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).

Solutions

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

Next > < Previous

Related Solutions

Construct a portfolio from the following assets: - SPY (SPDR S&P 500 ETF Trust) - BND...

Construct a portfolio from the following assets: - SPY (SPDR S&P 500 ETF Trust) - BND (Vanguard Total Bond Market ETF) - IYR (iShares US Real Estate ETF) - SHV (iShares Short Treasury Bond ETF) - DBC (Invesco DB Commodity Tracking) With an investment period of 01/01/2014 to 01/01/2019, the goal is to achieve a target return of 4% with minimum volatility. Estimate expected returns and volatility from the 5-year time series. Assume a portfolio of $100 million, allocating no...

You have invested $100,000 in the US stock market via the S&P 500 Depository Receipts ETF...

You have invested $100,000 in the US stock market via the S&P 500 Depository Receipts ETF (SPY) which tracks the S&P 500 Index. You are going to pull out your money once your investment triples in value (i.e. becomes $300,000). Assume, that the S&P 500 Depository Receipts ETF (SPY) which you have invested in earns a 9% per annum rate of return. How many years is it expected to be until you are going to pull out your money? Round...

You currently own SPY, which is an ETF replicating the S&P 500 index. You consider adding...

You currently own SPY, which is an ETF replicating the S&P 500 index. You consider adding another ETF to your portfolio and your options are: TLT (iShares 20+ year bonds), DIA (Dow Jones Industrial Average SPDR), and GLD (SPDR Gold Shares). The table below gives you the correlation matrix for SPY, TLT, DIA, and GLD. Which is the best (worst) ETF to combine with SPY to obtain the maximum benefit from diversification? Correlation matrix SPY TLT DIA GLD SPY 1...

Part 1: The following table shows historical stock prices of Spider S&P 500 ETF and Amazon...

Part 1: The following table shows historical stock prices of Spider S&P 500 ETF and Amazon stock. The prices listed are the adjusted closing prices on the first day of each month from 9/1/2016 to 8/1/2018. The monthly risk-free rates for the T-bills are also listed in the table. Using the price data, calculate the monthly returns for the Spider S&P 500 ETF and the Amazon stock, respectively, from September 2016 to July 2018 (note that the monthly return for...

1. Compare the expenses on two mutual funds that follow the same index: S&P 500. The...

1. Compare the expenses on two mutual funds that follow the same index: S&P 500. The first fund is PEOPX (Dreyfus S&P 500 Index) and it's expense ratio is 0.5% per year. The second fund is VFIAX (Vanguard S&P 500 Index) with an expense ratio of 0.05% per year. 2. Assume that both funds will return 10% per year until YOUR retirement (you will have your own number of years here) and that you will invest $5,500 per year starting...

1.Portfolio Investment. An investor has decided to invest $13,000 in an S&P 500 index fund and...

1.Portfolio Investment. An investor has decided to invest $13,000 in an S&P 500 index fund and $7,000 in 10-year treasury bonds (T-bonds). The index fund is expected to have an average annual rate of return of 6.8%. The T-bonds are guaranteed to pay annual interest of 0.70% (as of Oct 2, 2020). Assuming the stock market return is as the investor expects, how much will this $20,000 investment be worth the end of 10 years? 2.Refer to the Portfolio Investment...

P Company S Corporation Revenues $(700,000) $(400,000) Expenses 400,000 300,000 Investment Income Not given -0- Dividends...

P Company S Corporation Revenues $(700,000) $(400,000) Expenses 400,000 300,000 Investment Income Not given -0- Dividends declared 80,000 60,000 Retained Earnings, 1/1/18 (600,000) (200,000) Current Assets 400,000 500,000 Equipment 700,000 300,000 Copyrights 900,000 405,000 Royalty Agreements 600,000 1,000,000 Investment in S Not given -0- Liabilities (500,000) (1,380,000) Common Stock (600,000) ($20 par) (200,000) ($10 par) Additional Paid-in-Capital (150,000) (80,000) On January 1, 2018, P acquired all of S's outstanding stock for $680,000 cash. At the date of acquisition, copyrights (with...

Subjects