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 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 real data, the decomposition of risk into systematic and firm-specific parts, R-squared, and why not all alphas are equal.

The Treynor-Black Model Combining the market with an active portfolio of mispriced securities, the optimal weights, and the information ratio as the measure of how good an alpha is.

Fixed Income

Bond Pricing Coupon bonds and the yield to maturity, current yield, pricing with zero rates, holding-period returns, semi-annual conventions, and flat and invoice prices.

Forward Rates Synthesizing forward rates from zero-coupon bonds, and the expectations, liquidity preference, and segmented markets theories of the term structure.

Interest Rate Risk Management Bond price sensitivity, duration and convexity, and immunizing liabilities by matching the dollar durations of assets and liabilities.

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.