You are given the factor model for the assets whose return vector is r(t) with factor...

 

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You are given the factor model for the assets whose return vector is r(t) with factor returns f(t) and noise term (t): r(t) = a + Bf(t) + (t). The factors are, by construction, orthonormal; i.e., uncorrelated with variance 1. Let the mean factor returns be represented by the vector o. (a) Express the returns' mean vector and covariance matrix in terms of the factor model. (b) Given the mean-variance program below, explain how you can exploit the structure of the factor model to solve the program more efficiently? { / x Ex- \x} (c) Assuming there are n = 500 assets and m = 10 factors, compare the number of parameters needed to compute the covariance matrix under the factor model with one computed directly from the raw returns. You are given the factor model for the assets whose return vector is r(t) with factor returns f(t) and noise term (t): r(t) = a + Bf(t) + (t). The factors are, by construction, orthonormal; i.e., uncorrelated with variance 1. Let the mean factor returns be represented by the vector o. (a) Express the returns' mean vector and covariance matrix in terms of the factor model. (b) Given the mean-variance program below, explain how you can exploit the structure of the factor model to solve the program more efficiently? { / x Ex- \x} (c) Assuming there are n = 500 assets and m = 10 factors, compare the number of parameters needed to compute the covariance matrix under the factor model with one computed directly from the raw returns.

Answer rating: 100% (QA)

a Expressing the returns mean vector in terms of the factor model The mean vector represents the expected returns of the assets In the factor model the expected returns can be expressed as a The mean ... View the full answer