Stock Index Futures

Stock Index Futures

• A stock index future is a contract to buy or sell a stock market index (portfolio of individual stocks) underlying the futures contract
• Stock index futures are generally settled in cash
• Not all stock indices can be used for futures trading
  • The arbitrage bound should not be too wide
  • The market in individual stocks that comprise the index should be liquid

Standard & Poor's 500 Stock Price Index Futures Example

• Underlying: Standard & Poor's 500 Stock Price Index (S&P 500)
• Contract size: $250 times the S&P 500 Index
  • E-mini contract size: $50 times the S&P 500 Index
• Contract month: 8 months in the March, June, September, December cycle plus 3 additional December contracts
  • E-mini contract: 5 months in the quarterly cycle (March, June, September, December)
• Last trade: 3:15 p.m. on Thursday prior to the 3rd Friday of the contract month.
  • E-mini contract trading can occur up to 8:30 a.m. on the 3rd Friday of the contract month
• Final settlement price: Opening price of the index on the 3rd Friday of the contract month
• Quotes: S&P 500 E-mini Stock Index Futures, CME, 12.3.2018 include
  • March 18: Open 2784.00, High 2800.50, Low 2779.00, Last 2783.00, Settle 2784.00, Volume 1,210,960 Open interest 2,313,022
  • June 18: Open 2788.75, High 2805.25, Low 2783.75, Last 2788.25, Settle 2789.00, Volume 1,644,022 Open interest 1,166,354
  • Sept 18: Open 2800.00, High 2812.25, Low 2791.75, Last 2795.50, Settle 2796.25, Volume 2,062 Open interest 15,875
  • Dec 18: Open 2805.00, High 2813.00, Low 2799.50, Last 2800.50, Settle 2802.00, Volume 53 Open interest 24,922
  • March 19: High 2808.75, Last 2808.75, Settle 2809.00, Volume 3 Open interest 41
• The maintenance margin for S&P 500 E-mini Stock Index Futures is 5,800 USD
• Cash Market (S&P 500 Index): 2,783.02

DAX Stock Price Index Futures Example

• Underlying: DAX 30 Stock Price Index
• Contract size: €25 times the DAX 30 Index
• Contract month: 3 nearest months in the cycle March, June, Sep, Dec
• Last trading day: 3rd Friday of the expiration month, if that is an exchange day; otherwise the exchange day immediately prior to that Friday
• Daily settlement: Prices for the current maturity month are derived from the volume-weighted average of the prices of all transactions during the minute before 17:30 CET, provided that more than five trades took place within this period
• Final settlement: Cash settlement based on the final settlement price
• Final settlement price: Established by Eurex on the Final Settlement Day of the contract (=last trading day) and is determined by the value of the respective index, based on Xetra auction prices of the respective index component shares
  • The intraday auction starts at 13:00 CET (for MDAX component shares at 13:05 CET)
  • For the remaining maturity months, the Daily Settlement Price for a contract is determined based on the average bid/ask spread of the combination order book
• Quotes: Dax Stock Index Futures, Eurex, 12.3.2018 includes
  • Mar 18: Open 12,435.0, High 12,476.0, Low 12,357.5, Last P. 12,398.0, Settlement Price 12,425.0, Traded contracts 112,482, Open interest 139,012
  • Jun 18: Open 12,443.5, High 12,487.0, Low 12,374.5, Last P. 12,380.0, Settlement Price 12,439.5, Traded contracts 45,867, Open interest 42,308
  • Sep 18: Open 12,430.5, High 12,433.0, Low 12,360.0, Last P. 12,420.0, Settlement Price 12,425.0, Traded contracts 72, Open interest 1,053
• Cash Market (Dax Index): 12,418.39

Options to take the market risk of a particular stock market index

• Buying all individual shares comprised in the index (in line with the weighting of the index) on the spot market
• Buying stock index futures contracts
• Buying futures contracts has the advantage of no funding costs for the cash purchase (depart from margin account requirements) but the disadvantage of no dividend income

No-Arbitrage Equation for Stock Index Futures

• F0,T = S0 ⋅ (1 + r0,T ) − ΣDivj ⋅ (1 + rtj,T)
  • ΣDivj ⋅ (1+rtj,T) is the value of all dividends paid between t=0 (today) and t=T expiration of the contract) on a portfolio that mimics the index at time t = T
  • N is the number of dividend payments between t = 0 and t = T
  • r0,T is the spot rate between t = 0 and the expiration of the contract (t = T)
• Example: Suppose the S&P500 spot index is 1,122, to calculate the no-arbitrage price for a futures contract with a remaining time to maturity of 0.2 years the future value of expected dividends on the S&P500 till the last trading day of this contract amounts to 3.3 index points and the corresponding spot rate is 1.5% p.a., therefore
  • No-arbitrage futures price: F0,T = 1,122 ⋅ (1 + 0.015 ⋅ 0.2) − 3.3 = 1,122.07
• If d0,T is the dividend yield rate, the no-arbitrage equation changes to
  • F0,T = S0 ⋅ (1 + r0,T − d0,T ).
• Then the arbitrage free futures price is given by
  • F0, T = 1,122 ⋅ (1 + 0.015 ⋅ 0.2 − 0.003 )= 1,122.
• If the index is a performance index (like e.g. the DAX index) dividends are already included in the spot market price of the underlying instrument (the spot index value) and the no-arbitrage relationship can be reduced to
  • F0,T = S0 ⋅ (1 + r0,T ).
• If the arbitrage equations are violated arbitrage opportunities exist

The Basis of a Stock Index Futures Contract

• The basis (S0 - F0,T) can be positive or negative
• Negative basis (S0 < F0,T), negative cost of carry:
  • Funding costs > income from the spot market position (i.e. dividends).
  • The futures price is higher, the higher interest rates and the lower dividends are
• Positive basis (S0 > F0,T), positive cost of carry:
  • Funding costs < income from the spot market position (i.e. dividends).
  • The futures price is lower, the lower interest rate and the higher dividends are

Hedging

• The risks of an equity portfolio comprise on the one hand company-specific risks (unsystematic) and on the other hand overall market (systematic) risk
  • Unsystematic risks can be reduced mainly by holding a broadly diversified portfolio
  • Market risk can be hedged using index instruments
• The relationship between the return on a portfolio of stocks and the return on the market (i.e. a particular index) is described by the parameter β
  • β measures the sensitivity of an equity position and the corresponding stock (market) index, and characterizes the amount of systematic risk of the equity position
• Only the systematic (and therefore not the total risk) of an equity position can be managed via stock index futures contracts
  • The unsystematic risk of an equity position remains unaffected by futures transactions!
• The higher the unsystematic risk component is, the lower is the hedge efficiency
• Reasons for a high unsystematic risk component are
  • A badly diversified equity portfolio
  • The wrong stock index futures contract
• The stock market index futures contract which is closest to the characteristics of the equity portfolio should be used in hedging transactions
  • This is typically the "local" stock market index futures contract of a particular stock market
• The number of contracts (N) can be calculated by:
  • N = (MVP/MVUL) ⋅ βP
    • MVP = Market value of the portfolio
    • MVUL = Contract size (=market value of the underlying for one contract)
    • βP = Beta of the portfolio relative to the index

Short Hedge

• Used to hedge an existing equity portfolio (long spot market) against falling equity prices, stock index futures can be sold
• Example: In April 2002, a portfolio manager expects a significant price decline in the US equity market in the coming months
  • She manages a broadly diversified portfolio of US equities valued at $5,450,000
  • The beta factor of this portfolio, measured relative to the S&P500 index, is 1.20
  • The S&P500 is trading at 1,105 points (S0)
  • The portfolio manager sells 118 September 2002 contracts of the S&P 500 Mini Futures at 1,108 (F0,T) to hedge the equity portfolio against price fluctuations
  • The number of contracts is calculated according to: N= (MVP/MVI) ⋅ βP = ($5,450,000/1,105*$50) ⋅ 1.2 = ($5,450,000/$55,250) ⋅ 1.2 = 118.37
• Now the share prices have fallen (as they did), and the S&P500 is trading at only 890 points (ST) in September 2002
  • The value of the equity position has fallen to $4,177,000
• The investor closes out the S&P500 Mini Futures position shortly before maturity, by buying back the September contract at a price of 891 (FT)
  • Equity position outcome: Value in April $5,450,000, Value in September $4,177,000, Loss -$1,273,000
  • S&P500 Mini Futures position outcome: Sale in April (118 X 1,108 X $50) $6,537,200, Closing out in September (118 X 891 X $50) $5,256,900, Profit $1,280,300
  • The portfolio manager achieves the following overall outcome: Profit on the S&P500 Mini Futures position $1,280,300, Loss on the equity position -$1,273,000, Total change $7,300
  • The overall outcome of the investor’s hedging strategy is a profit of $7,300

