Foundations of Finance

01Defining Finance and the Financial System 02Valuation and Management: The Two Challenges 03Stocks, Flows, and the Five Cash-Flow Decisions 04Time, Risk, and the Six Principles of Finance 05How to Learn Finance: Practice and Study Habits Problem set0/10 Problem set 20/10

Present Value

01Information and Price: An Auction and Fannie Mae 02Who Pays for the Fannie and Freddie Guarantee?03What Counts as an Asset: Patents, Secrets, Brands 04An Asset as a Sequence of Dated Cashflows 05The Value Operator and the Cashflow Timeline 06Dates as Currencies: Building Net Present Value 07Discount Factors: Market Prices for Future Dollars 08A Worked Net Present Value and Its Assumptions 09The Opportunity Cost of Capital and Present Value Problem set0/10 Problem set 20/10 MIT problem set0/5

01Does the Currency Change an NPV's Sign?02Moral Hazard and Contagion: Where Bailouts Stop 03The NPV Rule at Work, and Choosing the Rate 04The Perpetuity: Why Cash Forever Is Worth C/r 05Reading the Rate Off a Perpetuity's Price 06The Growing Perpetuity, and When Growth Outruns r 07Building the Annuity from Two Perpetuities 08The Annuity Discount Factor and Mortgage Payments 09APR, the Effective Annual Rate, and Compounding Problem set0/10 Problem set 20/10 MIT problem set0/13

01Leverage: How a 10% Fall Becomes a 200% Loss 02Who Absorbs the Loss: Walking Away, Rate Cuts, Bailouts 03Last in Line: Chapter 11 and How Lehman's Equity Hit Zero 04Inflation vs. Time Value: Wealth and the Price Index 05Real Returns: Match the Discount Rate to the Cashflow Problem set0/10 Problem set 20/10 MIT problem set0/7

Fixed-Income Securities

01Fixed Income: How Treasuries Overtook Mortgage Debt 02Why Dealers Break When Everyone Sells: 1987 and 2008 03Pricing a Coupon Bond: Why It Trades at Par 04Zero-Coupon Bonds, STRIPS, and the Forecast in a Price Problem set0/10 Problem set 20/10 MIT problem set0/6

01Credit, Not Cost: Why the Fed Held Rates and Saved AIG 02Spot Rates and the Term Structure from Strips Prices 03Flight to Quality, and the Rates the Fed Cannot Set 04Forward Rates: Locking In Next Year's Rate Today 05Hedging with Forward Rates and Quoting a Forward Loan 06Yield to Maturity: Many Spot Rates in One Number 07Reading the Treasury Yield Curve: 1981 to 2026 08Yield Curve Theories and Pricing Bonds by Arbitrage Problem set0/10 Problem set 20/10 MIT problem set0/8

01Breaking the Buck: The Money-Fund Run into T-Bills 02The Law of One Price: Same Cash Flows, Same Price 03Why Arbitrage Needs Short Selling: The 2008 Ban 04Fixed-Income Arbitrage: No Solution Means a Trade 05Duration: How Far a Bond's Price Moves with Yield 06Convexity: The Bend That Duration Misses Problem set0/10 Problem set 20/10 MIT problem set0/7

01September 2008: Rising Yields and Forced Bank Mergers 02Default Risk and Credit Ratings: When Debt Acts Like Equity 03The Credit Spread: Default Premium, Risk Premium, Securitization 04Tranching: How Two Risky Bonds Make a Triple-A Claim 05Correlated Defaults: How the Triple-A Tranche Broke 06Where the Money Went: Ratings, Winners and TARP Problem set0/10 Problem set 20/10 MIT problem set0/1

