms of beta

{ {

M fi if M

MReward for delayingEquilibrium Expected Returnconsumption

Slope of SMLMarket price of risk

E rr E r COVr r r

VAR r,

1444442444443


Security Market Line

In equilibrium every asset should be priced as a linear function of its

covariance with the market.


Over- and Under-Priced Assets

Point U is an underpriced asset Has an abnormally high return for its systematic risk

Will experience high demand and a subsequent increase in price until return equates to U

Point O is an overpriced asset Has an abnormally low return for its systematic risk

Price will fall due to lack of demand Assets on the SML are in equilibrium and will remain so

until Systematic risk changes, the risk-free rate changes, etc.

Point N is a security with a negative covariance (beta) with the market


Stock Indexes

Uses Track average returns Comparing performance of managers Base of derivatives

Factors in constructing or using an Index Representative? Broad or narrow? How is it constructed?


Examples of Indexes – Canadian

S&P/TSX 300 Composite Index TSX 35 (also known as Toronto 35 or T35) TSX 100 S&P/TSX 60


Examples of Indexes - US

Dow Jones Industrial Average (30 Stocks) Standard & Poor’s 500 Composite NASDAQ Composite NYSE Composite Wilshire 5000


Examples of Indexes - International

TSE (Tokyo) - Nikkei 225 & Nikkei 300 FTSE (Financial Times of London) Dax Region and Country Indexes

EAFE Far East United Kingdom


Bond Indexes

Lehman Brothers Merrill Lynch Salomon Brothers Scotia Capital (Canada) Specialized Indexes

Merrill Lynch Mortgage


Construction of Indexes

How are stocks weighted? Price weighted (DJIA) Market-value weighted (S&P500, NASDAQ, TSX 300) Equally weighted (Value Line Index)

How returns are averaged? Arithmetic (DJIA and S&P500) Geometric (Value Line Index)


Contrasting Two Well-Known Stock Market Indicators

Dow-Jones Industrial Average (DJIA)

Begun in 1884 with 11 stocks

Average has contained 30 stocks since 1928

Only large, successful firms are in the average


Dow-Jones Industrial Average

Misleading name Only large firms are in the average New firms are not included Some firms may be more utility than industrial firms

DJIA Divisor In 1928 the prices of the 30 stocks were summed and divided by 30

However, stock splits and stocks dividends impact the divisor


Stock Splits and DJIA Divisor

As an example, consider the hypothetical stocks

Stock Price

X $50

Y $10

Total $60

Average 60/2 = 30

Stock Price

X $25

Y $10

Total $35

Average 35/2 = 17.5

If Stock X undergoes a

2 for 1 stock split

The stock split changed the price per share, but the stockholder’s wealth has remained the

same—each stockholder in X has twice as many shares as before.

If the divisor remains at 2, the average will drop, even though the aggregate market value of X remains the same. The divisor value must drop to reflect

the stock split.


Dow-Jones Industrial Average

Points DJIA is price-weighted

More weight is given to higher priced stocks Each point represents a few pennies of stock price

Converting each point to a stock price is inconvenient


S&P 500 Stocks Composite Index

First developed in 1923 Contained 233 stocks Has been at the 500 stock level since 1957

Uses a market weighting scheme Each security’s weight is based on the total market value

of the firm Corresponds to the investment opportunities that exist in U.S.



Equation used to calculate S&P500

1,t 1,t 2,t 2,t 3,t 3,t 500,t 500,t

t1,base 1,base 2,base 2,base 3,base 3,base 500,base 500,base

10P N P N P N P NS&P500 P N P N P N P N

Automatically adjusts for stock splits, etc. Base period of 1941-1943 with a base index value of

10 Index components change slightly each year 500 stocks in index are about 17% of the stocks

listed on NYSE But aggregate market value is > 50% of aggregate market

value of all stocks listed on NYSE & AMEX



S&P500 is more representative of U.S. common stock investing than DJIA

S&P500 Index is slightly less timely than DJIA Some of the component stocks are not as actively traded

as the 30 stocks in DJIA

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