Long Hedge

• Used if Equity prices are expected to rise, a long hedge can be used to lock in the current price level
• Example: An investor expects prices on the German equity market to rise
  • The DAX Index is trading that 2,605 points in March 2003
  • The investor plans to build up a diversified equity position amounting to €2,700,000. The beta factor of the planned portfolio will be 1.3
  • The funds required for the investment are tied up in a time deposit that does not mature for three months
  • The investor buys 54 June 2003 contracts of the DAX Futures at 2,623 to lock in the current price level
    • The number of contracts is calculated according to: N = (MVP/MVUL) ⋅ βP = (EUR 2,700,000/2,605*EUR 25) ⋅ 1.3 = (EUR 2,700,000/ EUR 65,125) ⋅ 1.3 = 53.90
  • Share prices rise until June 2003 and the DAX reaches 3,370 points in June 2003
  • The June DAX Futures position is sold later before maturity at a price of 3,375 points Equity position outcome: Value in March€2,700,000, Value in June -€3,731,000, Additional investment -€1,031,000
  • DAX Futures position outcome: Purchase in March (54 *2,623 *€ 25) €-3,541,050, Sale in June (54 *3,375 *€ 25) €4,556,250, Profit €1,015,200
  • The investor realizes the following overall outcome: Profit on the DAX Futures position €1,015,200, Additional investment required for the portfolio -€1,031,000, difference -€15,800

Changing the Beta

• Investors can change the beta factor of their portfolio depending on individual market expectations
• If the beta is not (or is no longer) in line with the desired value, they can manage the resulting market risk by buying or selling index futures
• When the market trend is bullish investors can increase the beta factor by buying index futures, to reap greater benefits from the anticipated rally
• When the market trend is bearish investors can reduce the beta factor by selling index futures, to reduce their (expected) losses
• In above short hedge example a portfolio manager needs 118 S&P500 Mini Futures contracts to reduce the beta of the (existing) portfolio to zero
  • To reduce the portfolio beta from 1.2 to 0.6, she only needs to go short 59 contracts rather than 118
• A long position of 59 contracts should be taken to increase the portfolio beta from 1.2 to 1.8 - Increasing the beta is appropriate, if equity prices are expected to rise
• The formula to reduce the beta (decrease in risk) of the portfolio from βold to βnew (βold > βnew) a short position is
  • N = (MVP/MVUL) ⋅ (βold − βnew )
• The formula to increase the beta (increase in risk) of the portfolio from βold to βnew (βold < βnew) a long position is
  • N = (MVP/MVUL) ⋅ (βnew − βold )

Bond Futures

• Main Bond Futures contracts include
  • Euro Bund Futures - EUREX 190.3 (2013) 179.1 (2014)
  • Euro Bobl Futures - EUREX 129.5 (2013) 113.6 (2014)
  • Euro Schatz Futures - EUREX 95.5 (2013) 71.4 (2014)
  • 30Y US-Treasury Bond Futures - CBOT 98.0 (2013) 93.2 (2014)
  • 10Y US-Treasury Note Futures - CBOT 325.9 (2013) 340.5 (2014)
  • 5Y US-Treasury Note Futures - CBOT 175.3 (2013) 196.4 (2014)
  • 2Y US-Treasury Note Futures - CBOT 57.8 (2013) 71.8 (2014)

Eurex Bond Futures Contract Specification

- Buxl Futures: German Federal Government Bonds (Bundesanleihen), Maturity 24-35 years
- Bund Futures: German Federal Government Bonds (Bundesanleihen), Maturity 8.5-10.5 years
- Bobl Futures: German Federal Government Bonds (Bundesanleihen); German Federal Debt Obligations (Bundesobligationen); German Federal Treasury Notes (Bundesschatzanweisungen, Schatz futures only), Maturity 4.5-5.5 years
- Schatz Futures: German Federal Government Bonds (Bundesanleihen); German Federal Debt Obligations (Bundesobligationen); German Federal Treasury Notes (Bundesschatzanweisungen, Schatz futures only) , Maturity 1.75-2.25 years
- Contract size: €100,000
- Delivery months: Up to 3 successive months within the cycle March, June, September, and December
- Delivery day: 10th calendar day of the respective month, if this day is an exchange trading day otherwise, the immediately following trading day is used
- Last trading day: 2 exchange trading days prior to the delivery day of the relevant month (trading ends at 12:30 CET)
- Minimum issue amount: €5 Billion

Bond Futures Example Quote

- Example Quote: Jun 18 157.00, 157.36,    156.91, 157.32, 157.27    440,187 1,824,378
- Example Quote: Sep 18 156.80 156.80, , 156.80  156.80,  156.84, 1, 141
- Example Quote: Dec 18, 156.84

