Tài chính doanh nghiệp - A course in financial risk management

Topic #3Using forward and option contracts to hedge equity risks: an end-user perspectiveL. GattisA Course in Financial Risk ManagementMcDonald Ch: 2-3 provide a review of forwards and optionsWhat Do Financial Risk Managers Do? (IMM)Identify risks that affects the viability of your firmMarket Risks: Equity, Interest Rates, Currency, CommodityCredit Risks: Bond and counterparty defaultMeasure exposure to identified risksPositions, VaR/CaR/EaR, Stress TestsMitigate risksLayoff, Hedge, Accept, Hold CapitalForward contractsDefinition: A binding agreement (obligation) to buy/sell an underlying asset in the future, at a price set todayFutures contracts are standardized and traded forward A forward contract specifies:The features and quantity of the asset to be deliveredThe delivery logistics, such as time, date, and placeThe price the buyer will pay at the time of deliveryGenerally, there is no exchange of cash until deliveryTodayExpirationdatePayoff on a forward contractPositions (each contract has two parties)Long: “buyer” will pay forward price and take delivery of assetShort: “seller” will deliver asset and receive the forward pricePayoff for a contract is its value at expirationPayoffs:Long = Spot price at expiration – Agreed upon forward (futures) price {St-F0}M“as if bought at agreed upon forward price and sold at spot price”M is the contract multiplier or (contract quantity for commodities)Short = Agreed upon forward (futures) price - Spot price at expiration {F0-St}M“as if Bought at spot price and sold at agreed upon forward price”Example 2.1: S&P 500 indexToday: spot price = $1,000, 6-month forward price = $1,020In six months at contract expiration: spot price = $1,050, M=1Long position payoff = $1,050 - $1,020 = $30 Short position payoff = $1,020 - $1,050 = ($30)Reading price quotesIndex futuresExpiration month“Delivery Month”The open priceHigh of the dayLow of the dayClosing price of the dayDaily changeLifetime highLifetime lowOpen interest “# of contracts outstanding”ContractUnderlying Index Spot PriceThese quotes skip two decimal places to save spaceMultiplierForward ExampleLook back at the S&P500 contract with March delivery. Assume you were able to take a position at the settlement price of 1,095.30. The multiplier is $250.What is your payoff if you take a long position and the S&P index closes at 1,200 on the expiration dateProfit= What is your payoff if you take a short position and the S&P index closes at 1,000 on the expiration dateProfit= A non-binding agreement (right but not an obligation) to buy an asset in the future, at a price set todayPreserves the upside potential ( ), while at the same time eliminating the unpleasant ( ) downside (for the buyer)The seller of a call option is obligated to deliver if asked Call optionsTodayExpirationdateorat buyer’s choosingExamplesExample 2.3: S&R 500 index “Buyer”Today: call buyer acquires the right to pay $1,020 in six months for the index, but is not obligated to do soIn six months at contract expiration: if spot price is$1,100, call buyer’s payoff = $1,100 - $1,020 = $80 $900, call buyer walks away, buyer’s payoff = $0Example 2.4: S&R 500 index “Seller”Today: call seller is obligated to sell the index for $1,020 in six months, if asked to do soIn six months at contract expiration: if spot price is$1,100, call seller’s payoff = $1,020 - $1,100 = ($80) $900, call buyer walks away, seller’s payoff = $0Why would anyone agree to be on the seller side? Payoff/profit of a purchased callPayoff = max [0, spot price at expiration – strike price]xMProfit = Payoff – future value of option premium x MExamples 2.5 & 2.6:, M=1S&R Index 6-month Call OptionStrike price = $1,000, Premium = $93.81, 6-month risk-free rate = 2%If index value in six months = $1100Payoff = max [0, $1,100 - $1,000] = $100Profit = $100 – ($93.81 x 1.02) = $4.32If index value in six months = $900Payoff = max [0, $900 - $1,000] = $0Profit = $0 – ($93.81 