Question 1: You are studying Rio Tinto Limited (RIO) stock performance during last years. Since RIO is listed in Sydney Security Exchange, you believe that the returns of RIO is correlated with ASX200...

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Question 1: You are studying Rio Tinto Limited (RIO) stock performance during last years. Since RIO is listed in Sydney Security Exchange, you believe that the returns of RIO is correlated with ASX200 index returns. As Rio Tinto is a multinational and the world's second largest metals and mining corporations, you also assume RIO returns are associated with S&P 500 index returns. You model the RIO returns () as below: + and are returns for S&P 500 index and ASX index, respectively, is the error term. After obtaining historical data, you run a regression and get the following output: ANOVA   df SS MS Regression 2.000 0.441 0.220 Residual 212.000 1.048 0.005 Total 214.000 1.489     Coefficients Standard Error t Stat Intercept 0.008 0.005 1.686 S&P 500 -0.094 0.171 -0.550 ASX 200 1.322 0.195 6.768 (1) Test if the first slope coefficient estimate of is significant at the 1% level? (2) Construct and interpret the 95% confidence interval for the second slope coefficient estimate of . (3) Determine if the two independent variables are jointly statistically related to at the 0.05 significance level. (5 + 5 + 5 = 15 marks) Question 2: You manage a U.S. core equity portfolio that is sector-neutral to the S&P500 Index (its industry sector weights approximately match the S&P 500's). Taking a weighted average of the projected mean returns on the holdings, you forecast a portfolio return of 12%. You estimate a standard deviation of annual return of 22%, which is close to the long-run figure for the S&P 500. For the year-ahead return on the portfolio, assuming Normality for portfolio returns, you are asked to do the following: (1) Calculate and interpret a two-standard deviation confidence interval for the portfolio returns. (2) You can buy a one-year T-bill that yields 5%. What is the probability that your portfolio return will be equal to or less than the risk-free rate? (4 + 5 = 9 marks) Question 3: Kevin works as an analyst in an investment bank, and he tries to build a time series model for monthly U.S. inflation (denoted) from Feb. 1971 to Dec. 2000. He first tried the Autoregressive AR(1) model using the previous month’s inflation as the independent variable: The table below shows the results of estimation. AR(1) model: U.S. Monthly Inflation Feb. 1971 to Dec. 2000 Regression Statistics R Square 0.3808 Standard Error 3.4239 Observations 359 Durbin-Watson 2.3059 Coefficients Standard Error t Stat Intercept () 1.9658 0.2803 7.0119 Lag1 () 0.6275 0.0410 15.3049 Autocorrelation of the Residual Lag Autocorrelation Standard Error t Stat 1 -0.1538 0.0528 -2.9142 2 0.1097 0.0528 2.0782 3 0.1657 0.0528 1.2442 4 0.10920 0.0528 1.7434 Based on regression results in the table, discuss whether the estimates of and are valid, and give reasons. If the model is misspecified, describe what is the next step you should take to determine an appropriate Autoregressive time series model. a b a b t SP r , 500 t Y . 1 t t t u Y Y + + = - b a