v3_20140217_cfa二級基礎班_derivative_紀慧誠1_W

1、CFA二級培訓項目Derivatives紀慧誠金程教育高級培訓師地點： 上海 北京 深圳Topic Weightings in CFA Level II2-169Session NO.ContentWeightingsStudy Session 1-2Ethics & Professional Standards10Study Session 3Quantitative Methods5-10Study Session 4Economic Analysis5-10Study Session 5-7Financial Statement Analysis15-25Study Session 8-

2、9Corporate Finance5-15Study Session 10-12Equity Analysis20-30Study Session 13Alternative Investments5-15Study Session 14-15Fixed Income Analysis5-15Study Session 16-17Derivative Investments5-15Study Session 18Portfolio Management5-15Total:2IntroductionFramework概念Level Derivatives定價Level Level 應用3-16

3、9Summary of Readings and Framework SS 16 - Forwards and Futures R48 Forward Markets and ContractsR49 Futures Markets and ContractsSS 17 - Options, Swaps, and Interest Rate and Credit DerivativesR50 Option Markets and Contracts R51 Swap Markets and ContractsR52 Interest Rate Derivative InstrumentsR53

4、 Credit Derivatives: An Overview4-169Derivatives（一級）重點內(nèi)容回顧Derivatives的基本定義 A forward contract is an agreement between two parties in which oneparty ,the buyer ,agrees to buy from the other party, the seller, an underlying asset or other derivative, at a future date at a price established at the star

5、t of thecontract.聯(lián)系基本概念Equity BondClassificationInterest rate (FRA) CurrencyHedge Speculate Arbitrage 報價問題 理解應用整個市場就是三種交易5-169Forward contractsForward Markets and Contracts - Framework1.2.3.4.Forward Contracts FundamentalsPricing, Valuation and settlement Forwards ArbitrageForward Contract Pricing a

6、nd ValuationT-bill Forward Contract Equity Forward ContractsEquity Index Forward ContractsForward Contracts on Coupon Bonds Currency Forward ContractsForward Rate Agreements (FRAs)5.Credit risk in forward contracts6-1691. Forward Contracts A forward contract is an agreement between two parties in wh

7、ich one party, the buyer, agrees to buy from the other party, the seller, an underlying asset or other derivative, at a future date at a priceestablished at the start of the contract. The party to the forward contract that agrees to buy the financial or physical asset has a long forward position and

8、 is called the long. The party to the forward contract that agrees to sell/deliver theasset has a short forward position and is called the short.7-1692. Pricing and Valuation The price is the predetermined price in the contract that the long should payto the short to buy the underlying asset at the

9、settlement date The contract value is zero to both parties at initiation The no-arbitrage principle: there should not be a riskless profit to begained by a combination of a forward contract position with position in other asset.Two assets or portfolios with identical future cash flows, regardless of

10、 future events, should have same priceThe portfolio should yield the risk-free rate of return, if it generates certain payoffs8-1692. Pricing and ValuationPricing a forward contract is the process of determining the no-arbitrage price that will make the value of the contract be zero to both sides at

11、 the initiation ofthe contractForward Price = price that would not permit profitable riskless arbitragein frictionless marketsFP=S0Carrying CostsCarrying BenefitsValuation of a forward contract means determining the value of the contract to the long (or the short) at some time during the life of the

12、 contract.9-1693. Forwards Pricing :No-Arbitrage Principle Cash-and-Carry Arbitrage When the Forward Contract is OverpricedIf FP S0( 1+Rf )T10-169At initiationAt settlement date Borrow S0 at the risk-free rate Use the money to buy the Underlying bond Short a forward contract Deliver the underlying t

13、o the long Get FP from the long Repay the loan amount ofProfit= FP- S0( 1+Rf )T3. Forwards Pricing :No-Arbitrage PrincipleReverse Cash-and-Carry Arbitrage when the Forward Contract is Under-pricedIf FP S0(1+Rf)T11-169At initiationAt settlement date Short sell the underlying bond to get S0 Invest S0

14、at the risk-free rate Long a forward contract Pay the short FP to get the underlying bond Close out the short position by delivering the bond Receive investment proceedsProfit=S0( 1+Rf )T-FP4. Forward Contract Pricing and ValuationT-bill (zero-coupon bond) forwardsbuy a T-bill today at the spot pric

