Question 1

An investor models the excess return for Amazon via the market model. Suppose that the sample size is 102 observations, the value of for Amazon is = 1.107, the standard error associated with the coefficient is SE() = 0.0348. She tests the null hypotheses that the value of the stocks beta is one, against a one-sided alternative that the stocks beta is greater than the markets beta. The level of significance is 5%.

a. Write down the regression model which uses the market models factors as explanatory variables and define the variables.

b. Write down the null and the alternative hypothesis.

c. Conduct the test. What do you conclude? Are the analysts claims empirically verified? You can find the t-tests critical values in Table A1 in the Appendix at the end of the exam paper.

d. The analyst also tells you that shares in Chris Mining PLC have no systematic risk, in the sense that the returns on its shares are completely unrelated to movements in the market. The value of beta and its standard error are calculated to be 0.5 and 0.25, respectively, and the model is estimated using 52 observations. Write down the null and alternative hypothesis. Form and interpret a 95% and a 99% confidence interval for beta. You can find the t-tests critical values in Table A1 in the Appendix.

e. Do the tested hypotheses concern the actual values of the coefficients (i.e. ), or their estimated values (i.e. ), and why?

APPENDIX A 1% Table A1 Critical values for the t-distribution at various significance levels Significance level Degrees of Two-tailed test: 10% 5% 2% 0.2% 0.1% freedom One-tailed test: 5% 2.5% 1% 0.5% 0.1% 0.05% 6.314 12.706 31.821 63.657 318.309 636.619 2.920 4.303 6.965 9.925 22.327 31 599 2.353 3.182 4.541 5.841 10.215 12.924 2.132 2.776 3.747 4.604 7.173 8.610 2.015 2.571 3.365 4.032 5.893 6.869 1.943 2.447 3.143 3.707 5.208 5.959 1.894 2.365 2.998 3.499 4.785 5.408 1.860 2 306 2.896 3.355 4.501 5.041 1.833 2.262 2.821 3.250 4.297 4.781 10 1.812 2.228 2.764 3.169 4.144 4.587 11 1.796 2.201 2.718 3.106 4.025 4.437 12 1.782 2.179 2.681 3.055 3.930 4.318 13 1.771 2.160 2.650 3.012 3.852 4.221 14 1.761 2.145 2.624 2.977 3.787 4.140 15 1.753 2.131 2.602 2.947 3.733 4.073 16 1.746 2.120 2.583 2.921 3.686 4.015 17 1.740 2.110 2.567 2.898 3.646 3.965 18 1.734 2.101 2.552 2.878 3.610 3.922 19 1.729 2.093 2.539 2861 3.579 3.883 20 1.725 2.086 2.528 2.845 3.552 3.850 1.721 2.080 2.518 2.831 3.527 3.819 1.717 2.074 2.508 2.819 3.505 3.792 1.714 2.069 2.500 2.807 3.485 3.768 1.711 2.064 2.492 2.797 3.467 3.745 1.708 2.060 2.485 2.787 3.450 3.725 1.706 2.056 2.479 2.779 3.435 3.707 1.703 2.052 2.473 2.771 3.421 3.690 1.701 2.048 2.467 2.763 3.408 3.674 1.699 2.045 2.462 2.756 3.396 3.659 1.697 2.042 2.457 2.750 3.385 3.646 1.694 2.037 2.449 2.738 3.365 3.622 34 1.691 2.032 2.441 2.728 3.348 3.601 36 1.688 2.028 2.434 2.719 3.333 3.582 38 1.686 2.024 2.712 3.319 