The SPDR S&P500 ETF's investment objective is to produce returns that match those of the S&P 500 Index. There also exist leverage and inverse leveraged ETFs having investment objectives that are multiples of that index. Specifically, these are the Direxion Daily S&P Bull 3x shares (ticker SPXL) that aims to return +3 times the daily index return and the Direxion Daily S&P Bear -3x Shares (ticker SPXS) that aims to return -3 times the daily index return. The spreadsheet data_PS_2_Fall2020.xlsx accompanies this problem set. There you will find daily prices and distribution amounts for these 3 ETFs. Use that data to answer the following questions.

1. [4 points] Use the daily prices and distributions to compute the daily returns to each ETF for the time period January 2017 to December 2019Note, the dividends appear on the ex-date, so the seller of the stock receives the dividend, not the buyer.
2. [3 points] Compute the arithmetic average daily returns to each of the funds.
3. [3 points] Compute the geometric average daily returns to each of the funds.
4. [2 points] Why does the geometric average return differ from the arithmetic average? To
5. what is that difference proportional?
6. [3 points] Compute the holding period return (across the full holding period) for each of the
7. funds.
8. [6 points] Assume that on the first day of 2017 you invested $100,000 in equal amounts of
9. SPXL and SPXS (i.e. use $50,000 to buy SPXL shares at the 01/02/2017 closing price, and $50,000 to do the same with SPXS).
10. What would that portfolio be worth at the end of December 31, 2019?
11. What would be the weights of SPXL and SPXS in the portfolio as of December 31,
12. 2019?
13. One might think since SPXL and SPXS return +3 and -3 times the daily returns to the
14. same index that the portfolio return would be 0%. Why is this not the case?