Arbitrage Pricing Theory

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Chapter 11

• ArbitragePricing Theory

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Arbitrage Pricing Theory

• Arbitrage - arises if an investor can construct a
  zero investment portfolio with a sure profit
• Since no investment is required, an investor can
  create large positions to secure large levels of
  profit
• In efficient markets, profitable arbitrage
  opportunities will quickly disappear

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Arbitrage Example from Text pp. 308-310

• Current Expected Standard
• Stock Price Return Dev.
• A 10 25.0 29.58
• B 10 20.0
  33.91
• C 10 32.5 48.15
• D 10 22.5 8.58

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Arbitrage Portfolio

• Mean S.D. Correlation
• Portfolio
• A,B,C 25.83 6.40 0.94
• D 22.25 8.58

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Arbitrage Action and Returns
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APT Well-Diversified Portfolios

• rP E (rP) bPF eP
• F some factor
• For a well-diversified portfolio
• eP approaches zero
• Similar to CAPM

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Portfolio Individual Security Comparison
8
Disequilibrium Example
E(r)
10
A
D
7
6
C
Risk Free 4
Beta for F
.5
1.0
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Disequilibrium Example

• Short Portfolio C
• Use funds to construct an equivalent risk higher
  return Portfolio D
• D is comprised of A Risk-Free Asset
• Arbitrage profit of 1

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APT with Market Index Portfolio
E(r)
M
E(rM) - rf Market Risk Premium
Risk Free
Beta (Market Index)
1.0
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APT and CAPM Compared

• APT applies to well diversified portfolios and
  not necessarily to individual stocks
• With APT it is possible for some individual
  stocks to be mispriced - not lie on the SML
• APT is more general in that it gets to an
  expected return and beta relationship without the
  assumption of the market portfolio
• APT can be extended to multifactor models