3.566 40 1.684 2.021 2.423 2.704 3.307 3.551 1.682 2.018 2.418 2.698 3.296 3.538 44 1.680 2.015 2.414 2.692 3.526 46 1.679 2.013 2.410 2.687 3.277 3.515 48 1.677 2.011 2.407 2.682 3.269 3.505 50 1.676 2.009 2.403 2.678 3.261 3.496 60 1.671 2.000 2.390 2.660 3.232 3.460 70 1.667 1.994 2.381 2.648 3.211 3.435 80 1.664 1.990 2.374 2.639 3.195 3.416 90 1.662 2 368 2.632 3.183 3.402 100 1.660 1.984 2.364 2.626 3.174 3.390 120 1.658 1.980 2.358 2.617 3.160 3.373 150 1.655 1.976 2.351 2.609 3.145 3.357 200 1.653 1.972 2.345 2.601 3.131 3.340 300 1.650 1.968 2.339 2.592 3.118 3.323 400 1.649 1.966 2.336 2.588 3.111 3.315 500 1.648 1.965 2.334 2.586 3.107 3.310 600 1.647 1.964 2.333 2.584 3.104 3.307 2.429 3.286 1.987 APPENDIX A 1% Table A1 Critical values for the t-distribution at various significance levels Significance level Degrees of Two-tailed test: 10% 5% 2% 0.2% 0.1% freedom One-tailed test: 5% 2.5% 1% 0.5% 0.1% 0.05% 6.314 12.706 31.821 63.657 318.309 636.619 2.920 4.303 6.965 9.925 22.327 31 599 2.353 3.182 4.541 5.841 10.215 12.924 2.132 2.776 3.747 4.604 7.173 8.610 2.015 2.571 3.365 4.032 5.893 6.869 1.943 2.447 3.143 3.707 5.208 5.959 1.894 2.365 2.998 3.499 4.785 5.408 1.860 2 306 2.896 3.355 4.501 5.041 1.833 2.262 2.821 3.250 4.297 4.781 10 1.812 2.228 2.764 3.169 4.144 4.587 11 1.796 2.201 2.718 3.106 4.025 4.437 12 1.782 2.179 2.681 3.055 3.930 4.318 13 1.771 2.160 2.650 3.012 3.852 4.221 14 1.761 2.145 2.624 2.977 3.787 4.140 15 1.753 2.131 2.602 2.947 3.733 4.073 16 1.746 2.120 2.583 2.921 3.686 4.015 17 1.740 2.110 2.567 2.898 3.646 3.965 18 1.734 2.101 2.552 2.878 3.610 3.922 19 1.729 2.093 2.539 2861 3.579 3.883 20 1.725 2.086 2.528 2.845 3.552 3.850 1.721 2.080 2.518 2.831 3.527 3.819 1.717 2.074 2.508 2.819 3.505 3.792 1.714 2.069 2.500 2.807 3.485 3.768 1.711 2.064 2.492 2.797 3.467 3.745 1.708 2.060 2.485 2.787 3.450 3.725 1.706 2.056 2.479 2.779 3.435 3.707 1.703 2.052 2.473 2.771 3.421 3.690 1.701 2.048 2.467 2.763 3.408 3.674 1.699 2.045 2.462 2.756 3.396 3.659 1.697 2.042 2.457 2.750 3.385 3.646 1.694 2.037 2.449 2.738 3.365 3.622 34 1.691 2.032 2.441 2.728 3.348 3.601 36 1.688 2.028 2.434 2.719 3.333 3.582 38 1.686 2.024 2.712 3.319 3.566 40 1.684 2.021 2.423 2.704 3.307 3.551 1.682 2.018 2.418 2.698 3.296 3.538 44 1.680 2.015 2.414 2.692 3.526 46 1.679 2.013 2.410 2.687 3.277 3.515 48 1.677 2.011 2.407 2.682 3.269 3.505 50 1.676 2.009 2.403 2.678 3.261 3.496 60 1.671 2.000 2.390 2.660 3.232 3.460 70 1.667 1.994 2.381 2.648 3.211 3.435 80 1.664 1.990 2.374 2.639 3.195 3.416 90 1.662 2 368 2.632 3.183 3.402 100 1.660 1.984 2.364 2.626 3.174 3.390 120 1.658 1.980 2.358 2.617 3.160 3.373 150 1.655 1.976 2.351 2.609 3.145 3.357 200 1.653 1.972 2.345 2.601 3.131 3.340 300 1.650 1.968 2.339 2.592 3.118 3.323 400 1.649 1.966 2.336 2.588 3.111 3.315 500 1.648 1.965 2.334 2.586 3.107 3.310 600 1.647 1.964 2.333 2.584 3.104 3.307 2.429 3.286 1.987