x 1.02) = - $95.68Reading price quotesS&P500 Index optionsStrike priceCall or PutExpiration MonthLong Call ExampleSuppose you purchased the March S&P Call with a strike price of 1100 at the Last Price (see slide 2-18). The risk free rate was 3%. Multiplier is $250.What is your payoff at expiration if the S&P is at $1050 or $1150.Payoff (St=1050)= Payoff (St=1150)= What is your profit at expiration if the S&P is at $1050 or $1150.Profit(St=1050)= Profit (St=1150)= Long Call ProfitPayoff = - max [0, spot price at expiration – strike price]xMProfit = Payoff + future value of option premium x MExample 2.7:S&R Index 6-month Call OptionStrike price = $1,000, Premium = $93.81, 6-month risk-free rate = 2%If index value in six months = $1100Payoff = - max [0, $1,100 - $1,000] = - $100Profit = - $100 + ($93.81 x 1.02) = - $4.32If index value in six months = $900Payoff = - max [0, $900 - $1,000] = $0Profit = $0 + ($93.81 x 1.02) = $95.68Payoff/profit of a written callA put option gives the owner the right but not the obligation to sell the underlying asset at a predetermined price during a predetermined time period The seller of a put option is obligated to buy if askedPayoff/profit of a purchased (i.e., long) put:Payoff = max [0, strike price – spot price at expiration]xMProfit = Payoff – future value of option premium x MPayoff/profit of a written (i.e., short) put:Payoff = - max [0, strike price – spot price at expiration]xMProfit = Payoff + future value of option premium x MPut optionsPut option examplesExamples 2.9 & 2.10:S&R Index 6-month Put OptionStrike price = $1,000, Premium = $74.20, 6-month risk-free rate = 2%, M=1If index value in six months = $1100Payoff = max [0, $1,000 - $1,100] = $0Profit = $0 – ($74.20 x 1.02) = - $75.68If index value in six months = $900Payoff = max [0, $1,000 - $900] = $100Profit = $100 – ($74.20 x 1.02) = $24.32Profit for a long put positionLong Put ExampleSuppose you purchased the March S&P Put with a strike price of 1120 at the Last price (see slide 2-18). The risk free rate was 3%. Multiplier is 250.What is your payoff at expiration if the S&P is at $1050 or $1150.Payoff (St=1050) = Payoff (St=1150) = What is your profit at expiration if the S&P is at $1050 or $1150.Profit (St=1050) = Profit (St=1150) = A few items to noteA call option becomes more profitable when the underlying asset appreciates in value A put option becomes more profitable when the underlying asset depreciates in value Moneyness: In-the-money option: positive payoff if exercised immediatelyAt-the-money option: zero payoff if exercised immediatelyOut-of-the money option: negative payoff if exercised immediatelyOptions can be exercised at maturity, exercised early, or soldOption Price = Intrinsic (exercise) Value + Time ValueBlack Scholes and the Binomial Models are the most common models for valuing optionsBlack-Scholes and BinomialPayoffs and Profit SummaryBuy(long) Stock IndexShort Stock IndexLong Call*Long Put*Long ForwardShort ForwardCost(CF0)-S0S0-c-p00Payoff(CFt)St-StMax(0, St-X)Max(0, X-St)St-F0F0-StEcon Profitt (CFt-FV(CF0)St-S0(1+r)-St+ S0(1+r)Max(0, St-X)-c(1+r)Max(0, X-St)-p(1+r)St-F0F0-StSt=Spot price at time =t S0=Initial Spot PriceC=Call premiumP=Put PremiumF0=Forward or Futures PriceX=Strike PriceWhere:*Write (-)*Write (-)Basic Insurance StrategiesOptions can be: used to insure long positions (floors)used to insure short positions (caps)Covered positions (selling insurance)A put option is combined with a long position in the underlying assetGoal: to insure against a fall in the price of the underlying assetUsing the notation from the profit summary, show the combined payoff and profits from this strategy if you buy a stock index (S0) and a put (strike=X) and at maturity St is below X? StLong StockPayoffLong PutPayoffCombinedPayoffCombinedProfitSt>XSt+0St+St-S0(1+r)-P(1+r)StX-St+St+-X-X-X+(S0-C)(1+r)St<X-St-0-St--St-+(S0-C)(1+r)Maximum Cost to CoverMinimum Profit Insuring a short position: Cap (Short Index + Call)Example: