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Study Session 17 Derivative Investments

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## Study Session 17 Derivative Investments

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**Study Session 17 Derivative Investments**70. Derivative Markets and Instruments 71. Forward Markets and Contracts 72. Futures Markets and Contracts 73. Options Markets and Contracts 74. Swaps Markets and Contracts 75. Risk Management and Applications of Option Strategies**LOS 70.a, p. 164**• A derivative security derives its value from the price of another (underlying) asset or an interest rate • Forwards, Futures, Options, Swaps • Uses, (abuses) of Derivatives • Enhance profitability (and risk) through leverage (speculative activity). • Both gains and losses amplified • Risk management • Hedging or eliminating an existing risk • Price Discovery; Lower transaction costs**Abuse of derivative BY speculation/ leverage**• Proctor and Gamble lost 150 million in 1994 • Barings Bank lost 1.3 billion in 1995 • Orange County 1.64 billion in 1994 • LTCM 3.5 billion in 2000 (1.2tr postn eq = 5b) • Option Backdating Scandal • Lack of risk management: Failed to USE hedging tools: Daimler Benz $ recvb depr. • LITTLE PUBLICITY FOR SUCCESS STORIES ABOUT RISK MANAGEMENT**LOS 70.b, p. 164**Forward Contracts • Long obligated to buy and pay; short obligated to sell and deliver • Specified asset (currency, stock, index, bond) • Specified date in the future • Customized: No active secondary market • Long gains if asset price above forward price • Short gains if asset price below forward price • Neither party pays at contract initiation**LOS 70.b, p. 165**Futures Contracts • Like forward contracts but standardized • Exchange-traded, active secondary market • Require margin deposit • No default (counterparty) risk Methods to Terminate Forward or Future • Reversal (offsetting trade): Common • Delivery of asset (< 1% of trades) • Cash settlement: May be required • Exchange for physicals: Off exchange**LOS 70.b, p. 165**Swaps • Equivalent to a series of forward contracts • Simple interest rate swap • One party pays a fixed rate of interest • One party pays a variable (floating) rate of interest • Payments can be based on interest rates or stock/portfolio/index returns • Can involve two different currencies**LOS 71.d, p. 174**Equity Index Forward – Problem • 90-day S&P 100 forward contract • Forward contract price = 525.2 • Notional amount = $10 million • In 90 days index is at 535.7 What is the payment at settlement and which party receives it? Long receives (535.7 – 525.2) / 525.2 × $10 million = $200,000 at settlement, paid by the short -1**LOS 71.d, p. 175**Forward on Zero-Coupon Bond Example: 100 day, T-bill forward Underlying: $10 million T-bill Forward Price: $9,945,560 (1.96% discount) • If interest rates rise, P↓, long loses/short gains • If interest rates fall, P↑, long gains/short loses Coupon bonds: Priced at YTM; same principle Risky bonds: Must provide for default possibility**LOS 71.e, p. 176**LIBOR-Based Loan Example Loan value = $1.0 million Term = 30 days 30-day LIBOR = 6% Interest payment = $1,000,000 (0.06) (30 / 360) = $5,000 Total payment in 30 days = $1,000,000 + $5,000 = $1,005,000**LOS 71.f, p. 176**Forward Rate Agreement (FRA) Exchange fixed-rate for floating-rate payment • Notional amount • Fixed rate = forward (contract) rate • Floating rate (LIBOR) is underlying rate • Long gains when LIBOR > contract rate**LOS 71.f, p. 176**Forward Rate Agreement (FRA) • Long position can be viewed as the obligation to take a (hypothetical) loan at the contract rate (i.e., borrow at the fixed rate); gains when reference rate ↑ • Short position can be viewed as the obligation to make a (hypothetical) loan at the contract rate (i.e., lend at the contract rate); gains when reference rate ↓**LOS 71.g, p. 177**FRA Example Term = 30 days Notional amount = $1 million Underlying rate = 90-day LIBOR Forward rate = 5% At t = 30 days, 90-day LIBOR = 6% Underlying floating rate > fixed rate Long position receives payment**LOS 71.g, p. 177**FRA Example: Net Payment Net payment due to the long 90 days after contract settlement: Payment at settlement: PV of interest savings**LOS 71.g, p. 178**FRA Settlement Payment to Long days = number of days in floating rate term**LOS 71.h, p. 178**Currency Forward Contracts • Currency forward contracts