In this problem we assume the market portfolio is the S&P 500 index. The top 5 stocks in the S&P 500 index, when ranked by market capitalization, make up 22% of the total market capitalization of the S&P 500 index. Numerical estimates of the beta values of these top five stocks are listed in the table below. STOCK TICKER BETA Apple, Inc. AAPL 1.16 Amazon.com Inc. AMZN 0.70 Microsoft Corp. MSFT 1.15 Alphabet, Inc. GOOG 0.98 Facebook, Inc. FB 1.01 Furthermore, the variance of returns (entries on the main diagonal) and covariances between returns of these top five stocks are as follows: AAPL AMZN MSET GOOG FB AAPL 0.21 0.12 0.17 0.13 0.16 AMZN 0.12 0.15 0.12 0.10 0.12 MSFT 0.17 0.12 0.19 0.14 0.15 GOOG 0.13 0.10 0.14 0.15 0.14 FB 0.16 0.12 0.15 0.14 0.21 The variance of the S&P 500 index returns is known to be 0.11. Suppose we desire to invest in the S&P 500 index portfolio, but find that it is impractical to invest in all 500 stocks. Instead we choose to invest in the five stocks in the table in a way that replicates or tracks the S&P 500 index portfolio most closely---in the sense of minimizing the variance of the difference in returns between our portfolio of 5 stocks and the S&P 500 index portfolio. Note that short positions (negative weights) are permissible and the sum of all the weights must be equal to one. What is the optimal portfolio weight for Alphabet, Inc. (ticker: GOOG)? Please express your answer in decimal (not percentage) form and round your numerical answer to two decimal places. In this problem we assume the market portfolio is the S&P 500 index. The top 5 stocks in the S&P 500 index, when ranked by market capitalization, make up 22% of the total market capitalization of the S&P 500 index. Numerical estimates of the beta values of these top five stocks are listed in the table below. STOCK TICKER BETA Apple, Inc. AAPL 1.16 Amazon.com Inc. AMZN 0.70 Microsoft Corp. MSFT 1.15 Alphabet, Inc. GOOG 0.98 Facebook, Inc. FB 1.01 Furthermore, the variance of returns (entries on the main diagonal) and covariances between returns of these top five stocks are as follows: AAPL AMZN MSET GOOG FB AAPL 0.21 0.12 0.17 0.13 0.16 AMZN 0.12 0.15 0.12 0.10 0.12 MSFT 0.17 0.12 0.19 0.14 0.15 GOOG 0.13 0.10 0.14 0.15 0.14 FB 0.16 0.12 0.15 0.14 0.21 The variance of the S&P 500 index returns is known to be 0.11. Suppose we desire to invest in the S&P 500 index portfolio, but find that it is impractical to invest in all 500 stocks. Instead we choose to invest in the five stocks in the table in a way that replicates or tracks the S&P 500 index portfolio most closely---in the sense of minimizing the variance of the difference in returns between our portfolio of 5 stocks and the S&P 500 index portfolio. Note that short positions (negative weights) are permissible and the sum of all the weights must be equal to one. What is the optimal portfolio weight for Alphabet, Inc. (ticker: GOOG)? Please express your answer in decimal (not percentage) form and round your numerical answer to two decimal places
