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. Meta Platforms Inc TICKER AAPL AMZN MSFT GOOG MEAN RETURN 0.69 0.65 0.44 0.36 0.41 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 AAPL 0.21 0.12 0.17 0.13 0.16 AMZN 0.12 _, w; = 1 i=1 0.15 0.12 0.10 0.12 MSFT 0.17 0.12 0.19 0.14 0.15 ij=1 wiWjo ij - W; Fi i,j=1 i=1 GOOG 0.13 0.10 0.14 0.15 0.14 0.16 0.12 Suppose we desire to invest in the five stocks in the table in a way that simultaneously minimizes the portfolio risk and maximizes the portfolio expected return 1 W;, where ; is the mean return for stock i given in the table 5 i=1 above. One method for accomplishing this objective is to find the optimal portfolio weights wi, 1 i 5 that solve the following problem: minimize 0.15 0.14 0.21 subject to 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 Meta Platforms, Inc (ticker: META)? Please express your answer in decimal (not percentage) form and round your numerical answer to two decimal places.