15、e (S0) and short a T-month T-bill forward contract at the forward price (FP)FP = S0 (1+ Rf)TEquity Forward (forward contracts on a dividend-paying stock) Equity Index ForwardBond ForwardCurrency Forward12-1694. 1 T-bill Forward Pricing and Valuation T-bill (zero-coupon bond) forwardsbuy a T-bill tod

16、ay at the spot price (S0) and short a T-month T-bill forward contract at the forward price (FP)FP = S0 (1+ Rf)TForward value of long position at initiation, during the contract life, and at expiration13-169TimeForward Contract Valuationt=0Zero, because the contract is priced to prevent arbitraget=tV

17、= S -FPV= -V=FP- Slongt(1+ R )T -tshortlong(1 + R )T -ttfft=TST-FP4.2Equity Forward ContractsForward contracts on a dividend-paying stockPrice:FP = (S 0 - PVD0) (1+ Rf)TValue:FP= S- PVD-Vlongtt(1 + R)T -tf14-1694.2 Equity Forward ContractsExampleCalculate the no-arbitrage forward price for a 100-day

18、 forward on a stock that is currently priced at $30.00 and is expected to pay a dividend of $0.40 in 15 days,$0.40 in 85 days, and $0.50 in 175 days. The annual risk-free rate is 5%, and the yield curve is flat. Ignore the dividend in 175 days because it occurs after the maturity of theforward contr

19、act.$0.4$0.4 PVD =+= $0.79461.0515/3651.0585/ 365FP = ($30 - $0.7946) 1.05100/ 365 = $29.615-1694.2 Equity Forward ContractsExampleAfter 60 days, the value of the stock in the previous example is $36.00. Calculate the value of the equity forward contract on the stock to the long position, assuming t

20、he risk-free rate is still 5% and the yield curve is flat. Theres only one dividend remaining (in 25 days) before the contract matures (in40 days) as shown below, so:$0.4PVD= $0.3987601.0525/ 365$29.6V= $6.16(long position) = （$36 - $0.3987) -601.0540/36516-1694.3 Equity Index Forward ContractsForwa

21、rd contracts on an equity indexContinuously compounded risk-free rate:cRf = ln (1+ Rf )Continuously compounded dividend yield:c( Rc -d c )TFP = S ePrice:f0Value:StFP -=Vlongdc(T -t )Rc (T -t )e ef17-1694.3 Equity Index Forward Contracts Example：The value of the S&P 500 index is 1,140. The continuous

22、ly compounded risk-free rate is 4.6% and the continuous dividend yield is 2.1 %. Calculate the no-arbitrageprice of a 140-day forward contract on the index.FP = 1,140 e(0.046 - 0.021) (140/365)= 1,151After 95 days, the value of the index in the previous example is 1,025. Calculate the value to the l

23、ong position of the forward contract on the index, assuming the continuously compounded risk-free rate is 4.6% and the continuous dividend yield is 2. 1%. After 95 days there are 45 days remaining on the original forward contract:1,025e0.021(45/365)1,151e0.046 (45/365)V(of the long position) =-= -12

24、2.149518-1694.4 Forward Contracts on Coupon BondsCoupon bondsSimilar to dividend-paying stocks, but the cash flows are couponsPrice:FP = (S 0 - PVC0) (1+ Rf)TValue:FP= (St- PVCt ) -Vlong(1 + R)T -tf19-1694.4 Forward Contracts on Coupon BondsExampleCalculate the price of a 250-day forward contract on

25、 a 7% U.S. Treasury bond with a spot price of $ 1,050 (including accrued interest) that has just paid a coupon and will make another coupon payment in 182 days. The annual risk- free rate is 6%. Remember that U.S. Treasury bonds make semiannual coupon payments:C= $1000 0.07= $352$35.00PVC = $34.001.

