4. APT

# 4. APT - α P ⇒ an arbitrage opportunity exists(1 borrow...

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1 Arbitrage Pricing Theory (APT) • this analysis follows directly from the single factor index model same ß formula and interpretation • less restrictive assumptions than CAPM • recall that M is an index of stocks, not the market consisting of all assets • returns are excess returns, i.e. R i = r i - r RF and R M = r M - r RF and R i = α i + ß i R M + e i • now construct a well-diversified portfolio with zero firm-specific risk R P = α P + ß P R M 1. suppose ß P = 0 R i = α P this is a riskless return because (1) no firm-specific risk (2) ß P = 0 no systematic risk (3) returns are excess returns this portfolio has a return that exceeds the risk-free rate by

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Unformatted text preview: α P ⇒ an arbitrage opportunity exists (1) borrow at r RF (2) invest in the portfolio and earn r RF + α P ⇒ net return (arbitrage profit) = α P ⇒ so, no arbitrage requires α P = 0 2 2. Simple Quantitative Examples ⇒ here we focus on r (actual return) in order to see the role of r RF A. • portfolio A with ß A = .80 • r RF = 4% • r M = 12% • actual market return of A = 11.80% 3 B. • portfolio C with ß C = 1.20 • r RF = 4% • r M = 12% • actual market return of C = 12.40%...
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4. APT - α P ⇒ an arbitrage opportunity exists(1 borrow...

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