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Ch12 - Chapter 12 Arbitrage Pricing Theory(APT Road Map...

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Chapter 12 Arbitrage Pricing Theory (APT) Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Part C Determination of discount rates. Historical asset returns. Time value of money. Risk. Portfolio theory. Capital Asset Pricing Model (CAPM). Arbitrage Pricing Theory (APT). Part D Introduction to corporate finance. Main Issues 1. Factor Models of Asset Returns 2. Arbitrage Pricing Model (APT) 3. Applications of APT
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12-2 Arbitrage Pricing Theory (APT) Chapter 12 Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 12-3 2 Factor Models of Asset Returns . . . . . . . . . . . . . . . . 12-4 3 Properties of Factor Models . . . . . . . . . . . . . . . . . . 12-6 4 APT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-9 5 Implementation of APT . . . . . . . . . . . . . . . . . . . . 12-14 6 Comments on APT . . . . . . . . . . . . . . . . . . . . . . . 12-17 7 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-18 15.407 Lecture Notes Fall 2003 c Jiang Wang
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Chapter 12 Arbitrage Pricing Theory (APT) 12-3 1 Introduction The CAPM and its extensions are based on specific assumptions on investors’ asset demand. For example: Investors care only about mean return and variance. Investors hold only traded assets. The CAPM has several weakness (as discussed in Chapter 12), which the APT attempts to overcome. The Arbitrage Pricing Theory (APT) starts with specific assump- tions on the distribution of asset returns and relies on approximate arbitrage arguments. In particular, APT assumes a “factor model” of asset returns. c Jiang Wang Fall 2003 15.407 Lecture Notes
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12-4 Arbitrage Pricing Theory (APT) Chapter 12 2 Factor Models of Asset Returns Suppose that asset returns are driven by a few ( K ) common factors and idiosyncratic noise: ˜ r i = ¯ r i + b i 1 ˜ f 1 + · · · + b iK ˜ f K + ˜ u i ( i = 1 , 2 , . . . ) (12.1) where ¯ r i is the expected return on asset i ˜ f 1 , . . . , ˜ f K are news on common factors driving all asset returns: ˜ f k = ˜ F k E [ ˜ F k ] b ik gives how sensitive the return on asset i with respect to news on the k -th factor - b ik is called the factor loading of asset i on factor ˜ f k ˜ u i is the idiosyncratic component in asset i ’s return that is unrelated to other asset returns ˜ f 1 , ˜ f 2 , . . . , ˜ f K and ˜ u i have zero means: E [ ˜ f k ] = 0 ( k = 1 , . . . , K ) E u i ] = 0 ( i = 1 , . . . ) . 15.407 Lecture Notes Fall 2003 c Jiang Wang
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Chapter 12 Arbitrage Pricing Theory (APT) 12-5 Example. Common factors driving asset returns may include GNP, interest rates, inflation, etc. Let ˜ f int be the news on interest rates. Before a board meeting of the Fed, the market expects the Fed not to change the interest rate. After the meeting, Greenspan announces that There is no change in interest rate — “no news”: ˜ f int . = 0 . There is a 1 4 % increase in interest rate — “positive surprise”: ˜ f int . = 0 . 25% > 0 . What should be the sign of factor loadings on ˜ f int . for fixed income securities stocks commodity futures, etc.? c Jiang Wang Fall 2003 15.407 Lecture Notes
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12-6 Arbitrage Pricing Theory (APT) Chapter 12 3 Properties of Factor Models 1. Any well-diversified portfolio p is exposed only to factor risks: ˜ r p ¯ r p + b p 1 ˜ f 1 + . . . + b pK ˜ f K .
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