Lecture 19 - Arbitrage.pdf

# Lecture 19 - Arbitrage.pdf - Arbitrage Fundamental of...

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Arbitrage Fundamental of Finance L19 1 Outline Arbitrage definitions Arbitrage pricing Arbitrage pricing with transactions costs 2 Arbitrage Definitions In finance theory an “arbitrage” is defined as: A zero investment trading strategy that generates a sure profit: No initial investment Non negative cash flows at all times A positive cash flow at some times On Wall Street “arbitrage” also often means a trading strategy that is expected to make a profit This is also called a “statistical arbitrage” (stat. arb.) In this class: finance theory tradition 3

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Arbitrage Pricing Important insight in finance: There cannot be arbitrage opportunities. If there were, arbitrageurs would trade aggressively to exploit them. Called the “ No Arbitrage Condition ”. Perhaps surprisingly, using the no arbitrage condition alone we can: Compute restrictions on security prices Compute explicitly prices of derivatives. 4 Arbitrage –Example Two risky securities, perfectly negatively correlated Hyper: E[R] = 3%, std = 4% Super: E[R] = 6%, std = 8% Construct risk-free portfolio T-bill: 3% Arbitrage opportunity? 5 Arbitrage –Example If ߩ ൌ െ1: ߪ ݓ ߪሺܴ ݓ ߪሺܴ 0 ൌ ݓ ு௬௣௘௥ ∗ 0.04 ሺ1 െ ݓ ௌ௨௣௘௥ ∗ 0.08 ݓ ு௬௣௘௥ =2/3 ; ݓ ௌ௨௣௘௥ ൌ 1/3 E(R)=2/3*3%+1/3*6%=4% RF gives only 3% Short RF -> buy 2/3 Hyper and 1/3 Super Fundamental of Finance L19 6
Implications of No Arbitrage Intuition If “something 1” (security, portfolio, trading strategy) has the same cash flow stream as “something 2” (security, portfolio, trading strategy) -> equivalent -> have to have the same price 7 Implications of No Arbitrage 1.
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• Fall '14
• EduardoDavila

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