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Please provide a unique, detailed and complete solution, and I will be sure to upvote your response. The following is a mathematical finance question; please
Please provide a unique, detailed and complete solution, and I will be sure to upvote your response.
The following is a mathematical finance question; please answer accordingly. Thank you :)
3.23. (Two Securities) Consider a portfolio with two securities having returns 1 and 2, risks 1 and 2, and a correlation coefficient that vanishes. To minimize this portfolio's risk-to-reward ratio, a natural quantity to minimize is f(w)=pw)P2(w), where w is the fraction of the total investment in the security with expected return 1. a) Determine an equation that any critical point of f must satisfy. What type of equation is it? b) Show that if 1=2, then we obtain a linear equation for w with solution w=12+2222 This critical point coincides with the global minimum w we found for the two-security portfolio when minimizing the variance P2 with =0. Why are the two critical points identical? 3.23. (Two Securities) Consider a portfolio with two securities having returns 1 and 2, risks 1 and 2, and a correlation coefficient that vanishes. To minimize this portfolio's risk-to-reward ratio, a natural quantity to minimize is f(w)=pw)P2(w), where w is the fraction of the total investment in the security with expected return 1. a) Determine an equation that any critical point of f must satisfy. What type of equation is it? b) Show that if 1=2, then we obtain a linear equation for w with solution w=12+2222 This critical point coincides with the global minimum w we found for the two-security portfolio when minimizing the variance P2 with =0. Why are the two critical points identicalStep by Step Solution
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