Techniques and Tools of Risk Management Unit III-DBM,OU (Forwards & Futures) Introduction The emergence of the market for derivative products can be traced back to the willingness of risk-averse economic agents to guard themselves against uncertainties arising out of fluctuations in asset prices. Thus, derivative products initially emerged as hedging devices against fluctuations in commodity prices. Commodity linked derivatives remained the sole form of such products for almost three hundred years. Derivatives Derivative is a product whose value is derived from the value of the underlying asset. Underlying asset can be Equity, Forex (Currency), Commodity, or any other asset. According to the Securities Contracts (Regulation) Act, 1956, derivatives are those assets whose value is determined from the value of some underlying assets. The underlying asset may be equity, commodity or currency. A common place where such transactions take place is called the derivative market. . they are referred to as 'derivative financial instruments' or simply 'derivatives.Derivatives Financial products commonly traded in the derivatives market are themselves not primary loans or securities. But can be used to change the risk characteristics of underlying asset or liability position. The world over.' These financial instruments are so called because they derive their value from some underlying instrument and have no intrinsic value of their own. derivatives are a key part of the financial system. Range of derivative Products Derivatives Forwards/ Options Futures Swaps Features of Derivative markets Centralization of Trading No counter party risk Standardization of contracts Liquidity Mark to Market (MTM) margining system Standardisation of Contracts The standardised items in any futures contract are: i. Quantity of the underlying asset ii. Quality of the underlying asset(not required in financial futures) iii. The date and month of delivery iv. The units of price quotation (not the price itself) and minimum change in price (tick-size) v. Location of settlement for contracts of .Derivatives . where settlement takes place on a specific date in the future at today¶s pre-agreed price.Demystified Four Variants: Forward: Contract is a customized contract between two entities. The forward price may be different different maturities. .Demystified Is an agreement between two parties to buy or sell an asset at a certain time in the future at a certain price. A futures contract may be offset prior to maturity by entering into an equal and opposite transaction. > 99% of futures transactions are offset this way. Futures Contract: Derivatives . Futures contracts are special types of forward contracts in the sense that the former are standardized exchange-traded contracts. but not the obligation to buy or sell a specified quantity of the underlying at a fixed exercise price on or before the expiration date. Swaps: Are private agreements between two parties to exchange cash flows in the future according to a pre-arranged formula. .Demystified Options: Contract gives the right. A call option gives the right to buy and a put option gives the right to sell.Derivatives . The two commonly used swaps are interest rate swaps and currency swaps. OTC Quantities and terms of the contract are fully negotiable. No money changes hands at the time the deal is made.Forward Contracts An agreement made today between a buyer and a seller to exchange the commodity or instrument for cash at a predetermined future date at a price agreed upon today. Secondary market does not exist and faces problems of liquidity and negotiability. . The agreed upon price is called the forward price. Two parties agree to do a trade at some future date. at a stated price and quantity. Features Custom Tailored Traded over the counter (not on exchanges) No money changes hands until maturity High counter party risk . . Such transaction would take place through a forward market. A wheat farmer may wish to contract to sell their harvest at a future date to eliminate the risk of a change in prices by that date. Gains or losses settled daily 5. Margin account required as collateral to cover losses . Guaranteed by the clearing house ± no counter-party risk 4. Exchange traded 3. Standardised contracts: ± (a) underlying commodity or asset ± (b) quantity ± (c) maturity 2.Features of Futures Contracts 1. Futures Contracts Traded on a futures exchange as a standardised contract. security or currency at a predetermined future date at a price agreed upon today. It is standardisation of the futures contract that facilitates the secondary market trading. Terms not negotiable A futures contract is a financial security issued by an organised exchange to buy or sell a commodity. subject to the rules and regulations of the exchange. Relates to a given quantity of the underlying asset and only whole contracts can be traded. Price is called µFutures Price¶ . 