Question 4 (12 marks) A fund manager has created two index funds. The manager did this by dividing all risky securities in the market into two portfolios: Value and Growth. Each security was assigned to only one portfolio. In each portfolio, the securities are weighted according to their market values. Assume that all securities are priced according to the Capital Asset Pricing Model (CAPM). The standard deviation of the return on the Value portfolio is 0.10 and the standard deviation of the return on the Growth portfolio is 0.4. The correlation of the Value portfolio's return with the return on the market portfolio is 0.4, and the correlation of the return of the Growth portfolio with the return on the market is 0.6. The standard deviation of the market portfolio is 0.20. Now as an investor, you are trying to create your own optimal risky portfolio with highest possible Sharpe ratio. You can only take positions in the fund manager's Value portfolio and Growth portfolio. a. Calculate CAPM Beta for the Value portfolio and CAPM Beta for the Growth portfolio. (4 marks) b. For every dollar invested in Value portfolio, what dollar amount should be invested in the Growth portfolio? (Hint: According to the CAPM, the optimal risky portfolio is the market portfolio) (8 marks) Question 4 (12 marks) A fund manager has created two index funds. The manager did this by dividing all risky securities in the market into two portfolios: Value and Growth. Each security was assigned to only one portfolio. In each portfolio, the securities are weighted according to their market values. Assume that all securities are priced according to the Capital Asset Pricing Model (CAPM). The standard deviation of the return on the Value portfolio is 0.10 and the standard deviation of the return on the Growth portfolio is 0.4. The correlation of the Value portfolio's return with the return on the market portfolio is 0.4, and the correlation of the return of the Growth portfolio with the return on the market is 0.6. The standard deviation of the market portfolio is 0.20. Now as an investor, you are trying to create your own optimal risky portfolio with highest possible Sharpe ratio. You can only take positions in the fund manager's Value portfolio and Growth portfolio. a. Calculate CAPM Beta for the Value portfolio and CAPM Beta for the Growth portfolio. (4 marks) b. For every dollar invested in Value portfolio, what dollar amount should be invested in the Growth portfolio? (Hint: According to the CAPM, the optimal risky portfolio is the market portfolio) (8 marks)