清华大学经管学院--金融工程1

1、INTRODUCTION TO FINANCIAL ENGINEERING Fred SongSeptember 20011Introductory What is Finance? What is Financial Engineering? Whats the role of Financial Engineering in New Economy? New economy Financial engineering and e-commerce2What is Finance? Money & Banking Monetary Economics International Fi

2、nance International Economics3Corporate FinanceCapital Market(Investments)Financial EconomicsMultinational Corporate FinanceInternational Financial MarketFinancial Engineering4What is Financial Engineering? Generalizing: Financial Engineering involves the design, the development, and the implementat

3、ion of innovative financial instruments and processes, and the formulation of creative solutions to problems in finance. Specializing: Financial Engineering is risk management via creative structural tools.5FINANCEI.T.ENGINEERINGF.E.6CHAPTER ONE: MM Theory and No Arbitrage1. MM Theory Two measuremen

4、ts of valueAccounting: book value historic costFinance: market value net present value7Assets = Liabilities + Equity Accounting Equality: duel entity systemBook value measurementFund useFund source Finance Equality: Fund use = Fund sourceMarket value measurement8 Corporate Finance Assets Liabilities

5、 and Equity Asset 1 Asset 2 Liabilities Asset 3 . . Equity . Asset nTotal Assets Total Liabilities and Equity?_1niiAssetAssetsTotalAccounting: Yes!Finance: No!Capital MarketReal EconomyNPVFirm Value + NPV9Liabilities Value Equity ValueLiabilities Value Assets ValueCapital StructureFinancial leverage

6、:orHas a change of financial leverage any impact on the firm value?10M&M TheoryM&M assumptions: Frictionless assumptions No income taxes No transaction costs No information asymmetry No cost to resolve interest conflicts among stakeholders All liabilities are risk-free11Notes: A mini - caseT

7、wo companies EBIT Capital structure Firm value$10 million p.abonds: $40 million, 8%shares: 600,0001. As share price: $100 per shareexpected return: 10%1 million shares $100 millionB ?A 2. Bs bond: risk-free the share number is supposed share expected return: ?12(Risk-free) NoPosition Immediate Cash

8、Flow Cash Flow in the FutureReplication of As Stock Using Bs Stock and BondsBs Total Payments = Bs Net Earnings + Interest Payments= ( EBIT - $3.2 million) + $3.2 million= EBITSuppose price of Bs stock = $90 per shareShort sell 1% As shares at $100 per shareBuy 1% Bs shares at $90 per shareBuy 1% Bs

9、 bonds+$1,000,000 1% of EBIT $540,0001%( EBIT $3,200,000 ) $400,0001% $3,200,000 Net Cash Flow$60,0000ArbitragePrice of Bs stock= $100 per share13 M&M Proposition 1 Proposition 1: Under M&M Assumption, i.e., in the frictionless environment, the total market value of a firm is independent of

10、its capital structure. Think of the firm as a gigantic pizza, divided into quarters. If now, you cut each quarter in half into eights, the M &M proposition says that you will have more pieces, but not more pizza. Merton Miler14Probability Distribution of EBIT and EPS for the Two CompaniesState o

11、f the EconomyEBITCompany A Company B EPS Net EPS(1 million shares) Earnings (600,000 shares) Bad business $5 million $5 $1.8 million $3.00Normal business 10 10 6.8 11.33Good business 15 15 11.8 19.67Mean 10 10 6.8 11.33Standard deviation 4 6.81Beta 1.0 1.0 1.67NOTE: Each state of the economy is equa

12、lly likely.15The cost of capital depends on its use and not on its source.Proposition!16Weighted Average Cost of CapitalCost of capital of the firm without liabilityEDDrEDErWACCfeEDrWACCWACCrfe%10ABWACCWACCRisk premium of WACCFinancial leverageM&M Proposition 2:The cost of capital of a firm equa

13、ls the cost of capital of the firm without liability and the risk premium of WACC multiplied by financial leverage.17All transactions in financial markets are zero NPV transaction activities.Proposition!18Implication of M&M Theory Frictionless environment does not exist in the real world. Taxes

14、Transaction costs Information asymmetry Costs resolving interest conflict Liabilities are risk-bearing19 Tax ShieldCompany A:Tax rate: T = 33%Company A Company BClaimantCreditorsShareholdersGovernment Tax Authority Total Firm Value before Taxation$100 million $100 million067 million33 millionCompany

15、 B:(1T)(EBITInterests)+Interests = (1-T)EBIT+TInterests40.0 million40.2 million19.8 million$13.2 million20 WACC with Taxes Other M&M assumptions holdEDTEBITEDDTrEDEETDrEBITEDDTrEDErWACCfffe1111erHas a change of financial leverage any impact on the firm value ?Answer: Yes !Discount rate for cash

16、flow of the firm21 Stock PriceShare Number Total Equity Share PriceCompany A:1 million67.0 million$ 67Company B:600,00040.2 million$ 67?If Company A were to announce an issue of $40 million debt to be used to repurchase and retire common stockAs capital structure = Bs capital structureMarket reactio

17、n: price of As share would go up to reflect the $13.2 million tax shield: $(67.0 + 13.2) million / 1 million = $80.2 per share.Where is the benefit of the tax shield?22State Prices100$AP107$AuP98$AdPu = 1.07d = 0.98103$5 .98$1$02. 1$02. 1$Risk-free security%2frRisk-free interest rateBond ABond B?BP2

18、3 Basic SecuritiesBasic Security 1 Basic Security 21$01$0ud= ?= ?Portfolio Basic Security 1, Basic Security 2AuPAdPreplicatingAuPAdPBond AAdAudPuPAP=1duduNo Arbitrage24 Replicating risk free securityPortfolio Basic Security 1, Basic Security 202. 102. 1replicatingfdfurr111=1$02. 1$11$fr02. 1$11$frLe

19、tffrr1fdudurdu115447. 04357. 0durrudurdrffdffuState Prices25 Replicating Bond A and Bond B100985447. 01074357. 0AdAuAdPuPP53.985 .985447. 01034357. 0BPNo ArbitrageQuestions ?1. Do there exist such kind basic securities in the real world?2. Are there enough basic securities that can be used to replic

20、ate all the payoff of securities in the market?Answers :1. Find some equivalent instruments instead of basic securities.2. It involves in market completeness.26 Replication via equivalent instrumentsPortfolio Bond A, market value risk-free securityL?BP103$5 .98$replicating Bond B5 .9802. 19810302. 1

21、107LL02. 15 .49,21L53.98100LPB27 Market Completeness Whenever the number of different instruments used to replicate securities equals the number of states so that we can attain any payoff of securities in future , in such a circumstance, the market is a complete one. Otherwise, themarket is incomple

22、te.Completeness is a c o r e c o n c e p t o f finance theories !28Summary of Chapter One1. No Arbitrage Equilibrium2. Replication Methodology3. State Prices Technology29CHAPTER TWO: Time Value of Money and Term Structure of Interest Discounted Cash Flow FormulaYes ! is the expected rate of return,

23、i.e., the mean of the discount rates for different termsrLetNo ! is the discount rate that cannot be used for so long periodntttrCPV1)1 (?01)1(PrCPVnttttnttttntttrCrC11)1 ()1 (0)1 (10ntttrCPNPVr30 Determination of Interest1. Capital production ability the more the capitals expected return, the higher the interest rates and vice versa.2. Uncertainty of capital prod