2010 to buy two December 2010 gold futures contracts on the XYZ Commodity Exchange. Since the contract size is 100 ounces. We suppose that the current futures price is $1250 per ounce. the investor has contracted to buy a total of 200 ounces at this price.Example Suppose an investor contacts his broker on July. The initial margin is $5000 per contract or $10. A maintenance margin of $3500 or $7000 is set. .000 total. Day Future s Price$ Daily Gain/L oss $ Cumul ative Gain(L oss) -1000 -200 -1400 -1000 -1800 -2800 -2000 -2600 3600 -4000 Margin Accou nt Balanc e$ 9000 9800 8600 9000 8200 7200 8000 7400 6400 13400 Margin Call July 9 July 10 July 11 July 12 July 13 July 14 July 15 July 16 July 17 July 30 1245 1249 1243 1245 1241 1236 1240 1237 1332 1232 -1000 800 -1200 400 -800 -1000 800 -600 -1000 -600 3600 . We can infer that: Standardisation makes futures liquid Margin and marking to market reduce default risk Clearing-house guarantee reduces counter-party risk . Types of Futures Types of Futures Futures contracts can be classified into four categories. They are: ± ± ± ± Interest Rate Futures Index Futures Currency Futures Commodity Futures . Interest Rate Futures Interest rate futures are based on an underlying security which is a debt obligation. On the contrary. . the futures contract seller compensates the buyer for the lower interest rate at the time of expiration. An interest rate future moves in value according to the changes in the interest rates. In a market condition in which the interest rates are moving higher. the futures contract buyer has to pay the seller an amount equal to that of the profit accrued by investing at a higher rate in comparison to that of the rate specified in the futures contract. when interest rates move lower. An interest rate futures price index was created in order to accurately determine the gain or loss of an interest rate futures contract. By now. when the interest rates increase. In other words. . Treasury-bond futures and Eurodollar futures. Examples include Treasury-bill futures. This price index fluctuates in accordance with the interest rates. the index will move lower and vice versa. it is quite clear that the interest rate futures are used to hedge against the risk of the interest rates that will move in an adverse direction. causing a cost to the company. Germany DAX 5. NYSE. India BSE SENSEX. RUSSELL 2000. CNX. 1982. Two months later. NIFTY 2. S&P 500. NSE. UK PTSE 100 6. the Standard and Poor (S&P) 500 Index futures contract was introduced by the Chicago Mercantile Exchange (CME). Others 1.Index Futures Index or Stock index futures are one of the varieties of futures contracts. NASDAQ 100 3. France . The first stock index futures contract based on value line index were introduced by Kansas City Board of Trade (KCBT) on 24th February. US DJIA. Japan NIKKEI 4. the order will have to be punched in the system. In the trading. . An investor is able to buy or sell futures on the BSE ± Bolt terminal or the NSE ± NEAT screen with his broker. Separate bids and ask quotations are available like shares. Trading in Sensex or Nifty futures is just like trading in any other security. Since the tick size and market lot size in futures are similar to individual stock. the feel of trading in stock index futures is the same as trading on stocks. The confirmation from the system will be immediate like the existing system. A trader can carry the stock index futures contract till maturity or square it off at any time before expiry. Upon execution of the order he would receive a confirmation of the same. . the investor has to punch in the order of the required quantity at a price he wishes to buy. Simply. sell or execute the same at the market price. The price of the futures contract of this type is hence measured in terms of US dollars per unit of other currency. so as to make the actual payments of each currency for those held at the end of the last trading day. for example. . Rs. More popularly. The trading unit of each contract is a particular amount of the other currency. currency future is called as foreign exchange future or FX future.Currency Futures Currency future. one of the currencies of exchange in such contracts is US dollar. is a futures contract to exchange one currency for another at a specified future date at a price (exchange rate) fixed on the purchase date. 290. Usually. Most of the currency futures contracts have a physical delivery.000. but there are certain significant differences between