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CAPM & Indices

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.

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CAPM & Indices

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  1. CAPM & Indices

  2. Investment Opportunities in Risk-Return Space Markowitz Efficient Portfolios Efficient Frontier—these portfolios contain only undiversifiable risk Individual assets

  3. Borrowing and Lending at the Risk-Free Rate

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

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

  11. 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

  12. 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?

  13. 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

  14. Examples of Indexes - US • Dow Jones Industrial Average (30 Stocks) • Standard & Poor’s 500 Composite • NASDAQ Composite • NYSE Composite • Wilshire 5000

  15. 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

  16. Bond Indexes • Lehman Brothers • Merrill Lynch • Salomon Brothers • Scotia Capital (Canada) • Specialized Indexes • Merrill Lynch Mortgage

  17. 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)

  18. 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

  19. 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

  20. 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. Stock Splits and DJIA Divisor • As an example, consider the hypothetical stocks 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.

  21. 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

  22. 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.

  23. 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

  24. 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 • Some of the component stocks are not as actively traded as the 30 stocks in DJIA

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