# CAPM & Indices

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CAPM & Indices. Investment Opportunities in Risk-Return Space. Markowitz Efficient Portfolios. Efficient Frontier—these portfolios contain only undiversifiable risk. Individual assets. Borrowing and Lending at the Risk-Free Rate. The Market Portfolio. - PowerPoint PPT Presentation

### Transcript of CAPM & Indices

InvestmentsMarkowitz Efficient Portfolios

Comm 324 --- W. Suo

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

But provide a concrete foundation

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

Comm 324 --- W. Suo

Market portfolio on the efficient frontier

It is also the tangent portfolio

Security Market Line

Comm 324 --- W. Suo

Security Market Line

In equilibrium every asset should be priced as a linear function of its covariance with the market.

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

Representative?

TSX 35 (also known as Toronto 35 or T35)

TSX 100

Standard & Poor’s 500 Composite

NASDAQ Composite

NYSE Composite

Wilshire 5000

FTSE (Financial Times of London)

Dax

Equally weighted (Value Line Index)

How returns are averaged?

Geometric (Value Line Index)

Comm 324 --- W. Suo

Average has contained 30 stocks since 1928

Only large, successful firms are in the average

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

As an example, consider the hypothetical stocks

If Stock X

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.

Stock

Price

X

$50

Y

$10

Total

$60

Average

35/2 = 17.5

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.

Comm 324 --- W. Suo

Each point represents a few pennies of stock price

Converting each point to a stock price is inconvenient

Comm 324 --- W. Suo

First developed in 1923

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.

Comm 324 --- W. Suo

S&P 500 Stocks Composite Index

Equation used to calculate S&P500

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

Comm 324 --- W. Suo

S&P 500 Stocks Composite Index

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

S&P500 Index is slightly less timely than DJIA

++++

=´

++++

Comm 324 --- W. Suo

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

But provide a concrete foundation

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

Comm 324 --- W. Suo

Market portfolio on the efficient frontier

It is also the tangent portfolio

Security Market Line

Comm 324 --- W. Suo

Security Market Line

In equilibrium every asset should be priced as a linear function of its covariance with the market.

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

Representative?

TSX 35 (also known as Toronto 35 or T35)

TSX 100

Standard & Poor’s 500 Composite

NASDAQ Composite

NYSE Composite

Wilshire 5000

FTSE (Financial Times of London)

Dax

Equally weighted (Value Line Index)

How returns are averaged?

Geometric (Value Line Index)

Comm 324 --- W. Suo

Average has contained 30 stocks since 1928

Only large, successful firms are in the average

Comm 324 --- W. Suo

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

Comm 324 --- W. Suo

As an example, consider the hypothetical stocks

If Stock X

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.

Stock

Price

X

$50

Y

$10

Total

$60

Average

35/2 = 17.5

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.

Comm 324 --- W. Suo

Each point represents a few pennies of stock price

Converting each point to a stock price is inconvenient

Comm 324 --- W. Suo

First developed in 1923

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.

Comm 324 --- W. Suo

S&P 500 Stocks Composite Index

Equation used to calculate S&P500

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

Comm 324 --- W. Suo

S&P 500 Stocks Composite Index

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

S&P500 Index is slightly less timely than DJIA

++++

=´

++++