Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

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

image text in transcribed

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 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 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 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 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

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Bakers Health Care Finance Basic Tools For Nonfinancial Managers

Authors: Thomas K. Ross

6th Edition

1284233162, 978-1284233162

More Books

Students also viewed these Finance questions

Question

What does an ANOV table summarize?

Answered: 1 week ago