MAF759 Analytical Methods

Please complete the following questions:
1. Calculate monthly discrete returns (hint: holding period returns) for the S&P 500 index, NASDAQ index, and Apple Inc. (APPL) stock prices, respectively.
2. Compute descriptive statistics for monthly Apple Inc. (APPL) stock prices, S&P500 index and NASDAQ index, respectively.
3. Construct the frequency distributions (including relative frequency and cumulative frequency) for APPL returns, S&P 500 index returns and NASDAQ index returns,respectively. Use 10 intervals.
4. What is the probability of the S&P 500 index returns above 10% What is the probability of the NASDAQ index returns being between 2% and 8%.
5. Is the distribution of monthly APPL returns Normal distribution Are the distributions of S&P 500 index returns and NASDAQ index returns different.
Provide evidences.
6. In order to predict the monthly APPL returns, your supervisor advised two simple linear regression models:
 Model A: Assuming a linear relationship between monthly APPL returns and
 S&P 500 index returns.
 Model B: Assuming a linear relationship between monthly APPL returns and
 NASDAQ index returns
6.1: For model A, test if the intercept coefficient is significant at the 5% level;Calculate 95% confidence interval for the slope coefficient.6.2: For model B, Predict the APPL return when NASDAQ index return being 2%, and calculate its 90 percent prediction interval.