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
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