Common Stock

01What a Share Is: Residual Claim, Limited Liability, Votes 02Primary vs Secondary Markets: IPOs and Trading Volume 03Deriving the Dividend Discount Model 04The Market, Not the Company, Sets the Discount Rate 05Backing Out a Discount Rate from an Auction Bid 06The Gordon Growth Model and Why Prices Explode Near r = g 07Cost of Capital: r = D/P + g 08Multi-Stage Dividend Valuation and Dividend Policy Problem set0/10 Problem set 20/10 MIT problem set0/7

Forwards and Futures

01Mark to Market, Currency Risk, and Why Firms Hedge 02Should a Firm Hedge? Irrelevance vs Financial Distress 03The Forward Contract: Forward Price, Spot Price, and Payoffs 04Why a Forward Is Worth Zero at Signing, and What F Forecasts 05Buy Forward or Buy Now and Store? Features of a Forward 06Counterparty Risk: The Soybean Forward That Fails 07From Forward to Futures: Settling Gains and Losses Daily 08Clearing Houses and Margin Accounts: How Futures Stay Safe Problem set0/10 Problem set 20/10

01Marking to Market: Daily Settlement on a Futures Position 02Futures vs Forwards: Credit Risk, Closing Out and Netting 03Pricing a Forward by Replication: The Cost of Carry 04Cost of Carry in Practice: Gold, Gasoline and Stock Indexes 05A Synthetic Index Fund Built from S&P 500 Futures 06Hedging 25% of a Portfolio with Short Index Futures 07Futures Leverage, Margin Risk and What Prices Reveal Problem set0/10 Problem set 20/10

Options

01Calls and Puts: The Right Without the Obligation 02A Put Option Is Insurance on Your Stock 03Option Payoff Diagrams: The Kink and the Premium 04Writing Options and the Straddle: A Bet on Volatility 05Call Spreads, Butterflies and the VIX 06Equity Is a Call Option: Options in Capital Structure 07Cardano to Bachelier: Fair Games, Random Walks and the Heat Equation 08Black, Scholes and Merton: Why Option Prices Ignore Risk Preferences Problem set0/10 Problem set 20/10

01The One-Period Binomial Model: Six Inputs to an Option Price 02Replicating a Call With Stock and Bonds: Why p Drops Out 03The Binomial Price as a Risk-Neutral Expectation 04From the Binomial Tree to Black-Scholes 05Calibrating u and d: Volatility Raises the Call's Value Problem set0/10 Problem set 20/10

Risk and Return

01Returns, the Risk Premium, and Standard Deviation 02Correlation, the Normal Curve, and Fat Tails 03Randomness: The Signature of an Efficient Market 04Real Rates and the Risk-Return Tradeoff, 1946–2001 05Stock Returns: Unpredictable Over Time, Correlated Across Stocks 06Size, January, Value, Momentum: Anomalies Out of Sample 07Why Most Mutual Funds Trail the Index Problem set0/10 Problem set 20/10

Portfolio Theory

01Portfolio Weights, Short Sales and Buying on Margin 02130/30 Funds, a Leveraged Home and Zero-Investment Portfolios 03Why Hold a Portfolio? Diversification, Mean and Variance 04The Risk-Return Graph: Why Investors Head Northwest Problem set0/10 Problem set 20/10

01Portfolio Variance: Why Risk Lives in the Covariances 02Two Stocks, One Covariance: The Risk-Return Bullet 03Estimating Means and Covariances: How Much History?04How Correlation Bends the Bullet, from +1 to −1 05Mixing In T-Bills: A Straight Line and Leverage 06Average Covariance, and Why Correlations Jump 07The Limit of Diversification: Systematic Risk 08Three Stocks, One Bullet: Long Horizons and Equilibrium Problem set0/10 Problem set 20/10

01Never Hold One Stock: Three-Stock Frontiers and Why Stocks Co-Move 02The Tangency Portfolio: Why Every Investor Holds the Same Stocks 03The Sharpe Ratio: Lending, Borrowing and the Steepest Line 04The Stock Nobody Can Find: Negative Correlation and Alpha 05Indifference Curves and the Four Conclusions of Portfolio Theory Problem set0/10 Problem set 20/10

