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Suppose asset returns are driven by two common factors, namely GDP growth rate (factor 1) and interest rate (factor 2). There are three correctly priced
Suppose asset returns are driven by two common factors, namely GDP growth rate (factor 1) and interest rate (factor 2). There are three correctly priced well-diversified portfolios A, B and C. Their factor sensitivities and annual expected returns are given in the following table: Factor Sensitivity for Factor Sensitivity for Annual Expected Factor 1 Factor 2 Return Portfolio A bA1 = +2.0 bA2 = -3.0 4.50% Portfolio B bb1 = +1.5 bb2 = -1.0 6.25% Portfolio C bc1 = -1.0 bcz = +2.0 4.50% The risk-free rate is 4% per year. (A) Construct the unit factor portfolio for factor 2 with portfolios A, C, and the risk-free asset. What is the weight of portfolio A in this unit factor portfolio? (5%) (B) What is the expected return for the unit factor portfolio for factor 1? (3%) (C) What is the expected return for the unit factor portfolio for factor 2? (3%) (D) ) a Suppose you invest in a well-diversified portfolio (X) which has a factor sensitivity of +4.0 for Factor 1 and a factor sensitivity of -3.0 for Factor 2. We can construct another portfolio Y with two unit factor portfolios for factor 1 and factor 2, and the risk- free asset to track portfolio X's factor sensitivities with respect to Factor 1 and Factor 2. What is the weight of the unit factor for factor 1 in portfilo Y? (2%) (E) What is the expected return of portfolio Y in question (D)? (2%) * Terminology: The unit factor portfolio describes the tracking portfolio for a given risk factor. The unit factor portfolio has loading 1 on the given risk factor and loadings 0 on other risk factors a
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