1. Investment Analysis and Portfolio Management Futures Market and Risk Management
Attila Odabasi
Main Points:
Motivation
Forward Contracts
Future Contracts
Valuation of Forwards and Futures
Applications

2. Futures and Forwards
Forward - an agreement calling for a future delivery of an asset at an agreed-upon price
Futures - similar to forward but has standardized terms and is traded on an exchange.
Key difference in futures
Futures have secondary trading (liquidity)
Marked to market
Standardized contract terms such as delivery dates, price units, contract size
Clearinghouse guarantees performance

3. Types of Contracts Agricultural commodities
Metals and minerals (including energy contracts)
Financial futures
Interest rate futures
Stock index futures
Foreign currencies

4. Trading With and Without a Clearinghouse
The clearinghouse eliminates counterparty default risk; this allows anonymous trading since no credit evaluation is needed. Without this feature you would not have liquid markets.
The clearinghouse eliminates counterparty default risk; this allows anonymous trading since no credit evaluation is needed. Without this feature you would not have liquid markets.

5. Mechanics- The Clearinghouse and Open Interest
Clearinghouse - acts as a party to all buyers and sellers.
Seller of the contract for the long position
Buyer of the contract for the short position
A futures participant is obligated to make or take delivery at contract maturity
Closing out positions
Take or make delivery
Reversing the trade
Most trades are reversed and do not involve actual delivery
Open Interest
The number of contracts opened that have not been offset with a reversing trade: measure of future liquidity
Avoiding delivery: It is common to have your broker automatically close out your position on the last trading day before delivery becomes an obligation, or to roll your contract over to the next closest expiration contract. Over 90% of futures contracts do not result in delivery. For stock index contracts, the contracts are cash settled only and no delivery can take place. Why this doesn’t really matter is explained after the marking to market example.

6. Key Terms for Futures Contracts
The Futures price: agreed-upon price paid at maturity
Long position: Agrees to purchase the underlying asset at the stated futures price at contract maturity
Short position: Agrees to deliver the underlying asset at the stated futures price at contract maturity
Profits on long and short positions at maturity
Long = ST – F0
Short = F0 - ST
F = Futures price, S = spot price
At contract maturity T: FT= ST
The book says spot price at maturity and this is correct due to convergence between the futures and the spot price at maturity.

7. Ex: Future Contract on oil
NYMEX crude oil (light) futures with delivery in Dec at a price of $75.06/b on July 27, 2007 with 51,475 contracts traded
Each contract is for 1,000 barrels
Tick size: $0.01 per barrel, $10 per contract
Initial margin: $4050
Maintenance margin: $3,000
No cash changes hands today (contract price is $0)

8. Ex: Future Contract on oil
NYMEX crude oil (light) futures with delivery in Dec at a price of $75.06/b on July 27, 2007
Each contract is for 1,000 barrels
F0 on July 27 = 75.06$/b
Contract value= 75,060 $
ST on July 27 = 77$/b
Long-position Profit= (77 – 75.06)x1000= 1940$
Short-position Loss= (75.06 – 77)x1000= -1940$

9. Payoff Diagram, Dec 2007 Contract
Long position (buy) Short position (sell)
$ Profit
Long Position
ST – F0 ST
Oil price, Dec 2007 F0
Short Position
F0 - ST

10. Marking to Market and the Margin Account
Each trader opens a margin account. Initial Margin: funds that must be deposited in a margin account to provide capital to absorb losses.
Initial margin set to 5-15% of the contract value.
On any day, future prices may rise or fall. Profits and losses are recognized as they accrue daily and reflected in the margin accounts (Marking to Market).
Pay- (or receive-) as-you-go method
Maintenance margin: an established value below which a trader’s margin may not fall.
Margin call occurs when the maintenance margin is reached, broker will ask for additional margin funds…

11. Marking to Market, Buyer’s account
Contract: 5000 bushels of wheat at 4$ per bushel. Contract value is: 5000x$4=$20,000.Buyer deposits an initial margin of 5% of the transaction value (that is $1,000).
Day
Settle Price
$ Value
Chng Buyer’s equity
Margin Account
Total % HPR (cum)
SPOT HPR (cum) $4
$20,000
$1000 1
$4.10
$20,500
$ 500
1500
50%
2.5% 2
$3.95
$19,750
$-750
750
-25%
-1.25%
Future contract, marking to market:
Day 1: 4.10x5000= 20,500 Buyer gains $500 and seller looses $500.
Day 2: 3.95x5000= 19,750 Buyer looses $750 ans seller gains $750.
Forward Contract:
Day 2:
3.95x5,000=$19,750, hence Buyer looses $19,750 - $20,000 = -$250 and seller gains $250.
This is registered at once at the end of the contract.
Maintenance margin: percentage of initial margin.

