The ProShares Ultra QQQ (ticker QLD) is a leveraged ETF that seeks daily investment returns that, before expenses and fees, correspond to twice (2x) the daily performance of the NASDAQ 100 Index. Assume an investor purchases 100 shares of QLD for $47.60. On the first day of the holding period, the NASDAQ 100 decreased 3.10%. On the second day, the index decreased 1.0%, and on the third day the index increased 2%.
a. What is the arithmetic average return on the NASDAQ 100 over the 3-day holding period?
b. What is the geometric average return on the NASDAQ 100 over the 3-day holding period?
c. Assume the ETF achieves exactly the stated target of 2 times the daily return on the NASDAQ 100. If this happens, calculate the 3-day holding period return on the levered ETF.