Stock Index =$1000 (So) Premium on 6-month call with a $1000 strike price= 93.809 6-month rate= 2% (r), M=1 Stock Price is 6-months = $500 or $1500 (St)StShort StockLong CallCombined$1500$500PayoffStShort StockLong CallCombined$1500$500ProfitCovered Call (Write Call / Buy Asset)Example: Holding the S&R index and writing a S&R call option with a strike price of $1,000If Call is exercised, deliver the asset you holdThe covered call strategy is a neutral to bullish strategy because the investor is expecting the stock to go up or stay constant. Often called an “income strategy”Maximum Profit: Premium Maximum Loss: Substantial Covered Put (Write Put / Short Asset)Example: Shorting the S&R index and writing a S&R put option with a strike price of $1,000If put is exercised, buy the stock to cover your shortThe covered put strategy is a neutral to bearish strategy because the investor is expecting the stock to go down or stay constant. Often called an “income strategy”Maximum Profit: Premium Maximum Loss: Unlimited Options vs. ForwardsForwardsNo upfront costNo upside potentialOptionsRetain upside of riskMust pay premiumCan reduce cost byshorter maturityChange strike (higher call strike, lower put strike)Hedge less than full exposure (hedge ratio)Stock + Derivative StrategiesTrade (stock position)Buy Call(Long)WriteCall(Short)BuyPut(Short)Write Put(Long)Buy Stock(Long)n/aCovered CallFloorn/aShort Stock(Short)Cap or Ceilingn/an/aCovered Put Strategies involve combining a long and short positionProblemsYou take a long position in 10 S&P 500 forward contracts at a price of $1250. Each contract has a multiplier of $250. At maturity, the S&P 500 is selling for $1,187. What was your profit?You take a short position in 5 S&P 500 forward contracts at a price of $1250. Each contract has a multiplier of $250. At maturity, the S&P 500 is selling for $1,187. What was your profit?You buy one $1150 strike, 6-month, call option on the S&P 500 index at a price of $35. Each option has a multiplier of $250. The annualized interest rate is 5%. What was your profit (including the opportunity cost of capital) if the index is selling for $1175 at maturity? You buy one $1150 strike, 6-month, put option on the S&P 500 index at a price of $25. Each option has a multiplier of $250. The annualized interest rate is 5%. What was your profit (including the opportunity cost of capital) if the index is selling for $1175 at maturity? You write one $1150 strike, 6-month, call option on the S&P 500 index at a price of $35. Each option has a multiplier of $250. The annualized interest rate is 5%. What was your profit (including the opportunity cost of capital) if the index is selling for $1175 at maturity? You buy the S&P 500 index for $1,050 and hedge the position by buying a $1000 strike, 3-month, put option for a price of $20. The annualized interest rate is 5%. What is your minimum profit (including the opportunity cost of capital) on this hedged position in 3-months? Assume no multiplier (i.e., the multiplier = 1).You sell short the S&P 500 index for $1,050 and hedge the position by buying a $1100 strike, 3-month, call option for a price of $40. The annualized interest rate is 5%. What is your minimum profit (including the opportunity cost of capital) on this hedged position in 3-months? Assume no multiplier (i.e., the multiplier = 1).You buy the S&P 500 index for $1,050 and write a $1,050 strike, 6-month, call option for a price of $25. The annualized interest rate is 5%. What is your combined profit if the index is at 1,100 at maturity? Or 1000 at maturity? Assume no multiplier (i.e., the multiplier = 1).Using the Black-Scholes option pricing excel model, value the following options. 3-Month,$1200 Strike, at-the-money, European style Call and Put on the S&P 500 index. The annualized risk free rate is 1% and the dividend yield is 2.3%. The annualized standard deviation is 15%. Use the excel object in the PowerPoint file. You are not responsible for BS valuation on exams.