PROBLEMS I. Given the following data sample, how confident can we be that the men greater than 40? 64 70 20 3 58 13 74 84 47 17 2. You are given the following sample of annual returns for a portfolio manage If you believe that the distribution of returns has been stable over time and wait continue to be stable over time, how confident should you be that the portfolio manager will continue to produce positive returns? -7% 7% 19% 23% -18% -12% 49% 34% -6% -20% 3. You are presented with an investment strategy with a mean return of 20% ap a standard deviation of 10%. What is the probability of a negative return if the returns are normally distributed? What if the distribution is symmetrical, bus otherwise unknown? s follow a uniform distril5. You are the risk manager for a portiond w a daily standard deviation of 2.3%. Assume the returns are normally distributed and (not a good assumption to make, in general). What is the 95% VaR? 6. You are told that the log annual returns of a commodities index are normally distributed with a standard deviation of 40%. You have 33 years of data, from which you calculate the sample variance. What is the standard deviation of this estimate of the sample variance? 7. In the previous question, you were told that the actual standard deviation was 40%. If, instead of 40%, the measured standard deviation turns out to be 50%. how confident can you be in the initial assumption? State a null hypothesis and calculate the corresponding probability. of 15% with a 10% standard devia