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

The Sharpe Ratio: Lending, Borrowing and the Steepest Line

What makes the tangency line's slope, the Sharpe ratio, the one number a mean-variance investor maximizes, and why can a new stock never lower it?

Loading…

←Previous The Tangency Portfolio: Why Every Investor Holds the Same Stocks Next The Stock Nobody Can Find: Negative Correlation and Alpha →

Your summary note

1. Lending, full investment and borrowing along the tangency line
  Sketch the line from $r_f$ through the tangency portfolio, label the lending, fully invested and leveraged regions, and give the weight in T-bills for one point in each region.
2. Limits of the picture: kink, shorting, static snapshot
  Record that unequal borrowing and lending rates put a kink in the line, draw the reflected down-and-right line from shorting the tangency portfolio, and note that the analysis is a one-period snapshot.
3. The Sharpe ratio $\frac{\mathsf{E}[R_p] - r_f}{\sigma_p}$
  Write the formula as rise over run of the line from $r_f$ , compute it for two numerical portfolios, and reproduce the geometric argument that the tangency portfolio has the highest Sharpe ratio.
4. Adding a security relaxes a zero-weight constraint
  Write the 20-stock portfolio as a 21-weight portfolio with $w_{21} = 0$ , state that the new frontier is never worse, and record that any correlation below $\rho = 1$ suffices to bend it left.
Attempt 1 of 2