The Daily S&P 500® Bull 3x ETF seeks daily investment results, before fees and expenses, of...

The Daily S&P 500® Bull 3x ETF seeks daily investment results, before fees and expenses, of 300% of the performance of the S&P 500® Index and Daily S&P 500® Bear 3x ETF seeks daily investment results, before fees and expenses, of 300% of the inverse (or opposite) of the performance of the S&P 500® Index. For the purposes of this question, disregard the effects of expenses and fees. Let the returns on S&P 500® Index on three consecutive days be, 5%, -5% and 1%. Then the ratio of the cumulative return over the three day period on, Daily S&P 500® Bull 3x ETF to the cumulative return on S&P 500® Index over the same period is X(round your answer to 2 decimal places). Whereas the ratio of cumulative return over the three day period on, Daily S&P 500® Bear 3x ETF to the cumulative return on S&P 500® Index over the same three day period is Y (round your answer to 2 decimal places).

Expert Solution

Part A - Ratio of (cumulative return on Daily S&P 500® Bull 3x ETF) to the (cumulative return on S&P 500® Index):

3 Day return of S&P 500® Index = 5%, -5% and 1% (Let S&P 500® Index be on 100 on day 1):

100 + 5% = 105
105 - 5% = 99.75
99.75 + 1% = 100.75

Hence the cumulative return on S&P 500® Index is 0.75%.

This can also be calculated by formula [[(1+5%)*(1-5%)*(1+1%)] -1]*100 = 0.75%

3 Day return of Daily S&P 500® Bull 3x ETF = 15%, -15% and 3%:

Cumulative return on Daily S&P 500® Bull 3x ETF = [[(1+5%)*(1-5%)*(1+1%)] -1]*100 = 0.68%

Ratio of (cumulative return on Daily S&P 500® Bull 3x ETF) to the (cumulative return on S&P 500® Index) = 0.68/0.75 = 0.91:1 = 91:100

Part B - Ratio of (cumulative return on Daily S&P 500® Bear 3x ETF) to the (cumulative return on S&P 500® Index):

3 Day return of S&P 500® Index = 5%, -5% and 1% (Let S&P 500® Index be on 100 on day 1):

100 + 5% = 105
105 - 5% = 99.75
99.75 + 1% = 100.75

Hence the cumulative return on S&P 500® Index is 0.75%.

This can also be calculated by formula [[(1+5%)*(1-5%)*(1+1%)] -1]*100 = 0.75%

3 Day return of Daily S&P 500® Bear 3x ETF = -15%, +15% and -3%:

Cumulative return on Daily S&P 500® Bear 3x ETF = [[(1-15%)*(1+15%)*(1-3%)] -1]*100 = -5.18%

Ratio of (cumulative return on Daily S&P 500® Bear 3x ETF) to the (cumulative return on S&P 500® Index) = -5.18/0.75 = -6.91:1 = -691:100

jeff jeffy answered 1 year ago

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