Conversion Factor

• LTIR futures: physical delivery
  • The holder of the short position has the obligation to deliver the underlying security, and the holder of the corresponding long position must accept delivery against payment of the delivery price
  • The Bund Futures contract provides for the holder of the short position to choose to deliver any German Federal Government bond that has a maturity of 8.5-10.5 years
  • When a particular bond is delivered, its conversion factor defines the price received by the party with a short position
• The delivery price of the bond is calculated as follows:
  • Delivery price = FT⋅CF + AI
    • CF = conversion factor of the bond delivered
    • AI = accrued interest since the last coupon date on the bond delivered
    • FT = futures price at maturity (final settlement price)
  • The conversion factor creates a price at which a bond would trade if its yield were 6% p.a. (Buxl: 4% p.a.) on delivery
  • The conversion factor is necessary because the bonds eligible for delivery are non-homogeneous. They have the same issuer, they vary by coupon level, maturity, and therefore price
  • For Bund Futures
    • Expiry month Jun 2018 DE0001102416 0.25 15.02.2027 0.619489
      • DE0001102424 0.5 15.08.2027 0.62028
      • DE0001102440 0.5 15.02.2028 0.604713
    • Expiry month Sep 2018

      • DE0001102424	0.5	15.08.2027	0.628154
        

      • DE0001102440 0.5 15.02.2028 0.612345

Assumptions

• Assumptions for Conversion Factor: yield curve is flat at Delivery and the Level = 6% p.a. Buxl = 4% p.a.
  • This might not always be the case

Cheapest to Deliver (CTD)

• The Futures prices will track the deliverable bond with the greatest amount of maturity which is the Cheapest to Deliver (CTD)

Formulae

• The party with short position gives the Zero Price
  • F₁ = S₁/CF
  • Modified Duration Method
• To calculate the zero basis futures price FT
  • Basis = ST − FT ⋅ CF = 0
  • F₁ = S₁/CF
• Hedge ratio
  • N = (MVP/MVCTD)*(MDP/MDCTD)*CFCTD
  • Where
    • MDP = is Modified duration of the bond portfolio
    • MDCTD = Modified duration of the CTD bond:
    • MVP = Market value of the bond portfolio
    • MVCTD =Market value of CTD bond with face value equal to size of one contract (e.g., €100,000 for BUND futures contracts)
    • CFCTD = Conversion factor for CTD bond

The CTD Bond

• Bond for the December 2000 contract has the following characteristics:
  • Price = 94.88
  • Conversion = 0.899414
  • Modified duration = 7.2%
  • ( 20,000,000/94,8808.7/7.2) 0.899414 = 229.1

Expectation Management

• Till November 2000 Interest rates may either Drop or increase . In this case
  • CTD increased to 98.55 = BUND increased and Market Value increased to 20,9000
• August 2000 105.4 24,136,600
• November 2000 109.5 25,075,500
  • The net change = 900,00= - 938,880 = -38,9K

Differences between perfect Hedge and Cross Hedge

 - The cash position may be lost

• Cross Hedge does not precisely hedge the performance of the portfolio.

Money Markets Futures

• Exchange and Mio numbers of Important Contracts listed
  • 3M Euro Dollars: 517.3 in 2013 and 66,4.4 in 2014
  • 3M EUROBOR (Liffe) 178,8K in 2012
  • • Months EUROBOR 0.3 in 2013 and 0.2 in 2014
• Underlining contracts on Euromarkets is timed deposit and the rate is the 3M EUROBOR
  • Time contracts are a time lock based on a rate that locks in and then prices sold are calculated

Time Frame Comparisons

• Dollar futures are CM with a rate of M
• EUROBOR are LIFFE for 1 Mill €. With 40 month quarterly and 28th delivery on a 6-month consecutive cycle.

Final Settlement

• cash at a set price on that day. The last day is banks days to WED of a contract worth
  • EDC = 100-LIBOR
  • EDC - 100 - Price +10 .0 on that dat.
  • Where rates are to be QUOTED before the market is before the expire price of future that is, FO.T 100: = 3M Future R

Interest Rates

• The futures price on these instruments is 100 - The 3MR The rate is interest that locked in

CME Info

• Stats on Trade data are listed ,

General Rules

• On a Long Position . there is profit when trade volume increases / interest rates descrese. The converse is also true.
• Profits/Losses equal changes in payments is 3M time to 1 million by future price
• Each Basis Point translates into Gain or loss of 25K / 25K per BPOR for each one rate.
• When we assume that AU 200 was bought / Sold at 8th for 93.3 If market decrease = Long lost and short won as future decrease to the point to 93.3 /
• This Loss exactly = interest payment 3M
• By going short ER - You would make money as interest = to pay will have an offset. And VICE Versa
• For instance in a 3month period we can see that Interes rates decreased from 6%pa to 4% Pa that translated to -1750. Net decrease .
  - In second = increased from 9% -1%4. 25*230 +5750 (Increase to 1)

Formulae for Payments

• The formulae to calculate this is 9 % of 4% = .225 And vice versa In the end though the firm payed roughly = 3k The 6.7pa is in every scenario allowing firm in borrowing