1. Use the monthly data (September 2013 - November 2014) provided on the closing prices for Gold (GLD), NASDAQ, Oil (USO) and Facebook (FB).
Date GLD NASDAQ USO FB
Sep-13 128 3771 37 50
Oct-13 128 3920 35 50
Nov-13 121 4060 33 47
Dec-13 116 4177 35 55
Jan-14 120 4104 35 63
Feb-14 128 4308 37 68
Mar-14 124 4199 37 60
Apr-14 124 4115 36 60
May-14 120 4243 38 63
Jun-14 128 4408 39 67
Jul-14 123 4370 36 73
Aug-14 124 4580 36 75
Sep-14 116 4493 34 79
Oct-14 113 4631 31 75
Nov-14 115 4713 29 74
a. What is the approximate value of mean absolute percentage error (MAPE) of forecasting based on 3 months moving average for GLD prices?
3.81%
8.74%
3.44%
8.54%
b. What is the risk as measured by the standard deviation of monthly return for Oil during the sample period?
7.90%
5.19%
2.80%
4.20%
c. What is the approximate value of mean absolute error (MAE) of forecasting based on 5 months moving average for GLD prices?
5.89
4.56
4.10
6.08
d. What is the correlation between prices of NASDAQ and Facebook during the sample period?
0.89
-0.54
0.73
-0.44
e. What is the mean monthly return for Oil during the sample period?
-1.60%
-0.68%
3.12%
1.64%
To answer these questions, we will use the given monthly data on the closing prices for Gold (GLD), NASDAQ, Oil (USO), and Facebook (FB) from September 2013 to November 2014.
a. To calculate the approximate value of mean absolute percentage error (MAPE) based on a 3-month moving average for GLD prices, follow these steps:
1. Calculate the moving average for each month by adding the prices of the current month and the two previous months, and divide the sum by 3.
2. Calculate the absolute difference between the actual GLD price and the moving average for each month.
3. Calculate the percentage error for each month by dividing the absolute difference by the actual GLD price and multiplying by 100.
4. Calculate the mean of the absolute percentage errors.
The options provided are 3.81%, 8.74%, 3.44%, and 8.54%. Perform the above steps and choose the value that matches the result.
b. To find the risk as measured by the standard deviation of monthly returns for Oil, follow these steps:
1. Calculate the monthly returns for Oil by finding the percentage change between the current month's price and the previous month's price.
2. Calculate the standard deviation of the monthly returns using the formula for population standard deviation.
The options given are 7.90%, 5.19%, 2.80%, and 4.20%. Perform the above steps and choose the value that matches the result.
c. To calculate the approximate value of mean absolute error (MAE) based on a 5-month moving average for GLD prices, follow these steps:
1. Calculate the moving average for each month by adding the prices of the current month and the four previous months, and divide the sum by 5.
2. Calculate the absolute difference between the actual GLD price and the moving average for each month.
3. Calculate the mean of the absolute differences.
The options given are 5.89, 4.56, 4.10, and 6.08. Perform the above steps and choose the value that matches the result.
d. To find the correlation between the prices of NASDAQ and Facebook during the sample period, use the correlation coefficient formula:
1. Calculate the mean of the NASDAQ prices and the mean of the Facebook prices.
2. Calculate the difference between each month's NASDAQ price and the mean NASDAQ price, and do the same for Facebook prices and the mean Facebook price.
3. Multiply the differences together for each month.
4. Sum up the multiplied differences and divide by the product of the standard deviations of NASDAQ and Facebook prices, respectively.
The options given are 0.89, -0.54, 0.73, and -0.44. Perform the above steps and choose the value that matches the result.
e. To calculate the mean monthly return for Oil during the sample period, follow these steps:
1. Calculate the monthly returns for Oil by finding the percentage change between the current month's price and the previous month's price.
2. Calculate the mean of the monthly returns.
The options given are -1.60%, -0.68%, 3.12%, and 1.64%. Perform the above steps and choose the value that matches the result.