A. Download DAILY adjusted closing prices [from 7/1/2008 to 10/1/2020] from Yahoo Finance for the following tickers: SPY, GBF, SDS, TBT, EEM.

B. Plot historical prices for the five ETFs on the same line chart.

[Note: remember to compute returns on the five ETFs first for the following questions. The return series should start at 7/2/2008]

[Hint: SDS and TBT are leveraged ETFs]

C. A portfolio is designed to gain exposure to US and international stocks and bonds by allocating 40% to SDS, 30% to TBT, and 30% to EEM. Compute the mean, standard deviation, skewness, kurtosis, and Sharpe Ratio of this portfolio and the three ETFs (SDS, TBT, and EEM). Sharpe Ratio is defined as the ratio of mean to standard deviation (assuming risk free rate is zero).

D. A 130/30 trading strategy means shorting an asset up to 30% of the portfolio value and then taking the funds to long positions on other assets. Consider a 130/30 portfolio that is 70% SDS, -30% TBT,and 60% EEM. Compute the mean, standard deviation, skewness, and Sharpe Ratio of this portfolio. Compare this portfolio to the one in C., what do you observe?

E. A portfolio is constructed by investing 60% in SPY and 40% in GBF. Compute the mean, standard deviation, skewness, and Sharpe Ratio of this portfolio and both SPY and GBF. Compare this portfolio to the one in C. and D., what do you observe? [Hint: How much return each fund can get for one unit of risk?]

F. Regress SDS on SPY and TBT on GBF and draw the following two scatter plots: SPY vs SDS and TBT vs GBF. What are your observations?

G. Janice wants to buy stock A whose return shows a mean of 2% and a standard deviation of 4% based on 250 daily returns. At the .05 level of significance (or 95% confidence level), she would like to test if the stocks daily return is equal to 5%. (a) write out the null and alternative hypothesis. (b) Compute the test statistic. (c) Should she reject or fail to reject the null hypothesis?