Q1 (ED futures): On Oct 5, 2011, you sold 10 Eurodollar futures contracts for Dec 2013 delivery at 98.995. You closed your position by buying 10 ED contracts at 99.015 on Jan 13, 2012. What is your gain or loss?
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F(Oct 5, 2011)=
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98.995
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F(Jan 13,2012)=
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99.015
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No of contracts =
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10
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Change in price quoted
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$ amount gain (loss)
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Show your calculations below:
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Q2 (T-Bill futures)
The spot discount rates for two T-bills, 80-day T-bill and 170-day T-bill, are given below.
A) Based on the two T-bills's discount rates, what should be the quoted equilbrium price of a 80-day futures contract? Assume $1,000,000 face value. Keep in mind the quoted price is 100 - (discount rate). What should be the dollar amount implied by the futures quoted price (the amount to pay or to be paid at settlement)?
B) You took 10 long T-bill futures contract for delivery in 80 days. It is now 20 days later since you took the long futures position and the T-bill futures for delivery in 60 days is quoted at 95.50. Calculate your gains(losses) on your position.
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Spot discount rates
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80-day T-bill
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6.00%
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170-day T-bill
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6.25%
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Face Value
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$1,000,000
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A)
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Dollar amount for the futures
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Price Quoted
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B)
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Gain(loss)
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Show your calculations below:
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Q3 (Treasury Bond Futures)
On September 10, 2009, 30-year U.S. Treasury Bonds futures for Dec 2009 delivery was traded at 116-20 at CBOT. On September 13, the futures was traded at 114-29. You opened your position by taking 10 long positions on the T-bond futures on Sept 10. As of Sept 10, the initial margin is $4,995 per contract and the maintenance margin is $3,700.
i) Calculate your gains (losses) on your position as of September 13.
ii) What is the highest price at which you will be required to deposit funds to your margin account (a margin call)?
iii) Would you have faced a margin call on September 13? If so, what is the amount to deposit?
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Dec 2009 T-Bond Futures Price
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9/10/2009
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116-20
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9/13/2009
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114-29
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Initial margin
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mce_markernbsp; 4,995
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Maintenance margin
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mce_markernbsp; 3,700
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No of contracts
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10
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i)
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Gain(loss)
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ii)
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Price triggering margin call
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iii)
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Amount to deposit
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Show your calculations below:
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Q4 (Stock Index Futures): On September 13, 2009, the S&P 500 Index futures settlement price was 1016.70 for December 2009 delivery contract. The actual S&P 500 index (spot market) was closed at 1003.35 on 09/13/2009. The dividend yield is estimated currently at 2.12% (source: https://www.indexarb.com/dividendAnalysis.html). The actual delivery date of the December contract is 12/19/2009. The LIBLOR rate is 3.675% on September 13, 2009, which can be treated as a risk-free rate.
A) Are the futures price and the spot index in equilibrium? That is, is there an arbitrage opportuity between the futures market and the spot market? What is the basis for your answer?
B) Show the steps to find any arbitrage profit opportunity. Calculate the arbitrage profit which should be zero if the market is in equilbrium, positive if not. Be sure to show your calculations step by step.
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S0=
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1,003.35
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9/13/2009
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T=
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97
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days
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12/19/2009
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f(0,T)=
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1,016.70
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Rf=
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3.675%
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DivYld
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2.120%
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A)
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Short Answer
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B)
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Arbitrage Profit amount?
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Show your explanation and calculations below:
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Q5 (Target Beta): An investment management firm wishes to decrease the beta of one of its portfolios under management from 1.15 to 0.65 for a five-month period. The portfolio has a market value of $200,000,000. The investment firm plans to use a futures contract priced at $102,500 in order to adjust the portfolio beta. The futures contract has a beta of 1.02.
A) Calculate the number of futures contract that should be bought or sold to achieve a decrease in the portfolio beta.
B) At the end of 5 months, the overall equity market is down 3.5%. The stock porfolio under management is down 4.025%. The futures contract is priced at $98,840.75. Calculate the value of the overall position and the effective beta of the portfolio.
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t=0
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t=5 mo
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S=
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$200,000,000
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-4.025%
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Beta(stock)=
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1.15
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Beta(tgt)=
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0.65
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Beta(fut)=
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1.02
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f=
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$102,500
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$98,840.75
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CHG(mkt)=
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1%
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-3.50%
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A)
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No of contract?
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Short or long?
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B)
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Value of position?
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Effective beta?
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Show your explanation and calculations below:
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Q5 (Target Portfolio) You expect to receive a cash inflow of $50 million in five months. Today, you want to take a synthetic stock position equal to $30 million and a synthetic bond position equal to $20 million. The stock would have a beta of 0.65 and the bond a modified duration of 10.5. A stock index futures contract with a beta of 1.01 is priced at $200,500. A bond futures contract with a modified duration of 8.5 is priced at $102,300.
A) How many bonds futures contracts and stock index futures contracts do you need to trade to achieve your desired synthetic positions in stocks and bonds?
B) Five months later when the futures expire, stocks have risen by 4.25% and bonds have declined by 2.5%. Stock index futures are priced at $213,741, and bond futures are priced at $100,230. What would be your net gain(loss) from your futures positions? Compare this with the change in the value of stocks and bonds during the five-month period.
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NOW
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ON EXPIRATION
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S=
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mce_markernbsp; 30,000,000
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4.25%
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B=
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mce_markernbsp; 20,000,000
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-2.50%
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Beta(target)=
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0.65
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Duration(target,modified) =
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10.5
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Beta(future)=
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1.01
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f(stock)=
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$200,500
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Duration(future)=
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8.5
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f(bond)=
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mce_markernbsp; 102,300
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A)
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Actual # of stock index futures contract
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Actual # of bond futures contract
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B)
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Net gain from futures
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Net gain from stocks and bonds
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Show your explanation and calculations below:
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