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 mean (or expected) rates of return values of these top five stocks, expressed in decimal (not percentage) form, are listed in the table below. STOCK Apple, Inc. Amazon.com Inc. Microsoft Corp. Alphabet, Inc. Facebook, Inc. STOCK Apple, Inc. TICKER Amazon.com Inc. AAPL AMZN MSFT GOOG FB TICKER MEAN RETURN AAPL AMZN 0.69 Numerical estimates of the beta values of these top five stocks are listed in the table below. 0.65 0.44 0.36 0.41 BETA 1.16 0.70 STOCK Apple, Inc. AAPL AMZN Amazon.com Inc. Microsoft Corp. Alphabet, Inc. Facebook, Inc. STOCK Apple, Inc. Amazon.com Inc. Microsoft Corp. Alphabet, Inc. Facebook, Inc. TICKER AAPL 0.21 0.12 AAPL AMZN MSFT GOOG Numerical estimates of the beta values of these top five stocks are listed in the table below. FB AMZN 0.12 0.15 TICKER AAPL AMZN MSFT GOOG FB MEAN RETURN 0.69 0.65 MSFT 0.17 0.12 0.44 0.36 0.41 BETA 1.16 0.70 Furthermore, the variance of returns (entries on the main diagonal) and covariances between returns of these top five stocks are as follows: 1.15 0.98 1.01 GOOG 0.13 0.10 FB 0.16 0.12 Facebook, Inc. Furthermore, the variance of returns (entries on the main diagonal) and covariances between returns of these top five stocks are as follows: AAPL AMZN MSFT GOOG FB AAPL 0.21 0.12 0.17 0.13 0.16 AMZN 0.12 0.15 0.12 0.10 0.12 FB MSFT 0.17 0.12 0.19 0.14 0.15 1.01 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 0.09. Suppose we desire to invest such that we earn double (2 times) the return of 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 double (2 times) the return of 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 double (2 times) the return of the S&P 500 index portfolic Simultaneously, we desire to choose the portfolio weights so that the portfolio mean return is equal to 0.20. Please round your numerical answer to one decimal place. 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)?