them. . the currency markets are not as controlled as the currency futures. One such difference is that the currency futures are traded through exchanges. Thus. such as the Chicago Mercantile Exchange (CME). but the currency markets are traded through currency brokers. Currency futures contracts are similar to the currency markets. Popular Currency Futures Markets Name Description EUR The Euro to US Dollar currency future GBP The British Pound to US Dollar currency future CHF The Swiss Franc to US Dollar currency future AUD The Australian Dollar to US Dollar currency future CAD The Canadian Dollar to US Dollar currency future RP The Euro to British Pound currency future RF The Euro to Swiss Franc currency future . The underlying commodity can be wheat. .Commodity Futures Commodity futures can be defined as those futures where the underlying is a commodity or physical asset. futures on soya bean. In India too. eggs and so on. Such contracts began trading on Chicago Board of Trade (CBOT) in 1860s. black pepper and spices have been trading for long. butter. cotton. Future Price Quotations Cost of Carry Model Expectancy Model . it is better to buy in the cash market and simultaneously sell in the futures market. If µFutures price¶ is less than the µFair price¶. . If µFutures price¶ is greater than the µFair price¶. then it is better to sell in the cash market and simultaneously buy in the futures market. This arbitrage between cash and future markets will remain till prices in the cash and future markets get aligned. for instance. This happens mainly when underlying asset or instrument is not storable or may not be sold short. in the commodities market.Expectancy Model of Futures Pricing Expectancy model says that many-atime it is not the relationship between the fair price and future price but the expected spot price and future price which leads the market. . Speculating & Arbitrage: Hedging is a mechanism to reduce price risk inherent in open positions. . by reducing the risk. Derivatives are widely used for hedging.Hedging. Its purpose is to reduce the volatility of a portfolio. A Hedge can help lock in existing profits. If one is bullish on the market. Arbitrageur helps price discovery. Arbitraging involves profiting from the price discrepancy between two markets. Speculating & Arbitrage: Speculation involves taking a view on the market and playing accordingly. . For example: Cash Market and the Futures Market.Hedging. and vice versa for a bearish outlook. one can buy Futures. Speculators and Arbitrageurs: Hedgers: Hedgers wish to eliminate or reduce the price risk to which they are already exposed. Speculators provide liquidity and depth to the market.Hedgers. Without them the markets would lose their purpose and become mere tools of gambling. . Hedgers and investors provide the economic substance to any financial market. Speculators: Speculators are those class of investors who willingly take price risks to profit from price changes in the underlying. Arbitrageurs bring price uniformity and help price discovery. All class of investors are required for a healthy functioning of the market. Speculators and Arbitrageurs: Arbitrageurs: Arbitrageurs profit from price differential existing in two markets by simultaneously operating in two different markets.Hedgers. . The market provides a mechanism by which diverse and scattered opinions are reflected in one single price of the underlying. Terminology The party that has agreed to buy has what is termed a long position The party that has agreed to sell has what is termed a short position 36 . . Futures Standardized in each contract Changes everyday Market to market everyday Margin paid by buyers and sellers Not present Restricted no. Most of the contracts are cash settled.Distinction -Forwards and Futures Market Difference Size of Contract Price of contract Mark to market Margin Counterparty Risk No.Most contracts result in delivery. Highly Liquid Exchange traded Standardized. contracts per year Perfect hedging is not possible. No Liquidity Over the counter Specifically decided. Hedging Liquidity Nature of Market Mode of Delivery Forwards Decided by Buyer and Seller Remains fixed till maturity Not done No margin required Present Any no. of contracts Perfect hedging is possible. of contracts in a yr. Margins In Futures Market A margin is cash or marketable securities deposited by an investor with his or her broker(collateral). The balance in the margin account is adjusted to reflect daily settlement (marking to market) Margins minimize the possibility of a loss through a default on a contract 38 . A margin is not a form of down payment on the balance due. Margin payments are made frequently (usually daily) in