The CAPM

01Why Everyone's Fund Must Be the Market Portfolio 02From the Capital Market Line to Beta and the CAPM 03The Security Market Line: Betas of One, Zero and Below Zero 04Portfolio Beta Is a Weighted Average: Microsoft vs Gillette 05Alpha: Same Return, Same Volatility, Different Beta 06Hedge Fund Alpha or Hidden Beta? Fund XYZ's 771 Basis Points 07Systematic vs Idiosyncratic Risk: Why Only Beta Is Paid 08Testing the CAPM: Is Alpha Zero? Biogen vs Motorola Problem set0/10 Problem set 20/10 MIT problem set0/1

01Testing the CAPM with Portfolios: Size, Beta and a Flatter Line 02Paid for Beta, Not Volatility: Multiple Factors and Equilibrium Problem set0/5 Problem set 20/5

Capital Budgeting

01The NPV Rule and Investment Criteria for Capital Budgeting 02Building Project Cash Flows: Cash, After Tax, Incremental 03After-Tax Cash Flow and the Depreciation Tax Shield 04Project Discount Rates: The Pure-Play Beta for Bloomberg Press 05Synergies, Firm-Wide Cost of Capital and Moving Discount Rates 06Oil Exploration: Two Risks, Two Discount Rates Problem set0/10 Problem set 20/10 MIT problem set0/2

01Payback and Discounted Payback: Flaws and Defensible Uses 02The Profitability Index: Right Sign, Wrong Size 03Scale and NPV: Why Firms Budget in Dollars, Not Returns 04IRR as Yield to Maturity: Four Conditions, Loans and No IRR 05Multiple IRRs, Scale and Timing: Why IRR Can't Rank Projects 06What Firms Use: Survey Evidence and Six Capital Budgeting Rules 07Descartes' Rule of Signs for IRR, and the Politics NPV Leaves Out Problem set0/10 Problem set 20/10

Efficient Markets

01Market Efficiency: How Stocks Found the Challenger Culprit 02Behavioral Finance: Loss Aversion and Ambiguity Aversion 03Risk Versus Uncertainty: Knight, Ellsberg and the Gorilla 04The Dutch Book Theorem: Inconsistent Beliefs Create Arbitrage 05Emotion and Rationality: Damasio's Patient and the Triune Brain 06Stress and Decisions: Fear, Pain and Unstable Preferences 07The Adaptive Markets Hypothesis: Efficiency Most of the Time Problem set0/10 Problem set 20/10

01Adaptive Markets: Why the Risk Premium Changes Over Time 02Cycles of Efficiency: 130 Years of S&P Serial Correlation 03Pain Protects: Profits as an Anesthetic, and the Case for Regulation 04After 2008: Innovation, Evolution and Better Regulation 05Course Summary I: Six Principles and Present Value Pricing 06Course Summary II: Risk, the CAPM and When to Trust Prices Problem set0/10 Problem set 20/10 MIT problem set0/7

Cardano to Bachelier: Fair Games, Random Walks and the Heat Equation

How did a Renaissance gambler's fair game lead Bachelier, in 1900, to price options with the heat equation?

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Your summary note

1. Cardano's fair game as a martingale
  Quote the equal-conditions principle, write $E_t[W_{t+1}] = W_t$ , and check it on a fair coin-flip bet of $1 per toss.
2. From fair game to random walk and Brownian motion
  Record the step from the fair game to the Random Walk Hypothesis, and date Bachelier's 1900 thesis on options on French government bonds against Einstein's 1905 work on Brownian motion.
3. Option pricing reduces to the heat equation
  Write $\frac{1}{c}\frac{\partial \mathcal{P}}{\partial t} - \frac{\partial^2 \mathcal{P}}{\partial x^2} = 0$ , record Poincaré's link to Fourier's theory of heat conduction, and state what carries over from physics to option pricing.
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