Course notes RSM332 - Class 10 - APT

Course notes RSM332 - Class 10 - APT - Arbitrage Pricing...

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Arbitrage Pricing Theory The CAPM says that ER i = R f + β i (ER M -R f ) If ER M – R f = 6%, R f = 7%, and β i = 1.5, then ER i = 7% + 1.5(6%) = 16%. It is easy to see that ER M is 13%. Now, if, this year, the actual R M = 27%, then we expect the actual return on S i to be 7% + 1.5(actual R M – R f ) = 7% + 1.5(20%) = 37%. The extra 27%- 13% = 14% increase in the market return causes us to expect an extra 14% x 1.5 = 21% increase in S i . The CAPM assumes the expected return is a function of only one systematic risk – market risk. Other models assume there could be more than one systematic risk factor, such as inflation, or GNP, or interest rates. If so, our model would generalize to (with k factors): ER i = R f + β 1i (ER 1 - R f ) + β 2i (ER 2 - R f ) + … + β ki (ER k – R f ) An Example of APT: Two Factors Suppose that there are two economic factors which determine the stock returns. They are: F 1 : actual GNP growth rate expected GNP growth rate, F 2 : actual oil price growth rate expected oil price growth rate. Four firms are in the following lines of business: A . An airline company B . A manufacturing company C . An oil company D . A utility company Suppose actual returns on stocks A,B,C,D follow the factor structure: R A = 0 . 30 + 1 . 2 F 1 0 . 4 F 2 R B = 0 . 16 + 0 . 8 F 1 1 . 0 F 2 R C = 0 . 24 + 0 . 6 F 1 + 0 . 2 F 2 R D = 0 . 12 + 0 . 2 F 1 0 . 2 F 2 So E(R A ) = 0.30, E(R B ) = 0.16, etc.
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