Assignment:
1. Futures/Forwards
Construct the theoretical arbitrage bounds for the futures price if the bid-ask spread is e and lending rate is 8 and the borrowing rate is s. Assume s>8.
Calculate the upper and lower arb-bounds for a 3-month futures price ïf the spot is $50, the bid-ask spread is 75 basis points, the risk-free rate is 4%, and the borrowing and lending rates are 150 basis points above and below the risk-free rate respectively.
Using the current spot and futures prices (settlement for all available contracts) for SPX and the Nikkei 225, calculate the implied continuous dividend rate for each index, assuming no transaction costs.
Assume you entered into a 5 short December (2019) futures contracts for SPX at today price, but on January 31% 2019; use February daiïly price levels and show your daily margin account balances.
How would those balances look different if you were in the dollar equivalent value of a forward contract.
Can we claim that the SPX is a better investment than the Nikkei based on the futures curve
2. Convenience Yields
a. Explain the relationship between storage costs and convenience yield?
b. Are forward prices upward or downward biased in the energy markets? Explain?
c. What is the average daily convenience yield for the crude oil prices using first three monthly futures contracts on WTI Cushing spot and 3-month Treasury rates for the past 10 years?
3. Swaps
a. Assuming you had 10 million dollars to invest 15 years ago, show the cumulative value of the following portfolios in a nice line graph.
• Buy and hold S&P 500 index portfolio
• A portfolio that invests in a receive equity (S&P 500)/ pay floating swap portfolio, assuming quarterly payments and Aaa rates using 50% margin.
b. Assume the swap was initiated at zero, show the value of the swap at each quarter.
UNSW:
4. You are the manager ofa highly levered company. All the debt will mature in a year. If the value of the company is higher than the debt in one year, you wilÏ pay off the debt. If the value of the company is less than the debt, you will declare bankruptcy, and the debtholders will own the company.
a. Express your position as an option on the value of the company and draw the payoff diagram
b. Express the position of the debtholders in terms of options on the value of the company and draw the payoff diagram
c. What can you do to increase the value of your position?
5. Download the current prices from yahoo for December 2019 options on SPY.
a. Using all the options for both call and puts, project forward the required rate of return needed to break even on each strike and plot the rates of return across strike prices (two separate graphs, one for calls/one for puts)
b. Explain why the returns are not equal across the strike prices?
c. Calculate and show the put call parity values at each strike using mid-point prices.
d. Now incorporate the bid-ask spreads, Does arbitrage still exist?