Assignment
Question 1
After you merged both datasets as described in the Instructions: Compute the market capitalization as [abs(PRC) * SHROUT] for each stock in each month. Why are some prices negative? (You might need to lookup the definition of PRC in WRDS, for example with an internet search, to answer this question.)
Why can closing prices at time "t" be negative? [select every answer that you think is correct]:
Missing bid quotes
the specific stock is not trading on the current exchange at time t
negative prices are averages across bid and ask quotes
prices can be negative, if the companies liabilities are higher than its assets
Question 2
For each stock, compute the average excess return and the standard deviation over the period from January 2000 to December 2010 (to calculate such summary statistics the PivotTable is very useful). Which stock has the highest average excess return? (Reminder: excess return is the difference between the return and the risk-free rate)
Stock with PERMNO 82526.
Stock with PERMNO 82542.
Stock with PERMNO 76544.
Stock with PERMNO 86302.
Question 3
Now compute the Sharpe ratio for each stock over this period. Which stock looks most attractive to you in terms of the tradeoff between return and risk over this period?
Stock with PERMNO 76695, because it has the highest Sharpe ratio.
Stock with PERMNO 82542, because it has the highest Sharpe ratio.
Stock with PERMNO 82526, because it has the highest average excess return.
Stock with PERMNO 76695, because it has the highest average excess return.
Question 4
Do you observe any pattern regarding the Sharpe ratio of a stock and its average market cap (computed per PERMNO over the whole sample period)? Run a simple cross-sectional regression to check.
A smaller market cap is associated with a higher Sharpe ratio, and this relation is statistically significant (i.e., t-statistic is below -2 or above 2).
A smaller market cap is associated with a higher Sharpe ratio, but this relation is not statistically significant ( i.e., t-statistic is between-2 and 2).
A smaller market cap is associated with a lower Sharpe ratio, and this relation is statistically significant ( i.e, t-statistic is below -2 or above 2).
A smaller market cap is associated with a lower Sharpe ratio, but this relation is not statistically significant ( i.e., t-statistic is between-2 and 2).
Question 5
Now run a formal CAPM ("market model") time-series regression for each of the 100 firms (you can use the "LINEST" function in EXCEL to do so). Estimate the market model over the entire sample period. Which stock has the largest beta estimate? Insert the PERMNO of the stock with the largest Beta coefficient below.
Question 6
Make a scatter plot with on the vertical axis the historical average excess return of all stocks and on the horizontal axis the stock's beta estimates over the full sample period. Also add a linear trend line, which is the security market line (SML). Does this plot support the CAPM predictions?
Indicate every correct statement from the list below.
The estimated slope coefficient is positive, which is consistent with the CAPM.
The estimated slope coefficient is positive, which is NOT consistent with the CAPM.
The estimated intercept is positive, which is consistent with the CAPM.
The estimated intercept is positive, which is NOT consistent with the CAPM.
The estimated slope coefficient is negative, which is consistent with the CAPM.
The estimated slope coefficient is negative, which is NOT consistent with the CAPM.
The estimated intercept is negative, which is consistent with the CAPM
The estimated intercept is negative, which is NOT consistent with the CAPM
Question 7
Please indicate the Coefficient of determination (R2) from the regression in Question 6 (i.e. the estimated SML) that is closest to what you find:
6%
8%
10%
12%
Question 8
Now run a cross-sectional regression. Explain the wholesample average excess returns of each stock by the wholesample average MARKETCAP of each stock and the estimated beta (from Question 5). What do you find? Assume statistical significance is indicated by a t-statistic below -2 or above 2. Select every answer that corresponds with your findings.
I find a negative and statistically significant effect of Beta to explain excess returns.
I find a positive and statistically significant effect of Beta to explain excess returns.
I find a negative and statistically significant effect of Market Cap to explain excess returns.
I find a positive and statistically significant effect of Market Cap to explain excess returns.
I find a negative but statistically insignificant effect of Beta to explain excess returns.
I find a positive but statistically insignificant effect of Beta to explain excess returns.
Question 9
Now run a so called Fama-MacBeth regression (2nd step), that is: each month regress excess returns on MarketCap only, then compute the average coefficient on Market Cap as well as the Fama-MacBeth t-statistic, which is avg(X)/[stddev(X)/sqrt(T)], where: X is the monthly estimated slope coefficient when explaining Returns by MarketCap and T is the number of observations (the number of months in the sample).
Higher MarketCap is associated with higher returns and this relation is statistically significant (t-statistic below -2 or above 2).
Lower MarketCap is associated with higher returns and this relation is statistically significant (t-statistic below -2 or above 2) .
Higher MarketCap is associated with higher returns but this relation is not statistically significant (t-statistic below -2 or above 2) .
Lower MarketCap is associated with higher returns but this relation is not statistically significant (t-statistic below -2 or above 2) .
Question 10
As before, run a so called Fama-MacBeth regression and compute the Fama-MacBeth t-statistic. But this time explain Returns by MarketCap as of January for each year, i.e. in February to December you use the market cap estimated in January of each year for each stock.
Higher MarketCap is associated with higher returns and this relation is statistically significant (t-statistic below -2 or above 2)? .
Lower MarketCap is associated with higher returns and this relation is statistically significant (t-statistic below -2 or above 2) .
Higher MarketCap is associated with higher returns but this relation is not statistically significant (t-statistic below -2 or above 2) .
Lower MarketCap is associated with higher returns but this relation is not statistically significant (t-statistic below -2 or above 2).
Question 11
Of course, smaller stocks are also associated with higher risk. Hence, redo the Fama-MacBeth regressions, use the MarketCap as of January for each year, and the CAPM-beta (estimated over the whole sample) as a control variable, to explain monthly returns (as before).
Higher MarketCap is associated with higher returns and this relation is statistically significant (t-statistic below -2 or above 2) .
Lower MarketCap is associated with higher returns and this relation is statistically significant (t-statistic below -2 or above 2) .
Higher MarketCap is associated with higher returns but this relation is not statistically significant (t-statistic below -2 or above 2) .
Lower MarketCap is associated with higher returns but this relation is not statistically significant (t-statistic below -2 or above 2) .
Question 12
Are your results so far consistent with the data you received from Ken French's website (using data from Jan-2000 to Dec-2010)?
Yes, because the average return of HML is negative over this period
Yes, because the average return of HML is positive over this period
No, because the average return of HML is negative over this period
No, because the average return of HML is positive over this period
Yes, because the average return of SMB is negative over this period
Yes, because the average return of SMB is positive over this period
No, because the average return of SMB is negative over this period
No, because the average return of SMB is positive over this period
Question 13
Report the Fama-MacBeth test statistic, i.e. sqrt(N)*avg(X)/stddev(X), where N is the number of observations (the number of months), and X is the monthly estimated slope coefficient on MarketCap when explaining Returns by MarketCap and CAPM-Beta (i.e. the slope coefficients from the previous regression).
Round the value to two decimal digits, and use the dot to separate decimal from non-decimal digits, i.e. enter like:
12.23
Use all slope coefficients from 2005 (i.e. N=12).
Attachment:- Sample_Data_wrds.rar