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Chapter 11. Arbitrage Pricing Theory. 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

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Chapter 11 l.jpg

Chapter 11

ArbitragePricing Theory

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Arbitrage pricing theory l.jpg
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

11-2


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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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E. Ret.

* P

* D

St.Dev.

Short 3 shares of D and buy 1 of A, B & C to form P

You earn a higher rate on the investment than you pay on the short sale

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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E(r)%

E(r)%

F

F

Portfolio

Individual Security

Portfolio &Individual Security Comparison

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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

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