Portfolio Management

Portfolio Management

  1. 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

  1. 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.
  1. 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.
  1. 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).
  1. 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
αi βi 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: α= R, Qi = σ2ε, Q= σ2M

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

  1. 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.]
  1. In your role as a portfolio manager you are asked to make valuations of a number of corporate bonds. Consider the following bonds:

Bond A: corporate bond issued by company X, annual coupon of 3% (paid semi-annually), expiry in 3 years, redemption price at 100,00, YTM = 2,75%.

Bond B: corporate bond issued by bank Y, annual coupon of 2% (paid annually), expiry in 5 years, redemption price at 100,00, YTM = 1,45%.

Bond C: corporate bond issued by bank Z, zero coupon bond), expiry in 7 years, redemption price at 100,00, YTM = 4,00%.

  1. For the bonds given above complete the following table
Price Duration Convexity
Bond A 2,89 9,47
Bond B 102,634 27,679
Bond C 75,992 7
  1. For bond B calculate the relative price change (in %) following a yield curve parallel shift of +25 basis points, specifying both the price change due to the price duration only and also due to the price convexity (Note: if you have not answered question a) assume the duration of bond B as 4,75)
  2. Suppose you create an equally-weighted portfolio with the three bonds given in the table. Calculate the portfolio convexity. Note: if you have not answered question a) use the following data
Duration Convexity
Bond A 2,7 9,5
Bond B 4,75 30,0
Bond C 7,0 50,0
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