Futures and Forwards

1
Futures and Forwards

• A future is a contract between two parties
  requiring deferred delivery of underlying asset
  (at a contracted price and date) or a final cash
  settlement. Both parties are obligated to perform
  and fulfill the terms. A customized futures
  contract is called a Forward Contract.

2
Cash Flows on Forwards

• Pay-off Diagram

Buyers pay-offs
Futures Price
Spot price of underlying assets
Sellers pay-offs
3
Why Forwards?

• They are customized contracts unlike Futures
• and they are
• Tailor-made and more suited for certain purposes.
• Useful when futures do not exist for commodities
  and financials being considered.
• Useful in cases futures standard may be
  different from the actual.

4
Futures Forwards Distinguished
FUTURES FORWARDS
They trade on exchanges Trade in OTC markets
Are standardized Are customized
Identity of counterparties is irrelevant Identity is relevant
Regulated Not regulated
Marked to market No marking to market
Easy to terminate Difficult to terminate
Less costly More costly
5
Important Terms

• Spot Markets Where contracts for immediate
  delivery are traded.
• Forward or Futures markets Where contracts for
  later delivery are traded.
• Both the above taken together constitute cash
  markets.

6
Important Terms

• Futures Series All with same delivery month with
  same underlying asset.
• Front month and Back month.
• Soonest to deliver or the nearby contract
• Commodity futures vs. financial futures.
• Cheapest to deliver instruments.
• Offering lags.

7
Important Terms

• Variation Margin
• Deliverables
• Substitute for Future Cash Market Transactions
• Settlement in Cash

8
Interest Rate Futures

• Two factors have led to growth
• Enormous growth in the market for fixed income
  securities.
• Increased volatility of interest rates.

9
Futures Risk Hedging

• Interest Rate Risk
• Exchange Rate Risk
• Commodity Price Risk
• Equity Price Risk

10
Hedging Interest Rate Risk

• A CFO needs to raise Rs.50 crores in February
• 20XX to fund a new investment in May 20XX, by
• selling 30-year bonds. Hedge instrument
• available is a 20-year, 8 Treasury -bond based
• Future. Cash instrument has a PV01 of
• 0.096585, selling at par and yielding 9.75. It
• pays half-yearly coupons and has a yield beta of
• 0.45. Hedge instrument has a PV01 of 0.098891.

11
Hedging Interest Rate Risk

• Hence, FVh FVc ? PV01c / PV01h ? ?y
• 50 ? 0.096585 / 0.098891 ? 0.45
• Rs.21.98 Crores
• If FV of a single T-Bond Future is Rs.10,00,000
• then, Number of Futures (Nf) 21.98/0.1
• 219.8 Futures

12
Hedging Interest Rate Risk

• If corporate yield rises by 80bp by the time of
• actual offering, it has to pay 10.55 coupon
• semi-annually to price it at par. Thus, it has to
  pay
• Rs.50,00,00,000 ? 0.0080 ? 0.5 Rs.20,00,000
• more every six months in terms of increased
• coupons.
• This additional amount will have a PV at 10.55
• 20,00,000 ? PVIFA5.275, 60
• Rs.3,61,79,720 ? Rs.3.618 Crores

13
Hedging Interest Rate Risk

• Since corporate yield increases by 80bp, T-Bond
• yield will increase by 178bp resulting in an
• increased profit on short position in T-bond
• futures
• 22,00,00,000 ? 0.0178 ? 0.5
• Rs.19,58,000 half yearly, which has a PV
• 19,58,000 ? PVIFA4,89,40
• Rs.3,41,09,729
• Rs.3.411 Crores

14
Why Not perfect Hedge?

• PV01 provides accurate and effective hedge for
  small changes in yields.
• PV01s of cash and hedge instruments change at
  different rates.
• PV01s need to be recalculated frequently
  (practice is every 5bps). This can change the
  residual risk profile.
• Additional costs related to recalculations need
  to be kept in mind.

15
A Transaction on the Futures Exchange

• .

1a
1b
Futures Exchange 3
2a
2b
Buyer
Buyers Broker
Buyers Brokers Commission Broker
Sellers Brokers Commission Broker
Sellers Broker
Seller
6a
6b
5a
5b
7a
7b
4
8a
8b
Futures Clearing House
9a
9b
Buyers Brokers Clearing Firm
Buyers Brokers Clearing Firm

• 1a 1b Buyer and seller instruct their respective
  brokers to conduct a futures transaction.
• 2a 2b Buyers and sellers brokers request their
  firms commission brokers execute the
  transaction.
• Both floor brokers meet in the pit on the floor
  of the futures exchange and agree on a price.
• Information on the trade is reported to the
  clearinghouse.
• 5a 5b Both commission brokers report the price
  obtained to the buyers and sellers brokers.
• 6a 6b Buyers and sellers brokers report the
  price obtained to the buyer and seller.
• 7a 7b Buyer and seller deposit margin with their
  brokers.
• 8a 8b Buyers and sellers brokers deposit margin
  with their clearing firms.
• 9a 9b Buyers and sellers brokers clearing
  firms deposit premium and margin with
  clearinghouse.

Note Either buyer or seller (or both) could be a
floor trader, eliminating the broker and
commission broker.
16
Exchange Rate Risk Hedging

• Currency hedge is a direct hedge and not
• a cross hedge as in case of interest rate
• risk hedging. Hence, a hedge ratio of 11
• works very well.

17
Forward Rate Agreements (FRAs)

• FRAs are a type of forward contract wherein
• contracting parties agree on some interest rate
  to
• be paid on a deposit to be received or made at a
• later date.
• The single cash settlement amount is determined
• by the size of deposit (notional principal),
  agreed
• upon contract rate of interest and value of the
• reference rate prevailing on the settlement date.
• Notional principal is not actually exchanged.

18
Determination of Settlement Amount

• Step-1Take the difference between contract rate
  and
• the reference rate on the date of contract
  settlement
• Step-2 Discount the sum obtained using reference
  rate
• as rate of discount.
• The resultant PV is the sum paid or received. The
• reference rate could be LIBOR (most often used)
  or
• any other well defined rate not easily
  manipulated.

19
Hedging with FRAs

• Party seeking protection from possible
• increase in rates would buy FRAs (party is
• called purchaser) and the one seeking
• protection from decline would sell FRAs
• (party is called seller).
• These positions are opposite of those
• employed while hedging in futures.

20
Illustration

• A bank in U.S. wants to lock-in an interest rate
  for
• 5millions 6-month LIBOR-based lending that
• commences in 3 months using a 3?9 FRA. At the
  time
• 6-month LIBOR (Spot Rate) is quoted at 8.25. The
• dealer offers 8.32 to commence in 3 months. U.S.
  bank
• offers the client 8.82. If at the end of 3
  months, when
• FRA is due to be settled, 6-month LIBOR is at
  8.95,
• bank borrows at 8.95 in the Eurodollar market
  and
• lends at 8.82.

21
Illustration

• Profit/Loss (8.82-8.95) ? 5 millions ? 182/360
• - 3286.11
• Hedge Profit/Loss D?(RR-CR)?NP?182/360
• 1 ? (8.95-8.32) ? 5 millions?182/360
• 15925
• Amount Received/Paid
• 15925/1.04525 15235.59
• Note 8.95 ? 182/360 4.525

22
Index Futures Contract

• It is an obligation to deliver at settlement an
  amount equal to x times the difference between
  the stock index value on expiration date and the
  contracted value
• On the last day of trading session the final
  settlement price is set equal to the spot index
  price

23
Illustration (Margin and Settlement)

• The settlement price of an index futures contract
  on a
• particular day was 1100. The multiple associated
  is 150.
• The maximum realistic change that can be expected
  is 50
• points per day. Therefore, the initial margin is
  50150
• Rs.7500. The maintenance margin is set at
  Rs.6000. The
• settlement prices on day 1,2,3 and 4 are 1125,
  1095,
• 1100 and 1140 respectively. Calculate
  mark-to-market
• cash flows and daily closing balance in the
  account of
• Investor who has gone long and the one who has
  gone
• Short at 1100. Also calculate net profit/(loss)
  on each
• contract.

24
Illustration

• Long Position
• Day Sett. Price Op. Bal. M-T-M CF Margin
  Call Cl. Bal
• 1 1125 7500 3750 - 11250
• 2 1095 11250 - 4500 - 6750
• 3 1100 6750 750 - 7500
• 4 1140 7500 6000 - 13500
• Net Profit/(loss) 3750-45007506000 Rs. 6000
• Short Position
• Day Sett. Price Op. Bal. M-T-M CF Margin
  Call Cl. Bal
• 1 1125 7500 - 3750 2250 6000
• 2 1095 6000 4500 - 10500
• 3 1100 10500 - 750 - 9750
• 4 1140 9750 - 6000 2250
  6000
• Net Profit/(loss) -37504500-750-6000 (-) Rs.
  6000

25
Pricing of Index Futures Contracts

• Assuming that an investor buys a portfolio
  consisting of stocks in the index, rupee returns
  are
• RI (IE IC) D, where
• RI Rupee returns on portfolio
• IE Index value on expiration
• IC Current index value
• D Dividend received during the year

26
Pricing of Index Futures Contracts

• If he invests in index futures and invests the
  money in risk free asset, then
• RIF (FE FC) RF,
• where
• RIF Rupee return on alternative investment
• FE Futures value on expiry
• FC Current futures value
• RF Return on risk-free investment

27
Pricing of Index Futures Contracts

• If investor is indifferent between the two
  options, then
• RI RIF
• i.e. (IE-IC) D (FE-FC) RF
• Since IE FE
• FC IC (RF D)
• (RF D) is the cost of carry or basis and
  the futures contract must be priced to reflect
  cost of carry.

28
Stock Index Arbitrage

• When index futures price is out of sync with the
  theoretical price, the an investor can earn
  abnormal risk-less profits by trading
  simultaneously in spot and futures market. This
  process is called stock index arbitrage or basis
  trading or program trading.

29
Stock Index Arbitrage Illustration

• Current price of an index 1150
• Annualized dividend yield on index 4
• 6-month futures contract price 1195
• Risk-free rate of return 10 p.a.
• Assume that 50 of stocks in the index will
• pay dividends in next 6 months. Ignore
• margin, transaction costs and taxes. Assume a
• multiple of 100. Is there a possibility of stock
• Index arbitrage?

30
Stock Index Arbitrage Illustration

• Fair price of index future
• FC IC (RF D)
• 1150 (11500.100.5)-(11500.040.5)
• 1150 34.5 1184.5 (hence it is overpriced)
• Investor can buy a portfolio identical to index
  and
• short-sell futures on index.
• If index closes at 850 on expiration date, then
• Profit on short sale of futures (1195 850) 100
  Rs.34,500
• Cash Div recd on port. (1150 0.04 0.5 100
  Rs. 2,300
• Loss on sale of port. (1150 850) 100 ( - )
  Rs.30,000
• Net Profit 34,500 2,300 30,000 Rs.6,800
• Half yearly return 6800 (1150100)0.0591
  5.91
• Annual return (1.0591)2 1 0.1217 12.17

31
Stock Index Arbitrage Illustration

• If index closes at 1300,
• (-) 10,500
• 2,300
• 15,000
• 6,800 12.17 p.a.

32
Application of Index Futures

• In passive Portfolio Management
• An investor willing to invest Rs.1 crore can buy
  futures contracts instead of a portfolio, which
  mimics the index.
• Number of contracts (if Nifty is 5000)
• 1,00,00,000/5000 100 20 contracts
• Advantages
• Periodic rebalancing will not be required.
• Potential tracking errors can be avoided.
• Transaction costs are less.

33
Application of Index Futures

• In Beta Management
• In a bullish market beta should be high and in a
  bearish market beta should be low i.e. market
  timing and stock selection should be used.
• Consider following portfolio and rising market
  forecast.
• Equity Rs.150 millions
• Cash Equivalent Rs.50 millions
• Total Rs.200 millions
• Assume a beta of 0.8 and desired beta of 1.2

34
Application of Index Futures

• The Beta can be raised by,
• Selling low beta stocks and buying high beta
  stocks and also maintain 31 ratio. Or,
• Purchasing X contracts in the following
  equation
• 150 0.8 0.02 X 200 1.2
• i.e. X (200 1.2 150 0.8) / 0.02
• 6000 contracts, assuming Nifty
  future available at Rs.5000, multiple of 4
  and beta of contract as 1.0
• No. of contracts will be 600 for a multiple iof
  40 and 240 for a multiple is 100.

35
(No Transcript)
36
Euro-rate Differentials (Diffs)

• Introduced on July 6, 1989 in US, it is a
• futures contract tied to differential between
• a 3-month non-dollar interest rate and
• USD 3-month LIBOR and are cash settled.

37
Euro-rate Differentials (Diffs)

• Example If USD 3-month LIBOR is 7.45 and
• Euro 3-month LIBOR is 5.40 at the settlement
• time, the diff would be priced at 100 (7.45
  5.40)
• 97.95. Suppose in January, the March
• Euro/dollar diff is prices at 97.60, this would
• suggest that markets expects the differential
• between USD LIBOR and Euro LIBOR to be
• 2.40 at settlement in March.

38
Euro-rate Differentials (Diffs)

• They are used for
• Locking in or unlocking interest rate
  differentials when funding in one currency and
  investing in another.
• Hedging exposures associated with non-dollar
  interest-rate sensitivities.
• Managing the residual risks associated with
  running a currency swap book.
• Managing risks associated with ever changing
  interest-rate differentials for a currency dealer
  

39
Foreign Exchange Agreements (FXAs)

• They allow the parties to hedge movements
• in exchange rate differentials without
• entering a conventional currency swap. At
• the termination of the agreement, a single
• payment is made by one counterparty to
• another based on the direction and the
• extent of movement in exchange rate differentials.