Futures and Forwards

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.

Cash Flows on Forwards

Pay-off Diagram:

Spot price of underlying assets

Seller’s pay-offs Buyer’s pay-offs

Futures

Price

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.

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

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.

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.

Important Terms

 Variation Margin

 Deliverables

 Substitute for Future Cash Market Transactions

 Settlement in Cash

Interest Rate Futures

Two factors have led to growth:

 Enormous growth in the market for fixed income securities.

 Increased volatility of interest rates.

Futures & Risk Hedging

 Interest Rate Risk

 Exchange Rate Risk

 Commodity Price Risk

 Equity Price Risk

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.

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

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  PVIFA

= Rs.3,61,79,720  Rs.3.618 Crores

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  PVIFA 4,89%,40

= Rs.3,41,09,729

= Rs.3.411 Crores

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.

A Transaction on the Futures Exchange

.

Buyer

3

Buyer’s Broker’s Commission Broker

Futures Clearing

House

Buyer’s Broker’s

Clearing Firm Buyer’s Broker’s

Clearing Firm Seller’s Broker’s

Commission Broker Seller’s

Broker

Seller

1a 1b Buyer and seller instruct their respective brokers to conduct a futures transaction.

2a 2b Buyer’s and seller’s brokers request their firm’s commission brokers execute the transaction.

3 Both floor brokers meet in the pit on the floor of the futures exchange and agree on a price.

4 Information on the trade is reported to the clearinghouse.

5a 5b Both commission brokers report the price obtained to the buyer’s and seller’s brokers.

6a 6b Buyer’s and seller’s brokers report the price obtained to the buyer and seller.

1a 6a 7a

2a 5a

8a

4

9a 9b

2b 5b

1b 6b

7b

Note: Either buyer or seller (or both) could be a floor trader, eliminating

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 1:1

works very well.

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.

Determination of Settlement Amount

Step-1:Take 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 ^.

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.

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%.

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

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

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 50×150 = 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

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) = 3750-4500+750+6000 = 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

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

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

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

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.

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

Stock Index Arbitrage: Illustration

Fair price of index future FC = IC + (RF – D)

= 1150 + [(1150×0.10×0.5)-(1150×0.04×0.5)]

= 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

A.

Profit on short sale of futures (1195 – 850) ×100 = Rs.34,500

B.

Cash Div recd on port. (1150 × 0.04 × 0.5 × 100 = Rs. 2,300

C.

Loss on sale of port. (1150 – 850) ×100 = ( - ) Rs.30,000

D.

Net Profit = 34,500 +2,300 – 30,000 = Rs.6,800

E.

Half yearly return = 6800 ÷ (1150×100)=0.0591 = 5.91%

Stock Index Arbitrage: Illustration

If index closes at 1300,

A. = (-) 10,500

B. = 2,300

C. = 15,000

D. = 6,800 = 12.17% p.a.

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.

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

Application of Index Futures

The Beta can be raised by,

a. Selling low beta stocks and buying high beta stocks and also maintain 3:1 ratio. Or,

b. 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.

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.

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

Euro-rate Differentials (Diffs)

They are used for:

1. Locking in or unlocking interest rate differentials when funding in one currency and investing in another.

2. Hedging exposures associated with non-dollar interest- rate sensitivities.

3. Managing the residual risks associated with running a currency swap book.

4. Managing risks associated with ever changing interest-

rate differentials for a currency dealer

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.