You manage a portfolio worth €1 Billion for a Dutch pension fund. The portfolio invests solely in 10 large European industry indices. The weekly euro denominated returns (including dividends) are...

You manage a portfolio worth €1 Billion for a Dutch pension fund. The portfolio invests solely in 10 large European industry indices. The weekly euro denominated returns (including dividends) are given in the attached excel file. You have currently allocated 10 percent to each of the industries, i.e. each industry gets an equal weight. a. Calculate the annualized portfolio return volatility. Briefly discuss the diversification benefits in this portfolio based on the return correlation matrix. b. Suppose that the global equity market portfolio is a good proxy for the market portfolio in the CAPM (returns also included in the attached excel sheet). Calculate the betas of the 10 industries with respect to the market portfolio. Interpret the numbers you obtain. c. Assume the expected return (in excess of the risk-free rate) on the market portfolio equals 5% and the risk-free rate equals 1%. Calculate the expected return for each of the industries and the equal-weighted portfolio. You will use this expected return in the questions that follow. d. Assume that the portfolio returns are normally distributed. Calculate the probability that the portfolio will incur a loss of more than 5 percent over the next month. Similarly, what is the probability that the portfolio will realize a loss of more than 10 percent over the next three months? e. Calculate the 1-month Value-at-Risk at the 1%, 5%, 10% level. Interpret your results. f. You consider selling 5% (absolute value) of your position in Oil&Gas to invest it in Utilities. Approximate the impact of this sale on the 1-month Value-at-Risk at the 5%-level calculated in e. Discuss how accurate your approximation is when compared to the exact VaR(0.05) of the new portfolio. g. In all your calculations until now, you have used full sample volatilities and correlations. In reality, both vary substantially over time. Use the exponentially-weighted moving average (EWMA) technique discussed in class to model the volatility of the equal-weighted portfolio returns over time. Use a smoothing parameter (lambda) of 0.94. Make a plot of the estimated time-varying volatility. Discuss your findings. h. Recalculate the 1-month Value-at-Risk at the 1%, 5%, 10% level using the most recent volatility estimate from the EWMA model. Compare your results to those obtained in e.