Applied Finance Lectures 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

What is Finance? Companies Investors Equity Capital expenditures Debt Portfolio management Dividends Operating cash flow Interests

Time Uncertainty Asset pricing models 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

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

Discounted cash flow method PV = C1 v1 + C2 v2 + …+Cn vn Cash flows Required rates of return

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

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

Markowitz (1952) Portfolio selection Return of portfolio: normal distribution Characteristics of a portfolio: Expected return Risk: Variance/Standard deviation

Calculation of optimal portfolio

Markowitz: the birth of modern portfolio theory

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

Capital Asset Pricing Model

Capital Asset Pricing Model Expected return rM r Risk free interest rate β 1 Beta

Net Present Value Calculation with CAPM

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

Jensen 1968 - Distribution of “t” values for excess return 115 mutual funds 1955-1964 Not significantly different from 0

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)

The Efficient Market Hypothesis S&P 500 2000-2004

The Efficient Market Hypothesis S&P 500 2000-2004

The Random Walk Model

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

Does the capital structure matters? Modigliani Miller 1958: NO, under some conditions Debt Equity

Trade-off theory Market value PV(Costs of financial distress) PV(Tax Shield) Value of all-equity firm Debt ratio

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

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)

Buy 1 Fortis share

Buying a put Stock + Put Stock Put

Buying a call Bond + Call Bond Call

f=(#shares)(Stockprice)+Bond 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

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

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

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

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

State prices Law of one price (no free lunches) Current price State Up Down Stock S Su Sd Risk free bond 1 1+rΔt Law of one price (no free lunches) Price of a digital option

Stochastic discount factors Valuing a derivative: Expectation operator Stochastic discount factor Random payoff of derivative

Growth of derivative industry

Explosion of the market for options