are commitments to buy or sell a certain amount of a foreign currency for a fixed amount of another currency in the future • As with other forwards, cash settlement is the amount necessary to compensate the party who would be disadvantaged by the actual change in market rates as of the settlement date**LOS 72.b, p. 189**A Futures Trade • April wheat futures call for delivery of 5000 bu. of wheat in April, futures price is $2 per bushel Contract value is 5000 × $2 = $10,000 • Long obligatedto buy 5000 bu. in April at $2 • Short obligatedto sell 5000 bu. in April at $2 • Both the long and short post same margin amount • If future price > $2 long gains, < $2 short gains**LOS 72.c, p. 190**Price Limits Price limits: Exchange-imposed limits on how much the contract price can change from the previous day’s settlement price • Exchange members prohibited from executing trades at prices outside these limits • If the new equilibrium price (at which traders would willingly trade) is above the upper limit or below the lower limit, trades cannot take place**LOS 72.c, p. 190**Marking to Market • Marking to market is the process of adjusting margin balance in a futures account each day for the change in the futures price (add gains, subtract losses) • The futures exchanges can require a mark-to-market more frequently (than daily) under extraordinary circumstances (increased volatility)**LOS 72.c, p. 190**Margin Calculation Example • Long five July wheat contracts • Size = 5000 bushels • Futures price = $2.00/bu • Initial margin deposit = $150 per contract • Maintenance margin = $100 per contract Total initial margin = 5 × $150 = $750 Total maintenance margin = 5 × $100 = $500**LOS 72.c, p. 190**Margin Calculation Example cont. • Each change of $0.01 in the futures price leads to a change of 5000 × $0.01 = $50 per contract in the margin account • On the 5 contracts in our example, a $0.01 increase in the July wheat futures price will increase the long’s margin by $250 and decrease the margin balance in the short’s account by $250**LOS 72.c, p. 190**Margin Calculation Example cont.**LOS 72.e, p. 193**Stock Index Futures S&P 500 Index Futures: • Value of a contract is 250 times the level of the index • Each index point in the futures price represents a gain or loss of $250 per contract • A smaller contract is traded on the same index and has a multiplier of 50 Futures contracts covering several other popular indexes are traded**LOS 72.e, p. 193**Currency Futures • In the U.S., currency contracts trade on the euro (EUR), Mexican peso (MXP), and yen (JPY), among others • Contracts are set in units of the foreign currency, and the price is stated in USD/unit**LOS 73.a, p. 198**Options Basics • Option buyer (owner, long position) Pays a premium to purchase the right to exercise an option at a future date and price • Option seller (writer, short position) Incurs an obligation to perform under the option contract terms**LOS 73.a, p. 198**Options Basics • Call option: Long has the right to purchase the underlying asset at the exercise (strike) price; short has the obligation to sell/deliver the underlying asset at the exercise price • Put option: Long has the right to sell the underlying asset at the exercise (strike) price; short has the obligation to purchase the underlying asset at the exercise price**LOS 73.a, p. 199**Options Terminology • American options can be exercised any time prior to expiration (early exercise) or at expiration • European options can be exercised only at expiration • American options are worth at least as much as otherwise identical European options**LOS 73.a, p. 200**Moneyness = Intrinsic ValueBalance = Time Value Call Options Put Options Examples from yahoo finance**Equity, Options & Leveraged Equity**Investment Strategy Investment Equity only Buy stock @ 100 100 shares $10,000 Options only Buy calls @ 10 1000 options $10,000 Leveraged Buy calls @ 10 100 options $1,000 equity Buy T-bills @ 3% $9,000 Yield**Equity, Options Leveraged Equity - Payoffs**IBM Stock Price $95 $105 $115 All Stock $9,500 $10,500 $11,500 All Options $0 $5,000 $15,000 Lev Equity $9,270 $9,770 $10,770**Rates of Return**IBM Stock Price $95 $105 $115 All Stock -5.0% 5.0% 15% All Options -100% -50% 50% Lev Equity -7.3% -2.3% 7.7%**LOS 73.b, p. 201**Types of Options: Underlying Assets • Commodity options: (e.g., call option on 100 ounce of gold at $420 per ounce) • Stock options: Each contract for 100 shares • Bond options: Like stock options, payoff based on bond price and exercise price • Index options: Have a multiplier (e.g., payoff is $250 in cash for every index point the option is in the money at expiration)**LOS 73.b, p. 201**Types of Options: Underlying Assets Options on futures: • Calls give the option to enter into a futures contract as the long at a specific futures price • Puts give the option to enter into a futures contract as the short at the indicated futures price At exercise, futures position is marked to market**LOS 73.c, p. 202**Interest Rate Options • Interest rate options: Payoff based on the difference between a floating rate, such as LIBOR, and the strike rate • Payoff on a LIBOR-based interest rate call is Max[0,(LIBOR – strike rate)] × notional amount (long gains when rates rise) • Payoff on a LIBOR-based interest rate put is Max[0,(strike rate – LIBOR)] × notional amount (long gains when rates fall) • Payoffs made at the end of the interest rate term (after option expiration)**2%**7 % 3 % = 5% -2% LOS 73.c, p. 202 Two Interest Rate Options = One FRA**LOS 73.d, p. 203**Interest Rate Caps and Floors • A cap puts a maximumon an issuer’s payments on a floating rate debt • Equivalent to series of long interest rate calls • Makes payments to issuer whenfloating rate > cap (strike) rate • A floor puts a minimumon an issuer’s payments on a floating rate debt • Equivalent to series of shortinterest rate puts • Issuer must make payments whenfloating rate < floor (strike) rate**LOS 73.d, 204**Cap and Floor Payoffs**LOS 73.f, p. 205**Option Value Option value = intrinsic value + time value Intrinsic valuealso equal to payoff at expiration • Call: max (0, S – X) • Put: max (0, X – S) Time value • Option premium minus intrinsic value • Also called speculative value**LOS 73.g,h, p. 208**Options Notation St = price of underlying asset at time t X = exercise price T = time to expiration RFR = risk-free rate ct, pt = European style calls and puts at time = t Ct, Pt = American style calls and puts at time = t**LOS 73.g,h,k, p. 209, 216**Minimum and Maximum Option Values European puts, no early exercise means lower maximum, PV of X at expiration**LOS 73.i, p. 212**Options That Differ Only By Exercise Price • Given two puts that are identical in all respects except exercise price, the one with the higher exercise price will have at least as much value as the one with the lower exercise price • Given two calls that are identical in every respect except exercise price, the one with the lower exercise price will have at least as much value as the one with the higher exercise price**X**0 X LOS 73.j, p. 214 Deriving Put-Call Parity (European Options) Protective put = stock + put If S ≤ X, payoff = S + (X – S) = X If S ≥ X, payoff = S + 0 = S Fiduciary call = call + X/(1 + RFR)T (bond that pays X at maturity) If S ≤ X, payoff = 0 + X = X If S ≥ X, payoff = (S – X) + X = S Same payoffs means same values by no-arbitrage Put-call parity: S + P = C + X/(1 + RFR)T**LOS 73.j, p. 215**Parity Conditions and Synthetic Options**LOS 73.j, p. 216**Put-Call Parity Example • Stock XYZ trades at $75 • Call premium = $4.50 • Expiration = 4 months (T = 0.3333) • X = $75 • RFR = 5% • What’s the price of the 4-month put on XYZ?**LOS 73.j, p. 216**Put-Call Parity Example**LOS 73.i,m, p. 212, 217**Time, Volatility, RFR, and Strike Price Longer time to expiration increases option values Except for: Some far out-of-the-money options and European style puts Greater price volatility increases option values Increase in RFRincreases call values and decreasesput values For X1 < X2: call at X1≥ call at X2 put at X1≤ put at X2**LOS 73.l, p. 216**Cash Flows on the Underlying Asset • If the asset has positive cash flows over the period of the option, the cost of the asset is reduced by the present value of the cash flows • For assets with positive cash flows over the term of the option, we can • substitute this (lower) net cost, S – PVCF , for S in the lower bound conditions and in all the parity relations**LOS 74.a, p. 225**Swap Contracts: Overview • If A loans money to B for a fixed rate of interest and B loans the same amount to A for floating rate of interest, it’s an interest rate swap • If one of the returns streams is based on a stock portfolio or index return, it’s an equity swap • If the loans are in two different currencies, it’s a currency swap