Task 1: Stock Return and Portfolio Analysis

In the file named as “Stock.csv”, you have been provided with the daily prices of three stocks from 2012 to 2018. 

a. Plot and present the stock prices in time series with appropriate labels.

b. Calculate the log returns of all the three stocks and express them in percentages. 

Pls report the descriptive statistics of log returns of three stocks in Table 1. Pls change the names in Table 1 to the stock names in your file.

Table 1: Summary Statistics

c. Pls report the correlation matrix of log returns of three stocks in Table 1. Pls change the names in Table 1 to the stock names in your file.

Table 2: Correlation Matrix

d.    There is a file named as “FF3factors.csv” in your folder. Merge your stock data with the Fama French three factors data, which are all in percentages.  Pls create a new variable Stock.Rf for all the three stocks, which equals to the difference between log return of each stock and RF (available in the FF3factors.csv), and run a regression of :

Stock.Rf=α+βMkt.Rf+u.

Report the regression results for all the three stocks in tables (you can use only one table to summarize all the results or three separate tables).

e. Pls run regressions of:

Stock.Rf=α+β_1 Mkt.Rf+β_2 SMB+β_3 HML+u.

Report the regression results for all the three stocks in tables (you can use only one table to summarize all the results or three separate tables).

f. Pls make your comments by comparing the results in d and e.

g. If an investor would like to form a portfolio with a targeted expected return of 0.11% and achieve the minimized standard deviation by investing in these three stocks in the “Stock.csv” file. If the daily risk free rate is 0.02%, what is the Sharpe ratio of this optimal portfolio, given there is no short sale constraint? [hint: can use the library of “quadprog”] [pls provide your R code used to form the optimal portfolio in the end of the word file].

h. If an investor would like to form a portfolio with a targeted expected return of 0.11% and achieve the minimized standard deviation by investing in these three stocks. If the daily risk free rate is 0.02%, what is the Sharpe ratio of this optimal portfolio, given there is short sale constraint (i.e., you cannot short sell the stocks)? [hint: can use the library of “quadprog”]

i. By comparing your answer in g) and h), is there any difference in their Sharpe ratios? Why that’s the case?

j. Given there is no short sale constraint, pls draw an efficient frontier that satisfies the following conditions: 1. The range of the mean return of the portfolio is from 0.75*min of the mean return of three stocks to 1.25*max of the mean return of three stocks; 2. Pls create 500 optimal portfolios in this range; 3 Then pls plot all the risk-return combination of the 500 optimal portfolios (i.e., the efficient frontier). [Pls provide your R code in the end of word file]

stock-1

ff3factors