small amounts relative to the size of the contract rather than as a big sum. Margins In Futures Market Other Key Points About Futures They are settled daily Closing out a futures position involves entering into an offsetting trade Most contracts are closed out before maturity 40 Futures/Forwards: Equity Markets Derivatives Products in Indian Equity Markets Futures on indices Futures on Single Stocks Options on indices Options on Single Stocks . . . . . Theoretical Pricing of Futures Futures Price = Spot Price + Cost of Carry Basis = Futures Price ± Spot Price (Positive/Negative) Insurance/Storage/Interest/Less Dividend Cost of Carry reduces as time to expiry reduces and futures & cash price start converging On expiry day. futures and cash price should be equal. Actual futures & spot price would depend on demand and supply of underlying and futures . . the holding cost is the cost of financing plus cost of storage and insurance purchased. In the case of equity futures.Futures Pricing: Equity Markets In the case of commodity futures. the holding cost is the cost of financing minus the dividends returns. Futures Pricing: Equity Markets . Futures Discrete compounding of Interest rates) Pricing: An example (Using . for example. annually or semiannually. Most books on derivatives use continuous compounding for pricing futures too. . When we use continuous compounding.Futures Pricing: Equity Markets The concept of discrete compounding. where interest rates are compounded at discrete intervals. Pricing of options and other complex derivative securities requires the use of continuously compounded interest rates. Futures Pricing: Equity Markets-stocks Using Continuous compounding of interest rate- S spot price of a equity share . Futures Pricing: An example (Using Continuous compounding of interest rates ) . Futures Pricing: Equity Markets.When dividends are paid on a stock When an Investment Asset Provides a Known Income F = (S ± I )erT where I is the present value of the income during life of forward contract S: Spot price today F: Futures or forward price today T: Time until delivery date r: Risk-free interest rate for maturity T 54 . 049 + 36. T=1.60 .900. calculate its 1 year futures price if dividend paid is Rs.10*1 F = (S ± I )erT = 38. is trading at Rs.900. r=10% I = 40e -0. 40 at the end of half year and year.Futures Pricing: Equity Markets.1*1 = 912.24) e0.193 = 74.5 + 40e -0.10*0.When dividends are paid on a stock An Example : When an Investment Asset Provides a Known Income ABC ltd.. If the risk free rate with continuous compounding is 10% per annum. Sol: S= Rs.24 F = (900 ± 74. When dividends are paid on a stock When an Investment Asset Provides a Known Yield F = Se (r±q )T where q is the average yield during the life of the contract (expressed with continuous compounding) S: Spot price today F: Futures or forward price today T: Time until delivery date r: Risk-free interest rate for maturity T .Futures Pricing: Equity Markets. T= 1.08) * 1 = Rs. The risk-free rate with continuous compounding is 12%. is currently trading at Rs.12-0. r = 12% F = Se (r±q )T F = 25 e (0.When dividends are paid on a stock An Example: When an Investment Asset Provides a Known Yield ABC Ltd. 26. 25 .02 . the yield/return is 8% per annum. Sol: S=25..Futures Pricing: Equity Markets.Calculate the 1 year future price of ABC ltd. Stock Index Can be viewed as an investment asset paying a dividend yield The futures price and spot price relationship is therefore F = S e(r±q )T Where q is the average dividend yield on the portfolio represented by the index during life of contract 58 .Futures Pricing: Equity Markets. Long & Short Hedges A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future and want to lock in the price 59 . NIFTY(NSE) Other index futures on NSE are: CNX IT . Bank Nifty. CNX Nifty Junior.Equity Markets: Index Futures. Nifty Midcap 50 . ITC.Equity Markets: Stock Futures-(NSE) Stocks available for futures trading: Infosys..Wipro.SBI.HUL. .NTPC etc.HPCL. Some Terminology Open interest: The total number of contracts outstanding ± equal to number of long positions or number of short positions Settlement price: The price just before the final bell each day ± used for the daily settlement process Volume of trading: The number of trades in 1 day 62 . . the basis reduces to zero.Basis & Convergence in Futures Basis: The difference between the spot price and the futures price is called the basis. This means that there is a convergence of the futures price to the price of the underlying asset. This happens because if the futures price is above the spot price during the delivery period it gives rise to a clear arbitrage. We see that as a futures contract nears expiration. Basis & Convergence in Futures Basis Risk: Basis is the difference between the spot and futures price. In a normal market basis is ±ve The variability of the basis is called basis risk Hedge eliminates the outright price risk and substitutes it for less volatile and more manageable basis risk. Basis risk arises because of the uncertainty about the basis when the hedge is closed out The effectiveness of any hedge strategy depends upon the stability of the basis 64 . Convergence of Futures to Spot: Basis & Convergence in Futures Futures Price Spot Price Futures Price Spot Price Time Time (a) (b) 65 . Convergence of Futures to Spot (Hedge initiated at time t1 and closed out at time t2) Futures Price Spot Price Time t1 t2 66 . Futures/Forwards: Commodity Markets . Commodities Defined Commodity Derivatives : Derivative contracts where the underlying assets are Commodities are called Commodity derivatives Every kind of movable good excluding monies. securities and actionable claims The commodity markets can be classified into: ± ± ± ± Agricultural Products Precious Metals Other Metals Energy . Ticker Format Ticker : AAABBBCCC AAA : Commodity BBB : Grade CCC : Location For Example : GLDPURMUM GLD : GOLD PUR : PURE MUM : MUMBAI . Instrument Type Instrument type denotes the type of contract COMDTY : Commodity (Spot) FUTCOM : Future Commodity OPTCOM : Option on Commodities Only trading in Futures is Allowed by FMC . Expiry Date Contract Expiry is on 20th of Every month If 20 is a holiday. . the previous working day would be the Expiry date Ticker: 20MMMYYYY For Example : Gold contract for the month of August 2004 would be : ³20AUG2004´ Expiring Contracts can only be traded up to the morning session on the closing date. Lot Size Specific lot size for every commodity For Example : For Gold Contracts Prices Displayed : Per 10 Grams Minimum Contract : Per 100 Grams (& in multiple thereof) Delivery Lot : Per 1 Kilo . castor seed. the contract's price changes relative to the fixed price at which the trade was initiated. As time passes. .Commodity Futures The buyer of the futures contract (the party with a long position) agrees on a fixed purchase price to buy the underlying commodity (gold. silver. The seller of the futures contract (the party with a short position) agrees to sell the underlying commodity to the buyer at expiration at the fixed sales price. This creates profits or losses for the trader. refined soy oil or rubber) from the seller at the expiration of the contract. Payoff for buyer of futures: Long futures . Payoff for buyer of futures: Long futures . Payoff for Seller of futures: Short futures Payoff for a seller of gold: Profit 6000 Loss . Payoff for buyer of futures: Long futures Payoff for buyer of cotton futures: Profit 6500 Loss . Payoff for Seller of futures: Short futures . Payoff for Seller of futures: Short futures iiiiii Short staple cotton Short . in case of commodity futures. The cost typically includes interest cost in case of financial futures. The cost of carry is the sum of all costs incurred if a similar position is taken in the cash market and carried to expiry of the futures contract less any revenue that may arise out of holding the asset. insurance and storage costs etc are also considered. The theoretical price of a futures contract is the spot price of the underlying commodity plus the cost of carry. Though one can compute the theoretical price. In general. Futures Price = Spot Price + Cost of Carry. Please note that futures are not about predicting the future prices of the underlying asset or commodity.Futures Pricing: Commodity Mkts. the actual price may vary depending upon the demand and supply of the underlying asset or commodity . Futures Pricing: Commodity Mkts. it follows that the futures price will be equal to . The futures price of a commodity that is an investment asset is given by Storage costs add to the cost of carry. If U is the present value of all the storage costs that will be incurred during the life of a futures contract. Assume that the payment is made at the beginning of the year.Futures Pricing: Commodity Mkts. and the variable storage costs are Rs.55 per week.6000 per 10 grams and the risk. For ease of understanding let us consider a one. What would the price of one year gold futures be if the delivery unit is one kg? 3 month gold futures price for above example: . Assume further that the spot gold price is Rs. Suppose the fixed charge is Rs.year futures contract on gold.310 per deposit upto 500 kgs. free rate is 7% per annum. it costs Rs.3170 to store one kg of gold for a year(52 weeks). Futures Pricing: Commodity Mkts. . Futures/Forwards: Currency Markets . .Currency Forwards The simplest derivative It