12. Marking to Market, Seller’s account
Contract: 5000 bushels of wheat at 4$ per bushel. Contract value is: 5000x$4=$20,000. Seller deposits an initial margin of 5% of the transaction value (that is $1,000).
Day
Settle Price
$ Value
Chng Seller’s equity
Margin Account
Total % HPR (cum)
SPOT HPR (cum) $4
$20,000
$1000 1
$4.10
$20,500
$ -500
500
-50%
-2.5% 2
$3.95
$19,750
$ 750
1250
25%
1.25%
Future contract, marking to market:
Day 1: 4.10x5000= 20,500 Buyer gains $500 and seller looses $500.
Day 2: 3.95x5000= 19,750 Buyer looses $750 ans seller gains $750.
Forward Contract:
Day 2:
3.95x5,000=$19,750, hence Buyer looses $19,750 - $20,000 = -$250 and seller gains $250.
This is registered at once at the end of the contract.
Leverage multiplier = 20, contract value of $20,000 versus initial margin of $1000

13. More on futures contracts
Convergence of Price: As maturity approaches the spot and futures price converge. A commodity available from two sources (spot vs futures markets) must be priced identically.
What happens at maturity:
Delivery of actual commodity: Specifications of when and where delivery takes place and what can be delivered written in the contract
Cash Settlement: Delivery of a cash amount equal to the value of the underlying asset at maturity (ex: Index contracts)

14. What Determines Forward or Futures Prices?
Forward/futures prices ultimately linked to future spot prices
Notation:
Two ways to buy the underlying asset for date-T delivery:
1. Buy a futures contract with maturity date T
2. Buy the underlying asset now and store it until T
Contract
Spot at t
Futures
Price St
Ft,T

15. Valuation of Futures Gold: Easy to store (negligible costs of storage)
No dividends or benefits
Two ways to buy gold for T
Buy now for S0 and hold it until T
Buy future at 0, pay F0,T at T and take delivery at T
No arbitrage requires that:
F0,T = S0 (1+r)T

16. Valuation of Futures, example w/ Gold
Date
A: Future Contract
B: Outright Asset Purchase
Cash flow at 0
Enter long posittion: $0 Invest: -F0,T/(1+r)T
Buy gold: -S0
Cash flow at T
Long position: ST - F0,T
Investment: F0,T
Gold value: ST
Total at T ST
Since both strategies end up with the same CF at T, their initial costs should be the same:
F0,T = S0(1+r)T
Otherwise arbitrage profites would be earned.

17. Example
Suppose gold currently sells for $1200 an ounce. If the risk-free rate is 0.1% per month, a six-month maturity futures contract should sell for:
F0 = S0(1+r)6/12 = 1200 (1.012)1/2 = $
If the equation does not hold, arbitrage opportunity possible.
Suppose, F0 is $1210 instead of $ , we can realize profits by pursuing the strategy: …

18. Arbitrage Ex: Gold
Action
t=0
T (six months)
Borrow $1,200, repay with interest at T
Buy gold at $1,200
$1,200
-$1,200
-1,200(1.012)^0.5
$ST
Enter short position (F0=1,210) $0
1,210 - ST
Total
$2.82
Net initial investment is $0. Cash flow at T is positive and riskless. The profit is equal to mispricing of the futures contract.
Risk is eliminated because profits and losses on the futures and gold positions exactly offset each other.

