Quiz III practice - E[R x ] = .05 + 1*E[f 1 ]+ -1*E[f 3 ] =...

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Quiz III practice birr.com/Using_Macroeconomic_factors.pdf Stocks X, Y, and Z have expected returns consistent with the Arbitrage Pricing Theorem. E[R n ] = a + b 1n f 1 + b 2n f 2 + b 3n f 3 Where E[R n ] is the expected return of n-th stock. The risk free rate a = .05 The betas of stocks X, Y, Z and a fourth stock, Stock A, can be found in the following table. Stock Expected Return B 1n b 2n b 3n X .1 1 0 -1 Y .15 0 -1 0 Z .15 0 0 1 A ? 1 2 1 i. What is the expected return of stock A? ii. What is the risk-premia for factor 3? Answer: #1: There is two ways to solve this problem. 1) find risk premia: E[f K ] = risk premia for the k-th factor. 2) pick weights w1+w2+w3 = 1 to form a portfolio with betas (1,2,1) To find the risk premia note that E[R n ] = a + b 1n f 1 + b 2n f 2 + b 3n f 3 implies that E[R n ] = a + b 1n E[f 1 ]+ b 2n E[f 2 ]+ b 3n E[f 3 ] Using the numbers in the table we get: E[R x ] = a + b 1x E[f 1 ]+ b 2x E[f 2 ]+ b 3x E[f 3 ] = .1 E[R y ] = a + b 1y E[f 1 ]+ b 2y E[f 2 ]+ b 3y E[f 3 ] = .15 E[R z ] = a + b 1z E[f 1 ]+ b 2z E[f 2 ]+ b 3z E[f 3 ] = .15 Plug in the values for the betas and a =.05
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Unformatted text preview: E[R x ] = .05 + 1*E[f 1 ]+ -1*E[f 3 ] = .1 E[R y ] = .05 + -1*E[f 2 ] = .15 E[R z ] = .05 + 1*E[f 3 ] = .15 So E[f 3 ] = .1 E[f 2 ] = -.1 E[f 1 ] = .15 And E[R A ] = a + b 1A E[f 1 ]+ b 2A E[f 2 ]+ b 3A E[f 3 ] = .05+(1*.15)+(2*-.1)+(1*.1) = .1 Alternativly we could solve this by picking weights w1+w2+w3 = 1 to form a portfolio with betas (1,2,1) b1 = 1 = w1*(1) + w2* (0) + w3*(0) b2 = 2 = w1*(0) + w2*(-1) + w3*(0) b3 = 1 = w1*(-1) + w2*(0) + w3*(1) Solve for w1,w2,w3 to get w1 = 1, w2 = -2, w3 = 2 Thus a portfolio with w1 = 1, w2 = -2, w3 = 2 will have betas = (1,2,1) No-Arbitrage implies the expected return of this portfolio must be the same as the expected return of stock A. E[R A ] = w1*(.1) + w2* (.15) + w3*(.1) = 1*(.1) + (-2)*(.15) + (2)*(.15) = .1 #2: What is the risk-premia for factor 3? From #1 we know that E[f 3 ] = .1...
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This test prep was uploaded on 04/12/2008 for the course ECON 435 taught by Professor Chabot during the Winter '08 term at University of Michigan.

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Quiz III practice - E[R x ] = .05 + 1*E[f 1 ]+ -1*E[f 3 ] =...

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