26、06182/365 The forward price of the contract is therefore:FP(on a income security) = ($1,050 - $34.00) 1.06250/ 365 =1057.3720-1694.5 Currency Forward ContractsPrice: covered Interest Rate Parity (IRP)F is Foreign Currency, not risk-free rate(1+ RD )TFP = S0(1+ R )TFFP and S0 are quoted in currency D

27、 per unit of currency F (i.e.,D/F)Value:StFP=-Vlong(1+ R)T -t(1+ R)T -tFDIf you are given the continuous interest ratescFP = S e( R-Rc )TDF0= - FPStVlongccR (T -t )R (T -t )eeFD21-1694.5 Currency Forward ContractsExample:Consider the following: The U.S. risk-free rare is 6 percent, the Swiss risk-fr

28、ee rate is 4 percent, and the spot exchange rate between the United States and Switzerland is$0.6667. Calculate the continuously compounded U.S. and Swiss risk-free rates. Calculate the price at which you could enter into a forward contract that expires in 90 days. Calculate the value of the forward

29、 position 25 days into the contract. Assumethat the spot rate is $0.65.22-1694.5 Currency Forward ContractsAnswer:rfc= ln(1.04)=0.0392 S0 = $0.6667T = 90/365rfc=0.0392rc=ln(1.06)=0.0583rc=0.0583F (0,T) = ($0.666 St = $0.65 T = 90/365 t = 25/365T - t = 65/365rfc= 0.0392e-0.0392(90/365) )(e0.0583(90/3

30、65) ) = $0.6698rc= 0.0583V (0,T) = ($0.65 e-0.0392(65/365) ) - ($0.6698e-0.0583(65/365) ) = -$0.0174tThe value of the contract is -$0.0174 per Swiss franc23-1694.6 Forward Rate Agreements (FRAs)A Forward Rate Agreement (FRA) is a forward contract on an interest rate(LIBOR).The long position can be v

31、iewed as the right and the obligation to borrow at the forward rate in the future;The short position can be viewed as the right and the obligation to lend at the forward rate in the future.No loan is actually made, and FRAs are always settled in cash at contract expiration.Lets take a 14 FRA for exa

32、mple. A 14 FRA isa forward contract expires in 1 month,and the underlying loan is settled in 4 months,with a 3-month notional loan period. The underlying interest rate is 90-day LIBOR in 30 days from now.24-1694.6 Forward Rate Agreements (FRAs)LIBOR: London Interbank Offered Rate .an annualized rate

33、 based on a 360-day year an add-on rateoften used as a reference rate for floating rate U.S dollar-denominated loans worldwide.published daily by the British Bankers AssociationSingle rateEuribor: Europe Interbank Offered Rate, established in Frankfurt, and publishedby European Central Bank.25-1694.

34、6 Forward Rate Agreements (FRAs): PricingThe forward price in an FRA is the no-arbitrage forward rate (FR)If spot ratesinterest rate:are known, The FR is just the unbiased estimate oftheforwardL(m) / mFR /nL(m + n) /m+ n(1+ Lm m / 360) (1+ FR n / 360)=(1+ Lm+n (m + n) / 360)26-1694.6 Forward Rate Ag

35、reements (FRAs): PricingPricing of an FRA:Example:Calculate the price ofa 14 FRA. The current 30-day LIBOR is 3% and 120- day LIBOR is 3.9%.Answer:The actual 30-day rate (Period): R(30)=0.0330/360 = 0.0025The actual 120-day rate (Period): R(120)=0.039120/360 = 0.013 The actual 90-day forward rate in

36、 30 days from now (period):(1+R(120)/(1+R(30) - 1 = 1.013 / 1.0025 - 1= 0.015.The annualized forward rate, which is the price of the FRA, is :RFRA=0.015360/90 = 0.042 = 4.2%.(1+ Lm m / 360) (1+ FR n / 360)=(1+ Lm+n (m + n) / 360)27-1694.6 Forward Rate Agreements (FRAs): ValuationThe value of an FRAV

37、alue of an FRA at maturityValue of an FRA prior to settlement Lt(k): the annualized LIBOR on a k-day loan t days after initiation The long can borrow $1 at expiration (at time m) and repay$1+FRn/360 at loan end (at time m+n), so the value of the long should be the difference between the present valu

38、e of the two cash flows28-1695. Credit risk in forward contractsCredit risk is the risk that the counter party will not pay when a positive amountis owed at settlement. The larger is the value or the forward to one party, the greater the credit (default) risk to that party.Market value is the most i