19. Valuation of Futures Financials: Let underlying be a financial asset
No cost to store the underlying asset
Dividend or interest on the underlying
Example: Stock Index futures
Underlying are bundles of stocks, S&P500, BIST30
Futures settled in cash (No delivery)
Let the annualized dividend yield be d; then
F0,T = S0 (1+r-d)T

20. Stock Index Futures

21. BIST-30 Contract Features
Dayanak Varlık
Underlying Asset
BIST-30 index value (Ulusal hisse senedi fiyat endeksinin hesaplama yöntemi kullanılarak bu endekse dahil olan şirketlerin hisse senedi fiyatlarından elde edilen değer.)
Sözleşme Büyüklüğü
Contract Size
(BIST-30 Index /1000)*100 TL
[Ex: (91,000/1000)*100 = 9,100 TL]
Kotasyon Şekli
Quotation
BIST-30 Index divided by Three digits in decimals.
[Ex: / 1000 = ].
Günlük Fiyat Hareket Sınırı
Daily Price Range
% +15 of Base Price
Minimum Fiyat Adımı
Tick Size
0.025 (or 25 index points)
Ex: from to
Or from to 91025
Contract value= from 9100TL to TL so Tick Size= 2.5 TL).

22. Vade Ayları
Expiration Months
February, April, June, August, October and December.
Sözleşmenin Vadesi
Contract Maturity Day
Last day of the maturity month.
Son İşlem Günü
Last Transaction Day
Last day of the maturity month
Uzlaşma Şekli
Settlement Type
Cash Settlement

23. Trading Strategies
Speculation: to profit from movements in future prices
Go short if you believe price will fall
Go long if you believe price will rise
Hedging: to protect against price movements
Oil distributor planning to sell 100,000 barrels of oil in March that wishes to hedge against a possible decline in oil prices. Because each contrat calls for delivery of 1,000 barrels, it would sell 100 contracts.
Any decrease in prices would generate a profit on the contracts that would offset the lower sales revenue from the oil.

24. Hedging of Equity Portfolios
Suppose you have a diversified portfolio of large-cap stock worth $5mio and are now worried about equity markets (downward risk) and would like to hedge your exposure to equity market. How could you use S&P500 futures to implement this hedge? (assume index level is 2000)
Short sell 10 S&P 500 futures contracts (why 10?)

25. Example (cont) Compare hedged and unhedged portfolio (in $mio):
S&P 500
Cash Portfolio (Equity bought)
Cum Change in Margin Account
Cash Plus Futures Portfolio
1800
$4.5
$0.5
$4.5 + $0.5 = $5*
2,000
$5.0
$0.0
$5 + $0 = $5
2,200
$5.5
$-0.5
$5.5 - $0.5 = $5
This is a 100% hedge. The outcome is constant at $5 mio.
* Equity + Profit on contracts= 4,500,000+(10x200x250)= $5,000,000

26. Hedging Systematic Risk
To protect against a decline in stock prices, short the appropriate number of futures index contracts.
Use the beta for the portfolio to determine the hedge ratio.

27. Hedging Systematic Risk Example
Portfolio Value = $30 million, and Portfolio Beta = .8
S&P 500 = 1,000
If Expected Decrease = 2.5% => S&P falls to 975
Projected loss for the portfolio:
(.8) (-2.5%) = -2%
30 mio x -0.02= $600,000
Change in S&P500 index contract value=
(975 – 1000)x 250 = $6250.
Hedge Ratio= H= Change in portfolio value / profit by contract
H = $600,000 / $6250 = 96 contracts
Strategy: Equity portfolio long and 96 index contracts short.

28. Application: Creating Synthetic Positions with Futures for market timing
Index futures let investors participate in broad market movements without actually buying or selling large amounts of stock.
Results:
Cheaper and more flexible
Synthetic position; instead of holding or shorting all of the actual stocks in the index, you are long or short the index futures

29. Investing on Index Futures, example
You have $1 mio to invest in the stock market and you have decided to invest in the S&P500. How would you do this?
One way is to buy the S&P500 in the spot market:
Buy the 500 stocks, weights proportional to the market caps
Another way is to buy S&P500 futures:
value of a futures contract is $250 times the S&P500 index
Assuming the S&P500 is at 2000, one index contract is worth= $250x2000= $500,000
number of contract to buy:
$1,000,000 / (500,000) = 2 contracts
Assume 10% margin, you deposit $100,000 and invest $900,000 at risk-free rate.