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##### 50 years of Finance

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**50 years of Finance**André Farber Université Libre de Bruxelles Inaugurale rede, Francqui Leerstoel VUB 2 December 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**What is Finance?**Companies Investors Equity Capital expenditures Debt Portfolio management Dividends Operating cash flow Interests Francqui Leerstoel - Inaugurale Rede 2 december 2004**Asset pricing models**Time Discounted cash flow method State PricesArrow-Debreu Option Pricing ModelsBlack ScholesCox Ross Rubinstein Capital Asset Pricing ModelMarkowitzSharpe Lintner Uncertainty Stochastic discount factors Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**Discounted cash flow method**PV = C1v1 + C2v2 + …+Cn vn Cash flows Required rates of return Francqui Leerstoel - Inaugurale Rede 2 december 2004**Penetration rate of discount cash flow**Callahan, C. and S. Haka, A Model and Test of Interfirm Innovation Diffusion: the Case of Discounted Cash Flow Techniques, Manuscript January 2002 Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**Markowitz (1952) Portfolio selection**• Return of portfolio: normal distribution • Characteristics of a portfolio: • Expected return • Risk: Variance/Standard deviation Francqui Leerstoel - Inaugurale Rede 2 december 2004**Calculation of optimal portfolio**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Markowitz: the birth of modern portfolio theory**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**Capital Asset Pricing Model**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Capital Asset Pricing Model**Expected return rM r Risk free interest rate β 1 Beta Francqui Leerstoel - Inaugurale Rede 2 december 2004**Net Present Value Calculation with CAPM**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**Jensen 1968 - Distribution of “t” values for excess**return115 mutual funds 1955-1964 Not significantly different from 0 Francqui Leerstoel - Inaugurale Rede 2 december 2004**US Equity Mutual Funds 1982-1991(Malkiel, Journal of Finance**June 1995) • Average Annual Return • Capital appreciation funds 16.32% • Growth funds 15.81% • Small company growth funds 13.46% • Growth and income funds 15.97% • Equity income funds 15.66% • S&P 500 Index 17.52% • Average deviation from benchmark -3.20% (risk adjusted) Francqui Leerstoel - Inaugurale Rede 2 december 2004**The Efficient Market Hypothesis**S&P 500 2000-2004 Francqui Leerstoel - Inaugurale Rede 2 december 2004**The Efficient Market Hypothesis**S&P 500 2000-2004 Francqui Leerstoel - Inaugurale Rede 2 december 2004**The Random Walk Model**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**Does the capital structure matters?**• Modigliani Miller 1958: NO, under some conditions Debt Equity Francqui Leerstoel - Inaugurale Rede 2 december 2004**Trade-off theory**Market value PV(Costs of financial distress) PV(Tax Shield) Value of all-equity firm Debt ratio Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**Options**• Right to: • Buy (CALL) • Sell (PUT) • an asset • at a fixed price (EXERCICE PRICE / STRIKING PRICE) • up to or at a future date (MATURITY) • at a future date (EUROPEAN OPTION) • up to a future date (AMERICAN OPTION) Francqui Leerstoel - Inaugurale Rede 2 december 2004**Buy 1 Fortis share**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Buying a put**Stock + Put Stock Put Francqui Leerstoel - Inaugurale Rede 2 december 2004**Buying a call**Bond + Call Bond Call Francqui Leerstoel - Inaugurale Rede 2 december 2004**How to value an option**• Standard present value calculation fails • Value of option = f(Stock price, Time) • Required rate of return = f(Stock price, Time) • Black Merton Scholes • Combine stock and option to create a riskless position • Law of one price (no arbitrage) f=(#shares)(Stockprice)+Bond Francqui Leerstoel - Inaugurale Rede 2 december 2004**The fundamental partial differential equation**• Assume we are in a risk neutral world Expected change of the value of derivative security Change of the value with respect to time Change of the value with respect to the price of the underlying asset Change of the value with respect to volatility Francqui Leerstoel - Inaugurale Rede 2 december 2004**And now, the Black Scholes formulas**• Closed form solutions for European options on non dividend paying stocks assuming: • Constant volatility • Constant risk-free interest rate Call option: Put option: N(x) = cumulative probability distribution function for a standardized normal variable Francqui Leerstoel - Inaugurale Rede 2 december 2004**Binomial option pricing model**Risk neutral probability Stock price Su Option fu Stock price S Stock price Sd Option fd Time interval Δt Risk free interest rate Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**State prices**Law of one price (no free lunches) Price of a digital option Francqui Leerstoel - Inaugurale Rede 2 december 2004**Stochastic discount factors**• Valuing a derivative: Stochastic discount factor Random payoff of derivative Expectation operator Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline**• 1. What is finance? • 2. The diffusion of the discounted cash flow method • 3. Markowitz and the birth of modern portfolio theory • 4. CAPM: the relationship between expected returns and risk • 5. The Efficient Market Hypothesis: do stock prices move randomly? • 6. Modigliani-Miller: does financing matter? • 7. Black – Merton – Scholes: how to value options • 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors • 9. Outline of following lectures Francqui Leerstoel - Inaugurale Rede 2 december 2004**Growth of derivative industry**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Explosion of the market for options**Francqui Leerstoel - Inaugurale Rede 2 december 2004**Outline of next lectures**• 1. Valuing option: inside Black-Merton-Scholes • 2. Option and portfolio management: portfolio insurance, hedge funds • 3. Options and capital budgeting: beyond NPV, real options • 4. Options and risky debt: Modigliani Miller revisited • 5. Options and capital structure: how much debt is optimal? • 6. Options and credit risk: when rating agencies fail All documents for these lectures will be available on my website: www.ulb.ac.be/cours/solvay/farber/vub.htm Francqui Leerstoel - Inaugurale Rede 2 december 2004