Class Notes

These are the lecture notes for the investments topics. Each chapter is available in HTML and as a PDF for printing, ends with a set of practice problems, and most chapters come with a deck in the slides.

Portfolio Theory

Statistics of Asset Returns Holding-period returns, expected returns and volatility, estimating and annualizing them from CRSP data, portfolio returns as weighted averages, and how the law of one price and ETF arbitrage tie a fund’s return to its basket.

The Fisher Model Choosing consumption today and tomorrow with a utility function and a production technology, how capital markets separate the firm’s investment decision from the investor’s consumption decision, and what happens when borrowing and lending rates differ.

Utility Theory Under Uncertainty Expected utility, risk aversion and concavity, the insurance premium and the certainty equivalent, absolute and relative risk aversion, and the compensation investors require to bear risk.

Optimal Capital Allocation The capital allocation line and the Sharpe ratio, mean-variance utility and indifference curves, and the optimal split between a risky portfolio and the risk-free asset.

Portfolios of Risky Assets Two-asset portfolios, the investment opportunity set, the minimum-variance portfolio, the limits of diversification, and the minimum-variance frontier with many assets in matrix form.

Perfect Correlation Riskless portfolios built from perfectly correlated assets, the synthetic risk-free rate they imply, and why the right weights, long-only or long-short, are what eliminate risk.

Beta Pricing The tangency portfolio and the efficient frontier, and how the efficiency of a single portfolio prices every asset through its beta, whatever investors’ preferences.

The Capital Asset Pricing Model Two-fund separation and market clearing, why the market portfolio is the tangency portfolio in equilibrium, the CAPM pricing equation, and how to interpret empirical tests of it.

The Index Model A single-factor model of returns estimated on CRSP data, the decomposition of risk into systematic and firm-specific parts, R-squared, why not all alphas are equal, how precisely betas are estimated and why they regress toward one, and the covariance matrix the model implies.

The Treynor-Black Model Combining the market with an active portfolio of mispriced securities, the optimal weights and the information ratio, adjusting alpha forecasts for their accuracy, and what happens when past alphas are used as forecasts.

Fixed Income

Bond Pricing Coupon bonds and the yield to maturity, current yield, zero rates and continuously compounded yields, the Treasury yield curve since 1961, holding-period returns, semi-annual conventions, and flat and invoice prices.

Forward Rates Synthesizing forward rates from zero-coupon bonds, the forward curve, the term premium as the gap between forward and expected short rates, and the expectations, liquidity preference and segmented markets theories as statements about it.

Interest Rate Risk Management Bond price sensitivity, duration and convexity, immunizing liabilities by matching dollar durations, and the level, slope and curvature factors that move the Treasury yield curve.

Evidence and Active Management

CAPM Anomalies Testing the CAPM with time-series and cross-sectional regressions, the flat security market line, size, value, momentum and other anomalies in decile sorts, and what happened to them after publication.

Beyond the CAPM Multifactor models from Fama-French to the q-factor and mispricing models, how well they price assets, the factor zoo, and their use for the cost of equity, risk models and benchmarks.

The Term Structure in the Data Average returns of Treasury bonds, the Fama-Bliss and Campbell-Shiller tests of the expectations hypothesis, the Cochrane-Piazzesi factor, estimates of the term premium, and the changing correlation between stocks and bonds.

Credit Risk and Corporate Bonds Promised yields and expected returns, a century of credit spreads, how much of the spread is default, the returns of corporate bonds from TRACE, factor models for bonds, and reaching for yield.

Estimation Risk and Shrinkage How precisely means and covariances are estimated, why the plug-in portfolio disappoints out of sample, shrinking the covariance matrix and expected returns, Black-Litterman, and the debate over complexity.

Performance Evaluation Time- and dollar-weighted returns, the Sharpe ratio, M², Treynor’s measure, Jensen’s alpha and the information ratio, multifactor alphas, style analysis, market timing, attribution, and gaming the measures.

Skill versus Luck What the average active fund earns, whether performance persists, separating skill from luck in a large cross-section, skill in equilibrium and value added, and the special problems of hedge fund returns.

Limits to Arbitrage and Investor Anomalies Why arbitrage may not correct prices, noise trader risk and performance-based arbitrage, twin shares and carve-outs, short-sale constraints, and the evidence on how individual investors behave.

Market Microstructure

Sequential Trading How a dealer sets bid and ask prices when some traders are better informed, and how quotes are updated as each trade reveals information.