Question 1 (a.) You have 4 stocks in a stock market index. At the end of 2018 and 2019 the stock prices were as follows. 33 (i.) (ii.) Asset Number of Price (End 2018) Price (End 2019) stocks 1 7500 1.25 1.21 2 5000 0.85 0.92 3 10000 1.15 1.17 4 9000 0.55 0.62 Calculate the weights in the market capitalisation index in the two years. Suppose you invest in an equally weighted index in 2018. What would the weights of your initially equally weighted index be at the end of 2019? (Fractional shares are possible) [35 marks] (b.) You have used 555 monthly return of a stock market to calculated the mean and standard deviation. The monthly mean return is 0.4% and the standard deviation 5.9. Calculate the lower boundary of the returns distribution (based on normality) for the 5%, 2.5% and 1% left tail. How many observations do you expect to fall into these lower tails? Suppose you count 28, 15 and 6 observations to fall into the 5%, 2.5% and 1% left tail respectively, what would you conclude regarding your stock market returns complying to normality? [30 marks] (c.) You have four one-period continuously compounded returns which are : 5%, -2%, 3% and 1%. Calculate the n-period continuously compounded return and the n-period arithmetic return where n is four. [35 marks]