Rubric for Online Discussion and discussion 5 answers

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Purdue University *

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57000

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Economics

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Feb 20, 2024

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Question 1 (10 points) No initial posting exists to evaluate. 0 Points Your final answer is incorrect but the work shows one or more steps that are correct. 1-6 Points The final answer is incorrect but most of the work is correct. 7 Points The final answer is incorrect with only a minor calculation error, or the final answer is correct but the work needs more detail. 8 Points The final answer is correct and the work is complete. 10 points Question 2 (10 points) No initial posting exists to evaluate. 0 Points Your final answer is incorrect but the work shows one or more steps that are correct. 1-6 Points The final answer is incorrect but most of the work is correct. 7 Points The final answer is incorrect with only a minor calculation error, or the final answer is correct but the work needs more detail. 8 Points The final answer is correct and the work is complete. 10 points Participation in Discussion (10 points) No responses to other classmates were posted in this discussion forum. 0 Points May include one or more of the following: 1-5 Points Comments to only one other student's post. Comments are not substantive, such as just one line or saying, “Good job” or “I agree. Comments are off topic. Comments to two or more classmates’ initial posts but only on one day of the week. Comments are substantive, meaning they reflect and expand on what the other student wrote. 6-7 Points Comments to two or more classmates’ initial posts on more than one day. Comments are substantive, meaning they reflect and expand on what the other student wrote. 8-9 Points. Comments to two or more classmates’ initial posts and to the instructor's comment (if applicable) on two or more days. Responses demonstrate an analysis of peers’ comments, building on previous posts. Comments extend and deepen meaningful conversation and may include a follow-up question. 10 Points
Chap15Prob23: When you use @Risk’s correlation feature to generate correlated random numbers, how can you verify that they are correlated? Try the following. Use the RiskCorrmat function to generate two normally distributed random numbers, each with mean 100 and standard deviation 10, and with correlation 0.7. To run a simulation, you need an output variable. Now run @Risk’s excel reports button and check the simulation data option to see the actual simulated data. A. Use Excel’s CORREL function to calculate the correlation between the two input variables. It should be close to 0.7. Then create a scatter plot of these two input variables. The plot should indicate a definite positive relationship. Step 1: Generate two normally distributed random numbers with a mean of 100 and a standard deviation of 10, and a correlation of 0.7. I used the below formula: =ROUND(RiskNormal(mean,std dev,RiskCorrmat(2x2 correlation)),0) Step 2: Create an output variable. Use =SUM on the two random numbers generated in the previous step. Select the Output cell, select risk “output” and click define. Step 3: Run the @RISK simulation. Step 4: Click on the Excel Reports button in @RISK and check the Simulation Data option. View the input and output data. Step 5: use Excel's =CORREL function to calculate the correlation between the two input variables. Step 6: Create a scatterplot of the two input variables. The plot should show a definite positive relationship, indicating that the variables are indeed correlated. B. Are the two variables correlated with the output? Use Excel’s CORREL function to find out. Interpret your results intuitively.
Step 7: Use Excel's =CORREL function again to determine if the two input variables are correlated with the output. Yes, the two variables are correlated with the output – (0.923382676 and 0.923627038). This means that anything that happens to the two input variables will change the output as well. Chap15Prob26: Suppose you are going to invest equal amounts in three stocks. The annual return from each stock is normally distributed with mean 0.01 (1%) and standard deviation 0.06. The annual return on your portfolio, the output variable of interest, is the average of three stock returns. Run @Risk, using 1000 iterations, on each of the following scenarios. a. The three stock returns are highly correlated. The correlation between each pair is 0.9. b. The three stock returns are practically independent. The correlation between each pair is 0.1.
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c. The first two stocks are moderately correlated. The correlation between their returns is 0.4. The third stocks return is negatively correlated with the other two. The correlation between its return and each of the first two is -0.8. d. Compare the portfolio distributions from @Risk for these three scenarios. What do you conclude? The distributions for each of the portfolio returns in the three cases are as shown above. The mean in all three cases is the same and is equal to the mean of the individual stocks. But the standard deviation in the first case, when the correlation is highly positive is approximately equal to those of individual stocks. The standard deviation when stock returns are uncorrelated or mixed correlated, is less than those of individual stocks. Also, the first graph is almost perfectly symmetric while the other two are slightly skewed. This is because; there is a high positive correlation between the stocks in the first case. The average will also be highly correlated with each, and the portfolio returns show the same properties as those of individual stock returns. In the second case, the stocks are uncorrelated. The portfolio return does not have a standard deviation equal to individual stock returns. In the third case, the mixed effect is observed, leaving the distribution is slightly skewed and the standard deviation is not the same as the stock returns. In the case of high correlation, you can see a mean of 1% as expected but a min and max that are very different from this mean. With a lower correlation, the possible gains and losses experienced are much closer to the average of 1%. With one stock negatively correlated, the variance is even smaller making this an example of diversification. e. You might think of a fourth scenario, where the correlation between each pair of returns is a large negative number such as -0.8. But explain intuitively why this makes no sense. Try to run the simulation. Another case is that the correlation between each pair of stocks is -0.8. But this case is invalid because if stock 1 is negatively correlated with stock 2 and stock 3, then stock 2 and stock 3 must be positively correlated with each other. Because, when value for stock 1 increases, then values for stocks 2 and 3 must decrease. So, the values for stock 2 and stock 3 vary in one direction. Hence stock 2 and stock 3 must be positively correlated. Therefore, this case where correlation between all three stocks is negative does not make sense. As further evidence, when you try to run a simulation, it generates an error as seen below: