1. 1 X. Explaining Relative Price – Arbitrage Pricing Theory

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5. 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

6. 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

7. 7 RGP APT

8. 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.

9. 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.

10. 10 Identify simultaneously the ’s and the I’s. Factor Analysis Let the data speak to the return generating process.

11. 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. 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

14. 14 FOUR FACTOR MODEL OF THE JAPANESE ECONOMY VERSUS ONE FACTOR MARKET INDEX NRI 400; 20 PORTFOLIOS

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19. 19 BARRA – MODEL SIZE LIQUIDITY GROWTH VALUE FINANCIAL LEVERAGE INDUSTRY MEMBERSHIP

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24. 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. 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. 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

29. 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. 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

35. 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