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1 X. Explaining Relative Price – Arbitrage Pricing Theory
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5 Assume a two index RGP Portfolio Expected Return A 15 1.0.6 B 14.5 1.0 C 10.3.2 Three points describe a plane
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6 Any weighted average of points on a plane where the weights sum to 1 lie on the plane – any portfolio lies on the plane Lies above a below – riskless arbitrage
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7 RGP APT
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8 What are the ’s? What are the I’s? What are the ’s? In general, I’s are systematic influences which have an impact on the return of a large percentage of stocks. ’s are characteristics of individual firms or sensitivities of industrial firms to systematic influences. ’s are the market price of the ’s.
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9 How to Identify; Five Approaches: 1)Statistical methods for identifying the I’s and ’s simultaneously – factor analysis or principle components analysis. 2)Identify the firm characteristics that are judged as most important – estimate the ’s from multiple regression. 3)Identify the I’s; a priori macro variable. 4)Identify the I’s; a set of portfolios sufficient to capture all influences. 5)Mixtures of the above.
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10 Identify simultaneously the ’s and the I’s. Factor Analysis Let the data speak to the return generating process.
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11 Conceptually most difficult to understand Takes return data for each member of a set of securities over time (e.g. monthly returns) and the mathematically determines a set of Indexes (portfolios) which best explains returns Simple Example 4 stocks (countries) Belgium, Canada, France, U.S. Returrn data – monthly 1979-1988
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13 WHERE 1. R INDICATES RETURN 2. f INDICATES FACTOR VALUE 3. B IS BELGIUM 4. C IS CANADA 5. U IS UNITED STATES 6. F IS FRANCE 7. t IS TIME PERIOD 8. BARS INDICATE MEANS
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14 FOUR FACTOR MODEL OF THE JAPANESE ECONOMY VERSUS ONE FACTOR MARKET INDEX NRI 400; 20 PORTFOLIOS
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19 BARRA – MODEL SIZE LIQUIDITY GROWTH VALUE FINANCIAL LEVERAGE INDUSTRY MEMBERSHIP
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24 Salomon Brothers Risk Attribute Model 1.Economics Growth = Monthly Changes In Total Industrial Production 2. Credit Quality = Return on High Yield Bonds – Return on Governments (10+Year) 3. Long Term Interest Rates = Yield Change in 30 Year Treasuries 4. Short Term Interest Rates = Yield Change in 3 Month Treasuries 5. Inflation Shock = Realization Inflation – Expected Inflation (CPI) 6. US Dollar = Change in Value of US Dollar Trade Weighted 7. Market (After 6 Factors Removed). S&P 8. Small-Cap Premium = Return Russel 2000 – S&P 500 (seven factors removed)
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26 PORTFOLIO APPROCH RETURN ON MUTUAL FUNDS RELATED TO: 1.RETURN ON S&P INDEX 2.RETURN ON SMALL STOCK INDEX 3.RETURN ON BOND INDEX
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28 FAMA – FRENCH 1.TERM = LONG TERM GOVERNMENT BOND RETURN – T-BILL RATE 2.DEFAULT – LONG TERM CORPORATE BOND RETURN – RETURN ON LONG TERM GOVERNMENT BOND 3.SIZE – RETURN ON PORTFOLIO OF SMALL STOCK - PORTFOLIO OF REGULAR STOCKS 4.BOOK TO MARKET = RETURN ON PORTFOLIO OF HIGH BOOK TO MARKET FIRMS – RETURN ON PORTFOLIO OF LOW BOOL TO MARKET FIRMS 5.RETURN ON MARKET – T-BILL RATE
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29 NORMAL DURATION RETURN RELATED TO RETURN ON A MARKET PORTFOLIO RETURN RELATED TO 1. RETURN ON A 4 YEAR PORTFOLIO OF BONDS (LEVEL OF INTEREST RATE) 2. DIFFERENCE BETWEEN 10 YEAR TREASURY AND 2 YEAH TREASURY (TWIST IN YIELD CURVE) 3. DIFFERENCE BETWEEN 4 YEAR AAA CORPORATE AND 4 YEAH TREASURY (PRICE OF RISK)
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34 Passive Management 1. Better Match an index 2. Match an index + or – certain stocks 3. Passive management with changed sensitivity a. Pension fund liabilities that go up with inflation will pay a price to have assets that go up with inflation. APT tells investors that the cost of zero inflation exposure is (-4.32x.37) = 1.60% b. Take on oil exposure may be free lunch
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35 Active Management 1.Make bets e.g. on interest rates or inflation 2.Look for stocks out of equilibrium 3.Long short zero risk portfolios
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