50 years of Finance André Farber Université Libre de Bruxelles Inaugurale rede, Francqui Leerstoel VUB 2 December 2004

Francqui Leerstoel - Inaugurale Rede 2 december 2004 |2|2 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 |3|3 What is Finance? Equity Debt Investors Dividends Companies Interests Operating cash flow Capital expenditures Portfolio management

Francqui Leerstoel - Inaugurale Rede 2 december 2004 |4|4 Asset pricing models Time Uncertainty Discounted cash flow method Capital Asset Pricing Model Markowitz Sharpe Lintner Option Pricing Models Black Scholes Cox Ross Rubinstein State Prices Arrow-Debreu Stochastic discount factors

Francqui Leerstoel - Inaugurale Rede 2 december 2004 |5|5 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 |6|6 Discounted cash flow method Cash flows Required rates of return PV = C 1 v 1 + C 2 v 2 + …+C n v n

Francqui Leerstoel - Inaugurale Rede 2 december 2004 |7|7 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 |8|8 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 |9|9 Markowitz (1952) Portfolio selection Return of portfolio: normal distribution Characteristics of a portfolio: 1.Expected return 2.Risk: Variance/Standard deviation

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 10 Calculation of optimal portfolio

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 11 Markowitz: the birth of modern portfolio theory

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 12 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 | 13 Capital Asset Pricing Model

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 14 Capital Asset Pricing Model Expected return Beta Risk free interest rate r rMrM 1 β

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 15 Net Present Value Calculation with CAPM

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 16 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 | 17 Jensen Distribution of “t” values for excess return 115 mutual funds Not significantly different from 0

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 18 US Equity Mutual Funds (Malkiel, Journal of Finance June 1995) Average Annual Return Capital appreciation funds 16.32% Growth funds15.81% Small company growth funds13.46% Growth and income funds15.97% Equity income funds15.66% S&P 500 Index17.52% Average deviation from benchmark -3.20% (risk adjusted)

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 19 The Efficient Market Hypothesis S&P

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 20 The Efficient Market Hypothesis S&P

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 21 The Random Walk Model

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 22 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 | 23 Does the capital structure matters? Modigliani Miller 1958 : NO, under some conditions Debt Equity

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 24 Trade-off theory Market value Debt ratio Value of all-equity firm PV(Tax Shield) PV(Costs of financial distress)

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 25 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 | 26 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 | 27 Buy 1 Fortis share

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 28 Buying a put Put Stock Stock + Put

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 29 Buying a call Call Bond Bond + Call

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 30 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 | 31 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 | 32 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 | 33 Binomial option pricing model Stock price S Stock price S u Option f u Stock price S d Option f d Time interval Δt Risk neutral probability Risk free interest rate

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 34 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 | 35 State prices Current price State UpDown StockSSuSu SdSd Risk free bond11+rΔt Law of one price (no free lunches) Price of a digital option

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 36 Stochastic discount factors Valuing a derivative: Expectation operator Stochastic discount factor Random payoff of derivative

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 37 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 | 38 Growth of derivative industry

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 39 Explosion of the market for options

Francqui Leerstoel - Inaugurale Rede 2 december 2004 | 40 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: