As a portfolio manager you analyze 3 components (A, B, C) of the EUROSTOXX 50 index You have estimated the expected returns of these components for next year as Ra 12 , Rb 6 and Rc 8,5 and the corresponding variance covariance matrix as 0,09 0,0175 0,041 0,0175 0,0625 0,0225 0,041 0,0225 0,04 Where Cov (Ra, Rb) 0,0175 Calculate Sharpe ratio of each component, where the annualized risk free rate is 1 Then comment on the results and on the use of Sharpe index as a performance measure (7p) You plan to invest in a portfolio P1 defined by the following weights xa 30 , xb 50 , xc 20 According to the risk return tradeoff compare your portfolio with the alternative proposal of your colleagues to invest in equally weighted portfolio of the three components (P2) Justify your decisions with appropriate calculations (10p) Now you are considering investing in a stock portfolio of only two of the three components A, B, C (short positions are not allowed) Discuss whether each combination give the benefit of the diversification effect in terms of lower variance (Hint compare the ratio of any two component volatilities with the corresponding correlation coefficient) (9p) By applying the Share single index model, you have computed the following parameters of the three components (A, B, C) and the benchmark (M) that is the EUROSTOXX 50 (10p) i i Qi A 0,025 0,76 0,15 B 0,014 1,3 0,07 C 0,030 0,97 0,11 M 0,055 1,0 0,12 Where M R M , Q i 2 i , Q M 2 M Calculate the expected returns of portfolios P1 and P2 defined in point b You plan to invest in a portfolio with a beta of 1with respect to the benchmark EUROSTOXX 50 The portfolio is composed of only two of the stocks A and B analyzed in Question d) Calculate the variance and determine the optimum weights for a portfolio with a combination of stocks A and B only Hint given two risky assets, the weights to be invested in each security are obtained easily from the formula used to calculate the beta of the portfolio (4p)

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Sep 18, 2024

As a portfolio manager you analyze 3 components (A, B, C) of the EUROSTOXX 50 index. You have estimated the expected returns of these components for next year as: Ra = 12%, Rb = 6% and Rc = 8,5% and the corresponding variance / covariance matrix as:

Where Cov (Ra, Rb) = 0,0175

Calculate Sharpe ratio of each component, where the annualized risk-free rate is 1%. Then comment on the results and on the use of Sharpe index as a performance measure. (7p)

You plan to invest in a portfolio P1 defined by the following weights: xa = 30%, xb = 50%, xc = 20%. According to the risk/return tradeoff compare your portfolio with the alternative proposal of your colleagues to invest in equally weighted portfolio of the three components (P2). Justify your decisions with appropriate calculations. (10p)

Now you are considering investing in a stock portfolio of only two of the three components A, B, C (short positions are not allowed). Discuss whether each combination give the benefit of the diversification effect in terms of lower variance (Hint: compare the ratio of any two component volatilities with the corresponding correlation coefficient). (9p)

By applying the Share single index model, you have computed the following parameters of the three components (A, B, C) and the benchmark (M) that is the EUROSTOXX 50 (10p)

Where: _M = R_M , Q_i = ²_i , Q_M = ²_M

Calculate the expected returns of portfolios P1 and P2 defined in point b.

You plan to invest in a portfolio with a beta of 1with respect to the benchmark EUROSTOXX 50. The portfolio is composed of only two of the stocks A and B analyzed in Question d). Calculate the variance and determine the optimum weights for a portfolio with a combination of stocks A and B only. [Hint: given two risky assets, the weights to be invested in each security are obtained easily from the formula used to calculate the beta of the portfolio.] (4p)