39、mportant measure of the credit risk in a forward contract. Default risk: Each party to a forward contract is exposed to default risk.One way to reduce the credit risk in a forward contract is to mark-to-market partwaythrough.29-169Summary of Readings and Framework SS 16 - Forwards and FuturesR48 For

40、ward Markets and Contracts R49 Futures Markets and Contracts SS 17 - Options, Swaps, and Interest Rate and Credit DerivativesR50 Option Markets and Contracts R51 Swap Markets and ContractsR52 Interest Rate Derivative InstrumentsR53 Credit Derivatives: An Overview30-169Derivatives（一級）重點內(nèi)容回顧 Futures與F

41、orward全面對比重點突出重點Standard LiquidityDaily settlement Credit riskT-bill Futures Eurodollar Futures Bond FuturesMargin的操作機制31-169Futures Markets and Contracts - Framework1.2.3.4.5.6.Futures Contracts & forward contractsFutures/Spot Price ConvergenceFutures Price vs. Forward Price Futures ArbitrageCosts

42、and BenefitsFutures Contract ValueT-bill Futures Contracts Eurodollar Futures ContractsEurodollar futures vs. T-bill futures contractsT-bond Futures Contracts Equity Futures ContractsCurrency Futures Contracts32-1691. Futures Contracts & forward contractsFutures contracts are very much like the forw

43、ard contracts we learned about inthe previous topic review. Similar in that:Deliverable contracts obligate the long to buy and the short to sell a certain quantityof an asset for a certain price on a specified future date.Cash settlement contracts are settled by paying the contract value in cash on

44、theexpiration date.Priced to have zero value at the time the investor enters into the contract.33-1691. Futures Contracts & forward contracts Differences34-169FuturesForwardsExchange tradedOver-the-counterStandardizedCustomizedMarked to marketUsually not marked to marketClearinghouse as counterparty

45、Originating counterpartyregulatedusually not regulated2. Futures/Spot Price ConvergenceThe spot (cash) price of a commodity or financial asset is the price for immediate delivery. The futures price is the price today for delivery at some future point in time (the maturity date).Basis = spot price fu

46、tures price = S0 FPAs the maturity date nears, the basis converges to zero, At the maturity date, the futures price must be the same as the spot price. Otherwise, there will exists arbitrage opportunity.FuturesSpot pricepriceFutures priceSpot priceTimeTime(a)(b)basis=spot price-futures price35-1693.

47、 Futures Price vs. Forward PricePrices of Futures vs. Forward Contracts3636-169If the correlation between the underlying asset value and interest rate isInvestors willPositivePrefer to go long in a futures contract, and the futures price will be greater than the price of an otherwise comparable forw

48、ard contract.ZeroHave no preferenceNegativePrefer to go long in a forward contract, and the forward price will be greater than the price of an otherwise comparable futures contract.4. Futures ArbitrageCash-and-Carry ArbitrageA cash-and-carry arbitrage consists of buying the asset, storing/holding th

49、e asset, and selling the asset at the futures price when the contract expires. The steps in a cash-and-carry arbitrage are as follows.At the initiation of the contractBorrow money for the term of the contract at market interest rates. Buy the underlying asset at the spot price.Sell (go short) a futu

50、res contract at the current futures price.At contract expirationDeliver the asset and receive the futures contract price.Repay the loan plus interest.37-1694. Futures ArbitrageReverse Cash-and-Carry ArbitrageAt the initiation of the contractSell asset short.Lend short sale proceeds at market interes

51、t rates. Buy (go long) futures contract at market price.At contract expirationCollect loan proceeds.Take delivery of the asset for the futures price and cover the short sale commitment.38-169Professors Note: It may help to remember ”buy low, sell high”. If the futures price is “too high,” sell the f

52、utures and buy the spot. If the futures price is “too low,” buy the futures and sell the spot.5. Costs and BenefitsCarrying Costse.g., corn, live cattle, and gold.Carrying BenefitsMonetary benefits: dividends, coupons, interest, etcNon-monetary benefits: convenience yieldFP = S0 (1 + Rf+ FV (Carrying C