is buying or selling of a currency against another at a fixed price at a future date. g. When the firm is short in the undelying asset ± a payable in currency A ± it should go long in futures. Futures Position: Receive A . The firm is long in the underlying asset. To hedge it should take a futures position such that futures generate a positive cash flow whenever the asset declines in value. it should go short in futures i. a receivable in a currency A.e.Currency Futures Hedging with Currency Futures A corporation has an asset e. it should sell futures contracts on A against its home currency. Futures Position: Deliver A Cash Position: Deliver A. Cash Position: Receive A. 5 -1 -1.5 G IN SS A /LO 0 -0.5 Seller 1 0.4 45 .4 45 45 .6 47 .Forwards ± Risk Reward FORWARD PAY OFF 1.8 46 .6 46 .5 Buyer 45 .6 46 .2 46 46 .2 45 .8 47 .2 PRICE Buyer Seller Price 47 .4 47 . Futures Pricing: Currencies F = S e( rd-rf ) T F = Futures or forward price S = current spot price rf = foreign risk-free interest rate rd = Domestic risk-free interest rate T =Time until delivery date . 12-0.S being 12% and 7%.45/$ . rd =12% .Futures Pricing: Currencies Calculate 1 yr futures price.07) 1 = Rs. Sol: F = S e( rd-rf ) T S = Rs. 1yr interest rates in india and U. spot Rs/$ : Rs45/$ . rf = 7%.47. T = 1 F = 45 e (0.307 / $ . Hedging Strategies Using Futures . a hedge ratio of one could be assumed.Hedge Ratio The ratio of the size of a position in a hedging instrument (like futures) to the size of the position (exposure) being hedged. a hedge ratio of one may not be optimal. In situations where the underlying asset in which the hedger has an exposure is exactly the same as the asset underlying the futures contract he uses. . In all other cases. and the spot and futures market are perfectly correlated. h * is the hedge ratio that minimizes the variance of the hedger¶s position 92 WS V WF .Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is h*= where WS is the standard deviation of (S. WF is the standard deviation of (F. the change in the futures price during the hedging period V is the coefficient of correlation between (S and (F. the change in the spot price during the hedging period. Optimal Hedge Ratio Optimal number of contracts: The no. of futures contracts required for hedging: N* = h* N A / Q F N* = optimal no. of futures contracts for hedging Q F = Size of one futures contract (units) N A = Size of position being hedged . 000 bales of cotton in three months. Suppose the standard deviation of the change in the price per Quintal of cotton over a three month period is calculated as 0.An Example on Hedge ratio A company knows that it will require 11. The unit of trading is 11 bales and the delivery unit for cotton on the NCDEX is 55 bales.8.032.040 and the coefficient of correlation between the change in price of cotton and the change in the cotton futures price is 0. The company chooses to hedge by buying futures contracts on cotton. The standard deviation of the change in the cotton futures price over a three month period is 0. What is the optimal hedge ratio? How many cotton futures contracts should it buy? . 64* 11000/11 = 640.An Example on Hedge ratio Solution: If the hedge ratio were one.64 No. of Contracts = 0.000/11 N* = 1000 But the optimal hedge ratio is: h* = 0.040 = 0. the hedger would have to buy 1000 units (one unit of trading = 11 bales of cotton) to obtain a hedge for the 11.8 * 0.000 bales of cotton it requires in three months. that is if the cotton spot and futures were perfectly correlated.032/0. Number of contracts = 11. N* = 640 . 85. The unit of trading is 11 bales and the delivery unit for cotton on the NCDEX is 55 bales. The hedge ratio works out to be 0.000 bales of cotton in three months.An Example on Hedge ratio A company knows that it will require 33. The company can obtain a hedge by . 85 * 33000/11 = 2550 Thus the company obtains hedge by buying 2550 units of 3-months cotton futures. of contracts is given by.An Example on Hedge ratio Solution: The company obtains a hedge by: The optimal no. N* = h* N A / Q F N* = 0. . Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.0. but you feel they have been chosen well and will outperform the market in both good and bad times.Why Hedge Equity Returns To hedge an equity portfolio May want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolio Suppose stocks in your portfolio have an average beta of 1. 98 . Hedging Using Index Futures : To hedge an equity portfolio To hedge the risk in a portfolio the number of contracts that should be shorted is P N* = F F where P is the value of the portfolio. and F is the value of one futures contract N* = optimal no. Fis its beta. of futures contracts for hedging 99 .