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# Chapter 11 - PowerPoint PPT Presentation

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

ArbitragePricing Theory

11-1

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

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

11-3

Mean S.D. Correlation

Portfolio

A,B,C 25.83 6.40 0.94

D 22.25 8.58

11-4

* 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

11-5

rP = E (rP) + bPF + eP

F = some factor

For a well-diversified portfolio

eP approaches zero

Similar to CAPM

11-6

E(r)%

F

F

Portfolio

Individual Security

Portfolio &Individual Security Comparison

11-7

E(r)%

10

A

D

7

6

C

Risk Free 4

Beta for F

.5

1.0

11-8

• 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%

11-9

E(r)%

M

[E(rM) - rf]

Risk Free

Beta (Market Index)

1.0

11-10

• 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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