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Unformatted text preview: Markets and Information Efficient Market Hypothesis and Performance Measures 2 CAPM and APT Riskreturn trade off Single market portfolio Unequivocal statement on the E(r) relationship for ALL assets Strong conditions Noarbitrage condition Set of factors Cannot rule out a violation of the relationship for any particular asset Factors are not specified 3 An Example: IBM versus Dell Assuming the riskfree rate is 6%, are IBM and Dell priced correctly? IBM Dell Boom Price (Prob=0.5) 140 160 Bust Price (Prob=0.5) 100 80 E(price) 120 120 Current Price 100 90 E(return) 20% 33.3% 4 Business Cycle Factor Set the business cycle indicator, F BC , equal one if the economy is booming, and zero if the economy is in recession Given the 50/50 probability of boom/bust, E(F BC ) = 0.5 The unexpected change, f BC = F BCE(F BC ), is 0.5 when booming, and 0.5 when in recession 5 Factor Loadings The factor model r i = E(r i ) + i,BC f BC + e i , i = IBM, Dell Conditional expectation in two states: 0.4 = E(r IBM ) + IBM,BC 0.5 0 = E(r IBM ) + IBM,BC (0.5) E(r IBM )=20%, IBM,BC =0.4 E(r Dell )=33.3%, Dell,BC =0.89 6 Factor Risk Premium The APT pricing based on IBM E(r IBM ) = r f + BC IBM,BC 0.2 = 0.06 + BC 0.4 BC = 0.35 E(r Dell ) = 0.06+0.35 0.89 = 0.3715 > 0.33 Dell is overpriced. The APT pricing based on Dell E(r Dell ) = r f + BC Dell,BC 0.333 = 0.06 + BC 0.89 BC = 0.307 E(r IBM ) = 0.06+0.307 0.4 = 0.183 < 0.2 IBM is underpriced. APT relative pricing example APT relative pricing 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 beta (business cycle) E(r) IBM Dell 8 Arbitrage Tracking portfolio T: riskfree plus IBM w IBM IBM,BC + w f 0 = Dell,BC w IBM = 2.225, w f = 1.225 Buy T and sell Dell What is the BC of the total portfolio? r Tr Dell = 3.87% Bust: r Tr Dell = 3.76% Position ($100 portfolio) CF now CF Boom CF Bust buy IBM Now: $100 Boom: $140 Bust: $100 2.225 shares$222.50 +$311.50 $222.50 Borrow@ 6% +$122.50$129.85$129.85 sell Dell Now: $90 Boom: $160 Bust: $80 1.1 shares +$100.00$177.78$88.89 Total $0 +$3.87 +$3.76 Arbitrage Example 10 Equilibrium Price Price equation: E(r Dell ) = 0.06 + 0.35 Dell,BC Factor model: r Dell = E(r Dell ) + Dell,BC f BC + e Dell Boom and bust 160/P 1 = 0.06+0.35 Dell,BC + Dell,BC 0.5 80/P 1 = 0.06+0.35 Dell,BC + Dell,BC (0.5) Dell,BC = 0.92 and p Dell = $86.8 [E(r)=38%] Relative to IBM, investors underestimated Dells exposure to business cycle ( Dell,BC = 0.89) and were willing to pay a higher price (p Dell = $90)....
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This note was uploaded on 05/02/2010 for the course ACCT 3756 taught by Professor Leung during the Three '09 term at University of Sydney.
 Three '09
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