[SOLVED] statistic /*Problem 1*/

/*Problem 1*/
/*Data set myclass.usmkt includes the overall U.S. market returns from 1927 to 2018. Imagine that you are a portfolio manager and
you are advising potential clients about investing in the market fund and the benefit of long-term investment.

Calculate average market returns for each month, i.e. average market return for January, that for February, , that for December.
Which month, on average, has the highest return? which month the lowest return?
Based on your calculation, what would you suggest your clients do in the month of May?

/*Problem 2 Construct a Tobins q factor using individual stock returns*/

/*The dataset myclass.tobinq contains the following three columns:
year
cusip number (stock ID number)
End-of-year individual stocks tobins q
Basically, Tobin q is the ratio of a firms market value over its intrinsic value.
It indicates if a firm is overvalued or undervalued: if the ratio is less than 1, the firm is considered undervalued;
if the ratio is larger than 1, the firm is considered overvalued.

The dataset myclass.crspdata contains the following columns:
date (year/month/day)
cusip number
price or bid/ask average
monthly returns
shares outstanding

Following Fama and Frenchs methodology to create a Tobins q factor:
1. At the end of every year (t), rank stocks based on their Tobins q ratio and form 10 portfolios.
2. With the data set myclass.crspdata, calculate the equally-weighted as well as the value-weighted portfolio MONTHLY returns for the holding periods,from July of year t+1 to June of year t+2:
Equally-weighted portfolio return is simply the arithmetic average of individual stock returns within the portfolio (caluclated for each month).
Value-weighted portfolio return is calculated as follows,
1). At the end of year t, for each portfolio, the weight of an individual stock is calculated by dividing its market value
by the sum of the market value of all the stocks within that portfolio. Note: market value = price multiplied with # of shares outstanding;
2). For EVERY month during the holding period(July of year t+1 to June of year t+2), within EACH portfolio,
multiply the weights of individual stocks with their corresponding returns. Then, simply sum up the
multiplications WITHIN EACH MONTH to obtain the value-weighted portfolio return.
3. Repeat the procedure until the end of sample data of myclass.tobinq.

Based on the returns of portfolios, calculate the average monthly returns and statistical significance
for the following portfolios:
1. the 1st portfolio (the undervalued portfolio that has the lowest tobins q ratios);
2. the 10th portfolio (the overvalued portfolio that has the highest tobins q ratios);
3. the zero-investment portfolio, i.e. the 10th portfolio minus the 1st portfolio, aka high minus low (Tobins q factor, TQF).

Is the average monthly return of TQF significantly different from zero?